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1 7 »77 ^^'^ Radiation Physics ^-7- ______^ ^ ^
Proceedings of the International Radiation (^^1 Symposium on Physics, held at Bose Institute, Calcutta, India
November 30-December 4, 1974
Edited by: . .
A. M. Ghose Nuclear Physics Laboratory Bose Institute, Calcutta— 700 009, India
D. V. Gopinath Safety Research Laboratory Reactor Research Center Kalpakkam 603 102, India
J. H. Hubbell Institute for Basic Standards National Bureau of Standards Washington, D.C. 20234
S. C. Roy Nuclear Physics Laboratory Bose Institute, Calcutta— 700 009, India
Organized by. Bose Institute, Calcutta, India
Co-sponsored by: Department of Atomic Energy, India
Assistance from: International Atomic Energy Agency
National Bureau of Standards
U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary
Edward 0. Vetter, Under Secretary
Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology U.^NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
Issued January 1977 -
Library of Congress Cataloging in Publication Data
International Symposium on Radiation Physics, Bose Institute, 1974. Radiation physics.
(NBS special publication ; 461) "CODEN: XNBSAV." Supt. of Docs. No.; C 13.10:461
1. Ionizing radiation-Congresses. 2. Radiation- Congresses. 3. Radia-
tion-Measurement-Congresses. 4. Cross sections (Nuclear physics)
Congresses. I. Chose, A. M. II. Bose Research Institute, Calcutta. III.
India (Republic) . Dept. of Atomic Energy. IV. Title. V. Series; United
States. National Bureau of Standards. Special publication ; 461.
QC100U.S7 no. 461 (QC474] 602Ms [539.7"2) 76-608379
National Bureau of Standards Special Publication 461
Nat. Bur. Stand. (U.S.), Spec Publ. 461, 268 pages (Jan. 1977) CODEN: XNBSAV
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PREFACE
Radiation Physics is an interdisci- All papers were retyped at Bose plinary science and in the past different Institute, Calcutta, on composition (25% aspects of the subject such as nuclear and reduction) guide sheets supplied by the atomic cross section measurements and National Bureau of Standards for direct analysis, shielding of accelerators, dosi- photo-reproduction. In some cases the metry, nuclear electronics, radiation inserted figures and tables, although the biophysics, etc., have been discussed in best available to the editors, suffer in specialized symposia and seminars. It has legibility, particularly after the size- been increasingly felt that a symposium reduction. In these cases we suggest that presenting the subject matter in an inte- interested readers write to the authors grated manner would be useful to special- for more detailed versions of these papers ists working in isolated areas of radiation which in most cases have been published physics as well as to those interested in elsewhere the global view of the entire subject. The International Symposium on Radiation When commercial equipment, instru- Physics held in Bose Institute, Calcutta ments and materials are mentioned or from November 30 to December 4, 1974, with identified in these proceedings it is these ends in view provided a forum for intended only to adequately specify exchange of experiences and ideas among experimental procedure. In no case does different vjorkers in Radiation Physics such identification imply recommendation from different countries. or endorsement by the National Bureau of Standards, nor does it Imply that the The symposium was organized by Bose material or equipment identified Is Institute, Calcutta. Moral and financial necessarily the best available for the support was received from the Departments purpose of Atomic Energy and Science and Technol- ogy, Govt, of India; National Bureau of We regret the inordinate delay in Standards, U.S.A. and International Atomic publishing the proceedings, the reasons Energy Agency, Vienna. Vie express our of which are beyond our control. appreciation to those organizations. The editorial board gratefully Apart from a few minor changes, the acknowledges the assistance of the U.S. papers published in these proceedings National Bureau of Standards Office of essentially represent wha.t the authors Technical Information and Publications submitted as the "final versions of their received for printing and publishing presentations in the symposium. The these proceedings. editorial board apologizes for any mistake that might have crept in inadvertently. A. M. Ghose D. V. Goplnath J. H. Hubbell S. C. Roy
ill I
ABSTRACT
These proceedings contain Invited and contributed papers presented at the International Symposium on Radiation Physics organized by and held at the Bose Institute, Calcutta, India Nov. 30-Dec. ^, 197^. The purpose of this symposium, recognizing radiation physics as the thread held in common by a variety of medical, engineering and scientific disciplines, was to bring together specialists from these disciplines to report on, exchange, and make available through these proceedings, information and experiences of common Interest to workers in these diverse disciplines. Topics thus brought together in this symposium Include new measurements, theoretical developments, compilations and applications of basic cross section and transport data for photon, electron, neutron and heavy Ion beams Interacting with matter.
Key words: Cross sections; dosimetry; electrons; neutrons; photons; radiation physics; symposium.
iv TABLE OF CONTENTS
Contents Page
Preface Ill Inaugural Address, by R. Ramanna 1
SESSION A : BASIC INTERACTION CROSS SECTIONS
CHAIRMAN: W. S. Snyder (USA)
Al. Present Status of Photon Cross Section Data 100 eV to 100 GeV (Invited Talk), by J. H. Hubbell 3
A2. Semiemplrical Formulation of Coherent Scattering of Gamma Rays, by S. C. Roy and A. M. Ghose 17
A3. Experimental Photoionization Cross Section of Gamma Ray Photons for Low, Medium and High Z Atoms, by B. Slnha (Goswaml) and N. Chaudhuri 20
7 SI A4. Inner Bremsstrahlung Accomipanying Electron Capture in Be and Cr, by H. Sanjeevaiah and B. Sanjeevaiah 23
A5. Inelastic Scattering of 279 keV Gamma Rays by Bound Electrons In Heavy Atoms, by D. S. R. Murty, V. Govlnda Reddy, E. Narasimhacharyulu and S.T.P.V.J. Swamy 26
A6. Gamma Ray Attenuation Coefficient Measurements at 1115, 1173 and 1332 keV, by S. Gopal and B. Sanjeevaiah 29
SESSION B : BASIC INTERACTION CROSS SECTION
CHAIRMAN: A. K. Ganguly (India)
31. Radiation Physics and Nuclear Technology (Invited Talk), by P. K. Iyengar 32
B2. Variation of Total to K-Shell Photoelectric Cross Section Ratios with Atomic Number and Photon Energy, by R. Gowda and B. Sanjeevaiah ^1
83- Optical Model Analysis of Non-elastic Interaction of 1^1.2 MeV Neutrons, by B. Pal, A. Chatterjee and A. M. Ghose 44
SESSION C : BASIC INTERACTION CROSS SECTIONS
CHAIRMAN: J. H. Hubbell (USA)
CI. Geometric Factors in Radiation Physics Measurements (Invited Talk), by A. M. Ghose 47
C2. Measurement of Angular Distribution of Incoherently Scattered
Gamjna Rays from Atoms , by B. Sinha (Gosvfami) and N. Chaudhuri 55
C3. Measurement and Analysis of a Few 14 MeV Neutron Capture Cross Sections, by M. Majum.dar and B. Mltra 57
C5. Intermediate Energy Approximation of B-H Formula for the Bremsstrahlung Cross Sections, by K. Gopala and B. Sanjeevaiah 60
V Page
SESSION C (Continued)
C6. A New Method for the Measurement of Differential Elastic Scattering Cross Sections of Past Neutrons, by S. Nath, A. Chatterjee and A. M. Ghose 64
C8. Compton Scattering of 1.12 MeV Gamma Rays by K-Shell Electrons,
by P. N. Baba Prasad, G. Basavaraju and P. P. Kane . 6?
C9. Nuclear Theory Based Cross Sections of Th-232, Th-233 and U-233 and Their Applications in Reactor Technology, by S. B. Garg and Ashok Kumar 70
SESSION D : RADIATION TRANSPORT: THEORY AND APPLICATIONS
CHAIRMAN: L. S. Kothari (India)
Dl. Development of Radiation Shielding Standards in USA (Invited Talk), by D. K. Trubey 7^
D2. Integral Equation Methods in Radiation Transport, by D. V. Gopinath 79
D3. Neutron Transport Problems in Spherical Geometry, by D. C. Sahnl 87
D4. Transport of Neutrons During Reactor Transients, by S. K. Kapil 91
D5. Criticality Calculations by Source-Collision Iteration Technique
for Cylindrical Systems, by V. K. Sundaram and D. V . Gopinath 9^
D6. Stochastic Method of Calculations for Fast Systems, by B. K. Godwal and M. P. Navalkar 97
D7 . A Random Sampling Technique for Choosing Scattering Angles from Arbitrary Angular Distributions in Dosimetric and Shielding Computations, by P. S. Nagarajan, C. P. Raghavendran, P. Sethulakshmi and D. P. Bhatia 100
D8. Monte Carlo Calculations on Dose Distributions from Plane Infinite Oblique Electron Sources, by C. R. Gopalakrlshnan and V. Sundararaman 106
SESSION E : RADIATION SCATTERING IN BULK MEDIA
CHAIRMAN: D. K. Trubey (USA)
El. Backscattering of Gamma Rays (Invited Talk), by T. Hyodo 110
E2. Transmission of Cf Fission Neutrons Through Various Shields, by Y. T. Song 119
E3. Back-scattering (Sky Shine) of Gamma Rays from a 65O Curie ^'^Co Source by Infinite Air, by J. Swarup and A. K. Ganguly 12H
Eh. Backscattering of Gamma Rays by Barriers from Various Media, by D. B. Pozdneyev 129
E5. Gamma Ray Streaming Through Annular Cylindrical Duct, by K. P. N. Murty, R. Vaidyanathan and R. Shankar Singh 132
E7 . Multiple Scattering of 12-40 MeV Heavy Ions Through Small Angles, by B. W. Hoot on, J. M. Freeman and P. P. Kane 136
vl Page
SESSION E (Continued)
E8. Charged Particle Transport In One-Dimensional Finite Systems, by G. Muthukrlshnan, K. Santhanam and D. V. Gopinath 140
E9. Passage of Heavy Charged Particles Through Matter, by Shankar Mukher J i and B. K. Srlvastava
SESSION F : RADIATION SHIELDING
CHAIRMAN: P. K. Iyengar (India) .... ,
Fl. Neutron Thermallzatlon in Hydrogenous Moderators (Invited Talk), by L. S. Kothari II49
F2. Neutron Transport Studies In Fast Reactor Shields, by R. Valdyanathan, K. P. N. Murty and R. Shankar Singh I63
F3 . Shielding for the Variable Energy Cyclotron at Calcutta, by G. Muthukrlshnan, Hari Singh and R. Mukher jee I66 F5. Computer Codes and Data Available from the Radiation Shielding Information Center, by D. K. Trubey, Betty F. Maskewitz and R. W. Roussin I7I
F6. Gamma Ray Build-up Factors for Finite Media, by K. John and D. V. Gopinath lyil
SESSION G : RADIATION DOSIMETRY AND INSTRUMENTATION
CHAIRMAN: V. G. Bhlde (India) -.
Gl. Physical Principles of Photon Dosimetry (Invited Talk), by W. S. Snyder 177 G2. Track Theory Applied to Physical, Chemical and Biological Systems, by S. C. Sharma and Robert Katz I83
G3. Spectrum Shapes of Low-Energy Photon Sources, by R. C. Sharma, S. Somasundaram, K. Unnikrishnan and Shlv Datta I88
G5. Dose Function for Beta Dosimetry, by S. J. Supe and Shlv Datta 193 .... G6. Actual Problems in Photon Dosimetry (Invited Talk), ' by D. F. Regulla and G. Drexler 197
SESSION H : RADIATION DOSIMETRY AND INSTRUMENTATION
CHAIRMAN: S. Makra (Hungary) - .. ,
HI. Neutron Dosimetry by Thermoluminescence Dosimeter (Invited Talk), by Y. Furuta and Shun-lchi Tanaka 209
H2 . Effect of Heat Treatments on Thermoluminescence of Pure AlpO.,, by A. S. Basu and A. K. Ganguly 219
H3a. Thermoluminescence Mechanisms in Lithium Fluoride, by S. P. Kathuria,
V. N. Bapat, C. M. Sunta and V. K. Jain . . 222
H3b. Thermoluminescence Response of LiF to Gamma Rays,
by V. K. Jain and S. P. Kathuria • • • 227
vii Page
SESSION H (Continued)
H4. Change in TL Sensitivity of Quartz due to Stress, by M. David and A. K. Ganguly 231
' H5. ESR-TL Correlation Studies in CaSO|,(RE) Phosphors, • by K. S. V. Nambi 23H
SESSION I : RADIATION DOSIMETRY AND INSTRUMENTATION
11. Neutron Dose Evaluation Using Calculated Neutron Spectra (Invited Talk), by S. Makra 238
12. Utilization of Plastic Scintillator in the Measurement of Uncharged Radiations, by P. K. Sarkar and K. N. Kirthl 2H7
13. Neutron Spectrometry by Sandwich Surface Barrier Technique, by 0. P. Joneja 252
15. Role of High Resolution Ge(Li) Detector in Trace Element Study in Water Activated with Thermal Neutrons, by J. M. Chatterjee (Das), E. Peeters and M. A. Castiaux 255 CONCLUDING SESSION
Summing up of the Deliberations of the International Symposium on Radiation Physics, by A. K. Ganguly 257
viii INAUGURAL ADDRESS
R . Ramanna Director, Bhabha Atomic Research Centre
Trombay, Bombay-400085 , India
Prof. Sircar, Prof. D.U. Rose, Prof, The performance of the nuclear jhose, Ladies and Gentlemen: physicists during this time can be rated very good considering the facilities I feel deeply honoured in being available. Notable contributions were asked to inaugurate this International made in the fields of nuclear structure, Symposi\im on Radiation Physics. It is fission and theoretical physics, apart gratifying to note the magnitude of the from the contribution of the nuclear participation in this symposium from physicists to the atomic energy programme, various countries and India. I hope all development of electronics and in the of you will have a pleasant and useful field of technical physics. time at Calcutta. It should be to the credit of the At this function, I v^ould like to nuclear physicists in the country that share some of my thoughts with you who the VEC facility is being built entirely represent a very wide cross section in with local effort. The commissioning nuclear physics on the future of nuclear of the VEC project is being eagerly research in countries like India. V/hile awaited by the nuclear physics community we are classified as a developing of the country. In the first phase, country, we happen to have a very large experiments are planned with particles number of nuclear physicists of ability of energy up to 60 HeV. The enthusiasm and some facilities for the study of of the physicists is evident from the nuclear reactions and nuclear structure experimental proposals submitted to the and at least one big facility for seminar on VEC utilisation to be held at nuclear physics, the Variable Energy the annual i'iuclear Physics and Solid Cyclotron which v/e are fabricating State Physics Symposium to be held in entirely ourselves. I would therefore December this year in Trombay. Experi- like to ask myself the question before ments are being made to study (a) the few all of you - what should be our future particle nucleus interactions through programme especially considering that elastic and inelastic scattering providing facilities for Huclear Physics studies (b) nuclear structure studies takes both time and money ? through their electromagnetic and strong interactions and (c) fission phenomenon. In the past, a greater part of the Further proposals to enhance the -luclear Physics research in India has so utility of the Cyclotron is also under far been closely connected with the consideration for the second phase of the expansion of the atomic energy programme. operation of the machine. For instance At the beginning of the programme, a it is planned to have heavy ion 1 IleV cascade generator was installed at facilities with Variable Energy TIFR, in the early fifties. This Cyclotron. Looking even more further together with radioactivity studies ahead we must ask ourselves whether we constituted the nuclear physics research should have a versatile heavy ion facilities in the country till the facility at the VEC, by combining it reactors in Trombay, were commissioned. with a straight accelerator like a .Vith the commissioning of the reactors, tandem machine which I believe can also fission physics and reactor-based be made in the country. Is it nuclear and solid state physics research worthwhile ? Can we afford it ? started. In the early sixties the 5.5 .leV van de graaff accelerator at Trombay This is as far as the immediate '.fas installed. >/hile the nuclear future is concerned. But what of the physics activity of BARC and TIPR more distant future ? Should we expand centred around these facilities, several our nuclear physics activity further or universities and DAE assisted institutes have we reached a stage where we cannot like the Saha Institute also started afford any further expansion ? In nuclear physics research using mainly discussing this question, we should radioactivity and low energy accelera- consider, forgetting for the time being tors. Since these came into existence, our economic situation, the performance there has been no further expansion of of the people so far, the experience nuclear physics research facilities they have gained during the past and except for the forthcoming VEC project. the trend which nuclear physics
1 :: , ,
activity is taking in general in the rest These studies require a machine with of the world. It is true, unfortunately an energy of 4-6 GeV_which is capable of that days when small groups of people giving K, n, ji , and p beams. working on a simple problem and can achieve useful result have gone. To The listing of possible experiments achieve tangible results, it is necessary under the circumstances can only be vague to concentrate our efforts in major and very restricted. But I have made national facilities. Granting that the such a listing only for the purpose of credibility of our nuclear physicists is discussion as to what should be done for established and that we should not let the future. It is seen that the set of their past experience go to waste, we experiments involving the whole nucleus could think of the ways in which nuclear or a large number of particles can be physics activity can grow in the country. undertaken in a upgraded VEC facility, we should therefore give it serious consi- The two major areas in v/hich deration and try to provide funds for it. nuclear physics may grow in the future However, in the case of phenomena of a are few nucleons and their correlations in nuclei, the need for a large machine is 1. Phenomena involving the whole beset by many question marks especially nucleus or a large number of particles from the point of view of the cost, time in the nucleus : viz. of construction and the need for various maintenance facilities. But I do not a) Production and study of exotic see why the nuclear physicists in the nuclei like super heavy nuclei country cannot start making feasibility and nuclei far off the stability studies just as we did when we planned line, the VEC project. Feasibility studies should not stop just because big b) physics of nucleus at low nuclear machines are entirely out of our range densities like at the nuclear financially though not technically as surface things stand.
c) new phenomena involving various I have great pleasure in inaugura- collective degrees of freedom ting the conference and wish all of you like the giant resonances, high a very successful meeting. spin states leading to nuclear Heissner effect.
d) study of features like viscosity of the nuclear matter, through heavy ion studies.
These experiments require a heavy ion accelerator with upgrading of the VEC facility as envisaged above.
2 . Phenomena involving a few nucleons and their correlations in nuclei are
a) nuclear radius and surface studies using n, K and p absorp- tion in nuclei,
b) importance of baryon resonances in nuclear systems, which should connect up the elementary par- ticle physics and nuclear physics,
c) Mesic and hyperonic atoms giving rise to a wealth of information about the charge, mass and current distribution in nuclei,
d) investigation of unstable ele- mentary particles themselves by secondary process, when they are produced in nuclei.
2 ) } ,
PRESENT STATUS OF PHOTON CROSS SECTION DATA 100 eV TO 100 GeV*
J. H. Hubbel± National Bureau of Standards Washington, D.C. 20234
Recent developments in theoreticaJ. and experimental cross sections for the basic photon interactions with atoms (photoef f ect coherent and incoherent scattering, and electron-positron pair production) are reviewed. Emphasis is on the extensive total and subshell photoef feet calculations by J. Scofield, and on atomic form factor and incoherent scattering function data calculated by D. Cromer and by R. Brown. Some comparisons of these theoretical results with available explicit cross section and total attenuation coefficient measurements are presented.
(Atomic form factor, attenuation coefficients, cross sections, gamma rays, incoherent scattering function, photoelectric effect, pair production, photons, x-rays
Introduction -'sessions, (2) show some comparisons of present theoretical cross sections with Dr. Ghose, Dr. Ramanna, Chairman available total and partial measurements Dr. Snyder, fellow Symposium partici- (3) look a little at Z-smoothness with pants it is my pleasure to re- its implications for Z-interpolation, visit on this occasion the city of Nobel and finally (4) make some estimates of laureate (literature, 1913), Rabindranath how well we are converging toward Tagore who in his G-itanjali wrote: "underlying reality" or the unique photon cross section set we would all "'ifhere the mind is without fear and like to have. the head is held high} Where knowledge is free} General Background Where the world has not been broken up into fragments by Any review of x-ray cross section narrow domestic walls data should start with Rbntgen, whom we Where words come out from the depth call to mind with figure 1. This of truth} picture, assumed to be of Frau R<3ntgen's Where tireless striving stretches hand, is reproduced from Rontgen's 1895
its arms towards perfection; discovery paper^ , and should have a Where the clear stream of reason "familiar ring" to it. has not lost its way into the dreary desert sand of dead habit; Where the mind is led forward by thee into ever-widening thought and action — Into that heaven of freedom, my Father, let my country [or, my world] awake."
30 appropriate to the spirit of this Symposium.
In this talk I will (1) touch bri- efly on some topics in photon cross se- ctions and dosimetry which will be explored in much more depth and detail by other speakers in this and other Fig. 1.
*Work supported by the NBS Office of Standard Reference Data.
3 ) "
As well as taking pictures of bones ' In figure 4 we indicate the princi- and other hidden objects, x-rays deposit pal photon interaction processes (see,
energy, or "dose", in the media through e.g. ref.4 ); (a) K , creation of ele- which they pass, as illustrated in ctron-positron pairs, (b) t, atomic figure 2 by a radiation-sensitive dye photoeffect and (c) a incoherent ^ solution developed by McLaughlin et al. . (Compton) scattering, contributing to 0-100 kilorads The s-ray dose range the above "energy deposition", and the illustrated in figure 2 is important in types of secondary radiations (annihila- a variety of practical applications tion radiation, bremsstrahlung, fluores- including, as shown in figure 3» insect cence and Compton scattered photons) popiilation control ard food storage-life which subtract from the energy deposited ;ension. at a photon interaction site. Sums over various combinations of these cross sections, corrected for the escape of secondary radiation appropriate to a given problem, are the so-called "true absorption coefficient" \^Q_/p, the "mass
energy transfer coefficienl? • \i-g/p, and
the "mass attenuation coefficient' t^gj^/p
(see ref . 5 for a review of this nomen- clatiire) as schematically shown in figure 4.
KILORADS 0 5 10/5 25 50 75 100
Fig. 2.
100 -r 1-
Codlmj Mcih 1
i J
Snoil, Grain Mo?h-
Grain M.1e_ lyp H-a/p P-^/P l^en/P Fruit Leof Roller- Sugo'Cdne Leafhcpper-
Fruit Fly- Fig. 4. Beon Weevil, Screw Worm Fly_
Tse' ".e Fly_ Pea V/eevil,l*(lowfever N'.asqjiro_ The "mass attenuation coefficient Boll Weevil, Block Blow Fly ^ Sit Rice Weevil - (x/p which should include, in addition to the processes shown in figure 4» a con- tribution from coherent (Rayleigh) sea™ CocKchorer Peefle ttering a is usuall.y defined for *• House Fly coh. purposes of tabulations as (see, e„g.re£ 4,6,7):
(1) 'tot ABSORBED DOSE (kilorods
Fig. 5.
4: N, = in which Avogadro's number to within a ± 2'/. uncertainty. A fea ture of interest in figure 6 is the (6.022045 X 10 atoms/g-atom) , M i3 the atomic weight (g/g-atom) and in existing measurements in the neigh borhood of 1 keV. = -X+ T tot coh. (2)
The mass attenuation coefficient ii/f is obtained from narrow-beam measiirements of monoenergetic photon beams transmitted by samples using the relations
(3) or
- ln(l/lQ)/t (4) ESTIMATED UNCERTAINTY where I and I are the beam intensities o with and without the interposed sample, respectively, and t is the sample thick- ness in mass per unit area.
The relative magnitudes of the above interaction processes as a func- tion of photon energy are shown in v1 .1 IMeV ISeV figure 5 for the case of copper, with PHOTON ENERGY the further addition of the photo- nuclear cross section a which has Fig. 6. ph. n. a broad peak, or "giant resonance" Comparisons of Theoretical with Experi - feature, centered at about 24 MeV for mental Total Cross Section Data light nuclei, decreasing in energy with increasing mass number to about 12 MeV In the next series of figures we for the heaviest nuclei^ . Experimental will compare some of the total cross total cross sections o^q^ for copper, section measurements indicated in figure 6 with some existing compilations derived from existing n/f measurements^ using the above relations in equations of theoretical or smoothed data. and are shown in figure 5 as (4) (1), In the small circles. figure 7 for hydrogen we see that the Henke et al. (67 He 01)-^°
COPPER (Z=29)
10 eV IkeV IGeV lOOGeV
The coverage of total cross section measurements for other elements is shown PHOTON ENERGY, keV in figiire 6 in which the solid black bars Fig. 7. indicate that we know a. . or u/p" tot '^'^
5 ' 1 total cross section measurements and In figure 9, moving up through the the Crasemann et al. photoeffect periodic table to nitrogen, we see the measurements suggest, as discussed by I keV region reasonably well measured, Cooper-'-^ that the photoeffect cross as gas targets lend themselves well to section for molecular Hp is roughly AO'/. studies in this region. Above 100 keV higher than for atomic H for photon we must still rely on either theory or energies 0.5 to 10 keV. An even larger interpolation across Z, although some enhancement (as much as a factor of two) data (not shown On this figure) for in the coherent scattering cross nitrogen in the range 0.66 - 1.35 MeV, section for Hp vs. H^is predicted by deduced from measurements on carbon (in Bentley and Stewart"*--^ (see also II hydrocarbons), boron carbide and integral data in ref. 14). Hence, boron nitride, were recently published although cross section compilations by Goswami and Chaudhuri-^" . (see, e.g. ref. 4,6,7) customarily present data only for the exactly- calciilable isolated H-atom, for practi- cal applications a table of molecular H- cross section data should perhaps also ' be included in subsequent compilations.
Figure 8 for lithium shows the gap in our experimental information around 1 keV mentioned earlier also the status of some of the calculated and fitted results. No significant difference is seen here between the Sandia (Biggs and
^^SANDIA (1971) 3*-' a 62 Bo 01 — 68 Ko 01 — ~ o 69 De 01 — V 60 Go 01 V 57 OJ 0! * 65 Pf 01 — N(I971) 0 21 He 01 — O 59 Ro 02 ~ — \ • JO Ma 01 — \ • 65 We 01 lo" \ « 35 Mo 01 ~ \ 35 Ge 02 ^ Z \
lO"' 10° lo' 10^ 10* lo'' PHOTON ENERGY. keV
1 \L SCOFIELD (1973) j-HARTREE - SLATER o ^ Fig. 9. YyHARTREE - FOCK
« 10 z < \ 10 V
10°
1 1 1 1 1 mill 1 1 i 1 (O'' i/inl Wiiiiiil mil Mini O' 10° lO' 10^ lO' 10 PHOTON ENERGY, keV
Fig. 8 . lighthill parametric fit and the
Kaman (Veigele et al.^° ) calculated values. In Scofield 's-"-' recent photo- effect calculation, covering the range 1 keV to 1.5 MeV for all elements Z = 1 to 101, he has suggested that his Hartree-Slater results could be improved by renormalizing to the Hartree-Fock model. Lithium happens to be the lo"' 10° io' 10^ id' id" element most affected in the K-shell by PHOTON ENERGY, keV this renormalizacion, here shown to decrease by ?/• . Fig. 10.
6 In figure 10 we see that silicon, NBS (McMaster et al.25,26) tabiilation an important detector material, again follows the. 1936 data by Biermann shows a wide gap in the ezperimental (36 Bi 01^ 'K which is 30/. higher than information in the vicinity of 1 keV the Scofieldl'7 or Kamanl6 calculations and in this case the K absorption edge. at 1 keV. Hence for tin, as for some Further measurements filling in the elements previously mentioned, new region around 1 keV woiild be usefiil. measurements in the neighborhood of In the region around 1 MeV the recent 1 keV would be useful. silicon measurements by Goswami and Chaudhuri^" (not shown in this figure) are in much better agreement with the theoretical curve than the indicated measurements by Mavroyannakis and Antoniades (70 Ma 01)19 and by
Boltaks et al. [5B Bo Olj^O .
In figure 11 we have germanium, another popular detector material. The region of interest to crystallographers from 4 to 30 keV and extending up to 100 keV is rather well mapped out, but down around the 1 edges (1.22, 1.25 and 1.41 keV) there are disagreements of the order of 10'/. The (not shown) recent Goswami-ChaudhurilS .0.66 - 1.35 MeV measurements are in good agreement with the theoretical curve shown. PHOTON ENERGY. keV
Fig. 12.
In figure 13 gadolinium is seen to have a good distribution of measure- ments, all of them more recent than 1967, all reasonably consistent. Below, 1 keV the Kaman photoeffect calculation is seen to agree within 20'/. with the measured points except for the absorp- tion peak at 150 eV observed by
Zimkina et al. (67 Zi 01)28 .
iiin| I I 1 I I i I -II' 1 Mii| I I I iimi'— — I 1 1 nil
PHOTON ENERGY, keV Fig. 11.
Figure 12 shows tin taken down on additional decade to 10 eV. Low-energy data reported by NBS (Codling et al. [66 Co 01] 21 and DESY [Haensel et al. 68 Ha 01]^^ synchrotron-light groups and by the Leningrad group (Lukirski et al. (66 Lu 02)^5 ) reasonably consistent, and can be compared with the PHOTON ENERGY. keV Mc6uire24 and Kamanlo calculations, and with the parametric fit by the Fig. 13. Sandial5 group. Above 1 keV the LLL-
7 . .
In figure 14 uranium measurements solid curves in figures 15 and 16 are gradually filling in toward lower (Kaman-l-^ below ~1 keVj Scofield^' -I r above 1 keV) energies. Where the Kaman and Scof ield-'-'^ photoeffect calculations overlap in the range 1.0 - 2.5 keV, and disagree by 10% , the recent 1-10 keV measurements by Del Grande and Oliver (75 De 01)29 favor the Kaman results. However at lower energies the new 130 - 450 eV uranium measurements by Cukier et al.^O (not shown), although
ENERGY (KEVt
Fig. 15.
The principal features in figure 15 for carbon are (a) the slight sys- tematic divergence of the "difference" photoeffect data points from Scofield^^ '. theory in range 10 to 30 keY, and (b) the complete breakdown above 30 keV of this method for experimentally deter- mining the carbon photoeffect cross PHOTON ENERGY. keV section.
Fig. 14. In figure 16 for uraniiijn we can now see more clearly the relation of the exhibiting a shape similar to that pre- Del Grande and Oliver^S measured points dicted by Veigele et al.^^ , are closer (open circles) to the Veigele et al.^^ in magnitude to the Sandia (Biggs and Lighthilll5) extrapolation down through calculation (0.1 to 2.5 keV for uranium) and ( this region. Further uranium measure- to the Scofield-^' calculation 1 to 1500 keV) ments at and below 1 keV are in .,-| progress at the University of Hawaii-^
A More Explicit Look at Photoeffect
A more sensitive graphical com- parison of measured total attenuation coefficients with calculated photo- effect cross sections can be achieved by subtracting cal ciliated coherent and incoherent scattering cross sections from the measured totals, then multi- plying these "photoeffect" differences by an appropriate power of photon energy. In figures 15 and 16 we see that the power is a convenient compromise for application to all elements Z = 1 to 100. Veigele and Briggs52 have constructed these and similar plots for all elements having measured data in the Kaman file, for purposes of evaluating theoretical photoeffect cross sections shown as Fig. 16. . '
Scattering Data
This section of the talk is a brief summary of a recent extended-range tabulation and discussion of the atomic form factor F(x,Z) and the incoherent scattering function 8(2, Z), to which reference can be made for further
detailsl4 .
The atomic form factor for hydrogen is shown in figure 17 for (a) a neutral u 1.0 \ Fix, H- F S.l/FIx, H 1 isolated hydrogen atom (solid curve) calculated using the simple closed-form \ F(x,-|H2)/FIx, H)
"exact* formula given by Pirenne53 , (b) the "floated sphere" (0.07 2. off the \ et proton into the bond) Stewart al. res- \ I ult34 (circles useful for approximating 2.0 3.0 4.0 terminally-bonded hydrogen, and (c) H in X, sin(8/2)/x(A) molecular H2 as calculated by Bentley Fig. 18. and Stewartl3 (triangles) using Kolos- wavefunctions fioothaan35 For elements other than hydrogen, the atomic fQrm factor in the present tabulations^^ was pieced together from available numerical calculations by 37 Brown^" and by Cromer and Mann , additional extended-range results -.g
supplied by Cromer to Veigele et al. ,
-o-ooo-co -o-
F(x. [Hi)
16'
FU.H), PIRENNE
• FU,H-FS.). STEWART, ET AL,. AND rC^ EXTRAPOLATION
- Fl«, jHj), BENTLEY-STEWART, F(x,Z) O CROMER AND X"* EXTRAPOLATION BROWN BETHE-LEVIN6ER PRESENT TABLES
8R0WN ( } , K < 2 fl"'
- B L , NORM TO BROWN AT 0.1 1.0 2A"'. ( 1, . , 2I'' X, sin(9/2j/x il)
Fig. 17.
0.1 1.0 In figure 18 the ratios of the X, Sin (9/2 )/x(A) above Stewart et al.34 and Bentley- Stewartl5 molecular-hydrogen results Fig. 19. to the Pirenne atomic-hydrogen results suggest that H2 molecule, at least for x<1.0 i""^, strongly resembles the He 13—0__p 000 00 o CD atom. That is, the effective c Bentley- 10' Stewart H2 form factor for x = -J- (~V2 2 0) as used in calculating the coherent 10' scattering cross section for H2 would
be of the form F(x,Z) O CROMER BETHE-LEVINGER IK-SHELL) id' PRESENT TABLES \ CROMER, K < 10 X"' 2(h^H2)|,^0^' = 2{.J2 ']=^4 (5) B.-L , , > 10 J-'
[) which can be compared with
I \.X 01 10 X, sin (e/2)/x(A) (6) Fig. 20.
9 and from the Bethe-Levinger58 closed- I 1 I 1 1 1 1 1 1 form expression for the asymptotic 1 high-x region. The composition of the MEAS. :
—\* ' the data- V 8 04 keV [36 Br 01] present tables from above = A 17.5 keV [55 Be Oil — \ o - keV 1 soiirces is indicated in figures 19, 20 175 [6 Ba 01 ] 0 430 kcV [68 Wa Oil and 21 for helium, aluminum and lead. — ^\ 145 keV [69 Gh Ol] — ': • 17.5 keV [69 Jo Olj F{x,Z) • \~ 1 1 1 1 I 1 1 1 ! I \ 1.0 ^ 2.0 3.0 Fix, Z) X, sin (9/2 A) Fig. 24. PRESENT TABLES CROMER. X 10 A"' 10 l~' 0.01 0 1 1.0 10 100 K, sin (e/2)/x(A) Fig. 21. In figure 22 through 26 we compare the above theoretical form factor tabu- lation with available measurements for MEAS^ • 8.04 keVl [69 Ha Ol] O 17.5 kev'} CALC : PRESENT (BROWN) 1.0 10 X, 5in(9/2)/'x(A) Pig. 25. 1.0 o 2.0 X, sin (e/2)X(A) 1 1 1 1 1 1 1 , l| 1 M 1 1 III I 1 r~DLQi [ lll ; Pig. 22. - F(x,Z) Z _ MEflS: . 1330 keV |157Be OIJ Vv O 1330 keV [SSBe Ol] y 2620 keV [58 Eb 01] ^\ — O 5 II keV [66 Ha Ol] J - & 1330 keV [71 Ho Ol] Z CALC _ PRESENT ( CROMER B -L 1 T F ' CROMER - VEIGELE 1.0 2.0 ^ 1 1 1 Mil! 1 1 1 1 1 , 1 1 1 1 1 i[ ,1,1 1 \ X, sln(e/2)/'x(A) 1.0 X, sin(9/Z)/X( Pig. 23. Pig. 26. 10 , ; 1 r the elements beryllium, neon, aluminum, tin and uranium, also with, form factors calculated using the Thomas-Fermi (TP) statistical model of the atom. In the measurement-reference symbols in figures 22-29, the first two digits refer to the year of publication and are followed by the first two letters of the first-author's last name and am additional number for uniqueness. For example, "[58 Sb 01]" stands for "Eber- hard, F., G-oldzahl, L. and Hara, E., J. MEAS, 280 ktV (64 An 01] Phys. Radium i^, 658-667 (1958)". A O 662 ttV (66 Qu Oil complete listing of measurement refer- PRESENT ( CROMER ) ences for these and other elements is given in reference of this paper. 20 40 60 80 X, sin(S/2)/X(A) Figures 27 to 29 show similar com- Fig. 29. parisons of the present theoretical ta- bulations-^^ of the incoherent scatte- ring function S(x,Z) with available tial, resulting in 20'/. to 30*/. diffe- measurements for carbon, aluminum and rences in the integrated incoherent lead. For the elements helium through scattering cross section at 1 keV. carbon we have used the configuration- interaction results of Brown35 in Pair Production preference to those of Cromer and Mann39 for S(2,Z) [also for F(z,Z)]. Recent total attenuation coeffi- As can be seen in figure 27 for carbon, cient measurements by Ahrens et al.40 the differences in S(z,Z) for Be, B suggest that calculated pair production and C between Brown and Cromer-I*Iann in cross sections in present tabulations^ , 6 ,7 ,15 may be too low by amounts the range z=0to0.5^ are substan- shown in figure 30 of 0.8'/., 2*/ and 4/. for the elements copper, tin and lead at "1— photon energies 10 to 11 MeV. Since no theoretical treatment is yet available for this intermediate energy region, various semi-empirical 9.13 HV [42 La 0 Ij CALC: schemes, as shown in figure 31, have PRESENT (BROWN ) CROMER been employed4 ,41 ,42 , to join the (Ahren ei % ^ (.) ^ (I). c«lculff;»d Or Mu96e\.L 5 1.0 2.0 X, sin(e/2)/x( A) Cu Fig. 27. 1 1 1 Sn S(», Z) z Pb MEAS 0 17.5 li«V [42 Lo 01 1 » i.05 keV [56 Wo 01 i 280 keV [S4 An Oil V 17.5 ktV (6 e Ph 01] CALC. PRESENT (CROMER) 1 / , 1 1. .J_ 1 , 1 J lO-o laz 10* fO s lae n.o 1.2 sm(8/2)/x(A) PHOTON EH£ROT / M.Y Fig. 28. Fig. 30. 11 . 1 — T 1 r I r ~i In figure 32 the ratios of various bound-electron incoherent (Compton) sca- ttering On^^ models to the free-electron EW Zlein-Nishina model are plotted vs. Z. Here we see that although the Thomas-Fermi (TF) statistical model predicts a smooth Z-dependence, the Cromer-Mann39 Hartree-Fock and Brown36 configuration-interaction models at 1 keV indeed display breaks where pre- dicted by Rau and Fano44 . On the other hand the coherent scattering cross section, plotted 10 20 30 i.0 =0 &0 70 90 '^0 100 110 against Z in figure for several PHOTON ENERGf / MeV 33 cons- tant energies, is seen to be insensitive Fig. 31. not only to Z-discontinuities in atomic structure, but also to the choice of threshold-region (1.022 to 5 MeV) re- atomic model except for the lowest-Z sults to the high-energy asymptotic elements region. In these schemes the high- energy Davies-Bethe-Mazimon43 Coulomb = 1 correction is usually modified to 1 keV prevent the cross section from going l^^, ' negative and, within the spread of Ml ""i^ 10 hev available data-points, to smoothly join K the threshold region. In subsequent y tabulations, unless this gap in o\ir theoretical iinderstanding is bridged in the meantime, the empirical corre- ^^^0^0f''^~^ 100 hev ction-function suggested by Ahrens et aL should be used in calculating pair- production cross section values. THOMAS-FERMI • GROMtR-VEIGELE Y A BROWN, BETHE - LEVINGER Z-Smoothness MeV Rau and Fano44 have suggested ^^fc.grt""*"'*'^! looking for breaks in Z-smoothness in • the various interaction cross sections 1 1 1 1 1 1 1 1 not only in crossing the rare gases but also in the vicinity of the "noble metals" copper, palladixim and gold Fig. 33. which mark the completion of the L, M and W d-electron shells. With the systematic all-Z photo-.g effect calculations by Veigele et al. and ScofieldlV now available, it is also possible to look similarly at the photoeffect cross section i for theore- tical predictions of departures from Z- smoothness. In figure 34 > based on the Scofield-^'7 results at 1 keV, the major Z-dependence between absorption edges is removed by dividing the cross section in barns/atom by Z^, and here various mul- tiples-of-ten factors have been applied to examine these regions side-by side. Although argon, krypton, palladium and gold fall well-between edge-regions for 1 keV, the pronounced structure seen for incoherent scattering is not present. The Veigele et al.lo calcu- \ I \ o.oiL__i__J i L I ! I lated photoeffect results at 1 keV are 0 20 40 60 80 100 Z qualitatively the same as in figure 34. Thus present theory, at least, would Fig. 32. suggest that the photoeffect and total 12 In addition to the experimental points and the MDP/B library arbitrary baseline in figure 35 the dash-dot line represents the LASL [Storm and Israel^ ] theoretical compilation and the dotted line is the Kaman [Veigele et al.-^° ] compilation which was fitted to experimental values. Such graphs indicate the rate of convergence (if o S20 any) of measurements and theory toward determining "underlying reality" in which the data-points and compilation- E = 1.0 KEV lines should coalesce to a single hori- zontal asymptote for each element as we proceed off to the right. . . In figure 35 copper is interesting in that the experimentally-based Kaman compilation appears 5"/ higher than the bulk of the data points, even though Fig. 54. the two high points. Dyer 46 and attenuation coefficient can be inter- Ehrenfried and Dodds47 were not given excessive weight polated across Z (except across absorp- in the fitting. This compilation assumed Z-smoothness, with tion edges) to 1 or 2'/, although for the heavier elements larger errors five iterations fitting alternatively could result if a gap between measured energy and on Z. Hence it is still elements is too large. possible that the "real world" is not as smooth in Z as suggested by the Convergence in Time Scofield and Kaman calculated results. Moving down to tin and lead we In figure 35 one final means of see examining and evaluating photon cross that the LASL° values, which are here sections is shown. The attenuation the Brysk-Zerby48 theoretical photo- - than the coefficient for the 8.04 - keV copper effect , are 3 4X lower emission line in various materials measured values. The Scofield-'-' values for \iranium, as we have noted, are also has been remeasured over the years, a few percent lower than the recent Del following the 1909 measurements by Barkla Grande and 01iver29 measurements in and Sadler45 . In this figure the this region. measured values have been divided by the ENDF/b"? [McMaster et al.25 ,26 ] com- pilation values, represented by the Conclusion unit-value solid horizontal lines. In summary, uncertainties in the available photon cross section infor- mation appear to be of the order of 20'/. or greater below 1 keV, 3 to lOX in the region 1 to 10 keV and 1 to 4*/ above 10 keV. Fig. 35. 13 . » References • 13. Bentley, J., and Stewart, R.P., Two-Center Calculations for X-Ray 1. Tagore, R., Collected Poems and Scattering, J. Comput . Phys. 11, Plays . (MacMillan, N.Y., 1936). 127-145 (1973). See also: Total X-Ray by 2. Rbntgen, W.C., Uber eine neue Art Scattering Ho. J. Chem. von Strahlen, Sitzungsber. Phys. 62, 875-878 (1975). Wtirzburger Physik. - Medic. Gese- llschaft. (1895). 14. Hubbell, J.H., Velgele, Wm. J., 5. McLaughlin, W.L., Hussmann, E.K., Briggs, E.A., Brown, R.T., Cromer, Eisenlohr, H.H., and Chalkley, L., D.T., and Howerton, R.J., Atomic A Chemical Dosimeter for Monitor- Form Factors, Incoherent Scattering ing Gamma-Radiation Doses of 1-100 Functions, and Photon Scattering krad, Int. J. Appl. Radiat. Isot. Cross Sections, J. Phys. Chem. Ref. 22, 135-140 (1971). Data 4, 471-538 (1975). 4. Hubbell, J.H., and Berger, M.J., Sections 4.1 and 4.2 in Jaeger, R. G . ( Ed ) : Engineering Compendium on . Biggs, F., and Lighthill, R., Radiation Shielding (IAEA. Vienna). 15. Ana- lytical Approximations for X-Ray Vol. 1, Ch. (Springer, Berlin 4, Cross Sections. II. Sandia Lab. 1968), pages 167-202. See also Hubbell, (Albuquerque, N. Mez.) Report SC- J.H., Photon Cross Sectio- RR-71-0507 ns, Attenuation Coefficients, and (1971), 140 p. See alsos Biggs, F., and Lighthill, R. Analy- Energy Absorption Coefficients from , tical Approximations fo^- Total and 10 keV to 100 GeV, Natl. Stand. Ref. Energy Absorption Cross Sections Data Ser. 80 for 29 (1969), p. Photon-Atom Scattering, SC-RR-72- 5. Berger, R.T., The X- or Gamma-Ray 0685 (1972), 131 p. Energy Absorption or Transfer Co- 16. Veigele, Wm. J., Briggs, E., Bates, efficient: Tabulations and Dis- L., Henry, E.M., and Bracewell, cussion, Rad. Res. 1-29 B., 1^, (1961). X-Ray Cross Section Compilation 6. Storm, E., and Israel, H.I., Photon from 0.1 keV to 1 MeV, Vol. 1 Cross Sections from 1 keV to 100 (225 p.) and 2(73 p.), Rev. 1, MeV for Elements Z=l to Z=100. Nucl. Kaman Sciences Corp. (Colorado Data Tables A7, 565-681 (1970). Springs, Colo.) Report KN-71-431(R) See also: Veigele, Wm. J., Wright, J.B., and Roussin, R.W., (1971). 7. Photon Cross Sections from 0.1 keV ENDP (Evaluated Nuclear Data File) to 1 MeV for Elements Z=l to Z=94, photon interaction data tape DLC-7E Atomic Data 51-111 (1973). (Dec. 1974), available from RSIC ^, (Radiation Shielding Information 17. Scofield, J.H., Theoretical Photo- Center, Oak Ridge Nat. Lab.). ionization Cross Sections from 1 to 1500 keV, Lawrence Livermore Lab. 8. Puller, E.G., Gerstenberg, H.M., (Livermore, Calif.) Report UCRL- VanderMolen, H., Dunn, T.C., and 51326 Photonuclear Reaction Data, 1973 (1973), 373 p. NBS Spec. Publ. 380 (1973) 131 p. 18. Goswami (now Sinha), B., and Chaudhuri, N., Measurements of 9. Hubbell, J.H., Survey of Photon- Gamma-Ray Attenuation Coefficients, Attenuation-Coefficient Measirre- Phys. Rev. Z 1912-1916 (1973). ments 10 eV to 100 GeV, Atomic 2, Data 2» 241-297 (1971) 19. Mavroyannakis, E. , and Antoniades, J., Mesure du Coefficient d 'Absor- 10. Henke, B.L., Elgin, R.L., Lent, ption Gamma par des Materiaux R.E., and Ledingham, R.B., X-Ray Utilises aux Constructions Nucl- Absorption in the 2-to-200 i eaires, Nucl. Res. Ctr. "Democri- I4., 112- Region, Norelco Reporter tus" (Athens, Greece) Report DBMO- 131 (1967). 70/11 (1970) 12 p. 11. Crasemann, B., Koblas, P.E., Wang, 20. Boltaks, B.I., Plachenov, B.T., and T.C., Birdseye, H.E., and Chen, Semenov, E.V., The Coefficient of M.H., Measurement of the Photo- Absorption of Co-60 y-Rays Semi- electric Cross Section of H2 at conductors, Dokl. Akad. Nauk SSSR 5.4 and 8.4 keV. Phys. Rev. A 2» 121, 72-75 (1958). 1143-1151 (1974). 21. Codling, K., Madden, R.P., Hunter, | Depende- 12. Cooper, J.W., High-Energy W.R., and Angel, D.W., Transmission Molecular-Hydrogen Pho- nce of the of Tin Film in the Far Ultraviolet. tolonization Cross Section, Phys. J. Opt. Soc. Am. 56, 189-191 (1966). Rev. A ^, 2236-2237 (1974). 14 . . , , , 22. Haensel, R. , Kunz, C, Sasaki, T., 33. Pirenne, M.H., The Diffraction of and Sonntag, B., Absorption Measure- I-Rays and Electrons by Free ments of Copper, Silver, Tin, Gold Molecules , (Cambridge Univ. Press, and Bismuth in the Far Ultraviolet, London 1946), page 9. Appl. Opt. 7, 501-306 (1968). See 34. Stewart, R.F., Davidson, E.R., and also Phys. Lett. A 2^, 205-206 Simpson, W.T., Coherent X-Ray Sca- (1967). ttering for the Hydrogen Atom in 23. Lukirski, A. P., Zimkina, T.M., and the Hydrogen Molecule, J.Chem.Phys. G-ribovski, S.A., Photoionization il, 3175-3187 (1965). of d-Electrons in Te, Sn, Pb, PbTe 35. Eolos, W., and Roothaan, C.C.J. and SnTe, Fiz. Tver. Tela 8, 1929- Accurate Electronic Wave Functions 1931 (1966). for the Hp Molecule, Rev. Mod. Phys. 24. McG-uire, E.J., Photo-Ionization 22, 219-232 (I960). Cross Sections of the Elements 36. Brown, R.T., Atomic Form Factor for Helixim to Xenon, Phys. Rev. 175 . Neutral Carbon, J.Chem.Phys. 55 . 20-30 (1968). 353-355 (1971)? See also: Phys. Rev. 25. McMaster, W.H., Del Grande, U.K., A 1, 1342-1347 (1970) 2, 614-620 Mallett, J.H., and Hubbell, J.H., (1970), 5, 2141-2144 (1972) and 10, Compilation of Z-Ray Cross Sections, 438-439 (1974). Lawrence Livermore Lab. (Livermore, 37. Cromer, D.T., and Mann, J.B., X-Ray Calif.) Report UCRL-50174, Sec. II, Scattering Factors Computed from Rev. 1 (1959), 350 p. ; Numerical Hartree-Fock Wave Functi- 26. Hubbell, J.H., McMaster, W.H., Del ons, Acta Crystallogr. A 24, Part 2, Grande, N.K., and Mallett, J.H., 321-324 (1968). Sec. 2.1 in Ibers, J. A., and 38. Levinger, J.S., Small Angle Sca- Eamilton, ¥.C. (eds.): International ttering of Gammas by Boimd Electrons, Tables for X-Ray Crystallography Phys. Rev. SJ, 656-662 (1952). (lUCr), Vol. 4 (Kynoch Press, Bir- 39. Cromer, D.T., and Mann, J.B., mingham, England 1974) , pages 47-70. Compton Scattering Factors for 27. Biermann, H.H., Die Massenschwachun- Spherically Symmetric Free Atoms, gskoeffizienten monochromatischer J. Chem. Phys. £1, 1892-1893 (1967). Rontgenstrahlen ftir Cellophan, Al, Also: Cromer, D.T., Compton Scatte- Se, Ag, Cd, Sn, Sb und Te bis ring Factors for Aspherical Free lois, Ann. Phys. 26, 740-760 (1936). Atoms, J. Chem. Phys. 4857- 4859 (1969). 28. Zimkina, T.M., Fomichev, V.A., Gribovski, S.A., and ZhTikova, I.I., 40. Ahrens, J., Borchert, H., Eppler, Some Peculiarities in X-Ray Absor- H.B., Gimm, H., Gundrum, H., Riehn, ption by Lanthanum Group Rare Earth P., Ram, G.S., Zieger, A., and Ziegler, B., Photo-Nuclear Cross- Metals, Fiz. Tver. Tela ^, 1447- 1450 (1967). See also: Izv. Akad. Sections and Pair-Production Cross- Sections in the Range of 10-150 Nauk SSSR Ser. Fiz. ^k* 874-882 (1967). Also Zimkina, T.M. MeV, Proc . Electron Accel. Working personal comm. Group Conf., Giessen, Germany (Sept. 1971), pp. 359-370. 29. Del Grande, N.K., and Oliver, A.J., Soft X-Ray Cross Section Measure- 41. Grodstein, G.W., X-Ray Attenuation ments for Uraniiim (Abstract), Bull. Coefficients from 10 keV to 100 MeV, Bur. Stand, Circ. Am. Phys. Soc. 18, 635 (1973). Natl. 583 (1957), Also Del Grande, N.K., personal 54 p. comm 42. Koch, H.W., Electromagnetic Cross Sections for Electron and Nuclear 30. Cukier, M. , Dhez, P., Wuilleumier, F., and Jaegle, P., Photoionization Research, Nucl. Instrum. Methods Cross Section of Uranium in the 28, 199-204 (1964). Soft X-P^y Phys. Lett. Region, 43. Davies, H., Bethe, H.A. , and A 48, 307-308 (1974) Maximon, L.C., Theory of Bremsstra- hliing Production. II. 31. Henke, B.L., personal comm. and Pair Integral Cross Section for Pair Production, Phys, Rev. 788- 32. Veigele, Wm. J., and Briggs, E. 795 (1954). personal comm. Also: Hubbell, J.H., and Fano, U., Atomic and Veigele, Vftn. J., Comparison of 44. Rau, A.R.P., Theoretical and Experimental Photo- Potential Wells and the Periodic effect Data 0.1 keV to 1,5 MeV, NBS Table, Phys. Rev. 162, 7-10 (1968). Tech- Note 901 (1976), 43 p. 45. Barkla, C.G., and Sadler, C.A., The Absorption of Rbntgen Rays, Philos. Mag. 17, 739-760 (1909). 15 . 46. Dyer, G.R., The Determination of J.H. Hubbell Low-Energy X-Ray Mass Absorption Coefficients for Copper, M.S. In my opinion, one of the most Thesis, Emory Univ. (1962), 80 p. urgent areas of need is the measurement of whole-atom incoherent scattering 47. Ehrenfried, C.E., and Dodds, D.E., differential cross sections, from which X-Ray Attenuation Coefficients Mass one can derive values to check present in the 1.49 to 11.9 keV Range, theoretical incoherent scattering AFSWC-TN-59-33 (I960), 56 p. functions. Although the K-shell and 48. Brysk, H., and Zerby, C.D., some L-shell measurements are very Photoelectric Cross Sections in valuable, we need the whole atom data the keV Range. Phys, Rev. 171 for compilation purposes. Dr. J.W. 292-298 (1968). Motz at N.B.S. plans to make some measurements, but more would also be Discussion useful. W.S. Snyder I refer to the fi^re showing the early calculated results of Jaeger and Hulme published in 1936. There were only three other calculations shown in the later years. Is it likely that more calculations would improve our knowledge of the photoelectric effect ? J.H. Hubbell The Jaeger-Hulme ( 1936 ) points were for pair production rather than atomic photoeffect. There are still some 1 5p/5t>orn o Jaeger-, Hulme (1936) D Davis, Bethe,MaxinRon (195A) — 0verb0 (197o) --expected energy dependence 1o loo looo Photon Energy /MeV 40 Additional figure from Ahrens et al. unresolved differences between experiment ' and present theory in the case of both ' photoeffect and pair production. Hence in either case further calculations based on improved atomic models would Indeed be desirable, A.M. Ghose ' What would you consider to be the \ most useful areas to which experimental investigation should now be directed ? ' • - i 16 , , SEMIEI-IPIRICAL FCRI-IULATION OF COHERENT SCATTERING OF GAi'RiA RAYS S.C. Roy and A.M. Ghose Nuclear Physics Laboratory Bose Institute, Calcutta-700009 India An empirical formula to estimate Rayleigh scattering cross- section of gamma rays depending on photon energy and momentum transfer involved was first developed by Nath and Ghose by consi- dering the available theoretical and experimental cross-section values. V/ith availability of much accurate cross section values in recent times by using lar^e volume Ge(Li) detectors [M.Schumacher et al, Hucl.Phys. A206, 531 (1973)4 Nucl.Phys. A213, 306 (1973) J it becomes necessary to recheck the existing formula. V/e observe reasonable difference in cross-section values in the region where theoretical calculations are not available due to the uncertainties in earlier measurements. In the present paper an analytical formula of coherent scattering cross-sections of photons valid for photon energy below 1.5 I'leV and upto momentum transfer 2.0 in units of mc has been developed. The calculated values for different photon energies have been compared with experimental results and is in good agreement within experimental uncertainty. (Analytical formulaj coherent scattering; cross section; gamma rays; photons; Rayleigh scattering.) Introduction analytical formula of coherent cross section valid for photon energies below For photons of energy less than 1.5 i'leV and up to momentum transfer 2.0 about 1.5 I-leV and momentum transfer mc units will be described. during collision below about 2.0 mc units [m is the mass of the electron, c the Derivation of the Empirical Formula velocity of light] Rayleigh scattering is the most dominant of the processes The empirical formula was proposed constituting coherent scattering of on the basis of the form factor approxi- gamma rays. Also, Rayleigh scattering, mation in the low energy limit. If the being one of the fundamental modes of coherent scattering cross section a(e,Z) interaction of radiation with matter, not is expressed in the follov-ring form: only requires careful investigations on its ov7n right but careful estimation of a(e,Z) - i(l+cos2e)r2 znf(q) ... (1) riayleigh scattering is important in various radiation physics measurements where, 6 is the angle of scattering and calculations. Unfortunately, Z is the atomic number of theoretical computation of Rayleigh scatterer scattering is a complex problem and it is f(q) is a function of momentum not practicable to compute the Rayleigh transfer q scattering intensity for all photon rQ is the classical electron energy and for all scatterers. radius Therefore, a simple analytical formula, even if it is obtained semi-empirically then a(e, Z)/i(l+cos2e) is a f^onction of vrhich can reproduce Rayleigh scattering only and has no explicit dependence cross section reasonably v/ell is useful either on the angle of scattering or on to radiation physicists. An attempt v/as the energy of the photon. Such depend en made by liath and Ghose-'- to develop such ce is implicit through momentum transfer a formula on the basis of the then q. Nath and Ghose plotted 0(q,Z) = available theoretical and experimental a(e, Z)/T(l+cos2e) as a function of q and cross section values. Recently more observed it to be a smooth function of accurate cross section values have been q for energies of the photon below 0.4 reported^''* and it has become necessary MeV, but above 0.4 HeV to be a family of to modify the above formula. In the curves falling systematically below one present paper the development of an another as energy increases. Nath and 17 . . Ghose ascribed this trend to relativistic In the present paper we shall derive effects and proposed empirical corrections the modified semi-empirical formula for to make the above expression a smooth a standard absorber which is taken as function of q for all values of photon lead for obvious reasons and the esti- energy. This was done by introducing a mation of cross section values for other factor 9(E,q) whose values is 1 for elements will be taken up later. The 0 a = 15. 3395-44. 4843q+127.56l7q2 -197.0323q5+343.6817q4 b = 0.2532q for O^q^O.7 mc a = 3.965 4-3.9848q b = 0. 0769+0. 2731q2*^'^^^' for q>0.7mc The general formula for the coheroit scattering cross section of any element Z can be written as : a(e,Z)=T(l+cos2e) ( Z/Zq)^^^'!^ exp[a+ (b/E) Jxl0-28cm2, where index n(q) obtained by l^ath and Ghose is given by n(q)=2. 90+0. 08q+l. 27^-0. 36q^ q>0.1 mc. for q below 0.1 mc an additional term -0.90 exp(-500q2) was found necessary. Discus sion The coherent scattering cross section calculated on the basis of the ' i:'.-. 1 III ui 01 mc present formula for lead was compared with the experimentally obtained values in Figure 2. Except for photon Fig. 1. Experimental a(q) data of lead energies 1.17 and 1.33 HeV the cross for different photon energies section values for angles greater than plotted as a function of q. 30° were taken from the measurements 18 . . . . , , section values for photon energy .1.33 HeV and angles 30° onwards were compared with tiie measured data of Dixon, Storey and Kardie et al; whereas for angles less than 30° were co:npared with measured values of i and standing and Jovan.ovich" . The comparison shows that agreement is quite satisfactory within the experimental uncertainties. SchumacherlO studied Z- dependence of coherent scattering cross L^*«. sections in the intermediate to high »o'(Ref.2,3) Z region for a few elements and more accurate measurements covering wider range of elements are necessary to recheck the values of n as obtained by i>Iath and Ghose. The present formula will be utilised to study electronic charge density distributions of various elements and to recheck the earlier calculations by Roy and G-hose-^-^ for lead. Our thanks are due to Prof. 3.M. Sircar, Director, Bose Institute for his kind interest in the work. Refer enc e s 1. Nath, A. and Ghose, A.ii. , NBS Technical l^ote 442 (1968). 2. Schumacher, K., Phys . Rev. 132, 7 (1969) 3. ochumacher, M, Smend, P. and Borchert, I., JJucl. Phys. A206 . 531 (1973). 4. Roy, S.C., Ilath, A. and G-hose, A.!-!., Nuclr. Instr. and Methods (accepted for publication 5. I'lath, A. and Ghose, A.r-'I., Wucl. Phys. ^, 547 (1964). 6. Dixon, W.R. and Storey, R.S., Can. J. Phys. 46, 1153 (1968) 7. Hardie, G., Merrow, v/.J. and Schwandt D.R., Phys. Rev. CI, 714 (1970). 8. Roy, S.C, and Ghose, A.ii., Ph.D. thesis of Roy (C.U'. 1971). g. Standing, K.G. and Jovanovich, J.V. Can. J. Phys. (1962) . 10. Smend, P., Schumacher, i-i. and Borchert, I., Nucl. Phys. A21'j . 309 (1973). 11. Roy, S.C. and Ghose, A.k., Phys. Rev. 1^ 8A, 2298 (1973). 6 55 10 So w 85 i25 rtS" -rtr SCATTERING ANGL£ W DEGREES 2. Comparison of the empirical formuJLa ^/ith the experimental data for different photon energies made by Schumacner. For angles loss than 3C°, except for 1.33 1-ieV, the cross section values are taken from the measurements made by Roy, iiath and Ghose^ and i>Iath and Ghose^. The cross section values of 1.17 ileV for angles 30° onv/ards v;ere taken frpm the measure- ments of Dixon and Storey*^. The cross EXPSRIM^:i;NTAL PHOTOIONIZATION CROSS Si:;CTI0N3 OF GMOTA RAY PHOTONS FOR LO\I, MBDITTM AND HIGH Z ATOMS B. Sinha (G-oswami) and N. Chaudhuri North Bengal TJniversity, Darjeeling India Direct measurements of subshell and total photoionization cross sections reported so far are relatively few. Total photo- ionization cross sections have been determined previously from the measured total photon attenuation cross sections using the available theoretical estimates of incoherent and coherent scattering cross sections and above 1.02 MeV the electron-positron pair production cross section. This method is suitable at an energy region for such atoms for which photo absorption contribu- tion is larger than or at least comparable to other individual contributions to the total photon attenuation coefficient. Theo- retical investigations have been continued to improve the accuracy of individual cross sections. J.H. Scofield has calculated screened relativistic photoionization cross sections for all 100 atoms (Z = 1 - 100) in the energy range from 1 keV to 1.5 MeV. Refined incoherent and coherent scattering calculations for all 100 elements over a wide energy range using SOP Hartree-Pock wave functions have been reported recently. Improved pair production cross sections are also available. In view of these accurate theoretical results and inadequacy of experimental information on photoionization in the energy from 10 to 100 keV and above, v/e have evaluated experimental total photoionization cross sections for lov7, medium and high Z elements in the range Z = 12 to 92, from the very accurately measured total cross sections using the accurate theoretical estimates of partial cross sections. An analysis of the experimental results has been made and interpreted in a compa- rison of the theoretical photoionization results recently published. The Z dependence and photon energy dependence of total cross sections have also been studied. (Coherent scattering, cross sections, gamma ray, incoherent scattering, pair-production, photoionization.) Introducti on Highly accurate relativistic treat- method is to measure the total attenua- ment of the photoionization process in tion of photons, from which photoioniza- the Hartree-Slater screened potential , tion cross sections can be obtained by model has recently been made by Scofiela subtraction of theoretical values for for all atoms with Z from 1 to 101 in the scattering (coherent and incoherent) the photon energy range from 1 to 1500 cross sections and pair production cross keV. In this energy range the only sections for photon energy above 1,02 other high-accuracy cross section cal- MeV. This method gives sufficiently culations are those for 14 atoms in the accurate resialts for such photon energies range of Z from 13 to 92 by Schmickley and atoms for which photoionization con- and Pratt 2 . tribution is larger than or comparable to the scattering and pair production In view of these highly accurate contributions. Further, these cross theoretical results, we feel a need for section values must be very accurately reanalysis of the earlier measurements known. Highly accurate theoretical and to carry out accurate measurements values of coherent scattering cross of photoionization cross sections for section and incoherent scattering cross low, medium and high Z atoms over a wide section are now available from the com- range of photon energies. The direct pilations of Veigele et al^ and of measurements of phot oab sorption cross Hubbell et al^. These cross section data sections so far reported are relatively are based on Hartree-Fock atomic form- few, because of experimental difficulty fact or and incoherent scattering fu^^-c- in separating the photoelectric process tion calculated by Cromer and Mann^ and from other processes involved. The other Cromer°. In the compilation of 20 Hubbell 9t al, Bethe-Levinger relati- dure the same as that adopted by G-hose . vistic K-shell form factor was used for the atomic form factor above a momentum Results amd Discussion transfer of 0.5 mc. New theoretical results for pair production cross sec- Accurate theoretical whole atom tions in the energy range from 1.02 - 5 cross sections for photoionization pro- MeV have been given by ^verb^jS ^ Since cess were not available in early sixties the individual photon cross sections are and the earlier experimental values of very accurately known theoretically at total atomic photo-absorption cross sec- present, the total attenuation method is tions were compared with the calculated well suited in the present energy range K-shell cross sections using the avail- where available experimental data are able values of total-to-K-shell cross found to be inadequate. section ratio. V/e have given in Table 1 the present experimental results and the Method new whole atom theoretical cross sections only for some atoms representing low, The total attenuation method has medium and high Z elements. The theore- been used to obtain photoionization tical results are those obtained from cross sections for 34 elements from our tabulations giveg by Scofield and own measurements and the recent measure- Schmickley-Pratt . The cross sections ments of Conner et al^*-* . The measure- of Scofield are found to agree within ments of total attenuation were made at about iX with those of Schmickley - a level of accuracy of about 1% . All Pratt for the common elements in these total attenuation data for each element two calculations. For a given element were converted to attenuation cross these cross sections were plotted against sections usin^ the recent data of physi- photon energy to obtain a smooth curve. cal constant s-^^. Theoretical scattering The cross sections were read from these (coherent and incoherent) and pair pro- curves at energies for which cross sec- duction cross sections at our photon tions were not directly calculated by energies were derived through interpo- Scofieldl and Schmickley-Pratt 2 . it is lation of published cross section data seen from the table that the new whole mentioned in the section 1. atom photoionization cross sections are in fair agreement with the measured data The total attenuation data analysed except for the cross section for lead here have been obtained by excluding or (Z = 82) at 88.1 keV which is almost the minimizing a number of systematic errors same as K-shell threshold energy of this which were present in many of the ear- element. By the method of least-squares, lier attenuation measurements. The the Z^ variation of the experimental error in the final photoionization cross sections in the range of Z from cross sections for each element and 12 to 92 has been studied at fixed pho- energy is a combination of errors of ton energies. The value of the exponent (i) the measured attenuation cross n has been found to increase from 4.2 to sections, (ii) theoretical scattering 4.6 in the energy range from 88 keV to and pair production cross sections and 1.33 MeV. An analysis has also been (iii) interpolation of theoretical made for the variation at fixed Z in cross sections. the energy range above K-shell threshold energy of the element. The exponent m The measiarement of transmission is found to decrease slowly from 2.8 to of photons through a spherical or a 2.5 in the range of Z between 16 and 30 cylindrical absorber totally enclosing and again from 2.5 to 2.3 in the range a point source of photons yields absorp- Z = 57 to 82. tion cross sections of photons for absorber atoms. Owing to the circular The results of our cylindrically symmetry of the source-absorber assem- symmetric transmission method are in bly, there is no preferred direction of agreement with those obtained in the„ photon scattering to a suitable photon sphere transmission method by G-hose detector and the transmission measure- This indicates that perhaps there is not ments by a uniform spectral sensitivity much practical distinction between two photon counter under the required geo- experimental arrangements. metric conditions give total absorption cross sections directly. Ghose-^^ devel- oped the sphere transmission method and measured photoelectric cross sections by employing a uniform spectral sensi- tivity photon coijinter. V/e have deter- mined absorption cross section by mea- suring photon transmission through cylindrical lead absorbers in a. proce- 21 . Table 1 Total phot oionizat ion croas sections 3. Veigele et al.,Kaman Sci.Rep., for some representative elements in the KN-71-43l(a) (1971). low, medium and high Z ranges. (The final 4. Hubbell et al. , J.Phys.and Chem.Ref. error to the experimental cross section is Data 4, 471 (1975). shown in parentheses). 5. Cromer, D.T. and Mann, J., Chem.Phys. Photon Z Experimental Theoretical 42,1892 (1967). energy photoionization values from 6. Cromer, D.T., J. Chem.Phys. ^,4857 (keV) cross section calculat ions (1969) . 7. Levinger, J. Phys. Rev. (barns/atom) of Scofieldl, S. , 87, 656 Schmickley and (1952). 8. 0verb0,I., Thesis Univ. of Trondheim Pratt 2 (barns/ at om) (1970) . 9. GoswamijB. and Chaudhuri, J. , Phys. 13 1, ,06(0.20 1.21 Rev. 1912 (1973). 26 28,,46(0.46 28.8 A2, 10. Conner, A. L. , At water, H. F. , Plassmann, 50 423^.8 3.50) 424.0 3.H. and McCrary , J.H. , Phys.Rev.Al, 88.1 74 1783 .1 (9.40) 1800.0 3 (1970). 82 2141 .9 (9.70) 2500.0 11. Hubbell, J. H., Nat. Stand .Ref. Data, 92 868, .9 (5.60) 895.0 Ser.NSRDS-NBS 29 (1969). 22 2 .95(0.10) 2.9 12. Ghose,A.M.,rTucl.Phys.2i, 539(1966), 145.4 40 38,.35(0.23 3.7 Nucl. Inst, and Methods li, 45 ( 1965). 57 167 .90(0.53) 165.0 79 584,.63(3.90) 580.0 26 1 .88(0.31) 1.8 208.4 50 33,,80(0.64) 35.5 74 174..1 1.50) 179.0 92 399. ,2 (2.00) 407.0 26 0, ,66(0.28 0.82 279 50 14. ,6 (0.50 15.4 74 80,.1 (0.80) 80.3 92 187, ,8 (1.40) 192.0 50 4, .87(0.50) 5.30 412 74 29. .4 (0.70) 29.2 92 73. .4 (0.2) 73.6 57 2, .94(0.53) 2.92 662 64 5. ,06(0.60) 4.92 82 al4. .8 (0.40) 14.,40(0.63) 14.9 92 23.,60(0.70) 23.9 57 0.815(0.35) 0.952 1115.5 64 1.50(0.40) 1.6 82 5.02(0.50) 4.97 57 0.67(0.34) 0.87 1173 64 1.51(0.38) 1.50 82 4.61(0.48) 4.52 1252 82 a3. 85(0. 50; 4.10 (mean value for Co-60 pho- tons) 57 0.663(0.32) 0.685 1332 64 1.23(0.36) 1.22 82 3.54(0.45) 3.56 a - Results by the direct method. References 1. Scofield, J.H. UCRL-51326(1973) 2. Schmickley, R.D. and Pratt , R.H. , Phys. Rev. 164. 104 (1967). 22 f INNER BREMSSTRAHLUNG ACCOMPANYING- ELECTRON CAPTURE IN '^Be Al^D 5-^Cr H. Sanjeevaiah and B. Sanjeevaiah Department of Physics, University of Mysore Manasagangotri, Mysore-570006 , India The inner bremsstrahlung spectra accompanying electron capture 7Be and 51Cr are studied in coincidence with the 477 and 325 keV ; • gamma rays respectively. The random coincidence counts are subtracted from the true plus random coincidence counts to get the inner bremsstrahlung spectra. The disintegration energies of "^Be and Cr leading to the first excited states of and V respecti- vely are determined from the Jauch plots. Using these values the total disintegration energies of 7Be ^Li and ^Icr ^ly decay processes are calculated. The total disintegration energies are also measured directly by studying the inner bremsstrahlung spectra emitted in the gro-und- to -ground transitions. The results obtained by these methods will be presented and discussed. (Coincidence; electron capture; excited state; gamma ray,- ground state; inner bremsstrahlung; Jauch plot; spectrum; transition.) Introduction Experiment When a nucleus captures an orbital The IB spectra accompanying electron electron there is a small probability capture in 7Be and„ 51Cr to the first that this process is accompanied by the excited states in 'Li and 51v are measured emission of electromagnetic radiation. in coincidence with the nuclear y-i'ays This effect, known alternatively as from the de-excitation of these states. radiative capture or inner bremsstrahlung Two Nal(Tl) crystals I'x li " and li " x 2" (henceforth denoted as IB) was predicted in size are used in a face-to-face geo- by Morrison and Schiff-'-. The energy metry. The resolving time (2t) of the spectrum of the electromagnetic radiation coincidence circuit used in the measure- was calculated to be continuous upto some ment is 40 ns. The bigger crystal maximum energy, the end-point, and to detects the IB photons and the signals have a characteristic shape. from it are scanned in a single channel analyser. The smaller crystal detects Most of the early experiments^"^ the nuclear Y-i"ays and the single channel performed to verify Morrison-Schif analyser which receives the signals from theory showed an excess of low energy this crystal is set on the required photons. This was explained in allowed photopeak. The IB detection assembly is captures by an improvement of the theory housed in a lead chamber of 3" wall presented by Martin and Glauber5»w which thickness. A lead plate of thickness included relativistic effects and the 1.7 mm is placed in between the source possibility of radiative capture from and the smaller crystal. This is done both S and P orbital states. However, with a view to reduce the spurious the predictions of both the theories coincidences due to escape X-rays and become nearly equal over a wide range of cosmic rays. energy below the end point. Therefore it may be assumed that the shape of the The IB emitted in the ground-to- IB spectrum in the higher energy region ground transitions is measured in each is essentially given by Morrison-Schiff case in the energy region beyond the theory. Then by constructing the photopeak using the shielded Nal(Tl) Jauch-plot of the IB spectrum one can crystal and the single channel analyser get the end-point energy. If the associated with it. The intensity of the K-shell binding energy of the daughter sources used in these measui'ements are nuclide is added to the IB end-point somewhat higher than those of the sources energy, one gets the disintegration used in the coincidence measurements. energy of the process. The present The purity of the sources used in the experiments are performed to measure the present investigation is checked by disintegration energies of electron recording the single spectrum over two capture processes in 7Be and 51cr. half-lives in each case. No significant 23 ) . . impurity peaks are detected. 51cr was shovm in Fig. 2. [The results of the obtained from Bhabha Atomic Research present measurements are given in Centre, Bombay, India in the form of Table 1 along with those of other CrCl2 obtained from the workers in the fieldj Radio Chemical Centre, Amersham, UK in the form of 3eCl2. 60p Results and Discussion The IB spectrum emitted in coinci- dence with the nuclear y-rays is obtained by subtracting the random coincidence counts at each channel from the corres- ponding true-plus-random coincidence counts. Corrections for Compton continuum, detection efficiency, energy resolution and K X-ray escape are consi- dered following the method of Liden and Starfelt'''. Correction for energy reso- Fig. 2. Jauch plot VN(E)/E in arbitrary lution and K X-ray escape are found to units versus E in keV for the IB be insignificant in the energy range of from ground- to=ground trans- present interest. A large contribution sition 'Be —> 'Li. to the error comes from counting statis- tics. Jauch-plots of the corrected The end-point energy of the IB spectra are constructed to get the end- spectrum in '^Be emitted in coincidence point energies. A typical Jauch plot with 477 keV nuclear y-^^ys is found to for the IB from electron capture decay be 394 + 16 keV. This is in good agree- of '^Be is shown in Fig. 1. ment with previously measured values^* 9. The K- shell binding energy in'^Li is very small. Therefore the disintegration energy of the process may be considered to be 394 + 16 keV. The end-point energy of the IB emitted in the ground-to-ground transition is found to be 867 + 10 keV. This agrees fairly well with that computed from the first measurement (394 + 16 + 477 = 871 + 16 keV) Table-1 End-point energies of IB spectra Transition End-point Refer- energy (keV) ence „ E.C (First 395+25 8 'Be excited 388+ 8 9 state) 394+16 Present 7 E.G -\± (ground-to 867+10 Present 'Be ground) Fig. 1. Jauch plot V'N(E)/E in arbi- ^'^ 51 .51y* (First 424+16 10 trary units versus E in keV ^-^Cr excited 427+14 Present for the IB from electron state) capture decay of '^Be to the E.C first excited state in 7Li. (ground-to 725+20 11 51cr— ground 794+60 12 The IB spectrum emitted in the 748+16 Present ground-to-ground transition is obtained by subtracting the background co^mts at each channel from the corresponding total counts in each case. After The end-point energy of the IB considering the corrections as before spectrum in 51cr e-iitted in coincidence the Jauch-plots are constructed. A with 325 keV nuclear y-Tays is found to typical Jauch plot for the IB from be 427 + 14 keV. This is in good ground-to-ground transition ^Be 7jjj_ is agreement with previously measured 24 . value . The disintegration energy References corresponding to this transition is 433 + 14 keV. The end-point energy of 1, Morrison, P. and Schiff, L., Phys. the IB emitted in the ground-to-ground Rev. 24 (1940) . transition is found to be 748 + 16 keV. 2, Saraf, B., Phys. Rev. 642 (1954). This is in good agreement with the value 3' Hadansky, L. and Rasetti, F. , Phys. computed from the coincidence measurement Rev. 2Ay 407 (1954). (427 + 14 + 325 = 752 + 14 keV) . 4. Lindquist, T. and Wu, C.S., Phys. Rev. 100, 145 (1955) • The results of the present experi- 5^ Glauber, R.J. and Martin, P.O., Phys, :nents clearly show that the predictions Rev. 10^, 158 (1956) . of Morrison-Schif f and Martin-Glauber 5. Martin, P.O. and Glauber, R.J., Phys, theories become nearly indentical with Rev. 102, 1307 (1958) regard to the spectral distribution of 7. Liden, K. and Starfelt, N., Ark. f. the IB photons in the higher energy region. I^s. 7, 427 (1954). This is indicative of the fact that the S. Lancman, H. and Lebowitz, J., Phys. major contribution to the IB spectrum in Rev. C2, 465 (1971) . the higher energy region comes from 9. Borje, I, Persson and Steven, E. radiative capture from L3 orbital state. Koonin, Phys. Rev. C^, 1443 (1972). The deviation of the Jauch-plot from 10, Koonin, Steven E. and Persson, Broje linearity in the low energy region, I., Phys. Rev. C6, 1713 (1972). however, shows the contribution from the 11. Offer, S. and Wiener, R., Phys. Rev. P orbital state as well. This is 107 . 1639 (1957). explained by I'lartin-G-lauber theory. In 12. Narsimha Murthy, K. and Jnanananda, addition, one might observe an interest- Swami, Ind. J. PureeAppl. Phys. 12, ing deviation in the energy interval 557 (1967). 40-140 keV in Fig. 1. This may be attributed to the inadequacy of even the relativistic theory to account for the shape of the IB spectrum from 'Be where it is expected to be quite accurate. 25 INELASTIC SCATTERING OF 279-KEV GAMMA RAYS BY BOUND ELECTRONS IN HEAVY ATOMS D.S.R. Murty, V. Govinde. Reddy, E. Narasln±iacharyulu, and S.T.P.V.J. Swaray Department of Physics, Osmania University Hyderabad, India The differential cross section for the inelastic scattering of 279-KeV photons by K-shell electrons of thorium was experimenta- lly determined and expressed in terms of free electron scattering cross section at scattering angles of 30°, 50"^, 70°, 105°, 125° and 150°. Two scintillation spectrometers and a fast-slow coincidence circuit were used. The differential cross section for the inelastic scattering vanishes as the scattering angle approaches zero and becomes larger than the free electron scattering cross-section at very large angles. The experimental results were compared with those computed on the basis of different theories. Total cross section for the bound electron scattering was also obtained by graphical method. (Bound electrons} cross section^ gamma rays; inelastic scattering; K-shell electron; photon; x-ray.) Introduction A 0.9Ci radioactive Hg source was used as the source of 279 KeV gamma rays. Among various types of interactions of gamma rays with matter, Compton effect Results and Discussion is of considerable importance in the energy region of few hundreds of KeV. The differential cross section of To study the effect of electron binding 279 KeV gamma rays scattered by K-shell on Compton scattering especially at lower electrons of thorium was calculated in photon energy is of considerable interest terms of free electron scattering. The and has-been studied by several workers ratio dav-/da-p (da-^ represents differen- ' . In this present investigation tial scattering cross section for K-shell the differential cross section of 279 electrons dap represents the correspond- KeV gamma rays scattered by the K-shell ing cross section considering the electrons of thorium was measured in the electrons as free) was presented in angular range of 30°-150° in terms of Fig. 1. The errors shown are standard free electron scattering cross section. deviations. The observation that the The total cross section was also obtained scattering ratio da-^/dap at 125° with from the differential cross section by two different thicknesses (11.59 and graphical method. 4.89 mg/cm^) of scatterers remained unaffected confirmed the findings of Method Krishna Reddy et al^ that the effect of scatterer thickness is negligible on the In the present investigation the bound electron scattering below 20 mg/cnr number of gamma rays scattered inelasti- for photon energy of 662 KeV. The ex- cally by the K-shell electrons were perimental values of dax/da-p increases measured in coincidence with the corres- from 0.264 at © = 30° to 1.191 at 9 = ponding fluorescent x-rays. Both the 150°. The increase of the ratio with scattered gamma rays, and the x-rays were increasing scattering angle can be detected using Wal(Tl) scintillation easily understood from the fact that spectrometer. A fast-slow coincidence higher and higher momentum is transferred circuit with an effective resolution of to the electrons at those angles and 30 ns along with 20-channel pulse height thereby increases the probability for the analyser was employed. The false coin- ejection of bound electrons. The ratio cidence contribution was determined by reaches unity beyond 6 = 125° with 279 using an equivalent aluminium foil and KeV gamma rays whereas the same ratio subtracted from the total coincidence reaches iinity belo^J 70° for the same counting rate. The thickness of the scatterer with photon energy, of 662 KeV thorium scatterer used throughout as observed by Krishna Reddy". The observed angular range was 11.59 mg/cm"^. general trend of the experimental curve Another observation was made for as presented in Fig. 1 is that the ratio scattering angle of 125° with a thinner doj^/dap approaches zero as the scatte- thorium target of thickness 4.89 mg/cm^. ring angle approaches zero. It may i 26 . 1 tuere is no agreement between the experi- THORIUM (Z.90) mental and calculated values. Jauch and Rohrli ch9 developed the idea that in Compton scatterin^j the sa initial electron is free but not statio- nary especially at large scattering angles when the momentum transfer is more than the momentum of the initial electron. Based on this idea they obtained an expression for the scattering of gamma rays by free electrons with non-zero velocity, i'rom this the average cross- section doiyd-Q- which is a good approxi- mation is given for any value of by the following expression at- ?')d(cos a) ,da;,, J } dIL 30 60 90 I20 150 "d(cos (p)d(cos a) SCATTEHINS C^^^v) J 1 where 9 is the angle between the planes formed by K, P and K,K- where K, K- are Fig. 1. Comparison of present values of the three momentum vectors of the photon dayr/da^ with the values obtained and P is that of the initial electron, from Eq. (1), Eq. (2) and Eq a is the angle between the incident (3). photon and initial electron; is the differential cross section for a given however be pointed out in this connec- value of 9 and a. tion that the exact relativistic cal- culation of V/hittingham'^ for the The average differential cross- incoherent scattering of 662 KeV photons section using the above equation was from K-shell electrons of lead gave a obtained by computing da-j^/dnfor non zero value even at zero angle. Wo different values of 9 ana a using IBM relativistic calculations are available 1620 computer and the mean value is for direct comparison with the present determined for each scattering angle. experimental results. The values thus obtained are shown in Figure 1 and are not in agreement with The effect of electron binding on the experimental results even at large Compton scattering was usually taken scattering angles. If one ignores the into account by introducing a scattering variation in 9 and considers the varia- function 3 as a correction to free tion in a alone as was pointed out by electron cross section and may be I-Iotz and Missoni^C' the average cross as: section can be given expressed , ., -1 da^(kQ,e,Z) d(cos a) .. < dJl/' -1 (3) k is the incident photon energy, 6 the d(cos a) angle of scattering, Z the atomic number of the element and Sv is the probability that the K-shell electrons The mean scattering cross section values receive a momentum k from the incident for different scattering angles calcula- photon. Jeglecting transitions to ted on the basis of this equation was excited discrete states Shimizu et al° shown in Figure 1 for comparison with obtained values. In obtained an equation for 3^^. The values the experimentally also the calculated values are of Sjj. obtained on the basis of this this case calculation was presented in Fig. 1. It not in agreement with the experimental is clear from the figure that excepting values. However the values obtained by the general trend of the two cixrves the equation (2) and (3) agree fairly 27 .. . , . , well for scattering angles upto 50° and diverges violently beyond 50°. From the above information we may conclude that tne experimental results do not agree with any of the existing theories throughout the angular range of observation. 60 By multiplying the ratios dov/dop with free electron (Klein-Wisnina j cross sections the bound electron scattering cross sections were obtained and these 60 were plotted in figure 2. The curve was ^ / X •. extended to 0° on the lower angle side "0 / and to 180° on the higher angle side. The free electron cross section was also 40 shown by dotted line in the same figure. The area under the bound electron curve represented the total cross section a-^ due to bound electron scattering while 20 the area countered by the Klein Nishina values represented the total cross section due to free electron scatter- ing and the ratio Oy/a^^ came out as about 0.5. Parthasaradhi reported this 0 ^ 60 90 120 150 33o ratio as 0.81 for lead. SCATTEP'^i''- iNGLF (DEC.) The differential incoherent scatte- ring cross sections have been computed Fig. 2. Comparison of experimental on the basis of Thomas-Permi bound differential incoherent scatte- electron model by Donaldson et al-"- for ring cross sections with calcu- different elements and energies and the lated values from Klein-Nishina interpolated values pertinent to the formula and Thomas-Fermi bound present case are shown by dashed curve electron model. (Kaman iMUClear) in figure 2. These values pertain to all the bound electro- ns but not to k-shell electrons alone. Krishna Reddy, D.V., Ph.D. Thesis, Osmania University, 1971. Acknowledgements V/hittingham, I.B., J. Phys. A (Gen. Phys.) 4, 21 (1971) . The authors express their grateful Shimizu, S., Rakayama, Y. and thanks to the Department of Atomic Mukoyama, T.,Phys. Rev. 140, A 806 Energy for generous financial assistance. (1965) The thorium foils were kindly supplied Jauch, J.M. and Rohrlich, F.,The by the Atomic o.'^aels Division of the theory of photons and electrons Bhabha Atomic 1-tesearch Centre. Thanks Cambridge, Mass. Addison-Wesley 1955- are also due to the Head of the Physics 10. Motz, J.W. and Missoni, G., Phys. Department for the facilities given. Rev. 124, 1458 (1961) . 11. Parthasaradhi K. , J. Phys. A 1, References 171 (1968). 12, Donaldson, M.E Henry, E.i-i. and 1. Hamalinga Reddy, A., Lakshminarayana Veigele, V/m.J. Ray transport, Vol. V. and Jnanananda, S., Proc. Phys 5, Kaman Nuclear, Colorado springs, Soc. 91, 71 (1967). Colorado, 1965. 2. Pingot, 0., iJucl. Phys. A 123 , 334 (1969) 3. Pingot, 0., Le Journal De Physique 33, 189 (1972) . 4. I'lurty, D.S.R., G-ovinda Reddy, . and Narasimhacharyulu, E., J. Phys. A (Gen. Phys.)6, 265 (1973). 5. Krishna Reddy, D.V., Narasimhachar- yulu, E. and Murty, D.a.R., Proc. Ind. Acad. Sci L XX 11, Sec. A, 185 (1971) 28 GAMT'IA RAY ATTSITUATION COSFPICI.^NT W jJASUxHSBTSNTS AT 1115, 1173 AND 1332 KB7 3. Gopal and B. Sanjeevaiah Department of Physics, University of Mysore Manasagangotri, Mysore-570006, India (lar^ma ray attenuation coefficients in C, Al, Cu, Zr, Sn and Pb v/ere measured for ^gamma ray energies 1115, 1173 and 1330 keV using the technique employed earlier by the authors for similar measurements at lower energies. The results will be presented here and discussed. (Attenuation cpefficient; counting sequence; cross section} gamma rayj photon.) Introduction Studies on the interaction of gamma of 1173 and 1332 keV are resolved by the radiation with matter yield useful infor- scintillation spectrometer. mation for designing experimental arrange- ments for handling the isotopes decaying The gamma ray attenuation coeffici- ents are determined by following the by gannna emission. The most important quantity characterising the penetration counting sequence of Conner et al° choo- sing the sample thicknesses such that and diffusion of garaTfia radiation in exten- (at = ded media is the attenuation coefficient 0.2 to 0.4 for 1115, 1173 and 1332 keV gamma ray energies in carbon, alumi- 'J.. This quantity depends on the photon num, copper, zirconium and lead. A suffi- energy S and the nature of the medium. cient number of counts was recorded so 3ramna ray attenuation coefficient mea- that counting statistics contributed s^areraents have been made from time to less time using narrow-beam-collimated geome- than O.3X error. The background counts were taken by placing a 15 cm long lead try-'-"-'-^. In these experiments it is tacit- cylinder of cm diameter in the sample ly assumed that the energy-degraded 1.5 position. The errors associated with photons due to multiple scattering in the measured gamma ray attenuation coeffici- sample do not reach the detector and hence have been calculated by the good geometry condition preserved. ents the method is described earlierll» 12. But it may be expected that the number of m.ultiple scattered photons reaching the detector would increase as the sample Results and Discussion thickness increa.ses. The recent investi- 12 The values of attenuation coeffici- gations^!' indicated that the gamma ray ents measured in this experiment are attenuation coefficients i'fould improve if given in Table 1. Also the attenuationg one follows the counting sequence of coefficients determined by Conner et al , ;onner et al8 toget her x-iith the criterion Henry and Kennett^ and Ooswami and Chau- at <^1, V7here u is the gamma ray attenua- dhurilO which are common to our measure- tion coefficient and t is the thickness ments are given for comparison. of the sample. In this paper we report the gamma ray attenuation coefficients It can be seen from Table 1 that the measured in carbon, aluminum, copper, present values are in general agreement zirconium, tin and lead at gamma ray with the results of Conner et al°, Henry energies of 1115, 1173 and 1332 keV using the above criterion. and Kennett9 and Ooswami and Ghaudhuril^ suggesting that the sample thicknesses Experimental Method used by them satisfy our criterion Lit<^l. Also it can be observed that in some cases The experimental set-up and the our values fill the gaps in the improved -3hape and size of the samples used in the gamma ray attenuation coefficient mea- present investigation are the same as surements. those described bv the authors earlier^W^. 65 The gamma ray sources of 10 mCi Zn flll5 keVT and 10 mCi o 29 . . ) Table 1 Comparison of measured total attenuation coefficients (cm /m). (In parentheses is given the uncertainty in the last one or two places ) 31eraent Snergy Present work Conner et al Henry and ' G-oswami and (keV) Kennett9 ChaudhurilO (error 1'/.) - C J—I—L J 0.060251(26) 0.06043(27) 0 .06017 0 0601 1 Garb on 1173 0.058261[24;) 0.0585( 1) 1332 0.05524<[24;) 0.0551(1) 1115 0.05842(31) 0.05807(45) 0 . 05781 O.C583( 2) A T TiTTi "i Ti inm 0.05655(29; 1332 0.05347(28) - 0.0531(2) XXJ. J 0.05586(28;] 0 • ^ J J i J 0.vV Wo ^nnPT^ ^ X n 73 0. 054341 1332 0.050961 1115 0.05407(27;) Zirco- 1173 0.05295(26;) nium 1332 0.04965(28; 1115 0.053671 ) Tin 1173 0.05227( 1332 0.04944(27;] 1115 0.06384(28;) 0.06324(32) 0 .06413 0.0640(1) Lead 1173 0.06167(32)1 0.0615(1) 1332 0.05556(31) 0.0557(1) References 1. Davisson, Q.¥. and Evans, R.D., Phys. 11. Copal, S. and Sanjeevaiah, B., Nucl. Rev. 8.1, 404 (1951). Instr. and Meth. 1P2, 221 (1973). 2. ColTatc', 3.A., Phys, Rev. 82, 592 12. Copal, S. and Sanjeevaiah, B., Phys. (1952). Rev. A8, 2814 (1973). 3. V.'iedenbeck,M. , Phys. Rev. 126. 1009 (1962). Discussion 4. Ramana Rao, P. V., Rama Rao, J. and . 3oc Lakshminarayana, V,, Proc Phys. A.M. Chose 82, 1081 (1965). and Douglas, A.C , Proc. 5. Perkin, J.L. . I would like to know what Phys. 3oc. 22, 618 (1967). special cares have been taken by you to 6. McCrary, J.H., Plassmann, 3.H., improve the accuracy of your measurements? Puckett, Conner, A.L. and Zimraermann, (T.V/., Phys. Rev. 153 . S. Copal 307 (1967). 7. Carter, R.W., Rohrer, R.H. , Carlton, We have adopted the geometry of V.'.R. and Dyer, ^.R., Health Phys. Davisson and Evans but the distance bet- 11, 593 (1967). ween the source and the detector is doub- 8. Conner, A.L., Atwater, H. F. , Plassman, led and the diameters of the slits are This makes the maximum angle for 3.H. and McCrary, J.H. , Phys. Rev. Al, halved. 539 (1970). scattered photons {'^^^y^ to rnach the 9. Henry, L.G. and Kennett, T.J., Can. J. detector equal to IS'-' and therefore the Phys. 41, 1167 (1971). contribution of coherently scattered pho- 10. Coswarai, B. and Chaudhuri, F., Phys. tons on the measured attenuation coeffi- Rev. A7, 1912 (1973). cients is less than 0.05X • Also in our 30 geometry the sample position becomes insensitive to garama ray attenuation coefficient measurements. Our investi- gationsH'^2 indicate that the multiple scattered photons reaching the detector can be largely minimized by selecting the sample thicknesses less than nt= 1 where |i is the attenuation coefficient and t is the thickness of the material and thereby improving the measurements. D. V. Gopinath Has it not been recognized much earlier that the foil thickness should be much smaller than a mean-feeei)ath for attenuation coefficient measurements ? ^3. ?opal I do not knov.' why it was not recog- nized earlier in the measurements of gamma ray attenuation coefficients. RADIATION PHYSICS AND SIUCLEAR TECHITOLOGY P.K. Iyengar Bhabha Atomic Kesearch Centre Trombay, Bombay-400085 India Understanding of basic interaction processes of radia- tions V7ith atoms, nuclei and bulk matter contributes a lot towards the advances in nuclear technology. Yet it seems that moi-e accurate and wide ranging measurements are required to make accurate predictions for the design of reactors, accelerators etc. The present article is a birds-eye viev; of the problems which need solution in new technologies - problems due to radiation effects, study and solution of which can arise from use of accelerators. (Cross section; energy transfer,- gamma rays,- moderator; neutron; radiation damage; reactor; scattering; spectrometer). Introduction material for use in nuclear research reactors, is the discovery of the unique The subject of radiation physics is tnermalising properties of zirconium a very general one. Long before man hydride. During the late fifties understood the structure of matter and physicists were interested in understand- atoms and started theorising interaction ing the effects of chemical binding on of radiation vjith matter, nature has been the scattering and thermalising proper- using it in various ways. Por example, ties of various hydrogen bearing plants nave been using optical radiation compounds. The object of the studies v;as In photosynthesis, met erological pheno- the difference in behaviour of the mena are a result of interaction of hydrogen atom when it is free and when radiation v/ith bulk matter. it is bound in various chemical compounds such as water polyethylene, zirconium and Confining our attention to nuclear other metallic nydrides. The emergence technology, the radiations we are concer- of pov/erful research reactors having high ned with here are m.ainly y-vays, neutrons neutron fluxes and the concurrent develop- and charged particles, that too in a ment of sensitive nev/ experimental small energy region. Parameters which techniques enabled the observation of govern tiieir interaction with atoms, phonons - by the inelastic energy nuclei and bulk matter have been measirred transfers betv/een incident neutrons and for several decades now, yet it seems crystal lattices. that more accurate and v;ide ranging measurements are required to make The tetrahedral structure of accurate predictions for design of zirconium hydride wnerein the hydrogen reactors, accelerators, in many of the atom sits at the centre of a tetrahedron applications. It is not my intention to of zirconium atoms, performing nearly cover all these, for there are several harmonic oscillations bestows this papers in this conference dealing with material with very interesting neutron basic theories, experimental measure- scattering properties. The tightly ments and computer codes. I shall bound proton is found to have quantized restrict myself to a fev/ examples which optical vibration levels spaced at equal to my mind have contributed significantly intervals of '^'0.14 eV. Although Fermi to nuclear technology. This also helps had predicted as early as 1936, while to remind us that research in understand- discussing neutron slowing down by ing the basic interactions of radiations hyurogenous moderators, that the boimd with both individual nuclei and collec- proton would act as a simple harmonic tive systems can contribute a lot oscillator bound to an infinitely heavy towards advances in nuclear technology. atom and have energy levels of nh-J , the first experimental evidence of such Uni q ue Mo derating Propertie s of a system was obtained only in 1957 in Zirconium hydride simple total transm.ission experiments with zirconium hydride^. Pig. 1 shows An interesting example of how a the total neutron cross section of the systematic study of interaction of slow hydrogen in zirconium hydride obtained neutrons v/ith matter lei to the deve- with a crystal spectrometer. The arrows lopment of a powerful, nev; moderating indicate the excitation levels for 32 . into the 0-0.14 eV region is xmiform (independent of energy) and is unaffected by molecular binding effects or moderator temperature. When the zirconium hydride moderator is heated, neutrons pick up energy from the vibrating protons in quanta of 0.14 eV; as at higher moderator temperatures, more number of vibrating protons are found in an excited state. The fraction of neutrons speeded up to the region hi) "tOu? ^^'{^^^ therefore propor- tional to e~ . This phenomenon has been very effectively exploited in the design of a research reactor possessing a strong ^"55 °C 05 .'0 .15 .20 .25 .30 .33 ^0 i;> prompt negative temperature coefficient INCi.-JEM NrjTRO.N £r..ESGY(»v) of reactivity. The TRIGA research reactor as it is called, uses enriched -ig. 1. xOtal neutron cross section of uranium mixed intimately with zirconium hydrogen in Zr H2 as a function hydride and fabricated into fuel rods. of neutron energy. V/hen this solid homogeneous fuel modera- tor rod gets heated following an hydrogen vibration in zirconium lattice. accidental power excursion the average Fig. 2 shows the energy distribution of energy of the neutron spectrum quickly neutrons scattered from zirconium increases resulting in significant loss hydride as measured^ at 296°K. The peak of reactivity, "instantly" shutting down at ~C.14eV corresponding to the first the reactor. The prompt temperature optical vibrational level is clearly coefficient of such reactor has been visible. (Below .02 eV there is some shov;n to be given by indication of the acoustic modes and at .28 eV a double phonon scattering peak is dk _ _d -h-i /kT just visible). Since these levels would dT " ^dT ® be excited or de-excited by collisions with neutrons, energy transfers betv/een a_(^)2 -To/T slow neutrons and zirconium hydride can - occur on_ly in multiples of h-i ~ 0.14eV, 0 , ; vrhich is verjf large compared to kT (~C.25 eV) , the thermal energy of the where = h /k ~ 1500°K moderator and T ~ 300°K a is a constant measuring the relative loss of importance of the speeded up neutron. The TRIGA class of reactors are very safe and have been operated success- fully as Pulsed reactors producing strong pulses of thermal neutrons. Slow ing Down Time Lead Spectrometer CO 0 20 C30 ENERGY TRANSFER, (eV) Tiu The Slowing Down Time (SDT) Lead Spectrometer^ represents another example Jig. 2. Energy distribution of scattered wherein certain special features of neutrons from Zr H2 at 296°K. neutron interaction with matter have been exploited. Unlike zirconium hydride Because of the above characteristics which is an efficient moderator by low temperature zirconium hydride virtue of the presence of hydrogen, lead has a high mass number of 207 because of - oderator exhibits an unusual neutron spectrum, significantly different from a which the neutron loses on an average MaxTx-ellian distribution. During the only 1/. of its energy per collision. blowing dovm process once the neutron This, coupled vrith the fact that lead is energy becomes less than 0.14 eV it scattering cross section of cannot transfer any more energy to the independent of energy, leads to a type lattice. However collisions down to of focussing with time during the ibout 1 eV is as if it v/ere with free slowing down of monoenergetic neutrons injected into a large lead assembly. - jdrogerii hence the slowing down source 33 : . Neutrons undergoing elastic collisions thus gather into a comparatively narrow velocity group which as a whole gradually shifts towards lower velocities with increasing slowing down time. Fig. 3 depicts this behaviour schematically. t • BOO/* sees By injecting short bursts of fast neutrons periodically into a large block of lead and by looking at events for a short interval of time -^t, delayed by time t with respect to the initial burst, approximately monoenergetic neutrons could be selected. The basic equations governing SDT spectrometer are given ^ 3M ^ 4B below ;i) where t : time after neutron pulse M : Mass Number scattering mean free path Va,1^ • neutron velocities at to, t 2 e-S^ • Tp-t/i :t) abc4- (2) 0-2 0-4 OS ^0 Slowing dovfn density at centre Q source intensity abc dimensions of the block r2 geometrical buckling neutron age neutron lifetime .3. Slowing down spectrum in lead as Dispersion D is given by a function of energy for various slovring down times. D = 2_ kT 3M + 4E (3; Fig. 4 gives the capture cross-section Equation 1 in this figure defines oflOS^ measured as a function of the relationship between the slowing neutron energy, using an SDT spectrometer. down time t and the energy of neutrons A second application is for the deter- corresponding to this time. Equation 2 mination of resonance parameters^. By give the slowing down density of measuring the capture gamraa rays and neutrons at time t. using an area method of analysis, the resonance parameters of -'- Ag, -^-'°Au, The velocity distribution of .L3lri>a^ iDPjjg etc., have been obtained. neutrons at any instant during slowing down is found to be a gaussian with a dispersion given by equation 3» where E is the neutron energy corresponding to time t The second term, represents the additional spectral broadening caused by the thermal motion of the lead nuclei- These characteristics enable a large block of lead together with a pulsed neutron soujrce to be used as a neutron spectrometer having several useful applications. The main advantage of the slowing down time (SDT) lead sooj ^see spectrometer is the large gain in SOOfOO 20 fO S 4 S ^ intensity by 3-4 orders of magnitude compared to conventional time-of- flight methods. It has been used in a wide energy range from 0.1 eV to ~1 keV for the measurement of capture cross Fig. 4. Variation of neutron capture Sections of a variety of nuclei- cross section of Ag-'-'-'" as a function of neutron energy. 34 An important application of the SDT extraction of energy but about the spectrometer is in the non-destructive radiation effects that take place (in assay of Pu in irradiated fuel rods. the process of energy deposition in the In the energy regign belov? 1 eV fission components and consequent behaviour of cross section of^-^^ij- and -^^Pu are the components) over long periods of -, similar except at 0.3 eV where ^^^pu. has time (of the order of a few years). a large resonance. This difference has been exploited to determine the 239pu On the microscopic scale, it is content of irradiated fuel elements by well-known that an energetic radiation measuring the fission yield as a bombarding a solid can impart sufficient function of neutron energy in the energy kinetic energy to a lattice atom, range 0.1 eV - 1 eV. Fig. 5 shows resulting in the lattice atom being different behaviour of 259pu and 235u displaced from its normal position. samples obtained during a calibration This was suggested by Wigner about experiment carried out at Trombay. thirty years ago. Since then a large number of physicists have been studying phenomenon of radiation bombardment of l:'r't as a fu/icfion tf _ Var/aiioH of // ^/g x t solids. In particular the stiidy of ' AND l^r ror Pu formation, combination and annealing of point defects in solids has been pursued in a number of laboratories. This forms a part of defect solid state studies. For example, materials like copper have been irradiated in nuclear reactors at very low temperatures lit of the order of 4°K and the resistivity of the samples has been measured, after bom- bardment, as a function of temperature. The recovery spectrum was studied to understand the kinetics of recovery and thereby the underlying atomic mechanisms. % This kind of v^ork is being pursued even after two decades; the recovery spectrum is rather complex particularly in alloys and there la a wealth of information to s5 be unravelled. Similarly interest in optical properties of defects and other studies are well known. These studies ti* rtt r(C tfi' are essentially of basic interest to time //}.<• sfc.f understand the defect solid state and can be pursued only when the defect Fig. 5. Variation of fission yield in U -^^ concentration is sufficiently low. When and Pu239 as a function of the defect concentration increases, neutron energy. although the radiation effects increase in their magnitude and importance Radiation Effects in Kuclear Technology theoretical understanding become difficult due to the complexity involved In the next few minutes, I v;ould in taking account of the mutual inter- now like to deal with the effects of actions between various kinds of defects radiation bombardment on the physical in the high concentration limit. On the and mechanical properties of materials. otherhand, during the lifetime of a In the field of nuclear technology, one reactor, various components of the is concerned with these effects since reactor get exposed to such large doses they turn out to be major problems in of radiation that they come to contain a the design and development of nuclear large concentration of defects within a reactor systems. The nuclear reactor, few years and consequently radiation as everyone knows, is a high intensity effects begin changing certain physical source of fast neutrons, heavy high properties that they become technologi- energy fission fragments, charged cally important. It is in this region particles and gami.-ia rays. The energy that physicists have begun taking in- contained in these various radiations terest in the last few years and my gets deiosited in various components of purpose in the rest of the talk is to the reactor system like the fuel high light this aspect of defect solid cladding and structural materials and state. I shall review briefly the ultimately we are interested in extract- nature of radiation effects and how ing this energy content in one form or these studies are conducted. another to produce electrical energy. Here I am not concerned about the 35 ' Radiation Damage carry enormous energies resulting in large scale localised damage. Secondly (a) Fast Neutron Bombardment the fission fragments decay ending up in gaseous products like Kryton and Xenon. To begin with let us consider the Another effect common to fissile and non- effect of fast neutron bombardment of a fissile materials is the formation of solid, in Fig. 6. Here the neutron ox hydrogen and helium due to (n,p) and energy let us say 0.1 MeV enters the (n,a) reactions in the material. solid on the left side and collides with an atom of the lattice. The atom is knocked out of its 'official' position and moves in some direction. The neutron follows a different path. The atom knocked out by the neutron is called the Primary Knock-on Atom (PEA). The kinetics of the collision like the mass of the atom, angle of scattering determine the energy of the PKA. It can, in its turn, have elastic and 'inelastic collisions with other atoms in the lattice. There can be excitation or ionisation of atoms in addition to other atoms in the lattice being knocked out of their sites. Hence the PKA produces secondaries in its path and secondaries tertiaries in their turn and so on. The net result is a cascade of collisions and atoms from, displaced their lattice ' NEUTROH PATH sites. This process goes on till the WH I I I PRIMARY energy transfer in a collision falls PATH belovr say 25 eV. This is the order of SECONDARY PATH energy required to displace atoms from .....o> TERTIARY PATH their sites. Below 25 eV, atoms cannot be removed from their sites but this • Vacancy energy gets transferred to a large number of atoms in the form of thermal O Impurity energy - kind of 'hot-spot ' in the material. In the literature these ^ St>ik» regions are known as 'thermal spikes', locally in such regions, the effective Fig. 5. Typical damage pattern in fast temperatures can exceed the melting neutron irradiation. point of the solid for short times and recr3'-stallisation can take place. So, (b) Charged Particle Bombardment therefore a single PKA can create a lot of havoc as it ploughs through the In the case of a charged particle lattice. Sites from where atoms are bombardment, shown schematically in removed can lie vacant-vacancies - and Fig. 7, the nature of radiation damage dislodged atoms can come to rest at is qualitatively and quantitatively irregular points in the lattice - inter- different from that in neutron bombard- stitials. Such PKA cascades occur in ment. In addition to phenomena like large numbers in a fast neutron bombard- back-scattering sputtering etc., the ment till the neutron loses all its essential characteristic is that the energy and comes to thermal equilibrium damage is rather dense and is confined with the solid. Unless the neutron to a thin surface layer because of the escapes from the lattice, it is couJLombic nature of the interaction. One absorbed by one of the atoms of the does find however displaced atoms at lattice resulting in formation of an larger distances because of focussed 'impurity' atom. The net result of all collisions. Impinging atoms can pene- this is that the order present in the trate deeper if they are 'channelled'. lattice changes to disorder and the solid is said to be damaged due to radiation. Certain components in nuclear V/hat we have discussed so far applies to reactors, controlled thermonuclear fusion all materials be they elemental metals reactors and space-vehicles are exposed or alloys. In the case of fissile to a high flux of radiations - neutrons, materials, in addition to 'radiation Y-rays, fission fragments and charged damage' as discussed above, vje have the particles. Several radiation effects process of fission taking place, a occur as a result of the materials being source of fission fragments, Y"^^-^^' in this hostile environment. more neutrons etc. The fission fragments 36 . H . exhibited nearly 6/. increases in volume i— I due to 'voids'. Void-swelling is '•OCU53IH0 I 5IM^7t) believed to arise from nucleation and growth of three dimensional vacancy o c^ o- - iHitmiitiAL agglomerates, possibly originating and 0 stabilised in the beginning by a few gas fACANCT o .o; o_^o atoms particularly that of He. Void formation is an important radiation effect usually in the temperature range o o o of 0.3 Tm to 0.5 Tjjj. ir.APVtO ATOM 0.^0 o o (h) loss of ductility at high tem- peratures above 0.5 Tj^ due to formation Q'lCmo o o of gas bubbles when voids anneal out. _ o o (i) blistering formation on surfaces IW) due to gases inside materials. VACANCr O.Q O O Technological Consequences «U»fArf VjAf.ANCy ^ I shall now pick up a few of the effects mentioned above and illustrate Fig. 7. Typical damage pattern in charged how these effects play an important role particle irradiation. in the economy and technology of reactor systems. Radiation Effects (Mechanical) (a) Change in NDT A few radiation effects part iciilarly those that affect the mechanical proper- I have already referred to the effect ties of materials are: a) radiation resulting in the change in ductile to growth in fissile materials like brittle transition temperatures. The uranium, for example, at room temperature, pressure vessels used to contain reactors when 1/. atoms have undergone fission in are made of some kind of steel let us say. monocrystal, the specimen increases in Steel as we all know is ductile above length by AOO'/. . a certain temperature but brittle below this temperature. This characteristic (b) a similar effect on a reduced temperature at which the materials goes scale occurs in anisotropic, non- over from ductile to brittle condition fissionable materials also when they are is referred to as NDT in literature bombarded by fission products. (Nil -Ductility Transition). The important point to note is that a small flow like (c) radiation hardening - increases a hair-line crack can propagate at great of the flow stress or yield stress of a velocities below the ED'S. Above the NDT crystal normally at low temperatures. this does not happen. A very large number of cases in shipping are known (d) change in the ductile-brittle wherein huge ships have just broken transition temperature - I shall refer apart as a result of their temperature to this in greater detail in a few coming down below NDT in cold waters. minutes Hence to remedy the situation the NDT must be as low as possible (much below (e) swelling due to gases - accumu- normal operating temperatures) which can lation of fission products like Kr or Xe be achieved by suitable change in carbon can, for example, cause swelling of the content of steel or by alloying the steel fuel when these gases are formed in with various elements. The pressure - sufficiently large concentrations. This vessels used in reactors also should phenomenon in uraniim is known to result therefore be made of such materials that in 'frothing' of uranium. its NDT must be below the operating t emp eratur e (f) radiation creep - neutron irradiation produces a weaker material More than a decade earlier it was when the material is under load. observed that due to radiation damage the NDT was found to shift to higher (g) swelling due to 'void' for- temperatures as a function of dosage. mation: Fig. 8 shows this behaviour qualitatively. o In other words, a pressure vessel Recently Cawthorne and Pulton of designed properly out of a material Harwell observed that certain fast having a low NDT was no longer suitable reactor structural materials like stain- after operation of the reactor for a few less steel irradiated by neutrons years since its NDT could move into the 37 operating temperat\are range of the other problems can arise from fuel pin reactor or can even move up beyond this buckling, core warping etc. due to non range. Technologically, therefore, a uniform temperature and flux distribu- new situation arose wherein there can be tions and consequent non-uniform void a catastrophic failure of the pressure density distribution) . Hence in fast vessel itself. Several nuclear and reactor technology, void swelling has non-nuclear solutions to this problem come to be looked upon as a greater bane have been proposed from time to time. compared to other problems such as low Suffice to say that a new element, temperatiire hardening, high temperature namely change in NJjT, has to be taken into embrittlement and the acceleration of account in the design and fabrication of diffusion controlled processes known reactor pressure vessels. earlier. Material assessment has become "" important. However in order to obtain IRRADIATION INDUCED NDT SI-! this data through fast neutron irradia- tion one has to go through tedious and time consuming irradiations Y t Y over ten or ORIGII-iAL INCHCM'^O twenty years in fast neutron environment NDT viELO i>iPi:;>:i._, if one were to use the materials for such periods of time in the reactor. This is clearly an unsatisfactory situation. It is here a new breakthrough has been achieved by charged particle irradiation using accelerators. Charged particles, though limited in their range, interact through atomic interactions which have cross sections four to six orders of magnitude larger than the nuclear cross- sections of the neutron. The damage rate is several orders greater than the neutron damage rate. So in principle the damage density produced during many years irradiation within a reactor can be 'simulated' in a few hours using ion beams. Experimental studies involve irradiation of materials by light or medium heavy charged, particles like G, Al, Ni etc. accelerated to energies of order of a few tens of MeV. These irradiated materials are then examined using transmission electron microscopes and parameters like void density and void diameter are measixred. It is 5: o l _J 1 L observed that when specimens are irra- diated for comparable damage doses as with fast neutrons, the micrographs , .IIMT5GRATEU NEUTRON EXPOSURE reveal almost similar void patterns. 'y, f ^ n/cm^>0.1 MeV) Fig. 9 shows comparison of 316 stainless steel which has been irradiated Fig. 8. Qualitative features of change in by neutrons and charged particles". The NDT as a function of irradiation figure on left corresponds to irradiation dose. by fast neutrons ( > Q.l MeV) at EBR-II to a fluence of 3x10^2 n/cm^ for a (b) Void Swelling duration of one year and that on the right hand side, the same material bom- which The fast breeder reactors are barded by 5 MeV nickel ions to a currently under design are expected to fluence of 3xlOl6 ions/cm^ over a provide fluences of order 10^3 to 10'^'^ duration of 30 minutes. You can see the to various reactor components like fuel context cladding etc. during the life of the similarity in voidage. In this fuel. The void swelling in such cases I wish to point out that the Variable could be 10/. or more. Such swelling is Energy Cyclotron that is being construc- expected to result in two important ted by Bhabha Atomic Research Centre at effects. It will decrease the breeding Calcutta could prove to be a very ratio (atoms of fissionable material powerful instrument for such studies. generated per atom, of fissionable Physicists who are conversant with material consumed) because additional acceleration techniques and solid state free space must be provided in the core physics can play a very important role to accommodate the swelling. (Secondly in this effort of materials assessment 38 . for fast reactors. Physics of void for sufficiently long time. The vacuum formation, void morphology, inter com- wall of the chamber containing the plasma parison of accelerator samples and is expected to operate at temperatures reactor samples (to take into account of order of 700° to 1000°G and is accelerated damage rate in case of exposed to bombardment of neutral atoms, simulation experiments) are areas neutrons, photons and charged particles. wherein physicists can contribute to our As a result of bombardment by these it is understanding expected that the wall can undergo large scale erosion. 5X rO rt/c^' Typical parameters'^ of a chamber n are given in Table-I and assuming very small sputtering coefficients of the order of less than l/. even, it is seen that the life time of such vessels could be very small indeed. In addition to this recently a new problem is expected to play a major role. The plasma is expected to contain H"*", He"*", T"*" etc. and these can bombard the wall. If radiation damage is caused by gaseous projectiles such as thege, the impurity concentration due to these atoms builds up in the material as a function of dose. Secondly such products can accumulate due to (n,p) and (n,d) reactions also. Due to low solubility of the gases in the metal, the gaseous atoms can precipitate out of the metallic solution and create 'bubbles' in the interior or 'blisters' on the surfaca (A) Depending on the size of the blisters Neutron irradiated at 585 °C (1 year exposure) and metallic strength, the blisters can get rupt\ired and skin defoliation can take place. Fig. 10 shows the kind of blisters observed by Das and Kaminsky-^^ is vanadium as a result of charged particle bombardment. Low energy accelerators (2-3 MeV) can be used for irradiating materials v;ith protons, particles etc. and one can examine the surface using scanning electron microscopes. This figure shows a sample of one such study in which 0.5 MeV particles were used to bombard the surface of polycrystalline vanadium film at 600°C. Interesting results are obtained as a function of irradiation temperature, projectile energy, pre- irradiation treatment, micro-structure etc. on other metals and alloys also. Table-I 500 MW(t) Fusion Reactor Parameters .2 (B) V/all area 400 m' Ni ion irradiated at 5«5 'C (30 njinutes exposure) Radial loss 10^5 IONS/SEC Fig. 9. Voids in 316 stainless steel due Particle flux 2.6 X 10^^ to neutron and Hi bombardment. lONS/Cm^/sec (c) Blist ering Average Spu- ttering Co- ATOM Tremendous efforts are underway all efficient 0.008 over the world to make the controlled low thermonuclear fusion a reality for Erosion rate 1.2 mm/Year meeting power needs of the future. One Wall thickness 1 cm of the problems in this area has been Permitted loss 20/. containment of the plasma in a vessel Life-time 2 Years 39 . . . , References He Reynolds, A.W., Nelkin, M.S., Rosenbluth, M.N. and Whittemore, W.L. PICG, 297 (1958). Woods, A.D.B., Brockhouse, B.N., Sakamoto, M. and Sinclair, R.N. Inelastic Scattering of Neutrons in Solids and Liquids - (IAEA) p. 487 (1961) Bergmanm, A. A., Isacoff, A.I., Murin, I.D., Shapiro, F.L., Shtranikh, I.V. and Kazarnovsky, M.7., PICG, 135 (1956) Chandramoleshwar, K., Naval kar, M.P., Ramakrishna, D.V.S., Nuc I.Inst, and Methods 60, 113 (1968). Chandramoleshwar, K., Navalkar, M.P., Ramakrishna, D.V.S., Ramanna, R. and Subramu, E.R., PICG (1964). Radiation Damage in Reactor Materials, Proceedings of an IAEA meeting Vol.1 Fig. 10. Blisters in polycrystalline and Vol. II (1969) vanadium produced by charged Proceedings of the BNES Nuclear Fusion particle bombardment. reactor Conference (1970) Gawthorne, C. and Fulton, E.O., AERE- Conclusion R 5269 (1966), p 446 and Nature 216, 575 (1967). I have tried to give a birds-eye Kulcinski, G-.L., Nucl.Inst. and view of new problems that need solution Methods 365 (1971). in new technologies - problems due to 10. Das, S.K. and Eaminsky, M. , J.Appd. radiation effects, study and solution Phys. ^, 25 (1973). of which can arise from use of accele- rators. Radiation Physics, in the broad sense of the word, has large scale implications in these new technologies. 40 VARIATION OF TOTAL TO K-SHELL PHOTOELECTRIC CROSS SECTION RATIOS WITH ATOMIC NUMBER AND PHOTON ENERGY Ramakrisiina G-owda and B. Sanjeevaiah Department of Physics, University of Mysore Manasagangotri, Mysore-570006, India The total to Z-shell photoelectric cross" section ratios are calculated from the measiired total and K-shell photoelectric cross sections (using a well type plastic scintillation spectrometer) in copper, zirconium, silver, tin, tantalum, gold, and lead for 145 '4, 279.1, 411.8 and 661.6 keV gamma rays. The ratios are plotted against the atomic number and also the photon energy. The theore- tical ratios obtained form the cross sections of Scofield [UCRl Report No. 51326] are also plotted and a comparison is made. The dependence of these ratios on the atomic niunber of the element and the photon energy is discussed. (Atomic nixmber; cross section; K-shell; measurement; photoelectric effect; photon) Introduction ratio is slightly energy dependent es- pecially at low energies. So the Until the 1960's the relativistic calculations using Kirchner 's values are calculations gave only the cross secti- found to be xinder- estimated above It was the pra- ons for the K-shell. K-shell threshold. ctice to estimate the contribution of by the all other higher shells using The total to K-shell photoelectric ratio o^/a-p,} where a-j; and are the cross section ratios are K-shell photoelectric cross measvired by total and Hultberg^^ using magnetic beta ray sections respectively. The law of spectrometer at the energies 1332, 662 "five fourths" simply claimed that and 412 keV gamma rays in uranium. a^/ag; = 5/4. This value holds good only Latyshev-'--'- gives the ratios for Z = 73 for Z materials above Hulme energy high and Z = 82 at 2.62 MeV. Experimentally limit MeV-^. and Evans G.35 Davisson , measured K-shell and L sub-shell ratios Grodstein' and Davisson^ tabulated the are tabulated in the recent review absolute photoelectric cross sections article of Pratt et al . together with cross sections for the various gamma ray intexaction processes Results and Discussion contributing to the total. In the tabulation of Davisson and Evans'^ the The total and K-shell photoelectric total atomic cross section was obtained cross sections are measured using a well by applying the 5/4 law to the K-shell type plastic scintillation spectrometer^ cross sections. Grodstein^ also -^"^ previously described by the authors^ '. followed a similar method, but instead Using these measured total and K-shell ratios of using the 5/4 law she used the photoelectric cross sections, the ratios jj/ag; as with Stobbe's ag^_i_T calculated are calci^lated in copper, zirconium, of Hall formura5 and similar formula , silver, tin, tantalum, gold, and lead which corrects the overestimation of for 145.4, 279.1, 411.8 and 661. 6 keV cross sections for the low Z values. In gamma rays. The ratios are plotted Davisson^ she used the later table of against the atomic number (Z) in Pig. 1. Kirchner's experimental ratios' measured and against the photon energy in Fig. 2. at the K-shell thresholds in which the The theoretical ratios obtained from the was found to Z-dependence of this ratio cross sections of Scofield-*-® are also vary monotonically from 1.09 for plotted in the ssune figure for compa- aluminium to 1.235 for uranium. rison. In the plot of total to K-shell Hubbell gives an empirical fit to ratios against the photon energy, one calculate the ratios ^ function ot/^K can observe the energy dependence at of Z with an accuracy of +2 to 3 percent with Kirchner values. This fit does not lower energies. Especially for high Z take into consideration any possible materials the dependence is found to be energy dependences^ Later calculations prominent. As the energy increases the of Rakavy and Ron-^ showed that the dependence decreases. The total to ill . . . < 1 1 1 i>25| 1 r i 100 300 BOO TOO 900 1 uiol 1 1 I L_ ,_ » 20 30 40 50 60 7C •ATOMIC NUVBER Fig. 1. Variation of total to K-shell Fig. 2. Variation of total to K-shell Photoelectric cross section Photoelectric cross section ratios with atomic number. ratios with photon energy. K-shell ratios obtained using the mea- 5. Stobbe, M. Ann. Physik 7, 661 (1930). sured cross sections are found to be 6. Hall, H. Rev. Mod. Phys. 8, 358 consistantly higher than those obtained (1936). from Scofield values at 145.4 keV, and 7. Kirchner, F. 1930, Handbuch der as the energy increases the agreement Experimental Physik, Ed. W. Wien becomes fair. These ratios are found and F. Harms ( Akademische, to vary monotonically as Z increases. Verlagsgesllschaft , Leipzig). The errors on these ratios are found to 8. Hubbell, J.H., Nat. Stand. Ref. Data. be about 97. in the case of photon Ser. NSRDS-NBS 29, (1969). energy 145.4 keV and 6'/. at all other 9 . Rakavy , G- . and Ron , A . Phys . Rev photon energies. 159 . 50 (1967). 10. Hultberg, S. Arkiv fiir Fysik 1^, 307 References (1959) 11. Latyshev, G.D., Rev. Mod. Phys. l^, 1. Hxilme, H.R., McDougall, J., 132 (1947). Buckingham, R.A. and Fowler, R.H., 12. Pratt, R.H., Ron, A. and Tseng, H.K. Proc. Roy Soc. (London) A149 . 131 Rev. Mod. Phys. 273 (1973). (1935). 13. Gowda, Ramakrishna and Sanieevaiah, 2. Davisson, CM. and Evans, R.D., Rev. B. J. Phys. (GB) A6, IO4I U973). Mod. Phys. 2±, 79 (1952). 14. Phys. Rev. A8, 2425 (1973). 3. Grrodstein, G-. White, N.B.S. Circiilar 15. J. Phys. B TgB) 2, 1772 (1974). No. 583 (1957). 16. Phys. Rev. A6, 2569 (1974). 4. Davisson, CM., Alpha-Beta-G-amma Ray 17. Can. J. Phys. 846 (1974). Spectroscopy, Ed. K. Siegbahn, Vol.1, 18. Scofield, J.H., UCRL Report No. 51326 Chap. 2 (1965) (North Holland, (1973) (unpublished). Amsterdam) 42 . Discussion Gaussians were fit. The areas under these Gaussians TjKJuld then give the number of Roy. 3.C . K-shell ph(t>toelectrons . Also the plot of observed K-shell photoelectron peak 1. Have you measured tj^ or energy against the pulse height amplitude "^^Q^g^l gives a straight line. or both, of them ? 2. Well, in case of measuring t^, 5. Although the experimental techni- how are you sure that you are considering que is similar to the conventional K-eleetrons only ? methods we have introduced some modifi- 3. Next, is there anything new in cations in the geometry and the detector the technique from the conventional size. We also observe the peak due to measurements ? photoelectrons in aluminium at 145.4 keV, 4. Can you assign any reason for the which was not observed in earlier experi- large observed discrepancy for some of ments. This shows that our experimental the elements ? set up is much better than the previous ones Gowda. R. 4. If we draw the error bars on the ratios there is agreement in the case of 1. We have measured both total and all the elements within the errors. The K-shell cross sections. errors are about at 279-1, 411.8 2. For monoenergetic electrons the 6X and 661.6 keV and 9X in the case of 145.4 pulse height amplitude spectrum in the keV. scintillators is mainly a Gaussian. The main peak in the photoelectron spectrum is attributed to the K-shell electrons and using the left portion of the peaks ^3 t OPTICAL MODEL .lii ALTS IS OF NOimASTIC INTERAGTIOl^" OF 14-2 I-IEV REUTH.OiiS E. Pal, Arun Ghatterjee and A. II. G-liose Nuclear Physics Laboratory, Lose Institute Calcutta-700009, INDIA I'Jon- elastic cross sections of several nuclei for 14.2 MeV neutrons have been measured using sphere transmission technique. The measured data together v/ith the results of others have been analysed with optical model using a least square criteria over a wide range of mass number (l2^A-^207). (Gross section; multiple bias; neutron; non-elastic; optical model-, param.eter; polynomial extrapolation; sphere transmission.) Introduction Optical I-Iodel Analysis In the present work, the experimental ilnalysis of non-elastic data obtained and theoretical studies on neutron non- from present measurement as well as from elastic interactions have been undertaken data obtained by others-^^ »-'--'- '^2 ^g^g in the 14 lieV region. Efforts have been performed using the widely used nine made here to find out an average set of parameter local optical potential given mass-independent optical model parameters, by the following form: ^ utilizing essentially the non-elastic j scattering cross section data measured by us. References 1 to 9 contain the works already carried out in this field. Measurement of Hon- el as ic Cross Section for Different Nuclei where the symbols have their usual sig- Non-elastic cross sections of seven nificance.- Volume absorption term in the nuclei for 14.2 MeV neutrons have been imaginary part of the potential has not measured by using reciprocal sphere been considered because of its negligible transmission teciinique. Two important contribution^^ on the absorption of 14 correction factors arising from (a) the MeV neutrons. The spin-orbit part of the recoil energy loss suffered by elasti- potential has practically no effect on cally scattered neutrons and (b) the non-elastic cross section. Therefore, multiple scattering in the finite throughout our present analysis we have scatter er thickness have been estimated fixed the param.eters Vs, Vq and as at by raul/tiple bias and polyno.mial extra- their reasonably expected values, namely, polation methods^*-' respectively. The results obtained are presented in V3:=7.0 MeV, Tq^1.25 fm, aa=0.65 fm Table 1. In the 14 MeV region the compound elastic Table 1 cross section is negligibly small-^^ and so we have disregarded this effect and IJon-elastic Cross Sections co:iip8,red the measured cross sections vrith the computed values directly. (barns) for 14.2 MeY Neutrons The experimental cross sections Og^-p may be compared with those predicted by Element a^g in barns optical model, Ofa^ simply by examining the sensitivity of cr's on parameters. The 0 0.82 + .02 difference between tiiese two cross secti- Al 0.94 ± .02 ons denoted by '^^^y ^® then ex- Cu .03 Oerror 1.49 ± pressed as a summation of variation of Cd 1.90 + .04 cross section with each free parameter aj Sn + .03 1.90 of the model about a fixed initially W 2.40 + .06 chosen value a? i.e. Pb 2.57 ± .05 *V.'ork carried out under a PL-480 Project sponsored by the National Bureau of Standards, U.S.A. 44 " , ' Table 3 a = a -cj,,=y ; ) . 6a -; error exra th / o J 6ai Comparison of the 14 MeV A-lndependent Average Parameters Obtained in the ... (2) Present Investigation with those Reported by Other Authors . We have started v/ith an initial set of parameters chosen from the works of Perey and Buck-'- and V/ilmore and Hodgson^, ilon-elastic cross section data for Paranet er Bj orklund Rosen^;^ Cassola Present several elements (seventeen) have been and et al^ and work taken from different soiirceslO'H»12 Pernbach ICoshel (14.2 Each of the six pararaeters was varied (14 MeV) (14.5 (14.0 MeV arbitrarily by 2'/. from its initial MeV HeV) value keeping others fixed. Thus partial 6ath.\ corresponding to eacn 44.0 44.5 derivative , ^^o 43.4 40.24 parameter was obtained. Least square ^0 1.25 1.25 1.25 1.26 criteria v^as applied to eqn. 2. A nass- 0.65 0.65 0.63 0.62 independent set of parameters which, in ^0 principle, should give optimiim fit to the 11.0 5.75 8.20 9.8 experimental data was then obtained. The 1.25 * 1.25 1.24 1.48 parameter set thus obtained has been presented in Table 2. 0.98* 0.70 0.47 0.45 Table 2 ( * indicates parameters pertaining to Optical Potential Parameters surface absorption potential of Gauss- from llon-elastic Cross Sections ian form) Pitting . 3.0 (MeV) (fm) (M^V) (fm) (fS) 40.225 1.261 0.618 9-795 1.477 0.452 A comparison of theoretically calculated values of cross section crth.» with the new parameter set against the measured '"'-lues of present investigation has been ".le in fig. 1. In table 3 we have corn- ered the potential parameters with the . /erage parameters obtained by Bjorklund and Fernbach^, Rosen et a35 and Cassola and Koshel7. I 1 " 1 1 1 I Discussion 1.0 2.0 3.0 4.0 5.C 6.0 The amount of variations from set to Fig.l. Experimental and theoretical , set noted in the values of a particular nonelastic cross section of 14.5, parameter is not surprising; that diffe- MeV neutrons as a function of i A J rent approaches of analysis would lead to *,j sets of slightly varying values, is the cross sections calculated with the I expected normally. The value of rj) new set of mass independent parameters / obtained in our analysis is notably agree well with the experimental results ly.rge compared to that of each set. over a wide range of mass numbers. The ^owe'ver, this value though large, is not variations for low A nuclei are not unrealistic . Optimum parameter searches surprising since the optical model is not ' for individual elements ha've quite often expected to be valid for low mass number 1 lead to values which vary over a wide elements. The parameters given in in mass , range from element to element. For Table 2, thus represent, the ; example7, maxira-um and minimum values of independent approximation, a set of ' rj) are foimd to be 1.49 (for K) and 1.04 reliable parameters for describing non- 'for ill) respectively. elastic scattering of 14 MeV neutrons from nuclei of mass number lying in It will be seen from fig. 1, that the range 12 4207. except for too low mass number elements. ^5 . . . Since our next endeavouir will be to 6. Becchetti, F.D. and Greenlees, G.V/., make another approach to fit the non- Phys. Rev. 182, 1190 (1969). elastic as well as elastic scattering 7. Cassola, R.L. and Zoshel, R.D., Uuovo data simultaneously, with a single set Cim. 363, 1968. of parameters, we have not attempted 8. Korzh, I. A., Kashuba, I.F., Kozin, multiple iterations for obtaining more B.D. and Pasechnik, i-i.V., Sov. J. accurate values of the parameters. Wucl. Phys. 7, 190 (1968). 9. Wilmore, D. and Hdgson, P.E., DjucI . References Phys. ^, 673 (1964). 10. Chatterjee, A. and Ghose, A.M., Phys. 1. Perey, P.G. and Buck, B., Nucl . Phys Rev. 161, 1181 (1967) 12, 353 (1967). 11. I'lacGregor, H.fl., Ball, W.P. and 2. Bjorklund, F.J. and Fernbach, S., Booth, R., Phys. Rev. 108, 726 (1957). Phys. Rev. lO^, 1295 (1958). 12. Flerov, N.K. and Talyzin, V.M., J. 3. Bngelbrecht, C.A. and Fiedeldey, H., Kucl. Energy 4, 529 (1957). Ann. Phys. 262 (1967). 13. Hodgson, P.E., The Optical Model of 4. Aver'Yanov, I.K. and Purtseladze, Z.Z., Elastic Scattering (Lond.) (1963). Sov. J. Nucl. Phys. 1, 193 (1968). 14. Lane, A.I-i., Rev. of Mod. Phys. 29, 5. Rosen, L., Beery, J.G-., Goldhaber, 191 (1957) A.S. and Auerbach, E.H., Ann. Phys. M. 96 (1965). 46 GEOMETRIC FACTORS IN RADIATION PHYSICS IffiASUREIffiNTS A.M. Ghose Department of Physics Bose Institute Calcutta-700009, India Optimisation of geometrical factors through symmetry considerations is a powerful means of improving the accuracy of measiirements in Radiation Physics. This has been illus- trated for the cases of spherical and axial symmetries. Design of double scattering fast neutron polarimeters as well as of gamma ray linear polarimeter systems have been discussed. Applications of the surface of revolution geometries to various fields have also been considered. (Absorption; accuracy; cross section; fast neutrons; geometric factors; photon; polarimeter; radiation physics; scattering; spectrometers.) Introduction Axial Symmetry One of the most important elements When the phenomenon or the process in the design of experiments in many under study shows no explicit dependence areas of Radiation Physics is the on the azimuthal angle, the symmetry spatial distribution of the component natural to the experimental arrangement parts of the entire experimental arrange- is axial (Fig. lb) . Thus in the measure- ment comprising the source, the absorber ment of the differential scattering cross and the detector. The purpose of the sections 03(6) of unpolarised radiations present paper is to indicate how the the symmetry is around the scatterer - effective signal strength at the detector detector axis. Other instances where and hence the accuracy of the measure- axial symmetry is important includes ments can be increased, sometimes even simple angular correlation experiments, by orders of magnitude, by making the study of nuclear fluorescence radiation distribution of the components symmetri- using Compton scattered gamma rays etc. cal. The symmetries correspond Extensively used ring geometry is the naturally to those inherent in the simplest version of axially symmetric quantities or processes under investi- arrangement and it has the additional gation. These considerations are virtue of being adaptable to the time-of- particularly important when scattering flight technique. However, in plane cross sections are either being geometry constant angle 9 corresponds to measured or differentiated from other an arc of a circle and this fact was interaction processes. utilised by Tandon and I-Iclntyre^ in their investigations on nuclear fluorescence Spherical Symmetry radiation (Fig. Ic). Obviously a surface of revolution shaped geometry of When total scattering from all the scatterer aroimd the soxxrce-detector directions is being measured (or dis- axis is a nattiral extension to the three criminated) the inherent geometry is dimensional case (Fig. Id); in a spherical. This is the basis of the separate paper^ we have shown how this well-known sphere transmission technique geometry has been utilised as the basis which can be used, at least in principle, for the measurement of differential to effect a separation of scattering and scattering cross sections of fast absorption processes (Fig. la). In neutrons. A version of the arrangement practice, the application of the sphere proposed for the measurement of differen- transmission technique depends upon the tial incoherent scattering cross validity of .several implicit ass-omptions section of gamma ray 3"+ is shovm in Fig. 2. and the accuracy obtainable depends critically on how closely these assum- A possible use of the axial ptions are obeyed by the actual experi- symmetry lies in the field of angular mental arrangement. Since the method correlation experiments involving prompt of spherical symmetry has been discussed radiations or radiations from short- elsewhere in other publications-^ we lived nuclei emitted by a source, which, shall not discuss it further. in turn, is produced by irradiation in a *Work carried out under a PL 480 project sponsored by the National Bureau of Standards, U.S.A. ^7 . t Double Scattering Fast Neutron PROCESS GEOMETRY TECHNIflUE Polarimeter In measurements involving linearly polarised radiations we come across symmetry considerations of a different type. We shall illustrate them first by e or* considering the design we have (ig. tie) proposed for a double scattering fast neutron polarimeter Fig. 4 shows the essential elements of a double interaction fast neutron polarimeter^ . Unpolarised beam of neutrons incident on the polariser gets polarised after scattering through an angle e^. The flux of particles V issuing out from the second target ^2 at a fixed angle of scattering 62 depends on the azimuthal angles 9 through the relation w(e2,9)=No(e2)[i+Pi(ei)P2(e2)cos 9] ... (1) Fig.l. Geometrical arrangement for dif- where Nq is the ferent types of symmetries. flux in absence of polarisation and Pi is the polarisation vector in the initial interaction while P2 is the polarisation that would result had an unpolarised beam been incident on S-p. Using the Basle convention", the differential cross sections for scatteri- S ngs to the "left" ((p=n) and to the "right" (9=0) in the common plane becomes respectively S- Soorce F FUUr D- lelecLor = a^(e2)[i-Pi(e^)P2(e2) J ... (2) X; ScaiUrer Direct Bedin Stopper arrangement for the Fig. 2. G-eometrioal Hence the asymmetry ratio A(e2), defined measiirement of differential in- to be equal to aj^/a^i, becomes coherent scattering cross section of gamma rays. i-P3_(e^) P2(e2) ••• wide beam. In the usual angular correla- ^^®2^ = rrprre^Tp^Tep- tion arrangement, source absorption and scattering can be reduced only at the i-A(ep) intensity. In the arrange- expense of so that •••(5) ment shown in Fig. 3 the source has the P^(e^)P2(e2)=CTep- shape of a surface of revolution about the line joining the two coincidence Hence a measurement of A(©2) yields detectors as axis; since the extended product Pi(9^)P2(62) > which, in turn, source can be thin there is considerable gives Pi(6i) or P2t62)» when one of the gain in intensity over the usual point two quantities is known. source geometry. The arrangement is also potentially useful for inner bremstrahlung The usual method for producing a experiments. polarised beam of fast neutrons is based on the polarisation during the produ- ction of neutrons e.g. by using d-t or d-d reactions well above their corres- ponding thresholds; P2(62) usually obtained from phase-shift analysis if the second interaction consists of elastic scattering from a spinless target like He or C. Near the thresh- old (e.g. for "14" MeV t-d neutrons) Fig.3« Proposed arrangement for angular Pl(9i) is very small and the above correlation measurements. method is therefore difficult to apply. . Fig. 4. Elements of a double interaction fast neutron polarimeter. Fig. 5. Double scattering fast neutron An alternative method is to use the polarimeter. technique of double scattering. If the second reaction is again an elastic where y is the number of nuclei per c.c. scattering from target nuclei which are not of the scatterer, t is its normal too light, the energy change during the thickness, Nq is the no. of neutrons scattering can be neglected and further emitted by the source S per sec, 21 is if is set equal to 62 » we can write the length of the SH axis, 6 is the 1*1(61) = 1*2 (©2) hence scattering angle, x = z is the distance along the axis SH of the projection of an element of scatterer from the centre of the axis and where the integrand f(x,6) = ^i^^i) rTirefy which is taken over the scatterer "^-^ given by Thus a measurement of A yields P and once the (l-:g)V^l+(l-x^)tan29-l polarimeter is calibrated, it can be f(x o)_ used to analyse diverse polarisation processes l+(l+x)tan^e-/l+(l-aP)tan^e In the conventional approach, 1 without optimising geometry, the double scattered beam intensity is lO"-'-^ to ^[sec^e-x2tan2ej'^ 10~-'-5 of the primary total beam strength 1 and this figure is too low to have any practical utility. A possible arrange- [l+(l-x)tan2e-Vl+(l-x'^)tarfe] ment of double scattering fast neutron polarimeter based on the surface of ... (8) revolution geometry is shown in Fig. 5. The neutrons are successively scattered The limits of the integral in P^n.. (7) by two sectors of angular width 6 and correspond to the two extreme positions forming a part of the surface of at the ends of the scatterer. In the revolution. The number of neutrons above derivation we have assumed that detected by the neutron counters in the the scatterer is "thin" enough to replace 3expressions of the type £s(i_e~°"^tY two symmetrical positions depend upon j the polarisation induced in the first ^t a is a numerical factor scatterer '^2.* -^^ S®"*' estimate of by aOgYt where the typical counting rate we note that of the order of unity. With this approsi- the number N]_ of neutrons issuing out mation the mean coimting rate after of and passing through a hole H of double scattering becomes effective radius a is given by C=€fi^[f^J^an8sec2e[ff(x,e)dx]2 aa^yN t . fr.^ +f (^f^)^=an4e sece f(x,e)dx %"g9/2j_2 j ... (7) ... (9) 49 . . where we have assumed that Xi and T2 have the same dimensions, € is^he efficiency of the detector and -^is the 9 solid angle subtended by at S. If ^SIq^ and"S^ are made of sulphur, typical mean counting rates (neglecting the polari- sation factor) obtainable by this method is shown in Fig. 6. It will be seen that C is several orders of magnitude more than the corresponding values using conventionsil geometry. In the calcula- tions we have assumed the following parameters, 6 = 0.1, f = 0,1, € = 0.01 ... (10) t = 1 cm and f = 0.75 32^ 208 If instead or S one uses v Pb, the double scattered coixnts are even higher as shown in Fig. 7. In the calculations we have used the same set of parameters as given in (10) The surface of revolution geometry thus promises to furnish us with a method for polarisation measurement of fast neutrons by double scattering. However the design of filters and slits poses a practical problem of some difficulty. ScalUrIn) angle indejrtti Fig. double ? 7. Expected mean scattering counts for lead in a typical polarimetric arrangement. Gamma Ray Polarimeter System For gamma photons the linear polarisation is transverse rather than longitudinal and this, therefore, calls for different type of geometrical considerations. We shall briefly consider a polarimeter system proposed by Rudra and Ghose' consisting of a ring ^1 of scatterer (and partial polariser) followed by an analyser ring X2 which scatters radiations through 90° to a specially shaped detector D in position I after channelling them through suitable filters. (Fig.8). The source of unpolarised photons S is placed on the axis of the system. Fig. 8 depicts the plane of the first scattering - the a-plane. To measure the polarisation, it is also necessary to measure the intensity of photons scattered by through 90° in 7[ - plane, which is normal to 0-plane. The detector D has now to be moved to the position II concentric with 51 to receive the photons. The path of typical ray in the ix-plane is shown in Fig. 9. The cross section of D transverse to the axis of the system is ring - shaped and the path of Fig, 6. Expected mean double scattering a photon through the ring is inclined counts for sulphur in a typical at an angle (p. In order that the polarimetric arrangement 50 . , where (D,h) are' the coordinates of 0 in the plane of the figure, with the source S situated at the origin and (X,Y) are coordinates of the projection of X t . But X = Y Cot (G - 9) 02) where © is the angle of scattering inS3_, This makes ^ ^-^ ^ = x-Y°co? e ••• ^3) and hence [X-i(D-ah) ]2+[Y4i(aD+h) = =J(DSh'^)(a%l) ... a4) Fig. 8. Basic elements of a double where a = Cot 6. This is arc of scattering polarimeter system for a photons circle, as expected from sec. 3. The loci of the projections of D are given by the same eqn. Y^ = (x-D)2 + (y_h)2 Thus as the point (X,Y) moves over an arc of a circle, the coordinates of 2? aarif describe two branches of the same parabola. The complete arrangement in space is obtained by generating surfaces of revolution by rotating the arc and the parabola around the symmetry axis of the system, nearly conical parts of the latter being suitable for practical systems. Fig. 9. Path of a typical ray in the u-plane. geometry of paths in -n and a positions of the detector be symmetrical, the photons must traverse the detector in position I in a similar manner and the , longitudinal cross section of D must be a section of a ring with the point 0 as centre. Hov^ever if D has a large efficiency these considerations need not be enforced rigidly. For a more extensive arrangement, it can be shown that if the points S and 0 are kept fixed, the locus of the projection of is a circle, while the points corresponding to ^'^'^ ^ Fig. 10. Earlier version of proposed y- lie on the same parabola. In fact, in ray linear polarisation. Fig. 10, the locus of the projection of "2 A more elegant system^ for linear 3_ on the plane is determined by the equation: transverse polarisation measurements can be derived from Fig. 11 which shows a Dj_ D2 D = X + (Y + h) Cot (p. 01) section through the positions and 51 . . of the detector in the a and n planes sections of a parabolic cylinder with a respectively. If the scattering planes right circular cylinder. are distributed normally to the plane of the Fig. 11, the rays PiUi, ^2^2 ^tc. For this system it is relatively are in the a-plane while the corresponding easy to design and fabricate systems of rays P1D2, ^2^2 '^^^ 71-plane, slits. Incidentally, gamma ray polari- where the points P]_, P2, etc. on X2» meter systems of the type discussed which now assumes the form of an arc of a above are going to be useful for esti- circle. To find the form of the mating the individual contributions of scatterer we consider the a-plane different types of coherent processes SQ]_P-lDq_ corresponding to the point to the total coherent scattering cross on X2 (Pig- 12). The ray SQ^ emerging section of gamma rays. from is the source scattered by 21 ]_ at the point Q-^ through an angle ©; QiPi Other Uses of Geometrical Factors corresponds to the scattered ray which is further scattered by ^2 ^'^ One of the early use of axial symmetry was made by Potenza and PuubbinoS in their Let the equation of Z j_ be design of fast neutron spectrometer. Another important area 2 _ I.e. X + y 2yll (Pig. 11; :6) where surface of revolution geometry can play an important role is the generation It vj-ill be seen that the projection of neutrons of predetermined energy from Z of Q-|_ along 3Dj_ satisfies the equation a intense source of neutrons of higher energy (e.g. 7 to I4 MeV neutrons from t-d neutrons) by elastic scattering in cos B - -r= (7) a low z scattering. If the sour-ce neutrons have anisotropic energy distri- bution in the laboratory system, the since the points P-^ and Q-]_ have identical scatterer might be shaped properly to X and y coordinates. From (6), we imme- take this account . For isotropic or diately have nearly isotropic sources the arc of a circle geometry discussed in sec. 3 is z2 = 2yR Cot^e (8) adequate. For practical systems, the difference of counts with equivalent amounts of paraffin (GH2)m and polythene (CH)n scatterers can be ascribed to elastic scattering from hydrogen Acknowledgement The author wishes to thank his students who have been associated with different phases of the programme out- lined here. He wishes to thank Dr. S.H. Sircar, Director, Bose Institute, for his interest in the present work. Fig. 11. Improved version of the proposed References Y-ray linear polarimeter. 1- Bethe, H.A., Los Alamos Sci.Lab. Report LA-1428 (1952). Ghose, A.i'I. and Gangiily, N.K., Ind Jour.Phys. 285 (1956). Bethe, H.A., Beyester, J.R. and Carter, R.E., J. Wucl. Energy ^, 275 (1956). Fast i\,feutron Physics, Vol. II, Edited by J.B. Marion and J.L. Fowler; Interscience Publications, (i960) and references contained therein. Fig. 12. Plane of polarimeter. Ghose, A.K. , Kucl . Inst . and Methods 45 (1965) . 2. Tandon, G.K. and Hclntyre, J. A. - Huclr.Instr. and Methods 181(1968). showing that for any given angle of 3. Wath, S. Ghatterjee, A and Ghose, A.M. scattering 6, the projection of the paper presented in this Symposium. points on on y,z plane describes a 4. Roy, S.G. and Ghose, A.li. (Private 1 parabola i.eT X.^ lies on the inter- communication) 52 . . . • . . 5. Elwyn, A.J. and lane, R.O., Nucl A.M.^ Ghose Phys. ^ 78 (1962) 6. Proc . Int. Symp . Polarisation Pheno- It is not always necessary to shape men of Neutrons (Basle 1970) ed. the detector to improve their characteris- H. Huber and K.P. Keyer (Birkiiauser tics. For example uniformity of res- Verlag, Basle, 1961). ponse in the gamma ray detectors can be 7. Rudra, N. and G-hose, A.M. Nucl . Phys. achieved by incorporating a suitable Solid State Phys. (India) 10, 581 detector in the system. Por fast (1967) neutrons multiple bias method developed 8. Ghose, A.M. (in press). by us achieves the same purpose. In 9. Potenza, R. and Rubino, A. Nucl. Inst. general the desired symmetry is also Kethods 2^, 77 (1963) applicable to the corresponding detectors and their fabrications etc. is not Discussion necessarily difficult. P.K. lyeni^ar P.P. Kane I must congratulate Prof. Ghose for 1. It is perhaps appropriate to inventing these innovations , however I point out that linear polarisation must stress that it is due to the measurements with gamma rays can some- situation of limited resources that he times be made more accurately through has been foimd to think of much clever the use of (p,py) reactions with tricks. selected targets such as magnesium. This has been done at 1.38 MeV for example. What will be the effect of non- uniform energy sensitivity and direction 2. There is a real problem with dependence of the detector on the over- regu.lar to Delbriick scattering amplitudes all resolution? at large angles. On our work (Wucl. Phys. 1970) and that of Schumacher et al A.M. Ghose (Hucl. Phys. 1973) shows that empirically the Delbriick amplitude at an angle such Optimisation of geometrical factors as 1200 interferes destructiveLy with the will not be effective unless suitable Rayleigh amplitude. Theory, as known at detectors are devised to exploit the present, predicts a constructive full benefit vrhich would result from this interferences between the two amplitudes optimisation. In ovcc laboratory we have at 1200. developed suitable detectors for photons and neutrons which have the desirable Geometrical factors are important properties. Iv'ith conventional detectors in all measurements. the resolution will be poor indeed. A.M. Ghose D.V. Gopinath I fully agree with Dr. Kane that The spread in the angle and thereby under suitable situations other methods the resolution of the system depends on might have the same order of efficiency; the distances between the detector and but here we have concentrated on general so-urce and their sizes. One can improve methods applicable to almost all the resolution to the desired extent by situations. Delbruck scattering is increasing the distances but thus one indeed an important area which requires has to use larger detectors for the same thorough investigation both theoretically efficiency and experimentally and polarisation measurements are expected to remove some A. i-l. Ghose of the uncertainties in this field. In fact by increasing the sizes, K. Gopala one only gets a scaled up version of the same geometry and angular resolutions Have you taken into consideration etc. are not improved thereby. It is the effects of multiple scattering essential that the improvement in amongst the various parts of the detector quality must match the improve- scatter er particularly in view of the ment in geometry. large size and closed shape of the scatterer B. B. Baliga A.M. Ghose Is it necessary to shape the detectors for good geometry ? If so Multiple scattering is an important uniform efficiency of one detector is a problem. We have considered this aspect real problem to achieve. and one of the incentives for the 53 present investigation came from the A.M. Ghose desirability of using thin targets in an optimised geometry so that overall I am afraid that experiments alone intensity remains at a reasonable value. are not sufficient to settle the rela- tive phase problem. However, at each S. Gopal angle of scattering, polarisation data will furnish additional data which are Can we really discriminate experi- sensitive to the choice of phases. mentally the phase differences exist Hence a judicial mixture of theory and between Rayleigh scattering and Delbruck experiment will certainly lead to a scattering ? better understanding of the coherent scattering phenomena. 5^ MEASUREMENT OF ANOTLAR DISTRIBUTION OP INCOHSRSNTLY SCATTERED QAMlIk RAYS FROM ATOMS B.Sinha ((xoswami) and N. Chaudhuri , North Bengal University, Darjeeling India There has been comparatively little experimental investi- gation on the whole-atom incoherent scattering of photons in the x-ray and gamma-ray regions. A rigorous theoretical treat- ment of this type of scattering has not yet yielded enough results and the incoherent scattering function approach is taken to calculate the incoherent scattering cross section. Recently, Cromer and Mann calculated using SCF Hartree-Fock wave functions the incoherent scattering function over a wide range of momentum transfer in the photon scattering process. These data are more accurate than the earlier Hartree-Fock data in the low momentum transfer range and form the only available most comprehensive set of data over the range of momentum transfer upto 3.9 mc. In the present work, the angular distribution has been measured for incoherent scattering of 662 keV and 1.115 MeV photons by atoms with low, medium and high Z in the angular range from l°to 165°. The experimental values of the incoherent scattering function have been interpreted on the basis of Cromer's theory. (Angular distribution) cross section} gamma rays; photon; scattering, incoherent; x-rays.) Introduction The incoherent scattering of pho- almost the same as the energy of photon tons by electrons of different atoms is scattered at a given angle from the a topic of current interest. In absence given scattering target. The measure- of exact theoretical calculations the ments were carried out with the main and incoherent scattering function approach the auxiliary aluminium scatterers under is taken in the calculation of incoherent the same experimental conditions using scattering cross section. Highly accurate multichannel analyzer with spectrum values of incoherent scattering function storage times in the range from 4 k sees over a wide range of momentum transfer to 100 k sees. Under the experimental upto 4 mc are now available from the conditions mentioned, the detector effi- recent SCF Hartree-Fock calculations of ciency and the solid angle factors cancel Cromer and Mann and Cromer2>3. Compa- out in the determination of the ratio of ratively few experiments on the whole- the differential scattering cross section atom incoherent scattering of photons for a given scatterer atom to that for a have so far been reported. The data from free electron in aluminium atom. This the available experiment s4-» 5 cover only ratio was divided by the atomic number small ranges of momentum transfer, have Z of the scatterer atom to obtain the large experimental errors and show con- incoherent scattering factor S. siderable discrepancies at small and large scattering angles. The cylindrical scatterers used were of pure aluminium, copper, tin, Method . mercury, tungsten and lead. The maximum value of iir (li-photon attenuation co- The whole-atom incoherent scatter- efficient, r-scatterer radius) for all ing experiment s4- reported have been the scatterers was 0.7. Even for such carried out by the auxiliary source small scatterers, the corrections for method. This method requires a photon absorption of primary and scattered pho- detector with efficiency independent of tons in the scatterer target were neces- photon energy. Instead of using this sary and made using Dixon's" results method, we have compared, in the angu.l8.r for calculating the self absorption cor- range 10° - 165°, the scattered counts rection in small gamma-ray sources. For from a given scatterer at each scatter- angles 10° and 150° at which \ir values ing angle with the scattered counts from were very small, S values were evaluated, an auxiliary aluminium scatterer of exactJy by extrapolating to zero scatterer radius the same size. The auxiliary aluminium a number of scattering measurements at scatterer provides a secondary (scatter- slightly different scatterer radii. Mea- ing target) source of photons of energy surements were made using a 150 mCi Zn-65 55 source collimated over a distance of The theoretical values of S included in 80 cm in iron block. The source, provided the Table are derived from the new work with adequate lead shielding, was at a of Cromer 2 and Veigele et al'. Agreement distance of 130 cm from the scatterer. between our results and Cromer values The detector, a 3" x 3". Nal(Tl) scinti- appears satisfactory at all values of llator head shielded -at sides, was couplFd momentum transfer studied. The earlier through a ND-52 PAD to a ND-1100 analyzer experiment s"* show greatest disagreement with 512 channels. The distance between with theory at low values of momentum the scatterer and the detector was 70 cm. transfer. For measurements at angles less than Table 1 10*^, a shadow-cone type experimental arrangement was used. The Cs-'-3' source Experimental whole atom incoherent in a conical shape collimator and the scattering factors for lead (Z = 82) with detector head, 1" x 1". Nal(Tl) scinti- the corresponding Cromer-Veigele values. llator, were provided with adequate lead (X = sin [e/2]/X , e - scattering angle, shielding for reducing the background to X- photon wavelength in angstrom units. a very low level. The scatterers of lead The experimental errors are in parenthe- in the form of narrow width rings {'^l cm) ses) . were used for scattering measurements by the auxiliary source method. At a fixed Experimental Cromer - source-to-detector distance of 3*3 m» the incoherent Veigele angle of scattering in the range 1°- 5° scattering values ofS. was chosen by taking scatterers of diff- factor S. erent radii. In the arrangement used, there was little background scattering 1. 92 0.894 0.374(010; 0.46 material, except the shadow-cone, the 2. 65 1.232 0.558( 010; 0.55 light suspension threads for the shadow- 3. 51 1.628 0.615 [010: 0.63 cone, the air mass between the source 4. 64 2.161 0.669 rolo 0.72 and the detector, and the foam rubber 10 7.84 0.937 030) 0.95 scatterer holder. The detector pulses 15 11.67 0.942( 032; 0.98 30 23.27 0.984 [022; 0.995 were recorded by the NT) 1100 analyzer using 512 channels and storage times in 45 34.42 0.984 :022j 0.996 the range 20 k sees to 100 k sees for a 60 44.96 0.990( 028] 0.998 75 54.76 0.978( 030 0.999 statistical precision near . The total 1% 0.980 scattering cross section at each angle 90 63.59 :038) 0.999 was determined and the incoherent scatter- 105 71.36 0.976(;o55; 0.999 120 ing cross section was evaluated by sub- 77.88 0.984 055 0.999 tracting from the total the accurate 135 83.10 0.990(,051 1 (^^^^ 150 86.86 1.007 100 1 theoretical value based on recent SOP 165 89.17 0.999 '098J 1 Hartree-Fock calculations-'-~3 , The results have been expressed as S. Results and Errors References The scattered counts in the shadow- 1. Cromer, D.T. and Mann, J.B.,J.Chem. cone method were corrected for any differ- Phys. H, 1892 (1967). ence in background counts with and with- 2. Cromer, D.T., J.Chem. Phys. ^,4857 out the scattering target. The experi- (1969). mental results for lead expressed as in- 3. Veigele, Wm. J. et al, Kaman Sciences coherent scattering factor S are given Report, KN-71-431(R) (1971). in the Table 1. The measurements on other 4. Sood, B.S. et al. Current Science, 33. elements mentioned above are not included 139 (1964), Indian J. Pure and Appl. in the Table. The measurements on all the Phys. 1,305 (1963). elements studied give S ^1 in the angular 5. Quivy, R., Nucl.Phys.l6, 362 (1966). range upto 165°. The errors of the expe- 6. Dixon, W.R., Nucleonics 8,68 (1951). rimental S values have been computed by taking into consideration statistical errors in all the measured counts taken for evaluation of the experimental results and errors in other factors involved in the evaluation of results. At scattering angles less than 5°* the energy change of the 662 keV photons in the inelastic in- coherent scattering is negligibly small and no correction for this effect is necessary in very small angle measurements. 56 MEASUREMENT AND ANALYSIS OF A FEW 14 MEV NEUTRON CAPTURE CROSS SECTIONS I'lanjushree Majumdar and B. Mitra Bose Institute, Calcutta-700009 INDIA Total 14 HeV neutron capture cross sections of seven represen- tative nuclei have been meas-ured by activation method, in a relative way. Data with an estimated error of + 2'/. have been presented. Analysis of a(n,Y) total has been attempt»ed with (a) Statistical evaporation type formula presented by Naguib and Luiyanov and (b) Direct reaction formula presented by Lane and Lynn. It has been shown that D.I. gives absolute estimate of values agreeing with experimental ones. Statistical model analysis with carefully adjusted neutron width function yields rather high radiative strength function. (Activation; P-counting error; capture reaction,- cross section; measurement; neutron) Introduction P-energies. For establishing such a relation they had to make very thin The Bose Institute 250 kT Cockcroft foils of elementary copper and V/alton accelerator has been used as a aluminium, irradiate them for generation 14 MeV neutron generator for quite a few of suitable ^-activity and draw effici- years in measuring cross sections of ency curves for a realistic thickness various nuclear reactions. V/e report of 20 mg/cm^ samples, neglecting here a few(n,Y) cross sections, with Z-dependence. We have tried to verify adequate stress on experimental methods the same analytic relationship, viz of obtaining reliable results by activa- tion method. by going down to much lower values of Method sample thickness in which tracer activities are uniformly dispersed. For The soirrce of maximum error in this, we first followed the method of activation results by p- counting has physically pouring out in pots, a been tracked down to errors arising out uniform suspension in solvent ether, of of self-absorption and self-scattering finest mesh metal dusts with tracer of p-rays . In case of 14 MeV (n.y) elements added. These tracers used were cross sections, additional trouble is 35s, 90sr, 204ti and 32p, all in liquid in low counting rate of the relevant chemical forms, to scan a P-energy activity. Hence we propose to deal, in range of = .047 to 58 MeV. this report , with our method of minimising p- counting errors in activation. The V/e have assumed that, as in fig. 1, result presented here are all relative the efficiency is defined by measurements, i.e. cross sections relative to a standard cross section. T] = l/cg ^1 = count This standard is (n,2n) cross section of i^Cu nucleus and (n,a) cross section rate at a minimum value of thickness in ^Al, the values of which are taken of the sample achieved and C2 = count as 540 mb and 117 mb at 14-8 HeV rate at a standard thickness of 20 ng/^m^ respectively. The results of obtaining (ct. rate vs thickness) ciirves in all the four above It has been reported previously cases are shown in figs. 2-5. from OTxr laboratory that self-interaction errors in jB- measurements can adequately Fig. 6 is the constructed (''tel'^^ be taken account of, even by using end Eq) curve. To construct this we window (j.M. counting set up. Mitra and determined the value of the constant Ghose^ proposed a semi /empirical formula 'b' from experimental t] for °*^Sr. for preconstructing efficiency curves of In fig. 5, the solid curve is the such G-.i-I. counters for different P-ray analytically constructed curve, and energies, where useful parameter the experimentally obtained values referred to j3-energies rather than maximum for 35s, 204T1 and 32p are plotted. 57 210- ThicKTwss in ms/en* Thickness m Tng^cm* 200 Thickrtess in mg/cm* 0 as O-i 06 0.8 1.0 1.2 H Average Energy Ep in MeV I I L. 8 12 16 Thickness in mg/cm^ 58 I ) . . . Therefore it is seen that the analytically and made a change in their method of sinple expression remains valid, within obtaining the values of K and y. the li.iiit_s of experimental error, for a ilaguib et al have proposed an arbitrary ran^e of Eg = C.C47 to C.5, HeV. energy, Eg, of incident neutrons in the experimental cr vs Ej-j^ curve and the value Our sole assumption is that, in the of a at the point so specified yields (Sp. count vs Thickness) carve, the so his K. But vre have shown that it is called 'Zero-thickness' value is given hy not necessary to have arbitrary E3 ' that actually obtained for the ' minimum values; instead, one could choose the prepared thickness. To give more exact E3 value at the point where the credence to the method, V7e are now last bump in the a vs E^ curve disappears producing very thin, doped saznples by for each nucleus, in their a(n,Y) vs E^ electro spraying. V/e assume albeit curves obtained from data accumulatedin drastically, that going dovm to a thick- a single set of experiments of a single ness one order of magnitude smaller, laboratory. Eor this, we have consulted will not appreciably alter the r\ values BI'IL 325 data4. In general, Johnsrud as defined. In electrospraying method, et al data (1959) and Stavissky's (1959) '.'e can go dow. to few iig/cm^ thickness. data have been compared as instances of The (n,Y) reaction cross section of a a single laboratory's single set of few nuclei relative to a(n, 2n) of °3Cu = data in the neighbourhood of E^.' 540 mb. and to a(n,a) of 27a1 = 117 mb, Presiimably, Eg is a critical energy obtained in our laboratory, are shown belov; which partial v/ave analysis is . in the Table 1. possible and at which point g-wave contribution comes in and the synthetic In this table we have also presented curve for that nucleus becomes exponen- tially decaying. cross section values ' as predicted by Above S^, the calculations according to a classical classical statistical formula with statistical model formula presented by suitable level density parameter is iJaguib and Lukyanov^, also presented are applied the values from crude Direct Interaction (D.I.) model calculations according to Conclusion Lane and Lynn^, along with the experi- mental values, '/e have analysed the V/e conclude from our comparison of ITaguib formula viz. values in Table that it is highly debatable v/hether at this high energy, a(n,Y)=Ka(c)E"-'-U^ exp[-2yVauJ a(n,Y) is quantitatively given by the classical statistical formula. Table- Certainly the Naguib formula has the character of a statistical formula, but- 14-l4eV (n,Y) cross sections there is no way of checking it, since it contains constants, t\io of v^hich, x and y are energy independent . Calcula- Target Exptal Author Calc. Calc. cT^^ tion from Perkin 's estimation of - the v^idth, the anv a ( mb 'y and Hi respective (mb) acc. (mb) statis- values of a obtained were 10-4 orders tical D.I. model lower than the experimental ones, while of Lane model D.I. calculations yield values nearly acc "and Lynn to Ilaguib of the same order of magnitude as the experimental ones, obtained by Perkin .37 .076 and the present author. 51y oo Csikai .49 Present References 1. Kitra, 3. and Ghose, A.k. - Nucl. ^^aa 1 .9 Perkin 1 .29 Present 1.44 0.2 Phys. 82, 157 (1966) 2. llaguib, K. and L\ikyanov, A. - J. of ilucl. Energy 20, 373 (1966). 1 .39 Present 1.55 0.129 3. Lane, A.K. and L^mn, J.E. - 2nd Geneva Conf. Report, 1^, 38 (1958). 127j 2 .5 Perkin 1.20 0,19 4. iTeutron Cross sections - EITL 325 pub- 2 .74 Present lished by Signa Center, Brookhaven National Laboratory, 2nd Edition (1966). 1 .3 Perkin 1.29 0.24 5. Johnsrud, A.E., Silbert , K.G. and . 1 .12 Present Bnschall , H . H -Phys . Hev . 116 , 927 (1955). 6. Stavissky, Y.Y. - Atomnaya Energiga (1959). 141pr 3 • 33 Perkin 2.727 0.6 I, 259 3 .00 Csikai 7. Perkin, J.L., O'Connor, L.P. and Cole- 2 .19 Present man, a.P.-Proc.Phys.Soc. 72,505(1958). 8. Csikai, J., Peto, G., BncZke, l-l. , . iiLlli/jv.Z* and Eissa, K . A -i-Iucl . Phys - A21, 2^5 tl967) 59 . . INTERMEDIATE ENERGY APPROXIMATION OF THE BETHE-HEITLER FORMULA FOR THE BREMSSTRAHLUNG CROSS-SECTIONS K. Gopala and B. Sanjeevaiah Department of Physics University of Mysore Manasagangotri, Mysore-570005 INDIA Bremsstrahlung cross section calculations are still attracting attention because of the inadequacy of the existing formulae. The Sommerf eld-Elwert formula holds good upto 0.1 MeV. Bethe and Heitler gave a relativistic expression for the bremsstrahlung cross sections using Dirac's electron theory and Born approximation. Coulomb and screening effects were not included in their calculations. Calcula- tions of the bremsstrahlung cross sections using the B-H formula are tedious. Approximations of the B-H formula in the nonrelativistic and extreme relativistic regions exist. But no such approximation is available in the intermediate energy region. An attempt is made to obtain an approximation of the B-H formula in the intermediate energy region. Several approximations are made to reduce the B-H formula into a polynomial in x, the ratio of the photon energy to the total energy of the incident electron. The coefficients of the polynomial turn out to be a long series of terms which are functions of incident electron energy. The validity of the approximate formula in the intermediate energy region will be discussed (Approximation; bremsstrahlung; cross section; electron; intermediate energy; photons.) Introduction where c< = fine structure constant=l/l37 Calculation of the bremsstrahlung Z = atomic number cross section using the Bethe-Heitler r^ = e^/m^c^ = classical electron (B-H) formula is tedious. Approximations radius of the B-H formula in the nonrelativistic 2 (NR) and extreme relativistic (ER) W = k/m c = photon energy in regions exist. But no such approximation terms of the electron is available in the intermediate energy rest energy regions = v^/c;(i = 1,2) is the velocity of the The present paper attempts to arrive electron in units of c at a simple form of the B-H formula by (subscript 1 refers to the affecting certain approximations to make incident electron and sub- it hold good in the intermediate energy script 2 refers to the region. scattered electron) - 2^-4 The B-H formula for the bremsstrah- Yi = (1 i = 1,2 lung cross section, diff erential in photon = = energy is given byl p^ momentum; i 1,2 |a ^ a(^^2 £2 a _ _2 (ii!:_i2!:!^ dk x^ ^2^2^ Y1Y2 2 , rIil2ii!?i?2Llii L = TT-TT— m [ rj j We now write -^1 3 Y1Y2 R 2fi 2 ' 2ytY 2 ^^2 1>2 YtP ^1 1^1 Y2 = Yi(l-x) ....(2) _ '^1"^^2^2 2W -L 2— ~^— ^ •••• (1) 2 Q 2 •[} ^2^2^ ^ Yl"'^2'^l"^2 60 . ) where x = W/y-i = k/E^ = photon energy in which are of course functions of incident terms of the xotal energy of the incident electron energy only) -electron Calculation of the cross sections taking three, four and five terms in ^2 '^2 /I 1 ..(3) equation (8) for various incident electron energies in the region 0.05 to 4. 54 MeV shows that the contribution of the fifth term is negligible. So, 2(1 - |2) ..(4) where K = ln(b) V If 0.o:r/(A^+A^x+A2x2H-A3x5). ..(9) can be taken as the required approximation of the 3-H formula in the inter-mediate energy regions. The coefficients A to A^ vary with Y]_ as shown in Fig. 1.° For 3 o 5 values of we ft Yt^ 3 can approximate the various coefficients as and ...(5) 2" 3 A^ = (18.5 + 0.55 Yj The appro xi 1 at i on made in (4) underestimates the B-H cross sections in A^ = -(42 + 0.33 Y^) the low photon energy region and over- (10; estimates them in the higher photon A2 = (37 + 0.20 Yi) energy regions. Calculations show that A^ = -(18.0 - 0.20 the overall effect of the approximation Yi ) made in (5) is negligible, 'rfith the above relations, equation (l) becomes ar 2 2 Z X ....(6) where a ,a-. etc. are ftmctions of and X i.e. functions of incident electron energy and fractional photon energy. ^2 can be written as , = - IT P2 tl 2m (7) using (7), ^2 ©"fcc. being expanded binomially upto the term containing 2 g 7-, (1-x) . Further simplification limiting to the term involving x^ leads to da = ar^^( Aq+A^x+A2X^+A3X-^+A^x^; Fig. 1 Variation of the coefficients dk A to A-, with Yn • o 3 1 (8) The cross sections calculated using where A , A-j^ etc. are functxons of xnci- equation (9) with the coefficients given dent energy of the electron only (each in (10) are plotted along with those of of A , A-, etc. comes out to be a long B-H formula (l) and the experimental l-j^ and results in Figs. 2. The experimental series 0f terms involving y^^ 61 —I r~ T. • 2.50MeV 10- 'GOLD • TIN « COPPER » ALUMINUM f 8 -ft 6 4 - 2- 0.5 W 1^ 2.0 2.5 PHOTON ENERGY.M«V 100 200 300 ''00 500 Fig. (e) PHOTON eNERC-y.-keV Fig. (b) 14 12- lO 2- 0.2 0.A 0£ 0.8 1X1 PHOTON ENERGY, MeV to 2J3 iO 4.0 SJ3 Pig. (c) PHOTON Efii5fi(5Y.WeV Fig. (f) as a function of emitted Photon Pigs. 2a to 2f Bremsstrahlung cross sections energy for different incident electron kinetic energies Uq-'- Bethe-Heitler formula, present approximate formula The points are the experimental data. 62 . . results were taken from Motz- for ^ 0.5 MeV electrons, from Dance et al for 0.2, 1.0, 1.7 and 2.5 MeV electrons and from Starfelt and Koch^ for 4.54 MeV electrons. It can be seen from the figures that the approximate formula (9) deviates considerably from the B-H formula for low energy electrons and in low photon energy regions of the spectra But the approximation is justified by the fact that it is closer to the experimental data. References 1. Jauch, J.M. and Rohrlich, F., The Theory of Photons and Electrons, Addison- V/esley Co., Mass., U.S.A., 1955, p. 369. 2. Motz, J.W., Phys. Rev. 100, 1560 (1955) 3 . Dane e , W . E . , Rainwat er , W.J. and Rester, D.H., Investigation of Electron Interaction in Matter, LTV Research Report No. 0-71000/ SR-2 Feb. 1968; see also Rester, D.H. and Dance, W.E., Phys. Rev. 161, 85 (1967). 4. Starfelt, N. and Koch, H.W., Phys. Rev. 102, 1598 (1956) 63 . A NEW ME'x^HOD FOR THE MEASUREtlEUT OF DIFFERENTIAL ELASTIC SCATTERING CROSS SECTIONS OF FAST NEUTRONS* S. Nath, A. Chatterjee and A.H. G-hose Nuclear Physics Laboratory Bose Institute, Galcutta-700009 , India A new method has been described which successfully reduces the problem of low scattering intensity. The scatterer has been taken in the form of a spheriod. The elastically scattered neutr ons have been discriminated from the inelastically scat tered ones by using multiple bias technique. Experiment ally measured values of differen- tial elastic scattering cro ss sections for sulphur at four angles for 14 I'leV neutrons have been presented. The resuJLts have also been comp ared with the optical raodel prediction (Cross section; differential; elastic; mialtiple bias technique; neutron; scattering). Introduction scatterer plotted against the length (measured along source - detector line) This paper deals with a new method of the scatterer surface, has also been suitable for the measiir ement of elastic shown in Fig. 2. This function is ob- scatterini- cross sections of fast neu- tained by theoretical evaluation of trons over a wide range of incident scattered intensity to be presented below energy. In the present method, eraphasis The length of the scatterer is determined has been laid on the geometric factors by the necessary aperture to be left to involved .in the experimental arrangemen tl make the entire surface of the scatterer so as to avoid two limitations encoun- available to neutrons emitted from the tered in the usual measurements. The target and by the intensity of the sca- size and shape of the scatterer, pre- ttered beam desired. The length and deterrp.ined by the design of the experi- position of the scatterer (symmetrically mental set-up, sets out a limit to the placed w.r.t. source and detector), in intensity of the scattered count. This our set-up, have been confined to the factor has been carefully considered in central section of the scatterer inten- designing the experimental set-up. The tionally; this is to avoid the steeply aethod also gives an effective v/ay to rising portion of the curve, incl"j.sion of discriminate betv;een the elastically which vfould have otherwise made the scattered counts and the non-elastically scattering more critically dependent upon scattered ones. The method described is the scattering angle. Referring to fig.l an absolute one in the sense that it does the number of neutrons scattered elasti- not require kno;:ledge of any other cally towards the detector D can be related cross section and the final shovrn to be. cross section value can be derived from ' the data obtained in the present ua'^y N^t da if +f experiment alone. ^1^. Secif' tan>J^ f(x,T/^)dx V 'jeometry and Underlying Theory wnere In this method, as mentioned earlier, the shape of the scatterer plays the (1- x) (^l+d-xS) tan^i^ -1) most important role. The scatterer is f(x,V^) shaped in the for;;! of a surface of revolution obtained by rotating an arc [l+d+x) tan^y) h+il-x^) tan^VJ of a circle about the corresponding 1 chord as axis. Fig. 1. depicts section [l+(l-x) tan^Y Xl + (l-x2) ta-n^f of such a surface truncated at sections AA ' and , and the positions of the B3 ' source and detector v/ith respect to it. The distribution of a function directly related to the exposed area of the (sec^Y c2 tan^lj/ )l/2 iVork carried out under a PL-480 Project sponsored by the National Bureau of Standards, U.S.A. 64 — and spectrum of elastically scattered neutrons (including distortion caused by the mul- = z/1 tiple scattering effects) while it is 21 = source to detector distance zero for neutrons of significantly lower No = ntunber of neutrons emitted/sec. energies. This scattered count is V = number of scattering nuclei/c.c. compared against the experimentally of the scatterer measured counts obtained as a difference t = radial thickness of the scatterer of counts with and without the shadow bar a = aperture of the detector in position. scattering angle Absolute knowledge ofeis not nece- ssary, as the expression for the direct count also involves 6 i.e. N ^ 2 and this € can be eliminated out by taking the ratio of N to n i.e. ^=^'t./2.ii.—I^.Sec^f' tan> r f(x,f)dx -f The count recorded by the detector has to be corrected, as it contains contributions from both elastic and non- elastic events. This has been done by the double bias technique developed in our laboratory. The method consists of recording the counts at two bias levels simiiltaneously and utilising the relative efficiency vs. energy curves^ for the of ths scatte^rtss^: Fig.l. Schematic corresponding set of biases. geoaetrj. 301PHUB DIP. ELASTIC COHJEAUB et al. PE2SEi'T EIPT. CAI/CULAIIOS .2 -A -6 -8 1.0 20^ Fig. 2. The intensity function f The coxinting rate registered by the detector D, is then given by 72 (iLi) . +f wa^Not da Cos e (C.K) N=^-=-75 5-. —2 tan^V^ Sec'^ f(x,V)dx -^^'^— ^\ 1 d-n. -f Fig. 3. Differential elastic apeetrm® of 14 MeV neutrons from sulphur. Here, the mean detector efficiency € is assumed to be independent of the 65 Results and Dlecusslons We are extending the measurements to large angles of scattering. The differential cross section of sulphur has been measured for 14.8 MeV The authors wish to thank the neutrons at 4 scattering angles 30°, 40°, Director, Bose Institute for his kind 60°, 70°. The results have been com- interest in this work. One of the pared with the experimentally measured authors (S.W.) wishes to thank the data of Conjeaud et al5 in fig. 3. The Council of Scientific and Industrial experimental values have also been com- Research for awarding him a scholarship pared with the optical model predict ion^ which enabled him to carry out this work (fig. 3). This set of average parameters has been obtained by simultaneously References analysing all the experimentally measured non-elastic cross section data in our 1. Ghose, A.M.; Proc. Int. Symp. Rad. laboratory by Pal, Chatterjee and Ghose^. Phys., India, 1974 (in press). The measured values, though in fair 2. Chatterjee, A. and G-hose, A.M.; Nucl. agreement with the other experimentally Inst, and Methods, 1967. measured ones, are not so close with the 3. Conjeaud, M.j Fernandez, B., Haror, theoretical values obtained with the S., Picord, J. and Souchere, G., above mentioned set of parameters. This Nucl. Phys. 62, 1965. is probably due to the over-emphasis 4. Pal, B., Chatterjee, A. and Ghos9, placed on the non-elastic set of data A.M., Proc. Int. Symp. Rad. Phys., while arriving at the set of parameters. India, 1974 (in press). 66 COMPTON SCATTERING OF 1.12 MeV GAMMA RAYS BY K-SHELL ELECTRONS P.N. Baba Prasad, G. Basavaraju and P.P. Kane Physics Department, Indian Institute of Technology Powai, Bombay-400076 Two sodium iodide counters in coincidence and a twenty channel pvilse height analyzer have been used to determine the pulse height distribution of 1.12 MeV gamma rays which are Compton scattered by the K-shell electrons of gold, lead and thorium. The angular vari- ations of the differential cross section ratio, "-^K , have already been reported. The present measurements were made at 60 and 100 scattering angles. At 60°, lead targets of 50 mg/cm^ and 143 mg/cm2 were used. At 100°, targets of gold (13 mg/cm^), lead (143 mg/cm^) and thorium (14 mg/cm^) were used. In all cases, pulse height distributions of false coincidence events were determined and subtracted from the measured distributions in order to obtain the true distributions. A broadening of the K-shell electron Compton peak has been observed. The results of these measurements •• are discussed. . * (Compton scattering; differential cross section; electron binding; gamma rays; K-shell; photons.) Intro duction In a recent paper"^ where references only thicker targets of lead (30 mg/cm to the earlier works have been listed, a and 143 mg/cm ) could be used on account report has been given regarding the of counting rate considerations. In all angular variation and the target-Z depen- cases, pulse height distributions of dence of the energy integrated cross false coincidence eveni s were determined sections for the Compton scattering of and subtracted from the measured distri- 1.12 MeV gamma rays by K-shell electrons. butions in order to obtain the true dis- The energy distributions of 0.662 MeV tributions. The usual procedure for the gamma rays Compton scattered by the estimation of false events is to record K-shell electrons of thin targets have a coincidence spectrum with an aluminium been studied in only a few of the earlier target of a thickness equivalent to that experiments. A broadening of the K-shell of the given target under consideration. electron Compton peak and a peak shift Such a procedure assumes that Z-dependent of about 35 keV towards lower energies false events are negligible. The relia- relative to the free Compton line were bility of this procedure has been observed by Missoni et al^ . The present examined experimentally at 60° as work was undertaken in order to provide follows. Firstly, the false event new information on Compton scattering spectra were measured with targets of by K-shell electrons at as high an aluminium and copper equivalent to 143 energy as practicable. mg/cm^ lead. For 1.12 MeV gamma rays, the binding energy of the copper K-shell Experimental Methods electrons can be considered relatively small. Moreover, on account of the Some of the details of our experi- narrow pulse height window used with the mental arrangement have been given x-ray counter, there was a negligible elsewhere^. The pulse height distri- probability of true events due to the butions of 1.12 MeV gamma rays Compton copper K-shell electrons being I'ecorded. scattered by K-shell electrons have been The integrated false coincidences measured at two scattering angles with a per hour determined with aluminium and coincidence gated twenty channel copper targets were 26.30 + 0.85 and analyser. At 100°, targets of gold 38.20 + 1.07 respectively. After (13 mg/car), lead (143 mg/cm^) and subtracting the 'target out ' coincidence thorium (14 mg/cm^) were used. At 60°, rate from these numbers and assujning the Work supported in part by a grant from the National Bureau of Standards under the Pl-480 programme. .67 leo differences to be proportional in each case to t2, where t is the thickness of t.l2 MeV LEAD (BO-ng/cm*^ 0=60° the target, we estimated the corres- iftlSO ponding differences for the thinner { COINCIDENCES targets of aluminium and copper equi- O - SINGLES valent to mg/cm^ lead. Then, with X 30.3 o the addition of the 'target out' coinci- 0120 dence rate, the false coincidence rates were calculated to be 18.09 + 0.97 and 18.54 + 0.97 respectively and, further, KEV 90 532 were in agreement with the rate 17.83 + uo 0.42 actually measured with a copper uUl target equivalent to the 30.3 mg/cm^ lead. In view of this agreement, the equivalent D aluminium substitution z. procedure can be seen to be reliable to about 3a in the case of thin targets for 30 - the determination of the false coinci- denc3 rates. However, the above mentioned data show that the same pro- cedure is unreliable in the case of thick targets. This is an important ^0 14 18 22 26 30 point to remember during any discussion of several early experiments. PULSE HEIGHT IN VOLTS_.., The true pulse height distributions Fig. 1. Pulse height distributions obtained at 60° with the lead (30 mg/cm^) obtained for 1.12 MeV gamma rays target and at 100° with the gold (13 for lead at 60°. mg/ cm^ ) target are shown in Figs . 1 and 2 respectively. The solid curve in each figure represents the pulse height dis- tribution of single events corresponding practically to scattering from free electrons. There is a noticeable rise in the coincidence spectrum at lower pulse heights. A similar rise was also observed by Missoni et al \iith 0.662 MeV gamma rays . On the basis of an 'exact ' non-relativist ic calculation, G-avrila^ has shown that such a rise is connected with the well-known infrared divergence in quantum electrodynamics. The present measurements also indicate a broadening of the K~shell electron Compton peak. In Fig. 2, a slight shift of the peak towards lower pulse heights is clearly seen. In each case, as expected, there is an appreciable number of scattered photons with energies considerably in excess of that corresponding to Compton scattering from free electrons at rest. The response of the gamma detector has been determined for several known energies so as to enable the determi- nation of the energy distribution, HEIGHT IN VOLTS d^av/d dE , of the scattered photons. PULSE ' 1.12 MeV is the highest photon energy Fig. 2. Pulse height distribution ohtaSor- at which electron binding effects have Bd for 1.12 MeV gamma rays for been studied so far. gold at 100°. 68 References Discussion 1. Baba Prasad, P.I^. and Kane, P.P. S. (jQpal ms J. Res. 78A, 15 (1974). Is it possible to measure K-shell 2. I'lissoni, G-. and Di Lazzaro, M.A., incoherent scattering cross section at Istituto Superiors Di Sanita Reports 0° scattering angle in view of the theo- ISS-66/7 and 65/8 (1966) (unpubli- retical prediction of non-zero cross shed) . section by Whittinghaan? 3. Baba Prasad, P. IT. and Kane, P.P., Ifuclear Physics and Solid State P.P. Kane Physics (India) 123, 81 (1969) and 13B . 187 (1970). a) Firstly, it does not seem possi- actually at 0°. 4. Savrila, H. , Phys . Rev. Ao, 1348 ble to do this (1972). b) G-avrila- et al have argued that this conclusion of Whittingham is probably an erroneous . one . 69 NUCLEAR THEORY BASED CROSS SECTIONS OF TH-232, TH-233 AND U-233 AND THEIR APPLICATIONS IN REACTOR TECHNOLOGY, S. B. Garg and Ashok Kumar Bhabha Atomic Research Centre, Trombay, Bombay, India. Thorium fuel cycle is an active subject of research - more so for us since we have large deposits of thorium. Because of various reasons thorium has not found much favour with the reactor technologists and therefore its cross sec- tions have not been studied with the desired accuracy. Cross sections make their impact on reactor design right from its inception to its completion and therefore a coherent study of the cross sections of thorium and uranium-253 has been made. In Reactor Physics studies emphasis is placed on total, fission, capture, elastic and inelastic scattering cross sections. Generally, the measured information on inelastic scattering cross section of heavy nuclides is not sufficient in the MeV energy range for reactor applications. In order to correctly predict the neutron spectrum and its effect on reactor parameters the inelastic cross sections have been evaluated with the local optical and statistical models. The total and elastic scattering cross sections have also been evaluated together with the angular distributions of elasti- cally and inelastically scattered neutrons. Multigroup tem- perature dependent cross sections have also been generated for thorium and uranium-253 in the entire energy range exten- ding upto 10 MeV. (Calculation ; cross section ; optical model } reactor technology; - scattering elastic , inelastic, total ; thorium ; uranium ) Introduction Thorium fuel cycle is an active spectrum, in a fast reactor, is very subject of research particularly for us sensitive to inelastic cross sections. since we have large deposits of thorium. Generally, the measured information on Because of various reasons thorium has inelastic scattering cross sections of not found much favour with the reactor heavy nuclides is not sufficient in the technologists and therefore its cross MeV energy range for reactor applica- sections have not been studied with the tions. This information can be generated desired accuracy. But, with the upcoming with the optical and statistical of fast reactor technology in this coun- modelsl' 2, 3,4 . For short lived elements try thorium is bound to find a place as such as thorium-233, the fission cross a fertile material to produce uranium- section can be estimated with the channaL 233. It is, therefore, imperative for theory of fission^' and the capture us to estimate the cross sections of cross section can be predicted either thorium-233 and uranium- thorium-232, with the dipole radiation theory of the , 233 in the MeV energy range based on compound nucleus" or with the direct^ ori nuclear theory. serai-direct-'-'-' dispersion theories. In reactor physics studies emphasis The reactor oriented studies of is placed on total, fission, cap-fcure, nuclear cross sections are concerned with elastic and inelastic scattering cross the generation of group cross sections sections. In the high energy region the neutrons lose energy mainly by inelastic collisions and therefore the neutron 70 , from the basic energy point data. In are given below: order to adhere to the spirit of this symposium we shall not discuss this U =40 MeV r = 1.32 f J ; subject in this paper but only concen- trate on the analysis of Th-232, Th-233 = (1.32A^/^ + 2.0)f. and U-233 cross sections in the energy = 20 range 0.1 MeV to 20.0 MeV. (i)W MeV ; 0.14E < 6.0 MeV. (ii)W = 26 MeV ; 7.0:^B ^ 20.0 MeV. Optical and Statistical Models 14 energy levels were used to obtain The local optical model with the the level excitation cross sections, but Saxon- Woods fonn of the real part, due to space limitation these cross sec- Gaussian form of the imaginary part and tions are not given in this paper. Thomas form of the spinorbit part of the potential has been used in these ana- b) Uranium-233 : In this case the lyses. The Schrodinger equation is nume- energy dependence of the parameters was rically solved to obtain the reflection observed to be very weak. The following coefficient which is then used to eva- parameters were chosen for the entire luate the transmission coefficients, energy range: shape elastic, compound nucleus and the total cross sections. U = 40 MeV ; W = 24 MeV 5 r = 1.32 f ; 1/3 The statistical decay of the com- Rg= (1.32 A + 2.5) f. pound nucleus leads to the calculation of compound elastic, inelastic, (n, 2n) The total, elastic and inelastic (n>p ), (n>a) and other energetically cross sections are tabulated in Table IL possible reaction cross sections. How- The excitation cross sections were eva- ever, the customary application of the luated with 9 energy levels. statistical model is in the calculation of inelastic cross sections. This model c) Thorium - 233 J Because of very also yields the differential elastic and short haif-life of 22.2 minutes cross se- inelastic cross sections. The relevant ction of Th-233 have not been measured. formulae for these cross sections are Only the thermal neutron cross section given in reference 11. is reported in the literature. The cross sections of Th-233 may be very The X Criterion significant in the production of U-233 The six parameters of the optical when thorium is used as fertile material model potential, namely, U,W, r,a,b and in high flux fast reactors. The situa- V are varied in such a way that a tions in which the neutron captures in Th-233 occur at a faster rate than beta- minimum value of X? is obtained. A com- decay would not be conducive to the pro- puter programme AUTO, which allows the duction of U-233. Then the capture simultaneous variation of five para- cross sections of Th-233> in the MeV meters, has been coupled to another pro- energy range, assume a special signifi- gramme ABACUS-2 and the search has been cance. We have calculated the total, carried out for U,W and r. This search shape elastic and compound nucleus for- was terminated when the calculated elas- mation cross sections with the following tic scattering cross sections matched optical model parameters: with the measured ones. In this study it was, however, noticed that U and r U 40 MeV ; r = ,1.32 f did not show much variation with energy and therefore to save time they were not R = (1.32 A^/5 + 2.5) f. varied throughout the entire energy = range. The values of V , a and b were (i)W 20 MeV } 0.1 6/MeV. fixed at 7.0 MeV, 0.6 f^Snd 0.6 f res- = (ii)W 26 MeV ; T.O^E 4 20 MeV. pectively. Calculations Capture and Fission Cross Sections; The capture and fission cross sec- a) Thorium-232 : optical The local tions can be estimated in terms of com- model parameters have been derived by pound nucleus formation cross section obtaining correctly the elastic scatter- by knowing ' • given by ing cross sections in the energy range f P fy 0.1 MeV to MeV. Since no measurements the We iskopf^ formula^. Using Newton's 15 Cameronl^ have been reported beyond 15 MeV, the level spacing fonnula recently model predictions of total, elastic and obtained an expression for (y in terms inelastic cross sections have been ex- of the effective total angular momenta tended upto 20 MeV and they are recorded of single particle states near the Fermi in Table I. The optical model parameters surface. These momenta are listed by 71 . ^ ITewton . Based on this fonnula and 16 Fujimoto and Yamagnchi have derived an choosing the appropriate values of expression for in terms of fission i various parameters we have obtained ?^/Vf Py threshold and neutron binding for Th-233 at 0.1 MeV to be 22.5 MeV, energies. Based on these considerations we obtain In general, fy for even-odd nuclei V^/Vf c:3^ so that Fy /p = . 003 and (Z>90) in the MeV energy region is = .024. We now assume that these negligibly small and for Th-233 Cramer Twf ratios of reaction widths and Brittle have neglected it in their do not vary with energy and calculate recent evaluations. the various reaction cross sections. These cross sections are given in Table III. Table I Total, Elastic and Inelastic Scattering Cross Sections of Th-233. Table III . m; \o)( n\ i (m) Reaction Cross Sections of Th-233 E (MeV) ''t ^t ^e ^in (c) (c) (c) (c) —T^l—ITT in IP -LX • U y u B(Me^ t ce cn f r seat 0.57 6.91 7.29 5.37 5.41 1.36 0.1 10. 85 7.07 2.88 0.069 0.0086 9.87 1.5 6.61 6.55 4.06 3.96 2.37 0.5 7. 13 4.63 2.50 0.060 0.0075 7.06 3.0 7.35 7.60 4.62 4.63 2.54 1.0 6. 30 3.57 2.73 0.066 0.0082 6.23 4.0 7.18 8.00 4.61 5.00 2.40 2.0 6. 97 3.86 3.11 0.075 0.0093 6.89 6.25 7.0 5.93 3.38 3.37 2.20 3.0 7. 33 4.39 2.94 0.071 0.0088 7.26 15.2 5.44 5.70 2.92 2.95 0.98 4.0 7. 18 4.45 2.73 0.066 0.0082 7.12 17.0 5.58 3.06 0.97 5.0 6, 82 4.18 2.64 0.063 0.0079 6.76 19.0 5.75 3.23 0.98 6.0 6. 40 3.76 2.64 0.063 0.0079 6.34 20.0 5.82 3.30 0.98 7.0 5. 97 3.28 2.69 0.065 0.0081 5.91 8.0 5. 70 3.00 2.70 0.065 0.0081 5.64 Table II 9.0 5. 51 2.81 2.70 0.065 0.0081 5.45 Total, Elastic and Inelastic 10.0 5. 40 2.69 2.71 0.065 0.0081 5.34 Scattering Cross Sections of 12.0 5. 34 2.69 2.65 0.064 0.0079 5.28 U-233 15.0 5. 41 2.83 2.58 0.062 0.0077 5.35 (°) ("1) 17.0 5. 57 3.00 2.57 0.062 0.0077 5.51 E(MeV) a a a. e e 20.0 5. 81 3.26 2.55 0.061 0.0076 5.75 0.1 10.63 11.03 8.06 8.24 0.15 0.5 7.23 7.66 4.82 5.04 0.40 Discussion 1.0 6.44 6.41 4.81 3.71 0.74 72 . , lations serve to fill this void. The cross sections of Th-233 have not been measured and their evaluation based on various nuclear theories may be of some use in certain applications. Acknowledgement s Our grateful thanks are due to Shri V.N.Meckoni, Director, Reactor G-roup for encouraging us throughout the course of this work. Also, we owe our sincere thanks to Dr. P.K. Iyengar, Director, Physics G-roup for suggesting to us to undertake the cross section study of Th-233. References 1. Feshbach,H., Porter, C. and Weisskopf, Y., Phys. Rev. ~96, 448 (1952). 2. Hauser, W. and Feshbach, H., Phys. Rev. 87, 366 (1952). 3. Auerbaoh, E.H., BNL-6562. 4. Moldauer, P., Engelbrecht, C. and Diuffy, G., AKL-6978 (1964). 5. Hill, D.L. and Wheeler, J. A., Phys. Rev. Q3_, 1102 (1953). 6. Strut insky, V.M., Nucl. Phys. A95, 420 (1967). 7. Vandenbosh, R. and Huizenga, J.R., 2nd UN Intern. Gonf. on Peaceful Uses of At. Energy, 1^,284 (1958). 8. Blatt, J.M. and Weisskopf , V. Theoretical Nuclear Physics, John Wiley, New York (1952). 9. Lane, A.M. and Lynn, J.E., Nucl. Phys. 11, 646 (1959). 10. Brown, G.E., Nucl. Phys. 57, 339 (1964) 11. Garg, S.B. and Rastogi, B.P., Fast Reactor Physics (IAEA) 1, 339 (1967). 12. Cameron, A.G.W., Can. J. Phys. 37, 332 (1959). 13. Newton, T.D., Can. J. Phys. 34» 8O4 (1956). I 14. Cramer, J.D. and Britt, H.C., Nucl. Sci. Eng. 11, 177 (1970). 15. Bohr, N. and Wheeler, J. A., Phys. Rev. ^, 426 (1939). ! 16. Pujimoto, Y. and Yamaguchi, Y., Progr. Theoret. Phys. 5, 76 (1950). i 1 73 . . THE DEVELOPMENT OF RADIATION SHIELDING STANDARDS IN USA* D.K. Trubey+ Radiation Shielding Information Center Oak Ridge National Laboratory Oak Ridge, Tennessee,, 37830, U.S.A. The American Nuclear Society (ANS) is a standards- writing organization-member of the American National Standards Institute (ANSI). The ANS Standards Committee has a subcommittee denoted ANS-6, Shielding, whose charge is to establish standards in connection with radiation shields, to provide shielding information to other standards writing groups, and to prepare recommended sets of shielding data and test problems. This paper is a progress report of this subcommittee. (American Nuclear Society, radiation, shielding, standard) By Standards, we mean voluntary Our interest here, however, is pri- Standards - sometimes called industry marily in American National Standards, of Standards - promulgated through the which about 5,000 exist. Perhaps the best American National Standards Institute known to the lay public are a few PH2 (ANSI) consensus procedure whereby all Standards defining the speed of photogra- interested parties have an opportunity phic film and Cl-1971 which, when given to comment on and contribute to the con- legal stature through adoption by a muni- any conflict of tent in a manner avoiding cipguLity, is the well-known electrical ; interest code. The purpose of a Standard is to set The organization responsible for forth acceptable practices, procedures, promulgating voluntary standards is ANSI. dimensions, material properties, specifi- The Institute, a nonprofit corporation, is cations, etc., which have been agreed a federation of leading trade, technical upon by representatives of a broad seg- and professional organizations, government ment of the subject activity. agencies and consumer groups. ANSI's principle functions are to coordinate The management organization of standards development, minimize duplicati- Nuclear Standards has accepted a defini- on and overlap, and provide a neutral tion propounded by an international forxun to consider and identify standards standards organization as, first, needs. •Standardization: The process of The Institute does not develop stan- formulating and applying rules for an dards. It makes use of the combined orderly approach a specific activity for technical talent and expertise of its the benefit and with the cooperation of member bodies j technical, professional, all concerned and in particular for the and trade organizations together with the promotion of optim\im overall economy companies and industrial firms that taking due account of functional condi- comprise the Institute. A standards tions and safety requirements. writing organization, such as a technical society, having developed a standard and It is based on the consolidated seeking approval by ANSI, prepares a list results of science, technique, and expe- of the organizations, companies, and rience. other groups with substantial concern and competence in the scope of the standard It determines not only the basis and then conducts a canvass of them on I for the present but also for future de- approval of the proposed standard. velopment and it should keep pace with The final results are reported to the progress," and a Standard is "The result MSI Board of Standards Review for deter- of a particular standardization effort mination that a consensus exists and approved by a recognized authority." declaration of the proposed standard as a *Research sponsored jointly by the U.S. Atomic Energy Commission and Defense Nuclear Agency under contract with Union Carbide Corporation. "''Chairman Shielding Standards Subcommittee, ANS-6, Standards Committee, American Nuclear Society. 74 yoluntary American National Standard. ANS-6. 1; Shielding Cross Section Standards The standards-writing organization Because of the changing state of of interest here is the American Nuclear knowledge of neutron cross sections, no Society (ANS). Among its several admi- standard is possible with anything near nistrative committees is one on Standards the time constant of the usual standard composed of nearly 30 Subcommittees (see such as, for example, the classical ASTM list below) . Parenthetically, as presen- code for unfired pressure vessels. At tly constituted, the Committee consists present it is better to think of recomm- of all individ-uals assigned to Standards ended cross-section sets as reference tasks within the Society, some 800, and sets rather than standards. Within is, obviously, not a working or workable ANS-6, "Shielding Cross Sections' has a group. There is, therefore, an eleven- broad interpretation, which includes member Steering Committee. The ANS neutron interaction cross sections for Standards Subcommittees are grouped along all common reactions, photon-production lines of common interest and assignments cross sections, photon interaction cross- \inder supervision of a Steering Committee sections, and secondary angular and member. The Subcommittees, in t\im, have energy distributions for all these inter- established ad hoc Working G-roups for actions. Since the Evaluated Nuclear preparation of individual Standards! Data File (ENDF) represents current reference data, no action in this area ANS-1 Performance of Critical Experiments seems to be required. The group did recommend in that the Lawrence ANS-2 Site Evaluation 1970 Livermore Laboratory evaluated photon ANS-3 Reactor Operations interaction cross section set be accep- ANS-4 Reactor Dynamics and Control ted as reference data and be distributed ANS-5 Energy and Fission-Product Release with the EI\[DF neutron data. ANS-6 Shielding ANS-8 Fissionable Materials Outside Reactors Current projects include standard ANS-9 Nuclear Terminology and Units flux-to-dose rate conversion factors and ANS-10 Mathematics and Computation reference coupled neutron-gamma-ray multigroup cross sections ANS-11 Radioactive I'laterials Handling for the Facility and Specialized Equipment elements normally found in concrete. ANS-13 Fuel Assemblies Criteria ANS-6. ANS-14 Operation of Pulse Nuclear Reactors 2; Benchmark Problems ANS-I5 Operation of Research Reactors The primary objective of the bench- ANS-16 Isotopes and Radiation mark ANS-18 Environmental Impact Evaluation problems effort is to compile in convenient ANS-19 Physics of Reactor Design form a limited number of well- ANS-20 Systems Engineering documented problems in radiation ANS-21 PWR Design Criteria transport which will be useful in testing ANS-22 BWR Design Criteria computational methods used in shielding. ANS-23 GCR Design Criteria ANS-24 Design Criteria The compilation and publication of LMFBR benchmark problems are ANS-30 Power Plant Systems solutions to Nuclear accomplish several ANS-31 Engineered Safety Features expected to things: Systems 1) attention will be focused on typical ANS-32 Reactor Plant Process work Containment problems where careful should ANS-33 produce which are representative Radioactive Waste Systems solutions ANS-34 of the state-of-the-art in solving radia- ANS-35 Fuel Handling and Storage tion transport problems, 2) specifications of standard configurations and data will The subcommittee on shielding stan- make comparisons of different computa- dards, ANS-6, now composed of seven tional methods and theory- experiment working groups, was established in 1964 comparisons more meaningful, 3) discre- with the sponsorship of what is now the pancies between calculation and experi- Shielding and Dosimetry Division of the ment may suggest refinements in the Society! The standards development numerical approximations or nuclear data, of the subcommittee is carried on within or may suggest new experiments to resolve working groups composed of members from the disagreement, 4) reliable solutions by reactor vendors, architect-engineers, several methods will be made available national laboratories, the Atomic Energy to help judge the precision and effici- Commission, and universities. The goals ency of different computer codes, and to and accomplishments of the working groups suggest if new codes ought to be deve- are briefly described below. loped, 5) newly acquired codes and codes 75 s . converted to new machines may be verified ANSI Glossary of Terms in Nuclear Science by duplication of the benchmark problem and Technology. It is planned to have solution, and 6) mistakes in existing or the special shielding terms and defini- new codes, or their options, can probably tions prepared by the ANS-6. 5 working be detected by independent calculations group published separately since the list of the benchmark problems. is sufficiently long and specialized to not be included in the glossary covering Four problem solutions were publi- all of nuclear science. A draft glossary shed in 1969 in loose-leaf form in Ref is presently being reviewed. [2j by the Radiation Shielding Infor- mation Center. Revisions and a new ANS-6. 6; Calculation and Measurement of problem were issued as a revision in Direct and Scattered Radiation from 1970. Two new problems were recently Nuclear Power Plants issued as Suppl. 2 of Ref. [2j and are available from RSIC upon request . They Organized in late 1973. the group has are Neutron and Secondary Gamma Ray adopted the following scope: Fluence Transmitted Through a Slab of Borated Polyethylene by C . E » Burgart and "This standard will define calcula- A Benchmark Experiment and Calculation tional requirements and measurement tech- for Neutron Trans port in Thick Sodium by niques for estimates of exposures near R.B. Maerker et al. The work slowed for nuclear power plants due to direct and a period but now additional problems are scattered radiation from contained sour- being developed including several for ces on site. On site locations outside typical reactor configurations. plant buildings and locations in the off- site iinrestricted area will be considered. ANS-6.3i Shield Performance Evaluation All sources that contribute significantly to exposure levels will be identified and The initial goal of this group was methods for calculating the source stren- attained in 1972 with the publication of gth of each will be given. This standard Ref. [3]- Shortly after publication, the specifically excludes radiation from U.S. Atomic Energy Commission issued a gaseous and liquid effluents. The stan- Regulatory Guide^ based on this dard will review the considerations _ standard for research and training reac- necessary to compute exposures, including tors. The current goal of the committee component self- shielding, shielding is to completely revise Ref. [3] to make afforded by walls and structures, and it more applicable to current practices scattered radiation. Finally, the in the nuclear power industry. requirements for measurements and data interpretation of measurements will be ANS-6.4; Shield Materials given. This standard will include normai operation and shutdown conditions Initial efforts involving materials but will not address accidental or normal per se , e.g., lead as a shielding mate- operational transient conditions. Nitro- rial, have failed. The current work has gen-16 gamma rays are a prime considera- produced the draft of a standard, ANSI tion. N403s on the Analysis and Design of Concrete Radiation Shielding for Nuclear ANS-6„7; Radiation Zoning for Design of Plant . The draft underwent balloting by Nuclear Power Plants ANS-6 in September of 1974 ^ The standard is much more general, in many respects, This group was organized in early than required for designing concrete 1974 to standardize radiation level shields only. That is, the approach to zoning in power plants. The tentative radiation analysis and the methods recom- goals were 1) definitions of radiation - mended can be applied to many shielding zone designations, 2) maximum and/ or analysis problems. average dose rates in each zone, 3) methods for determination of access time to each ANS-6 .5; Shielding Nomenclature zone, 4) precautions, posting, survey requirements, access control, and alarms, The effort of this group is directed and 5) responsibility of issuing entry to the preparation of a list of shielding permits for admission to areas of limited terms and definitions and maintaining access. liaison with the Nuclear Terminology and Units Subcommittee (ANS-9). The latter Related Standards Work subcommittee is assisting the Nuclear Most standards are listed in Terminologjr , Units, Symbols, Identifica- nuclear tion,, and Signals Committee of the Ref. [5,6]. Two other organizations American National Standards Institute in writing standards of direct interest to the preparation of definitions for the shielding specialists are: 76 » 1. American Society for Testing and Mate- Register. Regulatory Gruides are issued rials to describe and make available to the public methods acceptable to the AEC ASTM, publisher of the world-renowned Regulatory staff of implementing specific Book of ASTM Standards, is* the world's parts of the Commissions 's regulations, largest source of voluntary consensus to delineate techniques used by the staff standards for materials, products, syste- in evaluating specific problems or ms and services. Since 1898, the Society postulated accidents, or to provide gui- - mainly through the intensive activities dance to applicants. Regulatory G-uides of standards committees - has conducted are not substitutes for regulations and vast numbers of investigations and re- compliance with them is not required. searches leading to a better knowledge of Methods and solutions different from those the properties of materials and the deve- set out in the guides will be acceptable lopment of more than widely used if they provide a basis for the findings standards - specifications and methods of reqialsite to the issuance or continuance testing for materials. of a permit of license by the Commission. Beginning with the 1974 edition of Published guides will be revised the Annual Book of ASTM Standards , the periodically, as appropriate, to accommo- Society plans to provide a separate part date comments and to reflect new infor- of volume on ASTH's nuclear related mation or experience. standards. Part 45 of^ the 1974 Annual Book of ASTM Standards' contains all Copies of published guides may be ASTM standards dealing »/ith nuclear ma- obtained by request indicating the terials and materials related to nuclear divisions desired to the U.S. Atomic reactors. There are 104 standards in the Energy Commission, Washington, D.C. 20545 book of which 159 are new, revised or Attention: Director of Regulatory changed in status since 1973. Sixty-six Standards. Comments and suggestions for have also been approved by AI^SI and a improvements in these guides are encoura- number of others by other organizations. ged and should be sent to the Secretary The standards in Part 45 cover: concrete of the Commission, U.S. Atomic Energy products for nuclear applications,- gra- Commission, Washington, D.C. 20545? phite products for nuclear applications^ Attention: Chief, Public Proceedings Staff. metal products for nuclear applications (hafnium, nickel and nickel alloys, steel, The guides are issued in the follow- tantaliim, titanium and titanium alloys, ing ten broad divisions: zirconium and zirconium alloys) ; nuclear grade materials; radiation effects in 1. Power Reactors organic materials,- radioactivity-, inor- 2. Research and Test Reactors ganic materials in water; analysis, 3. Fuels and Materials Facilities dosimetry and radiation effects in metals; 4. Environmental and Siting and temperature measurement. 5. Ifeterials and Plant Protection 6. Products The ASTM Headquarters staff of 150 7. Transportation is located at 1916 Race Street, Philadel- 8. Occupational Health phia, Pa. 19103; William T. Cavanaugh, 9. Antitrust Review Managing Director. 10. General 2. U.S. Atomic Energy Commission The USAEC Division of Reactor Rese- arch and Development (RRD) is responsible Under the Atomic Energy Act, the for the safe development of reactor tech- Commission has the responsibility for nology in the U.S. Toward that end, they establishing licensing procedures and are concerned with the development of regulatory fimctions for the control of standards covering design, analytical materials and facilities essentiaO. to the methods, materials, equipment, systems, atomic energy industry. These functions fabrication, construction, quality assu- are carried out by a Director of Regula- rance, inspection, testing, operation, tions who reports directly to the Commi- and maintenance for government-owned ssion. The Director is responsible for civilian water reactors. Toward this end, the Directorate of Regulatory Operations. standards are being prepared, reviewed, The tvro basic reasons for the regulatory reproduced, distributed and revised in duties of the AEC are to protect the order to incorporate latest developments, public health and safety, and to promote information, techniques, and experience. the common defense and security. Regula- This work is being performed under con- tions of the AEG are included as parts of tract to Oak Ridge National Laboratory Title 10 of the Code of Federal Regula- (OREL) with the assistance of other AEG tions, and are published in the Federal offices and contractors as a continuing 77 activity in this program. The standards 6. Standards in Nuclear Science and Tech- program will serve as a base on v/hich to nologv, a Bibliography, TID-3336 build current and future reactor programs (1973) . Available from National Tech- with greater quality assurance and the nical Information Service, Springfield, attendant improvement in reactor reliabi- Va., 22151. lity and safety. A thorough investigation of records, experience, knowledge, exper- 7. Part 45, Nuclear Standards, 1974 Ann- tise, and evaluation from all available ual Book of ASTM Standards, Publication qualified sources is required for the Code No. 01-045074-35, successful attainment of the goals for the standards program. Initial efforts have been directed toward converting available standards into a form that may be used for engineering current (RRD) Discussion experimental activities and demonstration reactors and provide usable technical Shank er Singh guides for the AEC Directorate of Engineering Standards, Directorate of The shielding requirements for the Licensing, and the Advisory Committee of two types of Past reactor concepts namely Reactor Safeguards. ORNL is responsible Loop type and Pool type reactor being for overall management of the RDT different, are there any specific experi- Standards Program under direction from ments being conducted or planned for RRD. Standards are being prepared by either of these concepts and if so which ongoing development projects and by ORNL concept is being pursued more vigorously? in its specific areas of expertise for which each writer is qualified. Such D.K. Trubey standards, designated as RDT standards, are also listed in Ref. [5]. Experiments at Oak Ridge are in support of the US LMPBR program which References employs the pool concept. A.K. Gangxilly 1. Claiborne, H.C., Dudziak, D.J. and Schaeffer, N.M. , Activities of the 1. Do you measure the scattered ANS-6 Subcommittee on Radiation Shi- spectriim in open air below 0.21 MeV as elding Standards, ORWL-TM-3271 (1970) given in the table? Oak Ridge National Laboratory. 2. Do you still have a programme of A.E., Shielding Ben- 2. Profio, Editor, investigations on Multilayer shields? chmark Problems, ORNL-RSIC-25 (ANS- SD-9) Suppl. Suppl. (1969$ 1, 1970 J D.K. Trubey 2, 1974), Oak Ridge National Labora- tory. 3. Program for Testing Biological Shiel- 1. Not with sodium iodide detectors, ding in Nuclear Power Plants, ANSI but measurements at lower energies are N18-9-1972 (1972), American Nuclear made with Ge (Li) detectors. Society, 244 E. Ogden Avenue, 2. Many of the experiments are with Hinsdale, ill., USA. multilayer shields which mock-up particular 4. Shield Test Programs for Evaluation systems. Por example, iron-polyethylene of Installed Biological Shielding in and iron-sodiim systems have been studied. Research and Training Reactors, Regulatory Guide 2.1 (1973), U.S. Atomic Energy Commission, Washington D.C., USA. 5- Catalog of Nuclear Industry Standards (1974) , American National Standards Institute, Inc., 1430 Broadway, New York, N.Y. 10018. 78 ) INTEGRAL EQUATION METHODS IN RADIATION TRANSPORT D. Y. Gopinath Health. Physics Division Bhabha Atomic Research Centre Bombay - 400085 This paper presents a review o f the Work done on the devel- opment of integral equation methods for different problems in radiation transport. The cases con sidered are:(i) Three-dimen- sional (XTZ) geometry and (ii) One dimensional time-dependent transport for the transport of (a) Charged particles and (b) Optical- radiation. The methods are developed for arbitrary degree of ani- sotropy, and their simplification in the case of isotropic scattering are discussed. Few typical results are presented and the advantages of integral equation methods are di SGucsed. ( Int egral e quat i on radiation ; semi-numerical ; scattering; transport Introduction SCr,E,X)L,t) = radiation source at • r?,E,JT. ,t) • - In this paper we present a semi- numerical technique for the solution of T(E,-n.—^^,= spatial transmission radiation transport problems. The methods —>•,-',' . \ kernel r'->-r , t —j-t developed here are applicable to energy ). dependent radiation transport with arbi- G(r",E'->-E, = energy-angle transmission trary degree of anisotropy in scattering. -^s kernel The purpose of the paper is to give a brief review of the work done in our source. group on integral equation methods for S fr^, E,_Q,t)= external such problems. This is also intended to present a unified formulation for In the above formulation, eqn. ( 1) most problems in radiation transport and represents transmission of radiation to show that any variation in the treat- through space and eqn. (2) accounts for ment for different types of problems are what happens at a spatial point during only marginal. the collision. In obtaining the solution for the above equations, we have two Mathematical Formulation options: (i) develop the solution for the most general case and obtain the simpli- Basic equations : fications for particular problems, (ii) ^ obtain the solution for a simple system The essential feature of the and introduce modifications for more approach that is followad here is to general cases. separate the spatial and energy-angle While the first appnoach is definite- transmission in radiation transport. and scholarly, the second Whence, ly more elegant the transport can be represented advantage of being simpler as method has the and easy to follow. We adopt the second approach. • <^{t,E, Ji,t ) = dt dJT.' , dr' JjJ The simplest case is that of time- independent radiation transport in one- S(r',B, Jl.',t')z T(E, JiTh-Ti: ,!^'-). 7, . dimensional slabs. This problem has already been worked out in detail and 1;'-*t). .. (1) published elsewhere However for the sake of completeness and to introduce the broad principles of our approach, I start with this case. Further, in our formula- srr,E,2l, t) d^,dJi. 9S(r,B',Ji',t) =JJ tion, we consider only gamma rays and neutrons. Towards the end we deal with G(r',E'-»E,-n.'-»-n. )+ s'(r,E,jl ,t) the changes needed for other types of (2) radiation. where radidation flux at (r,S,^ ,t) , One dimensional slabs : 9f)'^(x^,Eg,Hg)=Z S^(x^,Eg,^g)T(g,l, j-i) In one dimensional slab geometry eqns.(l) and (2) simplify to (cf.Fig.l) 9^V,.Eg)=Z/(,^^,^,^^)p^(^^),^^ ^^^^^i'\^=^>^^^i'^g^^^^'«'-*s) + s;(x.,Eg) S^+l(x^,E^,H^) =^ S^(^i'Eg)P^(^ii) (7) Pig.l. Pictorial representation of spatial transmission of radiation in one dimensional where k is the iteration index. geometry. Starting with S'(x^,E the set of equations are solved fteratively till they are self-consistent within a pre- set criterion. .. (3) Spherical Geometry S(x,E,n) = JJ^^Cx.s'.^i') G (x,e'-^E, In this case, only the geometry differs from the earlier one. As such, Jl'->-0: )dil',dE'+ s'(x,E,(i) .. (4) equation describing the collision pro- cess remains unaltered. and Referring to fig. 2.,. the spatial (5) transmission equation for spherical sys T(E.,,x'->x)= tems can be written as (for a given energy) G(x,E'-)'E,3a'->.Jl) = Z^(E^E)6{:a.7l',|(E,E'')j (6) where ^ (E,e' )= 1 - + for Y-rays ' E ^ ?l±if~E— - O.' for neutron 2 • E' E elastic scattering. M is the target mass. For inelastic scattering of neu- trons ( , e'->- E , A' -^il ) = ( e'-^ E ( ) P G X 2 ) ^ X ^ n Pig. 2. Pictorial representation of spatial transmission {SI. JX ) of radiation for spherical Throughout our formulation we use dis- system. crete ordinate representation in n'andx for spatial integration and legendre polynomial approximation in |i for the 5ZS(r^,^^)= Jjs(r' ,nO T ( r'-^ r, evaluation of collision integral . Whence we obtain dti',dr'. .. (8) 80 and Tir-^T, \x-^\x^) = e~^^^^^ ^(r,-.,) =!l^.|^(r^,,,.(rj^,)) (- 1^)6 /.V l-r^/^2(l-4)}..(9) I - ^^-'i.r^^^.i.i )j.-2y(^j..) where (14) + \i jir)=T.^^ V"r2-r2 ^ for T ..(10) Having thus obtained expressions for flux in terms of source, further proce- in ezp.(8) and with the using exp.(9) dure is the same as that of slab geome- of space as in the slab discretization try. We go through the same iterative exp.(8) becomes, for case scheme till the final solution is obtain- ed . ^(r.,u^)= 9S(r._^.u(r._^))e-^y(^j-l> Next, before going to multi-dimen- sional geometry, we shall discuss one- dimensional time-dependent radiation transport. Of these the slab case is of + ( S dy ..(11) (r,n(r))e-^y little practical interest and only the o spherical case is presented here. Writing Time-dependent Radiation Transport in Spherical Systems . . . , = S(r,^i(r S(r,n(r))l )) As in the stationary case, even here the equation accounting for the change A3 during collision does not alter. (This ^"-"j-1^ Ar J,J-1 is strictly tirae only if we neglect meta- stable states of target nuclei and de- layed neutron emission. However this in exp.(ll) will be the integral assumption is not a serious restriction). The spatial transmission equation will be .-Zy(r, (cf .Fig.5): i{s(r...3_) - S(r._^,.(r._^)e-^^(-J-rJ As C o V y2-2yrj.^3_+ r^ (12) The integral in exp.(l2) cannot be integrated analytically. However one can note that the integrand contains the generating function for Legendre polynomials. Hence, expanding this, the integral can be obtained as fast converging series. Denoting this inte- fral as ^ and combining exp.(ll) and (12) Pig. 5. Pictorial representation for n + ve) of ti«e-d«p©jQden©e of radia- tion transport in spherical systems. <^(r.,^^) = !i^liill^ {^ir^_^,^(r._^)) S(r ^(rj,|i^,tj^) = dt,d^,dr. S(r,^,t) x i.i..(r.,, ))?-2y(r,_,)^43( JJJ T(r->rj., .. (15) .. (13) On exactly same lines it csm be shown that for ^ - ve 81 and Making the transformation t' = t, -t, the integral in exp.(18) becomes At js |r(tj^-t' ),n(t^-t' ),tj^-tj e-^^^'dt' ^[ti. Vl-rJ/r-^d-n^)! 6 t-tj^.iir)j • • (16) o I .. (20) where y(r) is, as before, given by eqn.(lO). To evaluate exp.(20), as before we use linear interpolation between spatial, Introducing eip.(l6) in (15), directional and time modal values of because of the '6' functions in ezp.(l6), source. Within the range of integra- we can either integrate over |i. and t and tion o to At, r(t) in exp.(20) may not obtain the final expression as an inte- be within r. and r. ^ but may fall bet- gral over r or integrate over r and \i ween different spatial nodes. Hence the to have the final expression as an inte- range of time integration is subdivided gral over t. Integrating exp.(15) over at ^2.*^2 that (cf.exp.6). t and (1 y(r ^) _ vt^ 2vt, r . .1 ^ = o of- t .= i/r 11 + \f^2 2/ , 2x „ 1 v| 2 1 -r.(l-^ll) - (21) .. (17) and the maximum of i given by Alternately, integrating exp.(l5) over r and \i t for ^ I^ax= ^.i^ VAt-^-r^(l-nf ) 7 i^(Tyix^,t^)^. J's(r(t).|i(t).t)e-'^^(^k-*^- .. (22) With this subdivision, S in exp.(20) in the interval t^ and t^^^ can be written as d(tj^-t) +^^r(tj^-l),ti(tjj.-l),tj^_^j J-i AS (18) ^J-i'^^ - At e-ZT(Wl) k,k-l Ar j-i+1 where _(r(t^-t.) - r._,j k,k-l r(t)=V(tj^-t)'^-2v(tj^-t)r.^+rJ A^S .t'ir(t -f)-r I At. Ar (19) j-i,j-i+i I ^ j-v v(t -t) - r Ai <^ -I' >i(t)= . i > r(t) (23) Expressions (17) and (18) are exactly equiv8.1ent. However in evaluating exp. Taking only upto first order differen- (17) one has to remember fluxes at all tial terms of exp. (23) in (20), comple- points for times earlier than t . ting the integration and using it in In case of exp. (18), it is necessary to exp. (18) know the fluxes and sources only at t, Purely from the causal considerations," this is also the necessary and suffici- ent information to compute the fluxes and sources at t, . Hence we deal only with exp. (18) in the sequel. 82 ht.J.k'l z -S + -.1-1+1. g' .k ".1-i.uJc (e-^'y-"-e--^yi+l)] 1-1 ^ As At t.J-t. A-» (24) Fig. 4. Pictorial representation of 1 radiation transport in three dimensional cartesian system. where along X axis is (25) j-Z.Ax ^i-l,J,k-^" Having thus obtained the expression for i.Ax flux in terms of source, we go back to the main iteration scheme. One difference + S(x',y.,Zj^)e-Z/'^j-^') dx' to be noted in this case would be that j the index k in eqn.(7) refers to time (1-1) Ax and not the iteration number. Next, we consider the multi-dimen- sional systems. In this, the two dimen- sional case (finite cylinder) will be discussed in detail by my colleague in S. . As another paper in this symposium. Hence, ^ "i>j>k ^ I will skip that case and go directly Ax to three- dimensional systems. Z 2 1,1-1 Stationary Radiation Transport in three .. (28) dimensional systems . Here we discuss only 3-dime-n- and this flux will be in the direction sional cartesian systems and as before we assume discrete ordinate representa- -1 Ax tion in X,Y,Z cordinates. The basic \X = 0, = COS equations in this case would be V Ax^+ Ay^ Similarly flux due to sources along ^(R,E,2t)= T(it,R'->-R)dR y Js(R;E,il ) axis is .. (26) - •'^>.l--^'^ S(R,E,2t)= id) ) e Jj . dE'd/l'+S' (R,E,^) .. (27) i,k -2Ay where R—>R(x,y,z) i k- , As ^ (l-e ) .. Ay (29) Referring to Pig. 4, the flux at a given space point will be computed in 26 direc- tions corresponding to 26 adjacent modal points. Thus flux at k,j,k due to sources and so on. 83 In general, we can represent the flux S(x. ,y . , z, ,-n, E ) 1 k equation as J g = L L S^(i, j,k,g)P^(ti)Cos mcp ..(32b) An n m the main iteration scheme described in eqn.(5) get modified, as : -2 = 1-1' k-k'/^ i'fS. . ^ - S. .,^,e-2^^k'- -V i,j,k 1-1, J, T(n,9,i'-).i, j'-^j,k'^k ) (33a; As 1, 1-1 V,j,k.g) = 2 Z.'J^i.j.k.g^^^n-'V) ~ i. j .k i, j-j' 2^ I in' ) Cos m m ,x w^ ..(33b) m' m,n,mjn'^ S^(i, j,k,g) = (i, j,k,g)G(n,g'-^g) 2, ..(33c) k'/s. . , - S. . - ,e~l^^ + ^'"^ i,J,k-k' 2 t ^i,j,k,g(^'^^-Z Z s;(i,J.k,g) n m ( (50) I k,k-k' P^ ( ^ ) Cos m ( x . , y . , z, , -fh , E ) 1 1 k In the case of charged particles g we consider two types of interaction j,k,g)P^^)Cos mcp with the media: , m m / n °- 1) Coulomb (32a) 2) Catastrophic collisions Though Coulomb interaction can also be considered as collision, because very 84 small angle and energy change per such In optical radiation we are mostly con- collision and very large number of such cerned with Rayleigh scattering which is collisions per unit track length, it is coherent. That is, energy (or wavelength) better to treat this phenomenon as to of the radiation does not change during continuous process. Thus, the charged scattering. Hence our second equation particle can change its direction and which accounts for the collision process lose energy continuously along its track reduces to even without any collision. To take into account such changes in energy and direc- tion our first equation describing the S(x,E,n)= J(^(x,B,n' )a(^^/3)d/L'+S' (x,E,n) spatial transmission modifies to (38) ^(R,E,2l ,) = S{R',E,jri! ) JIJ Of coarse, to be exact there is an -n. R E' indirect energy coupling in exp.(38) through S' . S'(x,E,|i), which accounts for the emission of radiation is a func- T(E^E,-a'-*il,R'-^R)dR;dXL',dS' . .(34: tion of temperature at x, which in turn depends on the absorption of radiation of However if we are considering heavy par-* all energies. However for the case pla- tides the directional change is negli- netary radiation, with which we are inter- gible and the eqn.(54) simplifies to ested S' does not contribute to the wave- lengths of our interest. Further, for Rayleigh scattering ^(R,E,5i) = s(r',e;Ji) J I R E aiSl-^Sl) = T(2l ,R'-»R,E'-?-S)dR'dE' ..(35) using exp.(39) in exp.(38), in our for- mulation, the source eqn. further redaces where to T(J1, E R'-^-R) = e"*^-^^"^'^ S^(x,E) = 0^ (x,E) S^(x,E) = o 6| r-r; ^(E,S') ..(36) The function -^(E.E') in exp.(36) is 'AO) obtained by the relation For the intensities of our interest, the system could be non-linear. That is the radiation intensity may be sufficient R-R' dE f dE /dz to change the characteristics of trans- E port medium while this may pose a serious problem in other methods, in the present Because of the 6 function in exp.(36), approach it is handled in a natural way. eqn.(35) can again be expressed as an In our main iteration scheme (cf.eqn.5) integral over space only. Beyond this each iteration corresponds to a collision point, the treatment is essentially the generation. Hence the only change nece- radia- same as in the case of non-charged ssary would be to have T and G matrices, tion. As I mentioned earlier, the de- which are dependent on medium properties, tails will be discussed in another paper. as a function iteration number. Of course, evaluation of the change in the media can Optical Radiation be very much involved but that is an input for this problem. The three characteristics that make optical radiation transport diff- Any analysis of optical radiation erent from others are: transport is not complete unless we con- sider the polarisation status of the 1) Energy decoupling in the radiation. Even in this case, equation collision, governing the spatial transmission does 2) non-linearity of the system, not change. But equation governing the 3) polarisation status of the collision process does alter. Following radiation. Chandrasekhar*^, we specify the polarisa- tion status of the radiation by the vectors 85 . , S — S (S^,S^,u,, v^) Then, to take into account the change in polarisation during scattering, instead of eqn.(40) we will have the matrix eqn. where the elements of the matrix |;P| are given by Chandrasekhar* References 1. (ropinath, D.V. and Santhanam,K. Wucl.Sci.Eng. 186 (1971). 2. Gropinath, D. V. and Santhanam, K., Nucl.SGi.Eng.,il, 197 (1971). 5. G-opinath, D.V., Santhanam, K. and Burte, D.P., Nucl . Sci . Eng. ,^2, 494 (1973). 4. Chandrasekhar, S. , Radiative Transfer, Dover (1948) P. 25-42. 86 s NEUTRON TRANSPORT PROBLEMS IN SPHERICAL GEOMETRY D. C. Sahni Reactor Engineering Division Bhabha Atomic Research Centre Bombay - 400085 The density transform method has been extended to cover spheri- cally symmetric neutron transport problems. The density transform is expanded in plane geometry normal modes and explicit singular integral equations are derived for the expansion coefficients. The method is thus an extension of Case's method of singular eigen-functions to spherical geometry problems. The Green's function approach for trans- port problems in spherical geometry has been considered. It is shown that the reduction operators used in this method can solve only some of the problems in the interior of a solid homogeneous sphere, (Density transform ; expansion coefficient ; Green' s function ; neutron ; spherical ; symmetric ; transport) Introduction Density transform method Analytical solutions of neutron We consider one speed spherically transport equation have been obtained S3rmmetric Boltzmann equation with iso- only for the narrow class of one dimen- tropic scattering and isotropic source sional plane geometry problems by using density Q(r), in which angular flux singular eigen -function techni-que of Njf(r,p.) depends only on the radial dis- Case^. Straight forward extension of tance 'r', measured in units of mean- Case method to spherical and cylindrical free-path, and 'n' the cosine of the geometries is not possible because in angle between the position vector r and these cases Boltzmana equation is not the direction of motion of the neutron. translationally invariant. In this paper we present a genera- lization of the density transform method for solving one speed spherically symmetric transport problems with iso- = I f(r) + Q(^) (1) tropic scattering. The method consists 2 2 of defining suitable integral transforms of the total flux (density) which satis- 'c' is the mean number of secondaries fy the plane geometry transport equation per collision and the total flux in transform variables. This gives an (density) P(r) is given by expression for the total flux (and hence the angular flux) in teras of plane geo- metry singular eigen-functions, the 1 expansion coefficients being determined f(r) = j \i'(r,n) dn .. (2) as the solution of a singular integral -1 equation. Finally we examine the Green' function approach for spherical geometry problems as given by Case at al^. These The transport equation (l) is to be sol- authors have introduced the expansion ved for range a ^ r ^ b and -1 ^.ji ^ 1, coefficients which are related to ones subject to the prescribed incoming dis- arising in the density transform method. tributions ^i'(a,n) } 04:^1^1 and y(b,n>, However, the singular integral equations — 1^(1^0. It is seen that equation (1) derived by them are not correct because can be integrated to the following form of the use of reduction operator. This can be seen most readily from their expression of linear extrapolation dis- >Kr,n) = ^{a, yi-r^(l-n2)/a2)exp(-fir + tance in spherical Milne problem which ^/a2-r2(l-^•2)) + 1 ^P(y)-HQ(y)]dy is independent of the radius of the f , black sphere, contrary to the well known JV y2^^ r^(l-fi2) result of Davison'. We indicate the procedure for deriving the correct equa- tions using the boundary values of a T^{l-\^) .. (3a) sectionally holomorphic function related .exp(-nr +^yj^- to their definition of expansion coeffi- cients. if /v/ 1-a^/r^ ^ 4 1 87 — ) — eip( -bn- b (1-^) (-|ir- 0\p y b' -r'^'-( l-ji'' ) ) b 2 ^ (5) 1r'J^^ ^2,, 2^ -b (1-n ) We define the density transforms by the equation for in >o r <^'(r,^) exp = (r/ii) ~j [y[c f(y)+Q(y ) ] 2 (5b) exp (y/|.i) dy + "2 \ |i' M'(a,|j') exp (a|a') ^ o Thufi csin t>6 determined once the density f(r) is determined. Integrating ^ equations (^a) and (^b) we find that ^o ( ? viiT"^!:^ r(r) is the aoliitlon of the inte>?;ral equatl on ' b _b r f(r) ^- \^ j*y[c\'y[c r(y)\Hy) ^f Q(y)] jK(^,y) y[c f(y) + Q(y)] dy I j I a - fx (r' ) r' exp (- r'/n) dr' [exp(-sly - r| )-exp ( -s\fy2-a2-s Vr^a^ )]dy 1 ^ 1 ^i' U(b,- )exp (-b ^' )Io . + a^ j'^i^ V|;(a,|i') exp ( a^' - ^ fr'-'-a"-(l-^'"' ) )d|ii(- o ^72 rri— 'r 7^ -a ( Vl - a2/ b2 . 1,2 U/ ^i/(b,-^l') exp(-bn'-Vr'^-b^l-n'2) )dn/+ b y ^' d (i' 2 iT^ 7 2 ) f l-a-/b^ (6a) 00 2 ^;.osh (sr) j'x(r')r'exp (-sr')dr' while for li 1 b '|>(r,n) exp (r/n) = - i_ ry[c p(y) .. (4) 2li J where the function x(r) is related to the incoming angular flux 4:'(b,-p)j |i > 0 at Q (y)] exp dy the outer surface of the shell a ^r 4 b by the equation ) r^ exp (r' /|i) dr^ .. (6b) 88 where fl^^ and are the noraaliaatlon constants while the unknown coefficients X a^^ and have to be determined by applying the following boundary condi- tions } n> 0 i) 4' (a,n)eip(a/ji) y)y an Ii (a/i/^2 1 exp (-1^7^/^/) . 1/^2 lj^(^)r'exp [cf(y)^Q(y)]dy - (7) o2 it (-r'/n)dr'+ -2 ji'M/(a,n')exp(an')I( Then it is seen from equation (4) that J r f(r) = dn .. (8) (ay- -p^W- 2 f, \i ' 1 - \i ' 1 - n' Prom the equation (6a), (6b) and (8) it 2 r- can be shown that 4)(r,^i) satisfies \ W ^(b,-n')eip(-t'|l')I„ plane geometry transport equation -1 ]i i-n ' i-fi (9) ii) 4>(b,-n)exp(-b/n) = i rx(r')r/exp Thus [exp (-Ir-r^lZ-t)^) - exp( - |r+r'l/Vo) ] + 1 D 1 b _ f cTdi' [t'G^(r')e^/^dy |r^(rOdH:exp(- |r-ri/V)- exp 0 ^ a (-|r + r'|/V)] .. (10) ... (12) 89 ^ while for <^e (~l,o) I.e. the e xpansion coefficients of equa- 1 tion (14) are related to the difference in the boundary values of the sectionally holomorphi c functions T (k) and A (k) of the comple X variable k having branch ctlte r ^ from {-±00 ,-i) U (i^i'-o ).A(k) in addi- tion, has two simple poles at + i/'^o- l^tie function IS (k) depends upon the angular flux M^(b, li) on the surface r = b T^(k) = - b^ In' vp(b,n')dn' 2(-i>o+i)) ^ (1) |;i^(2n+l)P^(fi') 1^ (kb) ffn^^^!! a n=o -1 (13) (19) These equations can also be derived from the Green' s function approach of (1) Case et al. They have shown that for f (kb) being the Hankel functions of interior problem (when a = 0) the angu- n of radius lar flux \p(r,n) in the sphere of first kind. By proving that the func- given by 'b' is tion H^(r,^)=VK,(r,,i) + h- (j,) = [ [iVill^/^W' ^^<^ii/^,r,n) vanishes everywhere and using Plamely 4 4>(i/»?,r,n)= f[p X('^)6(Y-t)]e-T^* formulae for the boundary values of a sectionally holomorphic function we ob- _| 2('y-t) tain the same equation as obtained by the density transform method above. Similarly we have also treated the other problem, (15) considered by Case et al, the exterior problem (b-»>oo) with same concliasions. A(^) ^ 1 - ^ (16) References -1 1. Case, K.M., Ann. Phys. (N.Y. )2, l( I960). 2. Case, K.M. , Zelazny , R. and Kanal,M., and , J. Math. Phys., 11 223(1970). 3. Davison, B., Proc.Phys. Soc.Lond. , 64, 981 (1951). 4. Muskhelishvilli, N. I . , Singular Inte- (i/'f) A'Ci/y) gral Equations} Foordhoff, G^roningen, Holland. .. (17) < ^ 1 T3^(-i/'»o) ' 2Y^A'(»i/^^) (18) 90 . TRANSPORT OF NEUTRONS DURING REACTOR TRANSIENTS Sushil K.Kapil Reactor Engineering Division ^ Bhabha Atomic Research Centre Bombay-400085. INDIA The study of time dependent behaviour of nuclear reactors is important from operational and safety considerations. In this paper, situations requiring an explicit time dependent solution of the transport equation are identified. The range of validity of the approximation methods in different situations is discussed. Finally, severe transients in a Fast-Thermal coupled reactor are computed with various commonly used approximations and also by an explicit time-dependent solution of the Boltzmann equation, using a set of computer codes which were specially developed for the purpose. It is shown that the commonly used approximate methods can lead to erroneous results. The reasons for the deviation of the solutions for the different approximations from the correct behavipur of the reactor under transient are discussed. (Approximations } fast-thermal couple reactor > neutron jreactor transients } solution } time-dependent j transport ; transport equation) Introduction defined in terms of initial distribu- tions would be inaccurate. In such a system point kinetics equation cannot The of a behaviour neutrons in be expected to be accurate. reactor is described in detail by the linearised Boltzmann equation. Analyti- Adiabatic Approximation cal solution of this equation for situa- tions of practical interest is not possi- In this approximation-'-'^ the ble at present and various approximations flux is factorised into shape and time have to be used. Time dependent Diffusion functions, the shape function is taken Equation is one of the most commonly used to be step wise constant in time. Although approximations. It is quite satisfactory this is more accurate than the point for most situations encountered in the kinetics approach the use of a static dynamic studies with spatial effects. But calculation for shape function involves a consequence of this approximation is the assumption that the flux changes that the effect of a disturbance any- adjust instantaneously everywhere to all where in the reactor is instantaneously perturbations made in the system. This felt at all points i.e. the transport could be valid only if the time deriva- time for neutrons is zero (though the tive of shape function is small and the diffusion time is not). Diffusion appro- flux distribution reaches its asymptotic ximation is therefore satisfactory for value within a span short compared to power excursions where neutron transport that for any significant change in power delays do not play a significant role. level. Furthermore, this approximation does not distinguish between the shapes Approximate Methods of prompt and delayed neutron sources and thus neglects the time lag in the Some of the other commonly used adjustment of the delayed neutron pre- approximations are given below: cursor distribution. If the power excur- sion produces any variations in spatial Point Kinetics flux distribution, the adiabatic approxi- mation cannot account for it. Spatial In the 'point' approximation^ the dependence of this type has been studied parameters for use in the equation deter- elsewhere and is not considered here. mining power variation are obtained on Quasi-static Method the basis of initial flux and adjoint distributions. D^iring an excursion in a This method^ lies between the large or coupled reactor appreciable time dependent diffusion equation and change in flux and adjoint distributions the adiabatic approximation since it can take place. The integral quantities includes a term for t ime derivative by 91 . . first order backward difference. This The calculations are performed method in spheri- also avoids the error due to the cal geometry with an appropriately derived neglect of the lag in delayed neutron four energy group structure. precursor distribution which is found directly from flux history. Calculation of Reactor Transients Exact Method The transient is induced in the fast core by a linear increase in the number It is 'exact' to the extent that of neutrons emitted per fission and tota- the Boltzmann equation is solved without lling 5*/. over a period of 0.1 msec, after any of the above assumptions and it can which it stabilises at the final value. be used as a touch-stone for validity Total reactivity change caused by this of these assumptions. A DSn solution is 4.66;;: . of the time-dependent Boltzmann equation is taken as 'exact' here. Rather than applying various appro- ximations in the conventional manner, the Computer Codes effects of these approximations are simu- lated directly as discussed below: A system of computer codes was A. Basic ' assumption of point ' kinetics developed^- which permits solution of is that all the subsequent behaviour of the time-dependent neutron transport the system can be described in terms of equation in various approximations dis- the initial flux and adjoint distribution. cussed above as well as by the 'exact' In Fig.l, Curve A shows the inverse of the method. The delayed neutron effect and feedbacks have not been utilised in the present study because it is intended to study only the space dependent effects arising mainly due to the neutron trans- port . System a Model S . "0 V o The system chosen for this study o is similar to thB one described by Avery and ToppeP for a coupled fast- thermal steam superheating reactor. It consists of a central steam cooled fast ' core and surrounded by a water cooled and moderated thermal region. To prevent thermal peaking at the boundary of the FRACTION OF THE MMP. X fast core the two are separated by a buffer region. The thermal region is then surrounded by a thermal blanket and a high density uranium blanket. The Fig.l. Plot of inverse of the region dimensions and core compositions period of power rise are shown in Table I. against the fraction of the ramp obtained from various approxima- tion methods. Table 1 Region No. 1 2 3 4 b Region Fast Core Buffer Thermal Core Thermal Blanket Uranium Blanket Outer Radii ^S cm 40 cm 52 cm. 58 cm. 98 cm. Material Pu02 .08556 •37369 .42016 .29456 .29611 .00075 .00084 .00214 .00059 Depleted U .3715 Pe .156 .157 Zr .4151 .4151 .4372 .014131 .01553 .2087 . 2087 .1350 92 . . period of the power rise against the return of thermal neutrons to the fast fraction of total addition due to the core is very important for maintaining raup, for this situation. the chain reaction, the effect CQuld be opposite. When reactivity becomes cons- B. ?or adiabatic approximation sequen- tant and flux transients have died, it is tial shape calculations are made in known that the asyroptotic inverse period w-mode (solution of Boltzmann equation would be the w-mode solution of the with inverse period as an eigen-value ) Boltzmann equation. Therefore, at the end The res'ults are shown by Curve B. The of the ramp, the inverse period quickly circles on the curve are the check points drops to that for the adiabatic case. calculated by a statics code. The ramp Physically, it corresponds to a redis- insertion in fast region reduces its tribution of neutrons. dependence on thermal region for criti- caiity and the effective prompt ^neutron D. Finally, if the reactivity is added lifetime for the system reduces . to the system infinitely slowly so that Therefore, the inverse period curve at any time the flux distribution in deviates from Curve A as more and more space is in quasi-static equilibrium for reactivity is added to the fast part. the reactivity at that instant the adia- Curve A does not take account of this batic approximation and the 'exact' fact and is significantly wrong as the method should coincide. To check this, excursion proceeds. the same reactivity is added at half the ramp rate in the 'exact' calculation. The C. The curve marked C shows the 'exact' result of the calculation is Curve D in space-time soluvion for the transient. Pigiure 1. It is seen that for a lower The curve shows the upward curvature as ramp rate the inverse periods are closer in Curve B but the inverse period is to the adiabatic case curve. A plot of significantly higher. fission density distribution for this case confirms that the differences ob- Diiring the ramp the inverse period served between Curves B and C are due to is higher for Curve C than for Curve B the reasons mentioned. due to the 'bottling' of low energy neutrons in the thermal core. They are Conclusions produced in the thermal core by mode- ration of fast neutrons created in The spatial effects in reactor power fission and by those coming from the transients may arise due to changes in fast core. Fast neutrons from the fast region and spectral coupling, delayed core can travel to the thermal region neutron precursors' lag, loose coupling in time short compared to that for sig- in parts of a large reactor and neutron nificant rise in power. On the other transport effects. For the particular hand, the low speed neutrons cannot case of neutrons transport/diffusion travel far out from their place of birth effect it is found that an accurate space- in the corresponding time. Thus finally time calculation may be required under a dynamic equilibrium is reached with certain conditions. Depending on the the neutron density higher in the thermal importance of various effects care must region compared to what it would have be exercised in the use of different been under the adiabatic assumption approximations. (Curve B). A plot of the difference in the fission density distribution between the adiabatic approximation (Case B) and References the space-time (Case C) calculations 1. Henry : Nucl. Sc. Sngg. 1, 52 , 1958 also shows that thermal neutrons which , are dynamically trapped in the thermal 2. Henry and Curlee: Mucl.Sc.Sngg.,22, region during the transient, are per- 171, 1965- Ott : I'Tucl, Sc. 3ngg. 26, 1966. mitted to spread (majority of which are 3. , 563, Kapil : SPURT series of Codes, Report lost by capt^are in surrounding region) 4. be published. in the adiabatic approximation. The same to Toppel and Avery: IAEA Seminar on fact is shown by a softer spectrum in the 5. Physics of Fast and Intermediate riermal region for Case G during the reactors, Vienna, 1962. 3.nip than for Case B. In the 'exact' 6. Avery : Second Geneva Conf . , P/1858, . ilculation this trapping leads to high- fission density in the thermal part 1958. and a higher contribution to reactivity due to it. On the other hand, feed back of the thermal neutrons to the fast core is reduced leading to some loss in over- all reactivity. Since in this system the fast core contributes most of the reactivity and drives the thermal core, :nis loss is small and there is a net over-all gain. In a system where the 93 . ' CRITICALITY CALCULATIONS BY SOURCE-COLLISION ITERATION TECHNIQUE FOR CYLINDRICAL SYSTEMS V . K . Sundaram and D.V.Gopinath Health Physics Division , Bhabha Atomic Research Centre Bombay-400085 This paper presents a fast-converging iterative technique using first collision probabilities developed for obtaining criticality parameters in two-region cylindrical systems with multigroup structure in energy of the neutrons. The space transmission matrix is obtained part analytically and part numerically through evaluation of a single- fold integral. Critical dimensions for condensed systems of uranium and plutonium computed using this method are presented and compared with published values. (Criticality; collision; cylindrical; energy; integral; iterative; neutron; transmission matrix.) Introduction all energies, S(E,r) is obtained as An analytic treatment of integral equations for neutron transport in S(E,r) = jc(E' ,r)G(r,E'-^ E) dE infinite, homogeneous, isotropic media on the one-velocity model is possible. (2) Beardwood et al-'- have used first collision probabilities along with successive over- V/here G(r, E'-^E) is the mean number relazation for the solution of group of secondary neutrons generated per unit fluxes in their computer code for energy interval at E and space point r calculations in finite systems with due to the collision of a neutron with multigroup structure for neutron energy. energy E'. S(E,r) and C(E,r) are Gaussian quadrature has been employed in uniquely determined by K(E, r'->r) and the Swedish code Flurig to obtain the G(r, E'-^E). Knowing K and G and same probabilities. starting with an arbitrary distribution of S(E,r), the true values of S and C A fast-converging iterative techni- can be obtained iteratively. que for criticalit;V calculations in two- region spherical systems with multigroup For a cylindrical system, dividing structure has been reported by Gopinath the cylinder into a finite number of et al-^. This paper presents an extension coaxial annular discs and the neutron of this technique to finite two region energy range into finite energy groups, cylindrical systems. The collision Eqs. (1) and (2) are transformed to probabilities are obtained numerically through evaluation of a single-fold ^g„n,l ^g,n •-^n,l'-^l int egral =ZZ^g,nM' Mathematical Formulation ....(3) Finite Difference Equations ^g,n,l T^g',n,l '^n,l,g'—>g 9' In an isotropic medium, the colli- ....(4) sion density C(E,r) per unit energy E and at space point r is given by Where Cr. and S„ , are the total g,n,x^ g,n,l = ' C(E,r) \s(E,r )K(E,r'-^ r) d r' first collision rate and total birth rate respectively for neutrons of gth energy group in the (n,l)'''^ coaxial annular disc (n referring to the number Where K(E,r'->-r) is the first collision of the cylindrical shell in the radial density kernel for neutrons of energy E direction and 1 the number of the axial rate at r segment), and Kg^j^!__^^ the collision • and represents 1 —> 1 due to unit neutron source at r'. total first collision rate of neutrons S(E,r') is the source density per imit th energy interval for neutrons of energy E in the (n,l) coaxial annular disc due g*^ and at space point r.' Given C(E,r) for to a unit source of neutrons of . I energy group in the (n',1')^^ disc. In the above, Z-^ i and Z-^ are the axial is the number of neutrons distances of the source and receptor n,l g' ^ J discs from the base of the cylinder. born in the th energy group due to the I g Lumping the total source in each disc collisi on of a neutron of group g ' in the I over a cylindrical surface of radius disc. It is given by^ equal to the mid radius of the disc (r^i) and of height equal to the mid- height of the disc n.l.g' n.l.s' n.l,g n.l. n,l,g'->g t t Z. n,lM ,n'->n,l n,l,f (5) ^g(^n"\"^n-l'2l^J Calculation of E ,n'-»n,l •- (6) If the uncollided flux integrated has different forms over a (receptor) disc of radius r^^ and thickness (Z-]_-Z-]_ t) due to a unit source depending on the position of r ,,Z-, ,,r n 1 n of neutrons of gtn energy group distributed and Z^« . uniformly over a cylindrical (source) surface of radius r^, and situated at an Computational Procedure average height, {Z-y-Z-y _^-2Z-^\) / 2, from i Z-j^ , On the basis the disc is denotealy^^ii , , r^^, Z-, ) , of the formulation in •the uncollided neutron*flux integrated Section 2, a computer programme has been over a coaxial annular disc with inner written for BESM-6. The scheme of and outer radii rj^_]^ and r^^ respectively computation is the same as given in-^ is given by Using the code, calculations have been done to obtain the critical dimensions of condensed bare as well as reflected ^(^n-'^.'^n'^i) -<^(^n"2i.'^n-l'2l) cylindrical systems. The results are presented in Table - 1, which include The total number of first collisions in the published values^ for comparison. the annular disc is then - X, t^a^^n-'^i.'^n'^l) Table - 1 Density Radius Critical Critical mass Published values o critical System 1 gm/cc cms height (core bulk parameters cms mass) Radius Height kgs ( core bulk mass) cms cms kgs 93.4/. 19.05 8.269 166.9 enriched 17.7 19.05 8.26 166.7 uranium 19.05* 8.259* 166.7* 93.5/. 9.434 11.52 60.56 enriched 18.8 9.434 11.509 60.5 uranium 9.434* 11.533* 60.6* 46/. 21.49 13.742 367.6 enriched 13.44 21.49 13.89 371.5 uranium 21.49* 13.720* 367.1* Plutonium 14-27 7.588 8.596 22.19 f 7.588 8.286 21.39 7.588* 8.579* 22.14^ Values obtained by treating the system as two regions. 95 Ref erences Beadwood, J.E., Clayton, A.J. and Pull, I.e., ANL-7050 (1965). Carlvik, I., Nukleonik, 8 Band, S. 226 (1966). Gopinath, D.V., Sundaram, V.K., Krishnan, L.V. and Santhanam, K., Nukleonik, 9 Band, 5 Heft, S. 252-256 (1967). Reactor Physics Constants, AITL-5800 (1963). STOCHASTIC METHOD OF CALCULATIONS FOR FAST SYSTEMS B.K. Godwal and M.P. Navalkar Bhabha Atomic Research Centre, Trorabay, Bombay INDIA Neutron slowing down is a Markov process in which the probability for being in a certain volume element in phase space (space-time-energy) at some future time depends only on the present state of the system and not on the past. The process has been approximated to a discrete time, discrete state by Williamson et al to determine state transition probabilities. In this paper, this approach has been extended to calculate Rossi-a which is an important dynamic parameter of the system. The values of Kg-ff as a function of B^ for the bare core of Zero Energy Fast Critical Facility, PURNIMA calculated from this method showed good agreement with the bare critical experimental parameters obtained from fission rate distribution. A method to extend this method of calcula- tions to reflected system has also been described. ( BESM-6 ; JBZEBEL; I'larkov process; neutron? PURNIMA; Rossi-a; slowing down; stochastic.) Introduction (a) Scattering, elastic and inelastic, (b) Non fission capture, (c) Multi-group calculations for fast Fission, (d) Leakage, (e) n,2n etc. systems are basically static in character. Apart from the cross-sectional uncertain- The flux^t'CEjt) for the source ties as well as errors arising due to neutrons can be obtained by operating averaging over broad energy groups, the the transition probability matrix on the multigroup method does not describe initial pulse. The source of first adequately the physics of the slowing generation fission neutrons is given by down in fast systems. k(t) = Jv(E) e^(E) <^>jE,t)dB An approach based on Markov chain process to calculate temporal and where symbols have the usual meaning. integral properties of fast reactors has The term k(t) can then be used to cal- been proposed by T.J. Williamson et al^. culate the relationship between the nth In this approach, the neutron slovring generation fission source S^ and (n-l)th down process is treated approximately as generation source, S^_3_. a discrete time, discrete state Markov Ob process from which state transition S^(t) = fSj^_i(*) K(t-f)dt' ...(2) probabilities based on collision physics o are determined. The matrix is then The Laplace Transform of K(t) is related applied to evolve the time dependence of to the Laplace Transform of a function a pulse of neutrons on a discrete time- (J(t) by energy mesh from which integral para- meters of the system are obtained. ... (3) In the present paper we have exten- ded the earlier work to calculate Rossi- This can be inverted by using con- a which is a dynamic and important volution theorem in Inverf'e Laplace parameter for the fast systems. In Transform to give the fur. tion G-(t) as addition, we obtain the neutron density t as a function of time due to a pulse of G(t) = k(t) + J k(u)k(t-u)du neutrons introduced in the system. The t o u' + k(t-u')du' k(u)k(u'-u)du calculations using 26 group cross-section I J library have been performed on BESM-6 to 0 o determine Rossi-a as a function of sub- criticality for JEZEBEL system which show k(u)du good agreement with the experimental data. + I k(t-u")du" I k(u-u')du'J Method Of Calculation When a piilse of neutrons having (4) fission energy distribution is injected in a finite multiplying assembly, the Thus Gr(t) gives total nvimber of fission following processes take place: neutrons of all generation at time t. 97 , Hence the slope of the logarithm of G(t) 1-K,ff AS A FUNCTION QF fuel PINS gives Rossi-a. FOR BARE CORE (PuOa) FOR PUffNIMA We have applied above method to calculate Rossi-a as a function of sub- criticality for JEZEBEL for which the results are shown in Fig. 1. It is seen that Rossi-a varies linearly with reactivity and intercepts the reactivity axis at prompt critical, thereby indi- cating the self consistency in calcula- tion of sub-criticality a. The delayed critical Rossi-a agrees fairly well with the quoted experimental results . tM ISO SSO too NOMBER OP FUEt PINS ^ ROSSI. «< AS A FUNCTION OF SUB- -I CWTtCALITY IN | FOR JEZEBEL Fig. 2, l-Kgff as a function of fuel pins for bare core (PUO2) for PURNI14A. FIG. 1 D(E)B^ LB (E) ... (5) ^j(E)+D(E)B'2 -8 -»!- The leakage in presence of reflector is given by D(E)B ,2 (6) OELAYEO CRITICAL^ ^j(E)+D(E)B ,2 -« -» -I -» 0 .1 .J RCACnviTV IN f Using Monte Carlo method and the leakage distribution given by stochastic for bare Fig. 1. Rossi-a as a function of sub- system, PlrCE) is calculated. This P^jjC^ criticality in $ for JEZEBEL. gives us equivalent D(E)B'2 which is used in the bare stochastic model. The advan- We have also done calculations of tage of using Stochastic-Monte Carlo Kgff for bare case of Zero Energy Fast approach is the saving in the computatio- Critical Facility, PURNIMA. The details nal time as well as increasing the of the critical facility have been des- accuracy over the conventional Monte cribed by Iyengar et al3. It consists Carlo method. This is due to the fact of six zones, the innermost being Pu02 that the neutron history is traced in th^ core whereas the outer most zone is reflector only in the Stochastic-Monte mild steel. Other reflectors such as Carlo approach unlike the complete his- molybdenum, stainless steel, copper are tory traced in pure Monte Carlo method. employed between the first and the last zone. Fig. 2 shows 1-Keff as a function Ref erenc es of fuel pins for bare core (Pu02 only) and gives a bare critical loading of 405 1. Williamson, T.J. and Alberecht, R.W., fuel pins. Using the axial reflector Stochastic Calculation of Fast savings as measured by Ramakrishna et al7 Reactor Generation Times , Fast a critical loading of 360 fuel pins is Reactor Physics Vol. I. p. 513 (IAEA, obtained which is in agreement with the Vienna, 1968). reported value^ for core consisting of 2. Reactor Physics Constant s, jUIL. 5800,-; Pu02 and molybdenum reflector. Prepared by Argonne National Labora- tory, Second Edition, July 1963. The stochastic method has been app- 3. Iyengar, P.K., Chandramoleshwar , K. lied to the bare fast system. In order Kapil, S.K., Krishnamurthy, T.N., to apply it ( 0 the reflected system, a Nargmdkar, V.R., Pasupathy, C.S., Ra^ combined Stochastic-Monte Carlo approach A.K., Seshadri, S.N., Srinivasan, M., is proposed. In this, the leakage term Subba Rao, K. , Preliminary Safety for the bare core which gets modified Analysis Report for Critical Facility due to reflector is calculated using of Pulsed Fast Reactor , B.A.R.C./I- Monte Carlo method. 134 - 1971. 4. Ramakrishna, D.V.S. and Navalkar, M.P The leakage lor bare core is given Power Calibration for Purnima lrac&€- dings of the Symposium on Nuclear 98 Science and Engineering, Bombay ,^^ndia_, (1973). / Ilargundkar, V.R., 3asu, T.K., Chandramolesiawar , K., Job, P.K., Subba Rao, K., Pasupathy, C.S., Srinivasan, H. and Faramsivan, C. - Internal Note No. 071 BARC - (1974). 99 . A RMDOM SAMPLINCt TECHJTIuUE FOR. CHOOSING SCATTERING ANGLES FROM ARBITRARY ANGULAR DISTRIBUTIONS IN DOSIMETRIC AND SHIELDING COMPUTATIONS P.S. Nagarajan, CP. Raghavendran , P. Sethulakshmi and D.P. Bhatia Division of Radiological Protection Bhabha Atomic Research Centre Trombay, Bombay-400085 A random sampling technique has been developed for sampling the cosine of the scattering angle of the neutron in the centre of mass system. This technique could be incorporated in existing shielding and dosimetry codes. Recent differential scattering cross section data (from BNL-400 (1970)) is expanded in double Legendre polynomials of incident neutron-energy and a random number. The necessary coe- fficients for the elements C, N, 0, Si, Ca, Fe and Pb for incident neutron energies upto 15 MeV have been obtained and the same are presented along with typical results, checking the method and coefficients (Angle; centre of mass; coefficients; computations, cross- section; Legendre polynomial,- neutron,- random sampling; scattering; shielding) Introduction -1 In shielding and dosimetric computa- tions it is necessary to take the anisotropy of neutron scattering from for [i-j (where R-, is a random number and F nuclei such as C, N, 0, Si, Ca, Pe and is the distribution of f) is almost Pb. In the course of our Monte Carlo impossible because F is usually a high work for the computation of leakage order polynomial in To overcome this spectra through shields and in dosimetry we have done the inverse interpolation to we have developed certain data and obtain procedures to sample the scattering angle of the neutron in the centre of mass ^ = ti(R,E) system, using available datal.2 . If sampling is needed from a unique angular Among the many choices for least square distribution, i.e., just for one angular interpolation in R and E, it was found distribution, f(|i), simple schemes can that the coefficients of a double normal be thought of, including the one due to polynomial expansion in R and E do not Coveyou3. However, the distributions lend themselves convenient and required a are functions of energy too. large number of terms- Hence a double legendre expansion in R and E was Method resorted to, giving, Garber et al-'- provide da/d-Q.as a m m function of cos for various incident = L Z a P (E'j P.(R) neutron energies. From this f(|i.,E) the i:o j:o ^-^ probability density function in |^ is obtained at neutron energy E, as given where P's are the legendre functionSi E' = (E-7.5)/7.5 and; R, a random mxmber in the interval 0 (-1, +1). where \i = cos and -1 Results ^ "C Graphically, the f(|i,E) data was The coefficients a^^^'s were obtained interpolated to obtain f(|i,E) at uniform for seven elements of interest in shiel- intervals in E, from 0.5 Me7 to 15 MeV. ding and dosimetry C,N,0, Si,Ca,Fe and Pb The usual procedure of sampling of value using data from ref.l.and in the case of \i by solving lead data from Langley^ was also used. 100 To increase the speed of sampling, coeffi- cients b-^j 's were derived from aj^j'S;thus enabling sampling as = Z 2 bij E'i P (R) Table 1 gives the coefficients b^j 's. Sample results for carbon are given in Figs. 1 and 2 to illustrate the efficacy of the method. The histograms are the sampled data and the dotted lines are the original data used. Complete check results of this nature for all the seven elements smd over the range of energies from 0.5 MeV to 15 MeV are avai- lable elsewhere5. CARBON I 1-0 MeV 1.0 OS 0 -05 .1.0 COSINETHETA^ CCM Sy6tei*>) 2BMeV E 10 Pig. 2. Comparison of BNIi-400 data and sampled results. b I / to ! +10 OS 0 -05 -1.0 COSINE THETA (CM eystem) Fig. 1. Comparison of BNX-AOO data and sampled results. 101 ' Table-1 NORMAL LEGENDRE COEFFICIENTS b^j 1 CARBON 0 4.34897=.n78?0-00l -3.6051R1816S8-0ni 7.06348637O03-00P 1 ?.^4'^66Q44l "^1-001 -1. 0070083 76 09-001 2 . 53021*^85634-001 2 -4,877?816710'^-O01 -4.(S219041';7n4-OOl 4.74898584566-001 1.118181lS2lO-n01 3 2 .7774066049'^-nn? -4. 3^^18614966^-001 -1.78755311314-00 1 4.89405090197-001 I. 1 .4"» 10307761^-001 1.28214626067-001 -4.61 694986644-00 1 -3.08714596571-001 5 3.87O7964726'^-n02 4. 16848722339-001 -7.27190210047-002 -1 .33865834776 + 000 6 -7.91 ni689011'=,-n02 1 .04642761837-001 1.C4085643497+0O0 -1 .63''37627586 + 001 7 -1 ,009 104019^^2-001 -3 . 82 78328S91 0-001 6.82361848404-001 1 .36778067023 + 000 -3 '^-^-001 7-001 + 000 8 2 . 387965'?64=S's-on? . 27^82'^1 1 1 -6.7 700474802 1. .27969383879 0 2.87873281502-001 7.822851324^0-007 •1.26081671612-001 -3.20610352200- 007 1 6.9''408923090-on] -4.7024507230^-003 7.05245659191-001 1 .34832057746- 00? 001 2 -1 .a^5863O8673-.0C I -1.172012115^7-001 1 .91732776638-001 1.15156202639- 3 -o. 174625«7760-OC 3 -3 .23386041 380-001 4.22680224343-002 1.17717243261- 001 2 .0^6261 Q8?'^^-"0l 2.0'^inp04Ci04o-nnT 4.01 f,7'^4641 12-001 -4,9q5O7'^40ftq?. 007 5 3.nflOi7;,ftl(SST_nni 1 .724017777^7 + 000 -',.9TQ754678'^4-001 -7,56500?^2776- • 001 6 -3.^86107'^0524 + O00 -3.06070^24611-001 3.85F7'=1'=.5299 + 000 ^.33729467946- 001 7 -2. 007978958^0 + 0 00 -1 .6uO37^774O8 + 000 2.73164727438+000 6.70039653361- •001 •001 8 1 .9204661 51 in+non -l.B'=i8 5 5'=.S5 4'^=. + 00 0 -2.08131 151038+000 8.86103324505- ,7''O08341 0 1 147-007 1 7,^^P74 -3 . 1-*16144043'^-001 5 1 .^01 280-S4?14-om 6 -1 ,371 7e;;jn7Sl 7 + O00 7 1 ,7O8876O7770+T00 ^ 8.ooo^ST5p7TO-,-\01 I 1 NITROGEN ,^R'^,q07c,O400- 0 3.41 6578^0470-noi 1 001 3.7'^7532O8490-002 1 . 86433332547 + 000 1 -1 ,09760SA90?q+000 1.10279115600- 001 -7.20311381148-001 7 .50699716537 + 000 2 -3.00629479720-001 6.^67^9831607- 007 -1 .472'^7096682 + 000 -2. 70521262012+000 1 . 11 629680701-001 -1.10612681 247- 001 4.81575447013-001 -1 .29724016087+000 I 2.21 O10227498-O02 •1.748832865] 8- 00] 0.212409=^6462-001 0.87740448172-001 5 -1 .3^124500084-001 -2.59829197176- 00] 4.6233^324974-001 1 .75597754812 + 000 6 -6 .'SO24601 8187-002 -2.34l004^qio7. 007 -3.468765976O3-001 -6.3O2585'^0513-001 7 4.O7843881 37'=.-O07 1 .34369401 0^"^- 001 -5.26102605959-001 -1.4 77279OO244+000 s 0 1.71 719805400+000 -3.51622420442+000 3.9988761 1047+000 1 . 70117466471+00O 1 •9.09583675308-0O1 -9. 27000057435 + 000 8. 7328779=^350 + 000 1 . 17006035143 + 001 2 1,71 504456271+COi 4. 14530'^761 S6 + 000 -3.07181128753+001 -6.21566179594-001 3 2 .08584552778 + 000 3.282069^0018+000 1 . 39343388752 + 0O0 -2 .14870996706+000 4 -4.5i=;8255 10 0 2 . 109 17S02586 + 000 o.ooooooonooo+ooo 0. onooOQOOOOO + OOO -4. 1 1 .3«^662431861 +001 78957183066+000 6. 1405=^977899 + 000 2 3 ,06970847500+001 -1 .016167=14777 + 000 -1 .08636268192 + 001 3 0,00000000000+000 0. 00000000000 + 0 00 0,00000000000+000 3»1'^322071 371+O00 1 .538528406^7 + 000 O.OOQCOQOOOOO+OOO 5 -1,21037305817+ 100 0, 00000000 000 + 0 0 0 0.00000000000+000 6 1 ,05087059879+ )00 3.51 166275844-001 O.OOOOOOOOOOO+OOO 7 4,91 016553820+000 9. 30600236660-001 -1 .88826998151 + 000 102 1 . 0 1 Oxygen 2 3 J \ 0 ,^«;370477367 -001 1.85071'=.86259-00l 2. 00751 228070 -002 1 .88937996427 -001 1 -1 .06?471«;4837+n00 9 .79104^16547-OOp 3.67167830906 -002 1 .1650^260199 -001 2 • Rt 3764fl00f,1 -oni -2 .796107: 4 6 0 -8 — 002 -1 .08570901 774-001 3.74007723628 -002 1 2 .18643886658 -001 -1 . 10051404381-001 -1.0Q312413580 -001 2 3 .4^851570651 -noi 7 .9294992''3'^l-007 -2.18116104162 -001 3 -1 .1^534732674-no3 8 .20805452888-007 -5.39018263208 -002 U 1 . 3*^757984759 -002 -7 .71117657259-003 *^ m\>*^ D >Vd f l:?oO -002 5 1 «n<;71Pm 9047 -O01 2 .23601 77^SQO-00l 7.84797620754-002 6 -3 .1132 64 74'^ 5 - 10 3 .^5227780889-001 1.01 170118192 —0 01 7 -7 , =;'^44 1 ft 1 66°'^ - 10 1 _p .37861 1 76467-007 ^.7'^21 581 10^ -001 0 1 Silicon 7 0 5 .2?46205403n-001 7 .6512401369^-007 -1 .68939193775 -001 -4 .90 7085^5384 -001 1 -9 ,01 448525670 -001 -4 .65451027651-007 -1.27119158331 -002 8 .56861430372 -007 -5 ..7 2 .8^513048824-oni .67928985787-007 4.8-^001593641 -002 4 . 1 4426 2 4U 8 2 3 -001 -1 •3 3 . 72562 1 3 1 801 -00 _> .91020394728-002 6. 10062390637 -002 1 • D 7^*50 3 96449 -001 — oo > 2 .'+' LOiV f D J X O 5 . 89320^74255-002 -1 . 57470074943-002 -1 . 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COOPnoooOOO + 000 o,no0ooooonoo+ooo 9 7.81 71267444'^-O0] 1 .08007733187-001 -1.57968764626+000 5,73690037485-001 H R 9 10 0 -1 .971 898O1704+000 3.63858O8730O+00O o.ooooooooooo+ooo 1 3,06878676518+000 3.00782o=,661 3+000 -7. 30790407168+0 00 2 -2. 4910071 346^ + 001 -5.49632436672+000 1.04522643326+001 3 -5 .68579697268-001 -1 .0l,568'^61 578+001 1 .80859492875 + 000 I, 2,47539070329+000 O.OOOOOOOOOOO+OOO 0. OOOOOOOOOOO + OOO 5 1 .54240453907 + 001 8.96781494046+000 -6.97815900783+000 6 -7,975660'^983^-O01 1 .9005705613=^ + 000 0. OOOOOOOOOOO + OOO 7 0,00000000000+000 O.OOOOOOOOOOn+ooo O.OOOOOOOOOOO+OOO 8 0,00000000000+000 0 .00 000000 0 00 + 0 0 0 0. oooooonnono+000 9 8 ,248264"0693-001 -4.7107068734''-00l o.ooooooooooo+ooo 104 . References Discussion 1. Garber, D.I., Stromberg, L.G., Godwal, B.K . Goldberg, M.D. , Cullen, D.E. and May, V.M. , "Angular distributions in Can the Coveyou technique be used for neutron- induced reactions". BNL-400, taking into account the anisotropic 3rd Edn. Vol. I (Jan 1970) and Vol.11 scattering in hydrogen due to neutrons ? June (1970). How is it at Legendre Polynomial 2. Langner, I., Schmidt, J.J. and Woll, preferred ? D., "Tables of evaluated neutron cross sections for fast reactor materials"- Nagarajan, P.S . KFE:-750 (Jan 1968) . 3. As reported by D.C. Irving, R.M. In the energy range of interest to Freestone and F.B.Z.Kam, "The Coveyou us i.e. upto 15 MeV, assumption of technique for selecting neutron isotropic acattering in the cm. system scattering angles from anisotropic is valid. Hence the cosine of ©Loa> distributions" in Appendix 1 of 05 [cos Qy^i} J ^® directly sampled as the R - A general purpose Monte Carlo larger of a pair of random numbers. At neutron transport code ORNL-3622 thermal energies I have not developed any (1965). sampling scheme. Perhaps one could assume 4. Langley, H.J., "Neutron cross sections" an isotropic law. - LA-2016 (1956) 5. Kagarajan, P.S., Sethulakshmi, P., Makra , S . Raghvendran, CP. and Bhatia, D.P. , "A random sampling procedure for Are the differential cross sections anisotropic distributions"BARC report data available for all the mate Trials and (to be published). energies and if so from which library ? Nagara.lan. P.S . The reports BNL-400 (1970) and KPK- 750 (1968) yield the required data for all the elements C ,N,0,Ca, Si,Fe and Pb. But in the case of Pb there is an energy gap where no data is available. We took the data from an old reference of 1956. 105 MOfTTS CARLO CALCULATIOrTS OW DOSS DISTRIBUTIONS FROM PLANE INFINITE OBLIQUE ELECTRON SOURCES C.R. Gopalakrishnan and V. Sundararaman Division of Radiological Protection Bhabha Atomic Research Centre Trombay,Bombay-400 085, India A modified Monte Carlo method has been developed for tracking electrons. In this method individual collisions wherein the electron suffers a large deflection or loses large fraction of its energy (denoted as catastrophic) are treated separately. The history of the particle is divided into sections, within which no catastrophic collisions occur and in which continuous- slowing down is assumed. The angular distribution at the end of a section follows a Gaussian distribution. In this method the correlation between energy-loss fluctuations and multiple scatter- ing deflections is preserved more faithfully. Dose distributions for electrons in carbon, aluminium and copper have been calcu- lated for oblique incidence using this method. Data have been obtained for five different initial angles and covering a range of energies from 0.05 to 10 MeV electrons. ( Aluminium ; carbon ; copper ; collision ; dose ; distribution ; electron ; Gaussian ; Monte Carlo ; scattering ) I ntroductioh to a distance in which the electron loses energy by a fraction 2"-^°, on an average. In this paper, we have reported The energy and angle at the end of each some of the results on electron dose dis- section are sampled from the Landau3 tributions obtained by Monte Carlo Meth- straggling distribution and Goudsrait and ods. First, dose distribution functions Saunderson^ multiple scattering distri- have been computed for infinite plane bution respectively . Since the computa- oblique sources of different energies tions are for infinite plane sources, the from 0.05 MeV to 10 MeV. These have been problem is one of one dimensional trans- obtained in Carbon, Aluminium' and Copper port. The details of the method are pre- for cosines of the angles varying from sented elsewhereS. The range of electron 0.2 to 1.0. Spencerl has calculated dose was divided into forty slabs and the distribution functions for plane perpen- energy absorbed in each block was computed dicular and point isotropic sources using 2000 histories were used in the calcala- the moments method with the continuous tion. The effect of secondary electrons slowing down approximation. Berger^ has was ignored. calculated these distribution functions using the Monte Carlo method. However, no For higher energies we have used a results are available for plane oblique modified Monte Carlo Method. This is a sources. These are of some importance in mixed procedure in which one excludes calculating doses in non-electronic equi- from the grouping individual collisions librium conditions on X or gamma ray denoted as major or catastrophic in which irradiation. Secondly, we have calculated either the electron loses a very large depth dose curves for high energy elec- fraction of its energy in an inelastic trons. These are required in treatment process or suffers a large change in planning for high energy electron beams angle due to elastic scattering. Here from accelerators. Also the perturbation again the electron track is divided intc in the depth dose curves due to the pre- sections. However, the section size is sence of cavity has been computed. not fixed earlier but is decided by the probability for catastrophic collisions. Method No catastrophic collision occurs in eacli section and each section is terminated i Two Monte Carlo methods were used. by a catastrophic collision. The sectio: The first one, for electrons of energy size is sampled from the probability dif less than 2 MeV, was similar to the one tribution function, used by Berger^. in this method, the electron track is divided into predeter- P(s)ds = exp j- (s')ds'jX (s)ds: sections, section size corresponding o total total mined J I 106 6 whers ^ (s) = (s) + (s) materials, viz., Carbon, Aluminium and total elastic inelastic Copper, the obliquity of the angle being Cos9c Cos 0 = 0.5. As atomic number of the material increases, peak of the distribu tion increases due to the increase in ilasLstic _ a (u,s)dLX -1 elastic backscattering. Fig. 2 gives the energy- 0.5 dissipation function for different ener- gies from 0.1 MeV to 10 MeV in Aluminium and . = ( a (£ ,s) d€ incident direction cosine being 0.8. inelastic € ^ melastic where Cos 9 is the cut off angle and£^ is the fracuional energy of the incident electron above which the collision is 2 MlV £i.ECTROiJ considered to be catastrophic. INCIOEHT ANC-.E COS 6 = C . In each section energy loss was com- pated using a continuous slowing down ^COPPER model. The change in the angle was com- \ ALUMINIUM puted using a Caussian distribution. 2C0 & z ?(«) dCO = exiD do) 2 6 z s CO was derived from the Moliere multiple Ui < scattering theory as -0.4 -0.2 0 0.2 04 0 6 DISTANCE (FRACTION OF R*NOE ) 6)^ = 2tiNS J 00 a (a) da Cos 0 Fig.l. Energy dissipation distribu- c tion for infinite plane oblique where M is the number of atoms per gram, (Cos 0 = 0.6) sources of ini- 3 is the step size. The actual distribu- tial energy 2 MeV in different tion was also obtained using (Joudsmit and materials. Saunderson'^ theory. It was found that the Gaussian approximation agreed well with the exact calculation. The catastrophic collision results in either a large angle scattering or production of a 6-ray.The large angle scattering was sampled from ALUMINIUM Mckinley-Feshbach' multiple scattering INCIDENT ANCLE distribution and 5-ray distribution from COS e = 0 the '!^ller° cross section. 6-rays above a certain cut off energy (100 keV) were tracked separately. Photons produced can also be tracked separately. In the present calculations, however, bremsstrahlung losses have been added to the stopping power. This is because, the total radiation yield for a 10 wev electron in carbon is only 4*/. This method has the advantage that the correlation between energy loss fluctua- 0.2 0 0.2- 0.« 0.6 1.0 ( RANGE tions and production of 6-rays is preser- DISTANCE FRACTION OF ) ved faithfully. The spatial location of the particle is also more accurate because large angle collisions have been excluded Fig. 2, Energy from the sections. Calculations for depth dissipation distri- for doses were carried out by tracking elec- bution infinite plane = trons in all the three co-ordinates. oblique (Cos 0 0.8) elec- tron sources 10,000 histories were used in these cal- of different culations. initial energies in Alumi- nium. Results and Discussion Fig.l gives the energy dissipation function for 2 MeV electrons in three 107 - L A Figs. show the energy dissipation function in Carbon for 0.05 WeV elec- trons for 5 different angles. (Cos 0=0.2, 0.4, 0.6, 0.8, 1.0). Here again, the peak increases for higher obliquity. 10 0 (3a) - •r 50 keV ELECTRON IN CARBON 7 5 z A = ION COS e 0, 5.0 I B COS e = 0 2 FIJI DISTANCE ( FRACTION OF RANGE ) 2.5 / — Fig. 4. Comparison of central axis 0 2 c 0.2 0.4 0 6 0 8 depth dose data for a 10 • F, MeV electron beam DISTANCE (FRACTION OF '.GE i in Carbon. 1 /K 50 k«V ELECTFCN i 2 / \ IN CARBON ISSIPAl ^^^^ 3 1 JNITS / 01 FUNCTION ENERGY / c\ \ \ A CCS 3 . 1.0 \^ \ ^. B COS 0 = 0 ,8 C COS.? =0.6 \.\\ - O.i -0 .2 0 0.2 0 4 C 5 0.8 -..0 DISTANCE (FRACTION OF Ri. 'Z) Figg„ 3a-, h : Energy dissipation distribution for infinite plane ob- lique electron sources of initial energy 50 keV in Carbon. Fig. Isodose curves for a 10 a) for incidence angles 5^ MeV electron beam in Car- Qos 9 = 0.2, 0.4. bon for a circular field b) for cos Q = 0.6, (14 cm d ia ) • 0.8 and 1.0. Fig. 4 gives the central axis depth dose curves for a 10 MeV electron beam for distribution in Carbon for a 10 MeV elec- the same field size. tron beam for a circular field of 14 cms. The perturbation due to an axis dose diameter. The central depth air cavity in the beam has been given data for this field size, of course, in Fig. 6. It can be seen that the depth corresponds to the data for an infinite dose curves are shifted downwards under source. This agrees plane perpendicular the cavity. Another effect is the pre- s data. The higher well with Spencer' sence of a region of overdosage under peak and lower doses at large distances the cavity (150X) This is because of obtained by Spencer^ are due to the fact 'focussing effect' associated with elec that stragglin.g has been neglected in tron beams, i.e., electrons scattered his calculations. Fig. 5 shows isodose into the cavity tend to stay there. 108 . . . electron beam. Also the experimental measurements were made with photographic films - the Cerenkov radiation produced in the phantom material would have con- tributed significantly to the blackening of the film. Attempts are being made to correct for this. Acknowledgements The authors are grateful to M.A. Prasad and P.S. Iyer for the many useful discussions and help during the course of this work. Thanks are also due to K.G-. Vohra for his keen interest in the work. References 1. Spencer, i.Y., Energy dissipation by fast electrons, NBS Monograph 1(1959). 2. Berger, M.J., Methods in Computational CM«64202468CH Physics Vol.1., ed. B. Acller, S. Fernbach and M. Rotenberg (New York and London Academic Press), pp 135- 6. curves for MeV ele- Fig. Isodose a 10 215 (1963) ctron beam in Carbon in the 3. Landau, L., J.Phys. USSR, 8, 201(1944). presence of a cylindrical cavity 4. Goudsmit , S. and Saunderson, J.L., (2.5 cm length, 2.5 cm diameter) Phys. Rev, , 24(1940) . at a depth of 0.64 cm. 5. Sxindararaman , V., Prasad, M.A. and Vora, R.B., Phys .Med .Biol 18, 208 whereas no electrons are scattered out . , (1973) from the cavity. This has been observed 6. Moliere, G., Z. Waturf . , 78(1948). experimentally also. (Starchman and Jen- 7. Mckinley, W.A. and Peshbach, H, , Phys. . However, there is quite a Htmg Chao9) Rev. 1759(1948) large disagreement between our results 14, 8. M011er, Zeits . f .Physik, 70, 786(1931). and those of Starchman ai;d Jen-Hung Chao-'. 9. Starchman, D.E. and Jen-Hung Chao, We are investigating the reasons for Radiology, 10^, 177(1972). this discrepancy. It may be because of the bremsstrahlung contamination in the 109 . BACKSCATTERING OF GAI-Il'IA RAYS Tomonori Hyodo Department of Nuclear Engineering Kyoto University Sakyo-ku, Kyoto Japan A survey of principal research on the backscattering of gamma rays is described. This is a macroscopic pheno- mena composing many photons scattered backward from a surface of material. After a historical survey as an introduction, principal theme of research is described; nomenclature of albedo, Monte Carlo calculation, measurement of albedos, semi-empirical formula of the differential albedo, exposure dose rate distribution outside a scatte- rer, distribution of scattered gamma rays on the surface. (Albedo, backscattering, distribution, dose rate, gamma rays, Monte Carlo, photon.) Introduction During last 20 years much progress albedos by a desk computer, Perkins^^^ has been made toward the calculation and Berger and Doggett^S and other workers^"" measurement of multiple scattering of ^ calculated total albedos using electro- gamma rays backward from the surface of nic computers. Total albedos and reflect- material, namely backscattering of gamma ion build-up factors were calculated rays. It may be said that the details using invariant imbedding method^-^, of this type of interactions are now Moment s^Methpd^ 4, and semi -analytical known to considerable accuracy. Most of method^-O^-l'^S papers are published in ten years, from 1959 to 1968. Review articles and books For the necessity of estimation of covering this field were published in exposure dose rate distribution outside a the end of this period. -^"^ This paper scatterer and estimation of duct streaming is a survey of works in this field gamma rays several Monte Carlo calculationi adding recent progress. of differential albedos have been carried out with increasing of calculation speed There are two large groups of pub- :5!?-4i^ Many experimental works measured lished papers in this field. One differential albedos to obtain total ° »-'--'•" concerns on the reflection characteris- albedos by integration"' . Precise tics of material, such as total albedo, measurements of differential albedos have differential albedo, reflection build an utility to compare calculated values. up factors, and the other concerns Steyn and Andrews'^^ and other workers^5-48 exposure rate field distribution outside measured them. Bulatov'^° compiled these and on a scatterer. data in a form having good availability to calculate exposure dose rate distri- Hine and McCall^ , Hayward and bution. Chilton and Huddleston^^'^-^ Hubbell' measiired backscattering of derived a semi- empirical formula for the gamma rays as a macroscopic phenomenon differential albedo of concrete and and they knew considerable amount of applied for the estimation of thej-distri- gamma rays were scattered backward. bution. Shoemaker and Huddi eston-'^" Bulatov and G-arusov""^ used a small proposed an approximation method to dosimeter without a collimator, Hyodo-'--'- reduce the number of necessary angles for used a small point isotropic source on the calculation and experiment. the surface of a scatterer and a Nal(Tl) scintillator without a collimator. Backscattered radiation of bremsst- After these experiments measurements of rahlung of betatrons was measured by total albedos have been continued-V^"^^ Pruitt^'^ and other workers55-57 Monte Carlo method has been applied Berger^^ calculated energy dissi- successfully for simulation of multiple pation in a medium with the scattering scattering phenomena of gamma rays in properties of wa,ter which consists of two ] material with the development of compu- semi-infinite regions, one of which is ters. Hayward and Hubbell"^-^ calculated much denser than the other. Titus-'" 110 - , simulated experimentally with iron. ^ , energy, and exposure dose rate are wri- Batter"'-' Clarke and and other workers tten by Jqn, Jjj; Jpj;, Jjj; Joi}» Jj)' measiired scattered gamma ray exposure respectively. Niimoer differential dose rate distribution. Chilton°4-65 and albedo a-^, energy differential albedo a-g, other workers"""""^ proposed calculation dose differential albedo a-^ is defined methods for the distribution and compared as follows: to the experimental results. Propagation of gamma rays at or near an air-ground interface was measured by many •^On/^^^O' ^0' ^' ®' ^^^^ vforkers°°~ ' 9 and a review article was written by Clarke^O. G-arrett proposed a = shielding benchmark problem and call for Je = Jqe ^^e^^o' ®0'' ®' theoretical calciilations and experiments. Jo:s[a^{SQ, eo; E, G, ^)dE ..(2) Emergent gamma rays at an interface with point source placed on the interface was investigated by Bulatov9, Hyodo-'--'-, Dag^s^gn and Beach°2 and other worke- JodJo:^(Eq, Oq; E, d,*)dE Scattered gamma rays at an air- Total number albedo A^, total energy groiand interface from air atoms is sky- albedo A-g, and total dose albedo A-q is shine. Several works has been published obtained by integration of differential on this problem"-^~94. albedos Several works95-98 -^ere published rrz on the backscattering from room walls, a " ^'^ ^^^^ ^® spherical shell and complicated confi- ^ J Jo^N^^O' ®0' ®' gurations . Ag = Id^ aE(EQ, Gq; e, 0) sinG dG As an example of application of albedo coi^^ej^^^ calculation of duct str earning :s shown. Aj^ = jd The quantities that characterized the reflection probability of material (3) are called albedo. The definition of the albedo is described in many books and 51? » op papers5~5 » ^ Traditionally, the albedo refers the ratio of the radiation entering in and leaving from a small area dS of the surface of a scatterer. In this usage the albedo is a ratio of current passing through dS and npt-pf flux density. Several papers^' discussed on this point in details. Consider, for example, a monodire- ctional source of radiation of energy Eq incident on a surface at polar angle Sq as shown in Fig. 1. The reflected current of energy E per unit energy per DETECTO« unit solid angle at polar angle G and azim.uthal angle ^ is given by, J(E,G,,^) = J(Eo,Go) a(Eo,Go; E,G,(#) ..(l) where J(Eq,Go) is the incident current and a(EQ,eQ; G, ^) is called (double) differential albedo or energy-angular distribution passing through the surface. The quantities of current incident and outgoing was measiired by photon number. Fig. 1. Reflejti on geometry, 111 . Scattered radiation flux and expo- sure dose rate outside a scatterer can be estimated if the value of differential albedo is known for every emerging angle of e and o. For the case of uniform monodire- ctional gamma rays are incident to a scatterer as shovm in Fig. 2 a. The nximber and energy flux and exposure dose rate at a detector caused by photons emerging from an. incremental area dS is nQ cosSq ttj^ dS n^ EqCOS&q dS d{Ei (4; n^ EqT] cosGq a-^ dS dD = Fig. 2. Geometry of scattered gamma-ray where n^ is photon flux at dS, r is the calculation, a. Plane distance between the center of dS and monodi- rectional source, b. Point the detector, t] is the conversion isotropic source. constant from photon intensity to expo- sure rate. where A is the value of albedo and N the number of histories. The value of For the case of a point isotropic A is between 0.01 to 0.6, so small value of source emitting Q photons/sec placed at standard deviation a is obtained. rQ from dS as shown in Fig. 2 b, formu- las are, The earlier works using Monte Carlo method were calculation of total albedos Q COS0Q a.^ dS _ _ and reflection build up factors for uniform materials having plane surfaces and spherical shell24-52. After these works sufficient histories for the Eq cose^ ttj, dS Q calculation of differential albedo have dS^ = (5) 2 2 been available since ten years ago 4nrQ r with increasing of calculation • speed of digital computers. Numerical tables and Q Eq T) cosBq a-j^ dS dD = _ graphs were ;published on several papers and books .5 » >'5-41 These calculated 4ixrQ r results are shown in the following paragraphs Monte Carlo Kethod Measurement of Albedos The backscattering of gamma rays has been the subject of a number of Measurement of differential albedos Monte Carlo calculations and got great has been carried out by many workers. success. Practical methods of the Host of these works had a purpose parti- application^are ally obtain 1°^"^^' described in several to total albedos by integra- books. tion of differential albedos, but several works had not the purpose The reason of success is following. because data of differential albedos Cross section of the interaction of were very important to get an information gamma rays with matter is well known and of scattered gamma rays in a definite monotonic functions with energy. The direction and to compare calculated standard deviation is given by^° results as a benchmark experiment. Measurement of photon current .(6) incident to and emergent from a small ~ VN - 1 112 . . area dS on the surface of a scatterer, truly to the definition, is difficult, because most of the photons incident to dS emerge from outside of dS or captured in the scatterer. Following three geometries are approximately possible to the measurement. The first geometry is a narrow, well-collimated beam of gamma rays incident on a scatterer at a desired angle, together with isotropic detectors around on a hemispheric shell centered around the irradiation area as shown in Fig.ja. Bulatov and G-arusov°, Efrimenko Cliff ord^^, and Elias et al48 measured scattered gamma rays with this well-collimated-beam geometry. The second geometry is the irra- diation of large scattering medium with a wide beam of gamma ray to simulate an infinite plane monodirectional source of gamma rays and use a well-collimated detector to observe the angtilar depen- dence of the scattered radiation emitted from a small surface region near the center of the irradiated area as shown in Fig. 3 b. §teyi^ ^^'^ Andrewr^, Haggmark et al^^, and Barran et al^' measured scattered gamma rays using well Fig. 3. Geometry of measurement for back- collimated detectors. scattered gamroa rays. Both case has a dead space of measurements caused by beam of radiation, shadow of collimator or shield. The third geometry Fig. 3 c, is rather special case, but it has not any dead space of measurement. A small point isotropic source placed on the surface of a scatterer and a detector without a collimator moves on a hemisphere of sufficiently large radii. Bulatov", Hyodo and his covrorkers-'--'-"!^, and Pozdneev-'- measured scattered gamma rays vrith this geometry Albedo Data Eg. Ur« Figure 4 shows Monte Carlo results of the total energy albedo for several elements as a function of energy. In Fig. 4. Energy albedo as function of the high energy region, the albedo value source energy (perpendicular decreases with increasing of energy incidence, G=0). (ref. 26) because the differential cross-section of large angle scattering decrease with where d is thickness of the scatterer and increase of energy. Figure 5 shows the a is a constant. Figure 6 shows the total energy albedo value obtained by total energy albedo obtained by third experiment. The figure shows the albedo geometry. Figure 7 shows the value of value increase with increasing of differential albedo. There is two scatterer thickness. Bulatov and distinct group of curves in the figure. Garusov^ derived following experimental Upper two curves obtained by third formijila geometry and lower group obtained by first geometry Aj,(d) = A2(°«)(l - e"'^/^) ...(7) 113 — | — C 1 —4 ;!os -|Fe h //, >• Cd -I r '> -k \ 20 30 40 50 Scoiierer trKkness, g/cm' ATOHIC MUMftCR Fig. 5. Energy albedo as fimction of scatterer thickness °'-'Go,9_.=0) ( ° (ref.8) ... . Fig. 7. Differential : energy albedo as function of scattering angle (ref.48). _ 1 1 1 _ 10 - E„ = 9.5 MeV nJl /" = / E„ 12.0 MeV POIYFTHVI.ENE ' _ ' . >y^t\^2^ " E„ = 15.5 MeV nu // r' 0.1 o.l 03 0.4 0.5 at 0.1 0.1 0.. oj ai o.S a* ».t 1 1 1 10.0 20.0 30.0 PHOTON ENERGY. MoV THICKNESS, g/cm» Fig. 8. Energy spectra of scattered radiation from aluminium, (ref.56 Fig. 6. Wixmber and energy albedos as fim- ction of scatterer thickness singly scattered gamma rays. Figure 9 ( Co, point isotropic source shows the differential dose albedo for placed on the surface), (ref.13) aluminium. Study of back scattered radiation SEMIEMPIRIGAL FORMULA OF DIFFERENTIAL ' caused by high-energy bremsstrahlimg ALBEDO ! from a betatron and a linear accelerator is very important for the estimation of For the application of albedo concej exposure distribution and for the under- for the calculation of duct streaming of standing of scattering phenomena of higa gamma rays, scattered gamma ray exposure energy photons. rate field, albedo values for many dire- ctions of emerging are necessary. A Figure 8 shows energy spectra of semi-empirical formula is very useful to photons back scattered from aluminium interpolate albedo values from calculate; scatterer, incident and emerging angles and experimental data; (Bq, e) = (0°, 20°). The energy of photons in the spectra is less than 0.5 Chilton and Huddl eston^*^ derived MeV or annihilation radiation because of a semi-empirical formula for the diff er- 114 ) — 1 EXPOSURE DOSE B.ATE DISTRIBUTION OUTSIDE A SCATTERER 1 It is necessary very often to "T" estimate exposure dose rate distribution !' a T . outside scatterer as shown in Fig. 10. (30.2C.C;.V ^ rk The j exposure dose rate at the detector is superposition of those primary gamma rays \l i3i°cc''': i from the source and those of scattered — gamma rays from the scatterer. 1 f.'O. J s.c ! r— -1 ,25 i 1 H < , ' i ! 1 1 ^ i! 1 \\ • i i 1 < S i 10 X MEOIIM 2. Fig. 9. Differential dose albedo as fun- ction of electron energy, (ref. Fig. 10. G-eometry of measurement. 56 Figures 11 and 12 show exposure dose ential dose albedo of concrete on the rate distribution in the case h = z in assumption: Scattered radiation can be Fig. 10. Medium 1 was air and medium 2 broken down into two parts, one is concrete. As shown in these figures the proportional to single Compton scattering ratios between the exposure dose rate and the other is isotropically scattered} caused by gamma rays scattered from the effective attenuation coefficient concrete and those of primary gamma rays |i does not vary greatly during a are fair agreement at the same h/D values. scattering history. The differential dose albedo a-^ is Chilton64»65 calculated scattered gamma-ray exposure dose rate using 26 formulas (5) and (8). The calculated C.IO ^^(Eq, e^) f c- = value is shown in Fig. 11. The cijxve "d cos e (8) shows fair agreement with experimental 0 1 + data. cos e 67 Kitazume proposed a calculation where is the scattering angle between 0^ method. The scattered gamma rays to the the incident and outgoing ray, given by detector was calculated following formula, follovring formula, ^Q tig/dA exp(-^j^p.^ -1^2P2^ cos0^= sin6Q sine cos0 - cos©q cosG _ { ^2 D _ ]-- -dv ^ „ 2 .2 ^^^ r' ...(9) and Kg(EQ, 9 ) is the energy scattering .(10) Klein-llishina crosssection per electron, and C and C' are constants. where N is electron number per cm-^, da/dJi is Compton scattering cross The value of differential albedos dep- section, p., and is path length of ends on the incident gamma ray energy and primary ani secondary gamma rays in the three angles 0^^, ©, ^, excluding axial scatterer, and B(pp) is the build up symmetry case, 6„ = 0 or point isotropic factor for scattered gamma rays. source placed on the surface of a Calculated results are shown in Figs . 11 scatterer. Shoemaker and Huddleston-'^ and 12. demonstrated a interpolation method to 62 obtain the differential albedo for the Hendee and Ellis calculated on the direction (G, ^) from those of (0, 0°) assumption of isotropic scatt ;ring and and (0, 180°). showed good fit for the experimental value 115 . , in the range of the ratio h/D is more measured emergent photons normally to than 0.5 as shown in Fig. 12 the surface. A review article on the propagation of gamma rays at or near an air-ground interface was written by Clarke^'^. Dislonc* from sowfCt,rjCm Fig. 11. POitio of scattered to direct Fig. 13. Radial distribution of energy °^Co exposure dose rate as back scattered from within function of h/D. (ref. 60) These data show that emergent energy*^ is fitted by following formula, -br 0 ... (11) where Vq andti^are constants. Differen- tiating xhis formiila, we can get I(r) as emerging energy an unit area at r, s-ar I(r) (12) where C and a^e constants. References 1. Bulatov, B.P. et al., Vop. Doz. Zash. Izluch. Vol. 5, pp. 5-35, 1966 ( in Russian) Fig. 12. of scattered to direct Ratio 2. Hyodo, T. Nippon Genshi-Ryoku "^Co exposure dose rate as Gakkaishi 8, 371 (1966) (in Japanese)} function of h/D. (ref. 62) ORNL-TR-1670 (English translation). 3. Selph, W.E. Neutron and gamma ray DISTRIBUTION OF SCATTERED QAmiA albedos, ORNL-RSIC-21 , ( DASA-1892~2 ) RAYS ON THE SURFACE 1968. 4. Leimdbrfer, The back scattering of Scattered gamma ray distribution on photons, in R.G-. Jaeger ed., the surface of a scatterer was measured Engineering Compendium on Radiation and calculated by several workers on the Shielding, Vol. 1, pp. 233-245, case of a point isotropic source was Springer-Verlag, Berlin, 1968. placed on the surface. 5. Bulatov B.P. et al., Al 'bedo gamma- izlucheniya, Atomizdat, Moscow, distribution of Figure 13 shows the 1968. emergent energy or the intensity of HcCall, R.C., photons emerging in an annulus of unit 6. Hine, G.J. and J.Appl, width at radius r calculated by Monte Phys. 2^, 506 (1954). Carlo method together with experimental 7. Hayward, H. and Hubbell, J.H., J. data. The experimental data were Appl. Phys. 2^, 506 (1954). 116 . . 8. Bulatov, B.P. and GerusoT, E.A., At. results, Technical Operations Rep. Bnerg. 5., 631 (I958)j Reactor Sci. No. TO-B-63-83,1963. 11, 159 (I960). 38. Wells, M.B .Differential dose albedos 9. Bulatov, B.P., At. Ene?rg. Z* 369 for calcuiation of gamma-ray reflec- (1959)» Sov. At. Energ. 1, 847 (1961). tion from concrete, AD 615 598,RRA-T I I 10. Bulatov, B.P. and Leipunskii, O.I., 46, 1964. At. Bnerg. 551 (1959)} Soc. At. 39. Berger, M.J. and Morris, E.B. , Dose Bnerg. 1, 1015 (1961). albedo and transmission coefficients 11. Hyodo, T., Nucl. Sci. Eng. ~12, 178 for cobalt-60 and cesium-137 gamma (1962) . ray incident on concrete slabs, NBS 12. Pujlta, H., Zobayashi, K. and j Hyodo, Report 9071,1966. ' T.,Niicl. Sci. Eng. 1^, 437 (1964). 40. 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TRAfTSMISSION OF ^^^CF FISSION WaUTROfTS THROUG-H VARIOUS SHISLDS Yo Talk Song Nuclear Physics Division U.S. Naval Surface Weapons Center White Oak, Silver Spring, Maryland, U. S. A. Measurements have been made of neutron transmission through various shield configarations. A ^^^Cf source, having a neutron yield of 1.02 x 10° n/sec was used with a US Navy neutron dosimeter, AN/PDR-70. This detector was used to measure the integrated neutron dose equivalent (DE). 3 by 5 ft. slab shields of various materials were used, such as iron, lead, polyethylene, combinations of iron-polyethy- lene, lead-polyethylene, and iron polyethylene-iron. The measured data were corrected for room-scattered contribu- tions. The scattered neutron DE was calculated using the differential dose albedo formula of Song, et all. The experimental data thus obtained were compared with calcula- ted values. The one-dimensionsal discrete ordinates neutron transport code, ANISN, with 40 energy groups, 22 groups for neutron and 18 groups for y-^ays, was used for the transmi- ssion calculations. Comparisons were made in terms of atte- nuation factors, the ratio of transmitted neutron DE to free-field neutron DS at the detector point. Agreement was within the expected dosimeter range of 20/. for all cases. For the case of two inches of iron and five inches of poly- ethylene, placing the iron on the source side was more effective than placing it on the opposite side. ( ANISN } Cf ; code ; configuration ; dose equivalent ; energy ; gamma rays; neutron ; scattering; shield ; trans- mission) Introduction The transmission of neutrons from radiation transport code ANISN The the 252cf source through various shields ANISN results are compared with experi- was measured by a neutron dosimeter, mental results of various shield confi- AN/PDR-70. The 252cf so urce is a small gurations. If the agreement between expe- cylinder of about 0.25 inches in diameter riment and computational results is and 2.5 inches long, and has a relatively favourable, the effective attenuation high neutron yield of /~ 10° neutrons/sec. kernel for further shielding calculations The AN/PDR-70^ is a U.S. Navy standard involving other shield configurations neutron dosimeter of a modified Anderson with other materials can be obtained and Brown type, that measures thermal neutron the confidence level in the computational flux with a BF-^ tube surrounded by cylin- results can be established. Furthei^ore, drical polyethylene moderator. The mode- the choice of group structure and multi- rator is 8.5 inches in diameter and 9.4 group cross sections used in ANISN may be inches in height. evaluated by comparing the experiment and computational results. The purpose of the study is to find out the effectiveness of steel and other Experiments materials for shielding fission neutrons. The steel is commonly used as structural The experiments were performed in a material in conjunction with neutron room about 28 ft. by 30 ft. in area and moderating materials such as the poly- about 20 ft. high. The walls, floor and ethylene. The experiment is simulated by ceiling are concrete slabs. The source the one dimensional discrete ordinate and detector were about 10 ft. above the + This dosimeter is calibrated to read dose -equivalent with units rem or millirem per hr. Hereafter, whenever neutron dose is used it will be understood to mean dose-equivalent 119 ) floor. The shields were 3 ft. by 10 ft. Center. Cross sections for polymers, with various thickness and placed on the (polyethylene) were obtained by mixing rack so that the centers of the shield carbon and hydrogen cross sections with faces lie on the source detector line the MACROMIX code. The basic cross and the faces are normal to it. The sections have apto P-^ components in 22 source-detector distance in transmission neutron and 18 gamma energy groups. Mono- measurements was kept constant at 2.5 ft. directional parallel beams of neutrons Various shields were placed on the rack nearly normal to the shields were assumed and the distance from the source to in calculations. Based on the spectrum source side face of the shield was kept in Table II, the neutron DE at 2.5 ft. at 10 inches. In Table I, the various from the scirce was estimated to 1.69 shields used in the experiments are mrem/hr, while the measured value was given. The left hand side material in 1.64 mrem/hr with corrections for neu- this table was facing the source. trons scattered from walls, ceiling and In order to aid in determining the floor. The neutron yield at the time of component of the neutrons scattered from the experiment was estimated to be walls, ceiling and floor, the neutron 1.02 X 10° neutron/sec. dose rates were measured for various The room scattered neutrons reach- distances from the source. Results are ing the detector were calculated by the shown in Figure 1. All data presented method described by Song et al-*-. Utili- in this paper were corrected for natural zing the differential dose albedo con- background and have fractional standard cept with energy dependent parameters deviations less than or equal to 5'/ of for the differential dose albedo formula, the measured values. The possible error the scattered neutron DE was estimated in measurements of distance between to be 0.05 mrem/hr at the source-detector- source and detector is no greater than separation distance of 2.5 ft, the expe- 3'/. of the measured values. rimental detector location. When the shields were placed between the source Analysis and detector, the scattered neutron DE was estimated to be 0.026 mrem/hr. In In the calculation an 316 quadra- Figure 1, the measured DE, measured DE ture with 22 neutron and 18 gamma ray with corrections for room scattered groups gas utilized. The group struc- neutrons and the inverse square line fit ture, ^52q^ source spectrum, and DS to the corrected data by the least squa- conversion factors used in ANISN, are res method are presented. From Figure 1, given in Table II. The 252cf source the room scattered corrections result in spectznm in 22 neutron groups is based a good agreement between experimentally on the data by Stoddard^. Basic cross observed data and calculations. There- sections are derived from the SNDP/B fore the room scattered data, 0.026 mrem/ library, and edited into ANISN Format hr with shield in between source and by Radiation Shielding Information detector, was subtracted to correct all Table I Shielding Material and Configurations Materials Thickness Materials Thickness (inches (inches) Iron 1 Polyethylene + Lead 6 + 1/2 Iron 2 Iron 3 Iron + Polyethylene Iron 1/2 + 5 4 Iron + Polyethylene 1 + 5 Iron + Polyethylene 2 + 5 Lead 1/8 Lead 1/4 Polyethylene + Iron 5 + Lead 1/2 3/8 Polyethylene + Iron 5 + Lead 1 1/2 Polyethylene + Iron 5 + 2 Polyethylene 2 Iron + Polyethylene + Iron 1+5+2 Polyethylene 4 Polyethylene 6 Polyethylene 8 120 the shield transmission data. In Table There are differences in the repre- III, the experimental results and calcu- sentation of the experimental geometry lated data for neutron transmission by AI^ISN. In the experiment, the source through various shields are given. In is a small cylinder, the shield is a this Table, the results are given in finite slab and the detector is a cylin- terms of the attenuation factors, the der. In ANISN, the source was assumed to ratio of transmitted neutron dose to free be plane-monodirectional beam normally field neutron dose at the detector point. incident upon a semi-infinite slab shield Further, comparison of the experimental and the detector to have an isotropic results and theoretical results are pre- response. Therefore, neutrons scattered sented in terms of the ratios of the cal- from beyond the actual geometry of the culated attenuation factor to the experi- shield in ANISN.were not detected in mental attenuation factor. experiment. Further, in experiment, the scattering angle of neutrons reaching the detector by a single scattering in the shield is larger than those in ANISN. Therefore, the expected neutron dose reaching the detector by a single sca- ttering in the shield will be larger in ANISN than those in experiment. Conse- quently, the thicker the shield, the greater the discrepancies between ANISN and experiment, as seen in Table III. It is also seen in Table III that iron is effective in neutron shielding if used with a moderating material such as polyethylene. Furthermore, the sandwich shield, iron + polyethylene + iron, was much more effective compared to the shield configuration of the same total amount of iron followed by polyethylene or polyethylene followed by iron, by about 257. . The attenuation afforded by one inch of iron followed by five inches of polyethylene was almost the same as five inches of polyethylene followed by two inches of iron. That is, if iron and five inches of polyethylene are to be used for shield- ing of fission neutrons, place the iron on the source side. This conclusion can be drawn from both experimental and ANISN results. In Figiare 2, the leakage spectrum from three different shields, one inch iron followed by five inches of polyethylene, five inches of polyethylene followed by two inches of iron and the sandwich shielding, are presented. Bet- ween about 0.1 to 1 MeV, there seems to be a window in the iron cross section that permits the neutrons to pass throu- gh. The contribution of a neutron to dose equivalent in the energy of 0.1 to about 1 MeV is about a factor of 3.5 higher than that of a thermal neutron. Fig. 1. Dose Equivalent Vs. Distance. Although the iron behind the polyethy- lene is more effective in removing ther- mal neutrons, placing the iron in front of polyethylene is more effective in Discussion reducing the total neutron dose. From Table III, it is seen that the Acknowledgement s experiment and the calculated results are Assistance provided by D.C. Hugus in good agreement. The agreement is gene- and his group at PANTEX Plant in experi- rally better for thin shields than for mental work, technical consultation by thick shields as expected. D.E. Hankins at the Los Alamos Scienti- fic Laboratory, CM. Huddle ston and N.E. 121 6957 ., 1 , - Table- II . 252 Energy Group Structure, Cf Spectrum and DE Factors NEUTRON GAMMA RAYS Energy Upper DE-' Source Spectrxim Energy Upper Dose" Group Energy Factors (Fraction/ Group) Group Energy Factor (Mev) (Mev; 1 15..0 5. 8(-8) 0.0 2 12., 2 4 . 0.0 3 10. 0 4.1 , 2., 70-3 23 10. 0 2 . 72(-9) . 4 8.. 18 4.1 1.,57-2 24 8. 0 2. 30 5 6., 36 3 . 3.,83-2 25 6. 5 1 .90 6 4,,97 3 . 4,,94-2 ZD 5. 0 1,. 60 7 4,.07 3.6 1.,19-1 27 4. 0 1 . 32 O O 8 3..01 3 . 9 ,05-2 zo 3. 0 1 . 10 ' 9 2,.46 3 . 2 ,27-2 29 2. 5 .97 . 10 2,. 35 3 . 1 .19-1 30 2. 0 83 •1 1 11. 1,.83 3.7 2., 30-1 31 1. 66 . 67 Iz 1..11 3.3 2,, 14- JZ 1. 33 .53 Q "it lie 13 5..50-1 1 . y .87-2 Jo 1. 00 . 445 1,,11-1 0 JM- 80 . 35 15 3 .35-3 .12 0 35 60 .256 16 5..83-4 .13 , 0 36 40 .177 17 1,.01-4 .13 0 37 30 .122 18 2,.90-5 .125 0 38 20 .066 19 1..07-5 .12 0 39 10 .039 20 3,.06-6 .115 40 05 .084 2l 1,.12-6 .110 S > 22 4,.14-7 .105 0 * rem/neutron/cm ^ , rem/gamma ray /cm Dose Attenuation For Cf^^^ Neutrons Through Various Shields Dose Attenuation D/Do (D/Do) Ratio Shield ANISN Experiment (ANISN/Exp) Material Thickness (inches) 0 1.000 .000 1.000 Iron 1 .992 .890 1.115 Iron 2 .878 , 793 1.108 Iron 3 .749 .663 1.130 Iron 4 .624 .588 1.061 Polyethylene 2 .568 .529 1..073 Polyethylene 4 .235 . .225 1 .044 Polyethylene 6 .096 .083 1,.156 Polyethylene 8 . 040 .. .033 1 .212 Lead 1/8 1..005 .929 1,.082 Lead 1/4 1,.009 1,007 1..002 Lead 3/8 1..011 .953 1..061 Lead 1/2 1,.011 .949 1,.065 Poly.+ Lead 6 + 1/2 .083 .083 1,.000 Iron + Poly. 1/2 + 5 .122 .109 1..119 Iron + Poly. 1+5 .099 .089 1..112 Iron + Poly. 2+5 .065 .051 1..275 Iron + .137 1..202 Poly. 5 + 1/2 .114 . Iron + Poly. 5 + 1 .123 .092 1..337 Iron + Poly. 5 + 2 .099 .082 1.,207 Iron + Poly. + Iron 1+5+2 .064 .057 1.123 122 1~ . — 1 1 1 ; — Discussion r.— =7: -1- f— -, 1 t- — ' 1 — - j- 1 ~— j 1 1 S. Makra :k H Thrcu gh Varlouj 5 nltldi («' • sure* rt ? 1 Could you give me the exact diff- J— i -4- erence in attenuation when reversing the of the layers? - sequence shield „ - Y.T. Song -I r: ^. 1 brH It will be shown in proceedings of this symposium. However, the following = r is one of the results of your interest. - 2 in. Iron + 5 in. Poly ANISN 0.065 Exp. 0.051 ;/ 5 in. Poly + 2 in. Iron ANISN 0.099 f 'ri- Exp. 0.082 ftT-F 4 As you see reversing the order, it gives as much as about 30? difference. I ran D.V. (jopinath = 5" - + tel7.-< : 1 1 1 \ -1 - ANISN is a one-dimensional code and 1 1 - -4 - 1 1 i be 1 your* experimental system seems to . i i 1 f r1 - H — _L .... away from one-dimensional geometry . Still i : i ! ! — the agreement between theory and experi- u J3 mental seems to be very good. Will you please comment ? Spectrum Fig. 2. Neutron Leakage Y.T. Song Through Various Shields (Cf source) Mock up of experiment depends large- ly on how you use the facilities. ANISN results and experimental results should agree very well for a thin shield if you properly. However, for thick Scofield at the Naval Surface Weapons use ANISN expected are poorer. for their giaidance and helpful shield, agreements Center arrangements of my assistance, and Jack Finkel at the Naval Note for the shield range of shield thick- Surface Weapons Center for his numerical paper within this rather good agreement in terms of calculation of room scattered neutron ness, D/D expected and we have it. dose, are all great fully acknowledged. is References 1. Song, Y.T., Huddleston, CM., & Chilton. A.B., Nucl. Scl. Eng. 35, 401 (1969). 2. Technical Manual, Set AN/PDR-70. NAVSHIPS 0967-871-5220, Nov. 1969. 3. WANL-PR(LL)-054, Nuclear Rocket Shielding Methods, Modification, Updating, and Input data prepara- tion, Volume 4, One-Dimensional, Discrete Ordinate Transport Tech- nique, Augiast 1970. a'. , Manual for 4. Bngle, Jr. , W. "A User's ANISN, A One-Dimensional Discrete Ordinate Transport Code with Aniso- tropic Scattering". 5. DP-939 Savannah River (Diipontj Ra- diation Properties of Cm^44 Produced for Isotopic Power Generators, Savan- nah River Laboratory, Aiken, S.C., Nov. 1969 by D.H. Stoddard. 123 . , BACK-SCATTERING (SZT-SHINE) OF GAMMA-RAYS PROM A 650 CURIE COBALT-60 SOURCE BY INFBflTE AIR J. Swarup and A.E. Ganguly Health Physics Division Bhahha Atomic Research Centre Trombay, Bombay- 400 085 The paper reports the preliminary results obtained on the sky- shine spectra from a 650Gi^'^Co source located at the centre of a gamma irradiation field of radius 90 m. fenced by a stone wall of thickness --^75 cm and height 3-66 m. The source is in the form of small pellet. The height of the source when raised for irradiation is 1.2 m above ground level and it is shielded on top by a lead cylinder of 10 cm diameter and 25 cm length. Thus, only the scattered radiation can reach the ground level beyond the fencing wall. There is a field Qf 100 mR/hr on the inner side and 2 mR/hr on the outer side of the wall with the source raised. Experiments are carried out for the measurement of sky-shine with a well-shielded Nal detector assembly coupled to a 400-channel analyser. The detector is placed 55 cm above ground looking vertically up through a lead collimator of diameter 12 mm (.or 20 mm; at distances from 150 m to 325 m away from the source. Energy calibrations of the spectra have been carried out before and after each experiment using standard sources of gamma-energy ranging from 60 keV to 662 keV. It is found that the spectrum extends upto 400 keV with a pronounced peak at 72 keV for all the distances. There is no evidence of the presence of primary gamma-photons in the spectra. Total eovmts under the sky-shine are observed to follow an exponential decline with distance, with a slope of -0.50 + 0.02 for both the collimators used. The ratio of peak counts (72 keV) to total sky-shine is 0.24 + 0.02 for both the collimators. Also, the nature and intensity of the spectra remain unchanged when the lead shield around the detector is provided with an internal lining of 2.5 cm thick aluminium. (Back scattering; ^^Co; gamma rays; sky-shine; spectrum) Introduction The height of the source when raised for irradiation is 1.2 m above the ground Swarup-^ has investigated the back- level. It is shielded on the top by a scattering of gamma rays obtained from plug of lead cylinder of 10 cm diameter 137gs inside a large room for different and 25 em length. ! source-to-detector distances. The present work is a preliminary report on The gamma irradiation field is ; an extension of the same work in the fenced by a stone masonry wall of height t ope , to study the back-scattering of 3.66 m, and thickness 1 m at the base ] cobalt-60 gamma, at different source-to- tapering to cm at the top. There is a 75 J detector distances, by infinite air field of 100 mR/hr on the inner side and above the source. This back scattering 2 mR/hr on the outer side of this wall is also known in literature as sky-shine. when the source is raised. Because of this wall, only the scattered radiations, Field Description and Experimental scattered by the air above the source, Arrangements can reach the ground level beyond the fencing wall The cobalt source for these obser- vations is located at the centre of a Observations on the sky-shine large (90 m radius) circular gamma spectra are taken with a 5.08 cm x 5.08cm irradiation field and has a calculated Nal (Tl) Harshaw integral assembly strength of 650 Gi. The active material coupled to a 400-channel analyser. The is in the form of small pellets of 1 mm detector is placed inside a cylindrical x 1 height filled in an cm high) lead shield made of inter- diameter mm (50 , annular stainless steel container of locking rings of 5 cm thickness, 5 cm , and 15 cm inner diameter (Fig. 1) 18.5 mm outer diameter, 11.5 mm inner height . diameter and 40 mm length. Thus, it is In the central hole of the top ring, a , effectively a point source when viewed lead collimator or a lead plug to close from distances beyond 100 m. It as the case may be, could be placed. 'j, i 124 . This whole assembly is motmted on a tro- On the side of the experimental lley of mild-steel 25 mm thick, for easy field is the sea and on the other side morement. Height of the detector head well beyond 400 m from the source, a in this position is 55 cm above gro\md. vegetation covered hill gradually rising to a maximum height of about 75 m above the sea level. The contribution to the sky-shine from the hill is negligible as the observations have been taken in a narrow collimated vertically upward direction. For taking the sky-shine spectra for distances between 325 m and 255 m colli- mator of 12 mm diameter and 5 cm length is used. The spectra with 20 mm colli- mator have also been recorded for distances of 150 m and 155 m. Recording of Spectra The procedure for recording the spectra is as follows: Fig. 1. Detector assembly inside the Pb shield with Al-lining. i) First the detector is calibrated with thin standard sources of gamma Whereas the detector is kept in the energy ranging from 60 KeV to 662 KeV open at atmospheric temperature, the kept at the opening of the collimator analyser is located inside an air-condi- (with the 6O00 source down) . The tioned room of constant {'^23°0) tem- strengths of these sources are known to perature. This necessitated long cables a confidence level of . The sources of 100 m length to couple the two. For used are 24lAm 109cd 57cp l4lce, driving the pulses through such a 203Hg, ^'-^Cr, l^^Au, ^^Sr, 137cs, length, the emitter follower of the pre-amplifier is fitted with a driver ii) Keeping the ^*^&'o source down, for coaxial cables which are appropria- the area-skyshine is determined for 30 tely terminated. mins. This shine is subtracted from the spectra of the standard sources. Then, To avoid large changes in tempera- by plugging the collimator, the back- ture of the detector in shade and simshine ground spectrum in the shield is deter- the entire set of observations are taken mined. Subtracting this from the area- in the night . Changes in the gain of skyshine, true area-skyshine is obtained. photomultiplier with temperature varia- As the area-skyshine could not be tions are discussed by Zinard^. E.H.T. determined for all the individual experi- of the photomul.tiplier is adjusted to mental points, it is measured at one less than the optimum working potential. point and assumed to be the same This helped in keeping the gain constant throughout throughout the interval of aboat five hours of one set of observations. By iii) The source is raised. First reducing the E.H.T. , sensitivity of the the spectrum is taken for 30 mins. with photomultiplier is reduced and inspite the lead-plug in position. This of temperature changes of upto 8°C spectrum is termed the back-ground during one set, the spectra from 0.662 spectrum in this work. MeV to 0.060 MeY remained reproducible. (iv) Finally, the plug is replaced To take the observations at diffe- with an appropriate collimator and the rent distances from the source, a road sky-shine spectrum is recorded for 30 radial to the source is used. This road, mins. The channel calibration is tested being inside the premises of Radioactive again with standard sources. From this Solid Management Site used for burying sky-shine the sum of the spectra of radioactive wastes, however, has a back-ground and the true area-skyshine significant background of its own is subtracted to^get the true sky-shine (0.5 mR/hr) and therefore its own area- spectrum due to °^Go source. skyshine. This area-skyshine is measured and subtracted from the sky-shine Typical spectra of sky-shine and obtained with "'^Co source raised. The area-skyshine with their respective back- spectra are taken with the detector grounds are shown in Fig. 2. looking vertically up for distances from 150 ffi to 325 m from the source at It is observed that the background intervals of 10 m. continued upto almost the 60co energy 125 . 0 50 TJ ISO 2m J50 300 3:0 «0 CHANWeL NUM3SR Fig. 2. Sky sliiae Bpectrum at 255 m. source dietanc© (Golliaater j20 mm). without any peaking at that energy and As a preliminary assessment of the increased continuously with decreasing spectra, the following important points source distance. A five-hours counting are observed. at 150 m source-distance did not show any °^Qo peak. At the distance of 255 m i) the counts of the true skyshine the back ground increased considerably spectra extend upto 400 KeV on energy (about 25*7. of the sky-shine at 72 KeV) scale for all the distances of observatkns. and it is reduced to 8/. when the shield is provided w^th a single layer castling The geometry of this set-up (Fig. 3) of 5 cm thick lead bricks all around. is such that all photons from the source But the back ground subtracted sky-shine and scattered ones from the lead-plug spectrum remained unaffected by castling. emanated below the horizontal plane The remaining sky shine spectra upto 150 passing through the source, strike the m are recorded with this 10 cm lead gamma field ground or its fencing wall shielding arrangement i.e. photons in a solid angle 2% do not give any sky-shine directly. Only those Discussions source photons go straight out which are emanated from its near ground periphery There is no data available in the and have their azimuthal angle, 126 . . . • scattered vertically down by air to come 155 m so"arce distance. Differences in "the field of view" of the detector observed are well within the limits of i.e. scattered to 90° with an energy experimental errors. Thus, the true of 353 K.eV, as obtained from the Compton sky shine spectrum observed in the formiila present work with a pronounced peak at 72 KeV is not related in any way to the scattering from Pb-shield. ! scattered E 1 + —pd-cose) I mc 1 • £ 0?: 1 This is the high energy limit of sky i shine spectrum and due to poor resolution 1 of the detector in this energy region, « 12 mm COLLJMaTOB ' the counts extend upto the channel 010 corresponding to ~ 400 KeV. ii 1 . . 0 . . 1 , , , , 1 , , J I 150 200 250 300 350 I Fig. 4. 72 KeV peak-to-total sky shine vs. source distance.: The inset in Fig. 2 shows spectrum jij^g obtained with ^98^^^ ^2.2 KeV photon in the present set-up does not contribute significantly to the Compton continuum in comparison to its photopeak. The con- tributions to the respective Compton portions of lesser energy photons are ^ i insignificant. If, therefore, as a first Fig. 3. G-eometry of photon scattering by approximation, the Compton portion be air neglected, about one-fourth of the inten- sity of sky-shine in vertical direction The photon with <^ equal to 45° comprises of 72 KeV photons. needs to be scattered by 135° to strike the detector from a minimum height of iii) The total CQ-unts under the sky- 150 m. above it, and the scattered photon shine (the intensity of the scattered has 240 J£eV of energy. The mean free- photons) follow an exponential decline path^, for 240 iieV gamma in air is ~ 70 with distance from the source (Fig. 5) m. This scattered gamma, therefore, The following relationship gives the best travels more than two mean free-paths fit with the recorded counts: for 150 m, and more than four mean free- paths for m source distance to be X 325 I.I • detected. The photons with angles 0 between 88.5° and 45° when scattered at where x is the source distance in meters appropriate heights by angles between and Iq is the intensity of a virtual ' 900 and 135° are detected. source, the value of which depends on the diameter of the collimator. ii) At all distances from the source the nature of the spectrum remains the iv) It is also found that the counts same. There is a peak corresponding to spectrum of the area-skyshine (Fig. 2), the channel of 72 K.eV. The ratio of too shows a peak at 72 KeV, but ends 1] counts in the range 64 KeV to 80 KeY at ^ 275 KeV. In the experimental field ' (taken as 72 KeY peak) with the total wastes containing different radioactive counts of sky shine (Fig. 4), for both substances of varying strengths are the collimators is obtained as 0.24 + buried deep in the groiind about 50 m 0.02 for all the distances; however the away from the detector, in about 30 cm effect of source distance is felt only thick concrete cells which are covered I in the count rates. also V7ith the same thickness of j concrete. These sources also give The 72 'B.eY peak obtained in the sky shine with a peak at the same energy. sky shine is very close to the Pb x-rays (K^^j 75 K.eV) . The spectra were Further work ia in progress taken with and without 2.5 cm of Al- lining inside the detector shield at 127 analyser through 100 m cables. The help 60 - in the experimentation given by M/s D.T. Khatri, A.R. Kamath, S.H. Shirke and K. Somanathan is gratefully acknowledged; the latter helped in calculations also. The facility of the source was kindly provided by Dr. h.M. Desai, in- charge. Experimental G-amma-Pield Station. References 1. Swarup, Indian J. Pxire Appl. Phys. 11, 331 (1973) 2. Kinard, I.E., Wucleonics 15" {Ho. 4j, 92 (1957). 150 200 250 300 350 400 SOURCE-DISTANCE fMETERS) 3. Alberg, M. , Beck, H,, O'Brien, K. and McLaughlin, Nucl. Sci. Engg. 65 (1967). [See also, E.T. Clarke, Nucl. Fig. 5. Total sky-shine counts vs. Sci. Engg. 27, 394 (1967) and Chilton, source distance. A.B., ibid, 403 (1967)J. 4. Hubbell, J.H., "Photon Cross Sections, Acknowledgements Attenuation Coefficients and Energy Absorption Coefficients from 10 keV The authors wish to thanl-L JVlr. G.H. to 100 GeV'iMSRDS - NB3, 29 (Aug. 1969). Vaze, Head, Electronics Division for the help given by his staff; i»ir. R.K. Balani supplied the 400-channel analyser, I4r. C Gr. Chatur developed and assembled the Pre-amplifier and matched it with the 128 . . BACESCATTERINQ OF GAMMA RAYS BY BARRIERS FROM VARIOUS MEDIA * D. B. Pozdneyev Gorki State University, Gorki, USSR Quantitative data about albedo of gamma radiation must be known to solve some problems of radiation shielding, radio- metry, nuclear instruments. Spatial - energy, differential and integral characteristics of gamma rays albedo for the case of the barriers of different thicknesses from beryllium, graphite, aluminium, concrete, iron, tin, and lead were deter- mined both experimentally and by means of Monte Carlo method. Energies of gamma rays from the point isotropic source and of monodirectional beam were 145, 279, 511, 662, 1000 and 1250 keV. Spectral - angular distribution of back-scattered gamma rays escaping from various portions of the barrier surface as a function of thickness and material of barrier, distance from the source, geometry of the source and energy of primary gamma radiation was also investigated. Systematized data about differential and integral albedo of gamma rays of various energies for the case of barriers of different thick- ness from various media are presented in the form convenient for practical uses. (Albedo; angular,- backscatt ering; barrier; differentials; distribution; gamma rays; integral; medium; Monte Carlo) Introduction reflector surface. Therefore we can write the function The quantitative data about the backscatt ering of gamma rays from a(EQ,H^ ; E, e, Cp, X, y, d) as barriers of various media must be known for the 8 olution of some problems of a(Eo,y ; E, e,Cp ,r, d) radiation shielding, in radiometry and dosimetry , in the elaboration and The spatial spectral albedo exploitat ion of some instruments dete- = cting bac kscattered gamma radiation a3(EQ,\p , E, r , d) ( such as thickness gauge, density gauge ^- //2 etc. ) dCp Ja(BQ,H/;E,e,'f, nd)sin 6 dO Method 0 0 characterizes the integrated energy Let us introduce the following spectriim of backscattered gamma quanta current characteristics of gamma rays escaped from various portions of the albedo reflector surface. The spatial number albedo (distri- a(EQ,M^ ; E, e,tf ,X , y, d) is the probability (per one quajitum with the bution of reflected ganma. quanta along energy Eq and angle of incidence vf* to the barrier surface) is characterized by normal to the plane barrier with the the value thickness d) of gamma radiation escaping from the reflector at the point with the ajj(EQ,v|^;y,d) = Cartesian coordinates (x,y,z=0) in the direction ( 6 ) ( 6 is polar and (f±s 1 azimuthal angle ) within the \init solid JdE dCp la(Eo,H^}E,e,9,y,d)sinede angle (tne energy of such radiation is 0 0 of backscattered equal to E) . In the cases of point Characteristics isotropic primary source with gamma rays were determined by us experi- the reflecting barrier, ana the mono- mentally and by means of Monte Carlo directional beam withH^= 0°, it is method convenient to introduce the If - coordinate E, Ai* ,d) characterizing the distance between the Some examples of ag( E^ ,y ; source and the studying region of the for Eg = 1.25 MeV are presented in fig. 1. For the sake of clearness all Presented by Mr. J.H. Hubbell 129 . . : ) the functions flgC Eg ,y i £,4^* , d) are nor- essential contribution to albedo was malized on Icm'^ of the reflector surface. rendered by the multiple scattered quanta issued from the depth of the reflector. Albedo from the thin barrier is condition- ed by gamma quanta penetrating along the reflecting surface of the barrier and scattering at small angles (therefore they throw down their energy insigni- ficantly see instance the spectra for d = 0, Imfp) The low-energy quanta corresponding to the multiple scattering are more intensively absorbed in the material of the barrier. Spectra ag(EQ,v|^;E, Ar, d) for the case of normal incidence of primary gamma rays beam are characterized by more finite energy field than in the geometry of point isotropic source. This is particularly characteristic for heavier media. Gamma quanta with energy lower than llOkeV (for lead lower than l60keV) are absent in the spectrum due to photoabsorption. The mean energy of the spectra of backscattered gamma radiation for the monodirectional source (normal incidence) is lower. In order to determine the meaning of albedo from the local portion of the barrier surface Ar (thickness of the reflector equals d) - a]^(Eo»'+'; •^r, d) the relative change of this value with d Fig. 1. Energy spectra of backscattered and aj,(Eo.vV ; ^r.co) .ust photons escaped from various portions of reflector surface. be known. Example of dependence on d of Eo=l,25MeV. ^J^»d) "uj^o'^ ^ - the ratio concrete a,b,c, graphite point iso- Ar,oo d,e,f - iron tropic source oJTe^TH^ } ) g,h,i - iron, monodirectional and isotropic source of primary gamma source ( =0°) d=0, Imfp rays is presented in fig. 2a. Fig. 2b d=0, 4mfp d=2, 5mfp characterizes the change of spatial spectral albedo ag(EQ,S';E, Ar,d) for While comparing spectra for various E = (10-160) kev with thickness of /IT there can be noted the following barrier d. The accumulation of low- points of principal importance: the energy gamma quanta due to multiple portion of backscattered gamma quanta scattering extends the range of change decreases with the increase of r, the of the value ag(Eo,H' ;E, Ar,d)/as(EQ,H' j dependence of albedo on d becomes less E, Ar,oo). with d for greater distances sharp with increase of r. With light r reflectors the increase of radius r is followed by the enrichment of the energy The analysis of the received data spectra with the low energy gamma quanta shows that the dependence of albedo on owing to multiple scattering in the the circular regions of the semi-infinite barrier matter. It is easy to understand reflector surface ajjQ(Eo,4^; t,oo) on r the deformation of spectra with r in- can be described by the following empi- creasing (fig. la,lb,lc) taking into rical formula (with accuracy + 5a ) consideration the small role of photo- absorption in such materials as bery- llium and graphite. V/ith gamma quanta 180° scattered at the angles nearing (1) essential contribution to albedo was observed in the region near the primary cv) source[Ar=(0-0, l)mfp - fig. laj (and where aM( Eq .H^ ; ) is the number in this situation the clearly expressed albedo from semiinfinite {6.-*°^) scatterer peak took place in energy interval with an unlimited area of the surface (r_^oo). (200-300)keV) . With the thick scatterer The values of aN(Eo,S';'^, oo 130 . , Table 1 Values 0*;( Eo* H' | Source Point Monodlrectlonal geometry =0") ieo tropic ( y a^i 6o, ^ )CD ,00) 0,'»36+0,002 0,242+0,002 0,42+0,04 (exp) (nfp)-'' f> 0,83 1 ,06 are given in Table 1 for concrete (alu- minium) according to the results of the experiments and of our calculation by- Monte Carlo method. The values p for the calculation of a]^jc(Eo»H^} r, 00) according to the formula (1) are given in the same table. It is easy to see 1 2 dtmfp) that a^{Eo,H^ ; ^r,oo) { Ar=r2-r±) can be found as Fig. 2a and 2b. Albedo from local portion of reflector surface (in arbitrary units) as fun- ction of barrier thickness The joint use of the formula {2) and d. Cs point isotropic graphs which are analogous to those on source fig. 2 permitted to determine the depen- a - E = (10-652)keV, b - E=(10-160) keV dence of albedo from local portion of 1 - r=(0-0,l)nifp, 4 - r=(0,5-l,0)mfp, reflector surface on the thickness of the 2 - r=(0,l-0,2)mfp, 5 - r=(l-2)mfp, barrier. 5 - r=(0,3-0,5)mfp, 6 - r=(2-5)mfp. 131 : , GAMM RAY STREAMING THROUGH AI^WLAR GYIIWDRIGAL DUCT K.P.N. Murty, R. Vaidyanathan and R . Shankar Singh Reactor Research Centre K:alpakkam-603102 Madras, India In this paper we present the study of gamma ray streaming through an annular cylindrical duct from an infinite plane source. A rigorous formulation based on the ray-analysis procedure has been developed to compute the resultant dose in the vicinity of the duct exit, A parametric study has been carried out to evaluate the accuracies obtained with the present rigorous treatment as compared to the simple formula developed for hand- calculations. Attempts are being made to incorporate the scattering component to the dose at the exit, in our present study. (Annular,- computation,- duct 5 gamma ray; integration; kernel; radiation-, streaming) Intro duction a . Radiation streaming through ducts is an important and difficult problem in nuclear reactor shielding. Methods of computing the streaming flux through straight cylindrical ducts have been 1 1 reviewed profusely by many peop2.e-'-~5 Only a few attempts have been made in 1 1 the study of radiation streaming through annular cylindrical ducts. This problem is of importance in reactor shielding, where one encounters cylindrical plugs with annular gaps all around. We present here a rigorous analysis of the problem of gamma streaming through annular cylindrical ducts using Ray-tracing procedure coupled v;ith point-kernel integration. Formulas for Uncollided Flux Figure 1 shows the configuration of the duct with an infinite plane source perpendicular to the Z axis at the duct entry. The source is divided into 3 regions, flegion 2 is further divided into two sub-regions, 2A and 2B. Region 3 is divided into 4 sub-regions 3 A, 3B, 3C and 3D. Let the uncollided flux from each region he %32 ; fl'^expU(r^^L')^(Rl/r)i n±l L ^-^(ritL^,)^(r4/r} ^,=^ ^ ^ fcexp ^2 2 (^2^^2)1+^/2 1P2A2U J J,^ (^2^j^2)i;n/2 r L"exp{-n(r2+L2)^(l+gInRl)] ^^i^ere r'^r^ when e Case 2 a 4Rj €t L^'exp J-^(r2+L2)^ (fi^fj^)? o (r .L) ' L:iexp{-.(r2.L2)i(.,/.4^ o ^,=f±i 1^9 ° (r'^+L^)^^^/^ ^1 J ^ ^ 2 2 4- L exp -^.(r ^-L")^ ^_=ii±i f def ^ 5B 271 J 2^2Nl+n/2 11 Ti f ? ? 4 ^1-^? 7 J . fj'^J'^^ rjT27l7H72 e; y L"exp -,.(r2+L2)%+4^) Case 3 Ri ~ 2.L2)^(l.r,/r)L ° (r2.L2)l-/2 o K J "tjig above formulas % = a cos e + (R^2_j^2 c-^y^^Q^i p 2 2 4- = a cos e + (R-g'-a sin = a cos e - (Rj-~a2 sin2G)^ de ln(l+(r'/L)^ n = 0 2 2 r^ = a cos e - (Rg'^-a^ sin 0)"^ = sin"l(R /a) - sin~l (R^a) o 10 E Where r' = r^ when 0^©<(eo Refer to the 2A component of the total uncollided flux at a = R^ in the r' = rp when ®^6q duct exit plane considered in case 3. For an isotropic source (n=0), this component can he approximated as follows: u ' 2 •! (r +1 j . I P'or a duct whose radial dimensions are small compared to its length, 3r L'^exp{-^(r2+L2)^(l-r2/r)j ln(l+r2/L2) r2/L2 and ln( l+r2/L2 )s.r2/L2 d r-li±l Iao f „.„ "3 271 2 T2Nl+n/2 Substituting thd expresions fo? anQ J^Jy {r( 00 "4i +1j ) integrating, we get % to L%xp(-^(r2.L2)^(l.^\ f3D=^. [ddf ^^ ^ , - Co.-lfR ) j J ^-R ,) Cos (R^/R^)/R (r2.L2)l--/^-rx, #2A=-72FR^« case 4 a RE ; ^^-j^ en r Vexp -,(.2,,2)i(i,^^) -H, fK^2_,^2 J - ^3 (r2+L2)lW2 133 . . Calculations and Results fraction of the total dose (25X to '55'/.) for all duct lengths. Dl contribution Calculations were performed using falls doim rapidly with increase of duct the formulas derived in section 1. The length (14.3/- for L = 6 cms to less than source considered was "'-'Co and the source .OOlX for L = 60 cms) angular distribution was considered to be isotropic (n=0). Various ducts in lead shields were studied. A part of the results obtained is presented in Fig. 2. as * " ' (cms) Rj I DJSTAfJCC 1' ' -I Fig. 3- Contribution of the components to the total dose. When 'a' increases from 0 to Rj-, Dl decreases while D2 and D3 increase - D2 increasing more steeply. For longer ducts D2 increases more rapidly with 'a'. 0 3 5 10 fi I— —-I I . D/S TANCl (cms) ^, I In the annular region D2A is the most predominant component. This com- j ponent alone accounts for about 65/- of Fig. 2. Total dose-rate distribution in | the total dose for a duct of length = 6 the duct exit plane. cms. For a duct of length - 60 cms, it accounts for about of the total dose. j total dose distri- 99X Fig. 2 shows the For longer ducts, the simple formula in bution in the duct exit plane for a duct section 1 which approximates the 2A = with the parameters as follows: Rj 3 component will provide a good estimate = cms, Rg - 5 cms, L 6 to 60 cms. From of the streaming flux. For shorter ducts a = 0 to a = Rj , the total dose components 2A and 3C together, will increases; the increase is steeper for Drovide a good estimate of the streaming ducts. It remains practically longer flux. For a »R^ Dl, D2A, D2B, D3C constant in the annular region and falls and D3D decrease with distance; D3A down rapidly for longer ducts increases slowly and reaches a constant = beyond a R-g, reaching a constant value, value. D3B also increases and reaches a and slab given by infxnite plane source constant value. Of these two components of cms. In the shield of thickness L D3B is the predominant one. It accounts annular region, thegdose is approximately for 92*/. of the total dose while D3A proportional to l/L . accounts for about 8% for longer dis- tances (L = 6 cms). This shows that for :''ig. depicts the relative 3 'a'^ R-g, the presence of the duct has various components contribution of the little influence on the total dose. to the total dose for a duct of Rj = 3 - cri;s, = 6 cms. These cms, Rjj 5 L Ref erenc es components are denoted by Dl, D2A, D23 etc. At a = 0, D3 predominates. This accounts for 50/. of the total dose for 1. Rockwell, III:Reactor Shielding L = 6 cms and 64/. for 1 = 60 cms. D2 Design Manual, McGraw Hill Book Co., contributes approximately the same New York (1956) 134 . Price, B.T., Horton, C.C. and Spinney, 4. Tsuruo, A., Shindo, I-I. and Kawabata, K.T., Radiation Shielding, Pergamon Journal of Iluclear Science and Press, ::ew York (1957). Technology, 2 (9), P. 325-330 (Sent. Tsuruo, -Lkira-, Shindo , i-iitsuo; 1965) Zawabata, I-Iasahiro, Journal of 5. Shindo, I-I. Tsuruo, A., Lliyasaka, iluclear Science and Technology, 2 (4) Shunichi et al, Nuclear Science and P. 121 - 126 (April 1965). Engineering 27, 450-463 (1967). 135 MULTIPLE SCATTERING OF 12 TO 40 MeV HEAVY IONS THROUGH SMALL ANGLES B.W. Hooton and J.M. Freeman Nuclear Physics Division AERE, Harwell, Didcot, U.K. and P.P. Kane Physics Department Indian Institute of Technology Powai, Bombay-400076 and AERE, U.K. Collimated beams of heavy ions were allowed to pass through thin foils. The angular distributions of the transmitted beams were measured with a position sensitive silicon detector. Oxygen, chlorine and iron ions of energy between 12 to 40 MeV were used in conjunction with carbon, aluminium, nickel and gold foils of thicknesses between 12 to 250 |ig/cm2. Values obtained for the half-angles of the distributions at half height are in fair agreement with the recent theoretical predictions of Meyer (1971). The data deviate substantially from the values calculated on the basis of the Moliere theory (1948) and even more markedly from those based on the theory of Nigam, Siindaresan and Wu (1959) • Reasons for the success of the recent Meyer theory in the interpretation of the new data will be clarified. (Angular distribution; foils,- ions; chlorine; iron, oxygen; measurement; moliere theory; scattering; multiple.) Introduction Experimental Details An experimental investigation of mul-' The experimental arrangement is I tiple scattering of heavy ions in foils shown in Fig. 1. An analysed beam from ! is important not only for the basic the tandem, after passing (in some of thi atomic physics interest, but also from experiments) through a 0.5 ^m Ni foil to j the point of view of a detailed under- produce a umiform and adequately i standing of the behaviour of ion beams in attenuated forward beam, was collimated | targets used in nuclear reaction studies. by two rectangular apertures 4 mm high [ Further, since foils are used for and 1 mm wide, with a spacing of 124 cm. stripping in the high voltage terminals The beam then passed through a target of tandem accelerators, and terminal foil mounted in a scattering chamber on voltages of twenty or even thirty million a moveable arm which could carry upto volts are now considered possible, such three foils at a time. After multiple an investigation is likely to be useful scattering in the foil, the diverging in the estimation of beam emittance in beam passed through a 202 cm length of future accelerators. We are not aware of beam pipe to a position sensitive any published work in relation to heavy silicon detector (PSD) with an active ion multiple scattering in the energy surface of 5.0 cm by 0.75 cm mounted wit range from about 5 MeV to 70 MeV. In the its long axis horizontal. The amplitudes f literature a study-'- on multiple scatte- of a pulse taken from the end of the ring has been found at aroirnd 4 to 5 MeV. resistive surface layer of the detector ; An investigation^ with a photographic was a measure of the position along the plate has been made of the multiple detector at which an individual ion scattering of fission fragments with impinged. From the distribution of the kinetic energies of about 81 MeV. scattered beam along the line normal to ) 164 MeV oxygen ic. 3 and 400 MeV argon the beam direction and the measured oi ions have also been used in another distance from the foil to the detector, ) c( experiment^ using a similar technique. the angular distribution due to multiply pj ) 5a ' 1 pe Ma I re: 136 Fig. 1. Schematic plan view of apparatus. coo scattering in the foil was simply obtained, ij; In order to prevent pile-up distortion and damage in the PSD, total counting rates were limited to 500 per second or less. The target foil could be rotated about a horizontal axis so that its normal moved from the direction of the beam through an angle upto 70 Thus the effective foil thickness seen by the beam could be varied from the actual thickness t to a value of almost 3t . The thickness of the target foils were measiired in a separate Rutherford type scattering experiment. The mean thick- 100 200 nesses of the scattering foils in |ig/cm CHANNEL NUMBER turned out to be 12 for carbon, 41 for aluminium, 45 for nickel and 127 for Fig. PSD spectrum obtained v;ith gold. 3. 12.5 MeV oxygen ions on Aluminium with an attempt for G-aussian fit at Figures 2 and show typical spectra 3 the centre of the peak. obtained with the PSD detector. In Fig. 2, we see spectra obtained with a 12 tig/cm^ carbon foil and an Fe beam this peak is around 1/4 mm. The spectrum in Fig. 2(b) was obtained with the plane of the carbon foil normal to the beam. The width due to multiple scattering in the scatterer was obtained by subtracting quadratically the 'foil out' width from the observed width. Fig. 2(c) shows the distribution obtained with the foil rotated through 60° so that the effective thickness seen by the beam was doubled. The half angle of scattering ©1/2 is defined as that corresponding to the half vfidth at half height of the observed — distribution, after correction for the tf^ Soof 'foil out ' width. CHAnc >u«a£R The overall uncertainties in the half-angle results are estimated to lie Fig. 2. Scattered spectrum obtained for between + 5/. and + 20/. . The accuracy no 37 MeV Fe beam with a) of the target thickness measurements was scatterer b) carbon foil placed estimated to be + 5/. for aluminium, nickel incident beam normal to the and gold foils, and + 10/ for the carbon through c) carbon foil rotated foils. 60°. of 37 MeV (calculated energy at the Discussion and Conclusions center of the foil). Fig. 3 shows the PSD spectrum obtained with 12.5 MeV A comparison of a few typical values oxygen ions on 50 [ig/ cm alumini\im and a of meas\ired half-widths with those^ Gaussian fit attempted near the central calculated on the basis of Moliere and peak. Fig. 2(a) in fact shows the NSW^theories is presented in Table I. natural width of the beam obtained in The NSW calculated widths are larger than this experiment without any foil scatte- the measured values by more than a factor rer. The half width at half height of of two in most cases. The Moliere widths 137 . . ) . . ) Table I A comparison of measured values of ©1/2 with those computed on the basis of the Moliere and the NSW theories Ion Ener^ Target Target Moliere NSW Measured ( MeV j foil thick- calculated calculated ei/2 ness ( ng/ cm^ ( degrees; (degrees) ( degrees 0 12.6 C 12 0.0782 0.110 0.054 0 12.6 C 35 0.142 0.200 0.110 0 12.6 Ni 45 0.470 0.162 0 21.8 Ni 45 0.262 0.099 CI 13.0 C 12 0.175 0.260 0.100 CI 21.8 C 12 0.104 0.155 0.066 Fe 37.3 c 12 0.096 0.140 0.043 ^ Fe 37.3 Ni 90 O.56I 0.820 0.241 are closer to, but substantially larger than, the measured values. Serious disagreement with the NSW theory had previously been noted by Kerr et al^ in their studies of multiple scattering of fission fragments of 81 MeV energy from silver and gold targets {94 4 ^ 4 848). These authors had tried successfully to restore agreement with the Moliere theory by the replacement, in the theore- tical formulae, of the primary nuclear charges of the ions with their effective charges. Bednyakov et al had made a similar attempt in the course of the analysis of their experiments with 4 to 5 MeV nitrogen and oxygen ions on alumi- ( oC:^ In a of the nium 30). study T scattering of I64 MeV oxygen ions and REDUCED TMICTNESS 400 MeV argon ions from zapon. aluininium, nickel and gold (2 .9 <: 30.8) , Simon5 Fig. 4. Comparison of experimental had noted that the NSW theory gave widths values with theoretical that were upto 60/. too large. calculations In order to compare our data with References the Meyer theory, the experimental ©1/2 and t values were converted to 61/2 1. Bednyakov, A. A. et al., Zh. Eksperim and T values. The resulting values are i Teor. Fiz. 50, 589 (1966); Soviet plotted in Fig. 4. The full curve repre- Phys. JETP 2^7^91 (1966). sents Meyer 's^ theoretical calculations. 2. Kerr, D. et al, Zeit . Naturf. 22a, The error bar shown on one of the oxygen 1799, (1967). on carbon points is an estimate of the 3. Simon, W.G., Phys. Rev. 1^, 410, total experimental error, which was (1964) larger for carbon than for the other 4. Moliere, G. , Z. Naturforsch. 2a., 133 i foils. The overall agreement with the (1947). theoretical curve can be considered to 5. Nigam, B. P., Sunderasan, M. K. and be satisfactory, within the experimental Wu, T, Y., Phys. Rev. 115 , 491 (1959) the possibility uncertainties. However, 6. Meyer, L. , Phys. Stat. Sol. 44b, 253 of a z-]_ dependence is not excluded, since (1971). the iron widths tend to lie slightly below the theoretical curve and the Discussion oxygen points are mostly above it. B.K. Godwal A more detailed report will appear elsewhere How do the quantiim mechanical effects appear only after a certain energy ? | 138 P.K. Kane The important paramet.er is tiie ratio of the de-Eroglie (reduced) wavelength to the significant dimension i.e. collision radius in this case. When this ratio exceeds unity, quantum mechanical theory of scattering has to be applied of course, there is no sudden transition from the semi-classical to the quantum mechanical situation. V/hen the above mentioned ratio is comparable to unity, the problem is quite complicated. S. Kukher.jee 1) has the scattering been consi- dered on the basis of unscreened - or screened Coulomb field ? 2) How is the effective charge of the ion taken into account ? P.P. Kane 1) The ion-atom interaction includes a screening factor. 2) The Lindhard prescription for calculating the parameter a, the screening distance, is supposed to take into account the ion-atom interaction fairly well. If 139 . CHARGED PARTICLE TRAl^SPORT IM ONE-DIMBNSIOITAl FINITE SYSTEMS G. Muthukrishnan , K. Santhanam and D.V. Gopinath Health. Physics Division Bhabha Atomic Research Centre Bombay- 400 085 India A semi-analytical technique for the charged particle transport in one-dimensional finite media is developed which can be applied to multi-energy mult i- region systems with arbitrary degree of anisotropy in scattering. For this purpose the transport equation is cast in the form of coupled integral equations separating spatial and energy-angle transmission. The spatial transmission is evaluated using discrete ordinate representation in space, energy and direction cosine for the particle source and flux. The collision integral is evaluated using discrete ordinate representation in energy and legendre polynomial approxi- mation in the direction cosine. A computer code based on the above formulation is described. (Anisotropy; charged particle; computer code; energy- angle; integral; legendre polynomial; scattering; semi analytical; spatial; transmission) Introduction polynomial approximation is used. Continuous slowing down approximation is The popular method for the study of used to fix the meshwidthe which charged particle transport is the correspond to different energy losses of MonteCarlo method in which the history the incident particles as they traverse of each particle is traced from the point through the medium. Angular straggling of its origin to the point where it is is neglected in the studies. absorbed or till it comes out of the medium. Because of the many kinds of Mathematical Formulation interactions involved, computer time needed will be quite considerable. To Let S(x,E,iJ.) and if)(x,E,|i) represent save computer time, condens edl case respectively the source and flux at histories are studied where a random position X with energy E and direction walk takes into account the combined cosine p.. effect of many collisions. At equilibrium, By solving the transport equations, one can study the particle transport. (|)(x,E,^) = Barish et al^ have studied the transport x'-^ particles and protons by ( x', B', iJ. ) T ( X e'^/, ]x ) dE'dx' of alpha j Js , solving the transport equations. In study nuclear reaction products - ' ... (1) their . . are neglected. S(x,E,n) = This paper describes a method of solving the transport equations for the ]J(^(x,B',tiOG(x,E^E, -^^^^)dEclXi.' charged particles. This is mainly based on the method developed for gamma ray ... (2) and neutron transport studies^. To solve the equations, discrete ordinate representation in energy and spatial transmission and Legendre Polynomial T(x^x,E''-*E,ia) = approximation in direction cosines are used. Source and flux terms are cal- culated at discrete angles but for - :^(x-^ evaluating collision integral, Legendre ^ 6(2=x',f(E',E) ... (2a) *Present Address :VEC Project, Bidhan Nagar, Calcutta-700 064 140 i G and T represent the energy-angle and Evaluation of the flux Terms space transmission kernels respectively. The 6 function in equation (2a) repre- The flux ^(x-,E , [a) is given "by sents the reduction in energy correspond- ing to the distance travelled. Because of this relationship, eqn. (1), after r^,A) /E,^) e spatial integration reduces to 0(x,E,^) = Js(f(E'),E'.n)rT-^^ ' '^ ^ ... (3) wlie -Kx-x) e P represents the space transmission kernel. In the transport study the mesh widths are so chosen that the delta function conditions are always satisfied; in other words, one can always find a source at x' with energy E' such that by the time the particle reaches the Here X represents the macroscopic position X without catastrophic collision non-elastic scattering cross section. f(E', Eg) can be linearly its energy would have been reduced to E. interpolated between En-'s If x' and E' are the initial position as and energy of the charged particle and X and E are the corresponding final f(E',E^) = a + bE' (12) values, then 0-= {Ei(2lrvK'E^,)--Ei(2UK^Eg)-||[ E x-oc/ _ f' - dE ... (4) AEl (13) _ _ ej_NJ. U(2tn^-uyil ..(5) 1 kK'2- (14) where the various notations have the To start with, while computing, the is divided various usual meaning. Equation 5 can also be medium into energy rewritten as bins and into corresponding meshes for one particular direction cosine of say [i = 1. Thus there will be one to one correspondence between the energy bins = iT^(K'E') (6) -If and the mesh vfidths, when the source term is interpolated linearly for energy and space transmission in that direction. substituting this in equation 4, But this no longer holds good at other 'X.--X. _ direction cosines. Hence the following procedure is adopted. Fixing the energy groups say Eg' and Eg' +1 for contribut- ing to the flux at xj , the minimum and maximum distances that particles have to KK'^ I ... (-7 travel so that the delta function condi- tion will be satisfied, are computed As stated earlier we make discrete using equation 7. ordinate representation in E and Legendre Polynomial representation in |i Thus the locations of the particles as follows: can be calculated. They may be either in one mesh group or in two adjacent S(x^,E^,^) = "Z:^S^(x^,E.)P3_(u) . groups. Taking a general picture, let us assume that the locations are in the adjacent mesh groups say between xj = ^(x^,E.,n) r^^^(x^,E^)P3^(u) ^'^^ and Xj ^^'^ -^j '+1 -^i '+2 corres- ponding respectxvely to the two energy . (8) limits Eg' and Eg' +1. Then the linear interpolation of the source term can be the out follows : , 3-,(x.,E.) and 0i(x.,E.) are carried , v / \ Legendreire coefficients ofox the somsource ajid flux respectively corresponding to the E^g'+l-E^/ . . .(15) spatial position i and energy group i Using linear interpolation of S(x',Eg'+]_, li) and S(x',Eg',!a) in spatial co-ordinate and converting Ei.E v+i spatial parameters into energy parameters . (9) using 12 and after substitution in(lG) and integrating we get 141 replacing ^(xj,E',ia') by Z Pl(^o)=Pl(n') .Pl(^i) ... (24) (16) Expressing S(xj,Eg,ii) in terms of Legendre coefficients, we get where A, B C and are constants, depending SnvC^i'Eg) P^(^) = on Eg's. E 0.47665 ZaJJc^^Cxj.E') . Hv(/u') C alculation of Source Terms WPtHln.''al^^'^^^'^'"'...(25) S(x. ,Eg,!i) = Jj0(x,E',u' )G(x^,B'-^Eg,^-^^) i-Iultiplying 25 by Pi(|J.) and integrating over (i dE'd-O.' ... (17) V/here G is the energy-angle trans- Sj(x., Eg) =0.47865 T^a^ Jj^n^^j'^'^ mission kernel. G can be split up into tvjo terms and Fp, P-j. I'epresenting the probability that the energy of the X l^g ||(E')xPj_(n')P^(|i')dB'dn' particle changes from B' to Eg as a result of scattering and E2 I'epresjenting E,, (26) the probability of the direction changing . from O.' to XI due to scattering. = 0.478.5 IS^.I j 0J-J.E'}r.et(E'A .• (- . G( X . , E Bg,Xl.^-n.)=Fj( E '-^E ) ^2 (18) ... (27) After Tucker <^(*j>£^and |^(E') can be linearly inter- polated between Eg' and Eg'+l. The cross ''Eg) dE (19) -ne section is assumed to be constant between Eg' and Eg'+l. 0.478656^^^0"-'-^ ( -a-<-=>-0-) (20) (23) Where is the energy spectre of the secondary particles and |j.o is the cosine of the angle betv:een the emitted and the incident particles, that is between JCI and-^- 'Sine is the non elastic scattering cross section. Equations 19 and 20 together give the differential spectra of the cascade particles. The evapora- tion process is not considered. Substituting for ^^(x^.,E') and f|(E') and integrating over Eg's, we get The angular distribution can be represented by e3(no-l) = Z a^P^da^) ... (21) 1=0 where a.^^ is the Legendre coefficient and - ^3'+'*'^a'+i/2 . •• (30a) is given by +1 c. = t^''i'h')^i(^r) ... (30b) ai = ^ J'e5(i^o-l)p,(,,) d^, (22) substituting 19, 20 and 21 in 17 and . . . A(dFl/d£) C - /a- P ^ Conclusion This paper describes a method that is being developed to study the proton + ^(Eg,).^ ... (30c) transport through various media. A computer programiie is being developed for this method. - "Al A (aN/4t) C'33 - ^ ' - References 1. Adler and Pernbach, "Methods . (30d) in computational Physics" I-Iethod of Computation 2. Barish, J., Santoro, R.T., Alsmiller, F.S. and Dividing the nedium into various Alsmiller, E.G., Jr. "Trapp, meshes, such that the variation in a computer Program for the transport of alpha particles and 2 W(K'Eg) is uniform, the transmitted protons vrith all flux is calculated at various meshpoints, nuclear reaction products neglected"ORWL-4763 The angular straggling is neglected in (1972). Gopinath, this case. Having computed the 3. D.V. and oanthanam, K., rluclear Science uncollided flux, at various mesh points and Engineering the first collision source terms are 42, 186 (1971) 4. Yucker, V/.R., computed analytically at these mesh "Empirical formulae points for various direction cosines. for secondary nuclear production cross sections" Proceedings of the Then iteration is carried out . special sessions of Accelerator shielding. Presented In integrating the right hand side at the 1965 V7inter meeting of the American of equation (4]l the relativistic correct- Nuclear Society AI^S-SD-3(1965 ) . ion to the dii/dx formula is not included; however this correction also can be incorporated in which case also the integral can be carried out analytically 143 PASSAGE OF HEAVY CHARGED PARTICLES THROUGH MATTER Shankar Mukherji and Brijesh K. Srivastava " . . Department of Cjhemistry Indian Institute of Technology Kanpur-16, U.P., India The energy loss of charged particles (much heavier than electrons) at energies where electronic collision predominates may be studied conveniently by separating the particles into two groups : completely stripped particles and partially stripped particles. Bethe's quantum mechanical stopping power equation is of limited applicability for the first group of particles and inapplicable for the second group. A general stopping equation valid for all ions upto relativistie energies has been developed which predicts the experimentally measured stopping powers and ranges of partially stripped heavy ions accurately. Prom the detailed analysis of the equation a simple formula to predict the number of orbital electrons with velocity less than a given velocity in an element of atomic number Z has been developed. Assuming the above equation to be valid for all the orbital electrons except the two K-shell electrons, it has been possible to calculate the mean excitation potential for any medium. (Charge; charged particle; collision; electron; ionic charge; ionisation potential; stopping power; stripped particle; velocity) Introduction Formulation For a completely stripped and com- Bohr's^ semi-classical stopping- paratively light ion like a proton or an power equation is alpha particle moving with velocity V the energy loss per unit path length in a medium containing n atoms per unit volume is given by Bethe's-*- equation: ff = np^{z:3(in.5ixr^.r3(in - 4tiZi^ e4 n ...(2) ^ 2mV^ , mV in which the symbols stand for: In the above equation, I, m and e ^2nz!el iV^,^,^'2,Z£ signify, respectively, the mean exci- ^. ...(3) tation potential of the medium of atomic number Z2, the mass and the charge of Further, ze is the charge of the parti- the electron, and Z-[_ is the atomic number of the moving ion. Mukherji and cle, V its velocity, Ug is the orbital Srivastava^ have shown that modification velocity of the si^ electron of the of a semi-classical stopping-power medium and Vq = e^/ti; m and e are the equation of Bohr3 leads to a general electronic mass and charge. The terms stopping-power equation valid for par- within the square brackets, if less than tially-stripped heavy ions like the unity, should be replaced by unity. The fission fragments. However, neither of summations were replaced by Bohr^ with these equations holds for many ions which integrals are heavier than alpha particles (i.e., ^ S, -'-"0 etc.) at energies which are too (in (in . low for the use of Eq. (1) and too high ^ .2uj-2) ri^L^J"!) for the equation of Mukherji and 's Srivastava^. This work attempts to present general stopping-power equations (In appropriate for different ions at X 'n^Lxj~^)dn (U ) + y (In energies at which electronic collision is the predominant mode of energy loss. [^J"^)dn(U ) ...(4) 144 ; , — where n(Ug) is the number of orbital The upper limits U^' and U " must be electrons of the medium with velocity- fixed corresponding to the actual physical less than Ug. It has been shown^ that situations so that the integrals make only in general, for a mediiim of atomic positive contributions towards the number Z^, nCUg) is given by energy-loss. The following cases may be considered: n(Us) = f(Z2) Ug/V^ ...(5) A. x> 1 ^2^0- where t^l^) = 0.28 2/3,^for Z2<45.5, (a) V> Z„ V X ...(6) 2 o Since x> 1, for V> J, would include all values of U upto the Velocity of the and f(Z2) = l^^^foT Z^;^ A5 .5 ...(7) K-shell electron which may be taken as Z2V0. Since (il)^ = 2mV^ where Ig is Is th The integrals in Eq.(3) may be written the ionization potential or the s as three integrals keeping in mind that electron, one obtains: ...... [x/Tig]-l = 1 for (x/rig) 1, < s 2 o ^2-0ZoV, = {ln(§I)2Uu„ = In2mV ^1 s flZ^ 2 j(ln dn(U ) + n f (In Ti . s s ...(10) in which = T stands for the mean ionization dn(U ) potential of the medium of atomic number Z^ and is defined by s=Z2 f(Z-) u' o o Z2 In I In ...(11) ;^(ln ri/[x]-2) dUg + Z [ 5 s=l 0 0 o Z V U " As for J2, since , in i^)^ ^-1) (In rig2)dUg + ln(iig3 jiUgJ would be positive for all possible values -1 of U„. Further, since the lower limit 2Vx for Ug in is 2Vx~ and this already corresponds to the highest possible value (8) for Ug(= Z2Vq), becomes redundant. Thus 2Vx~-'- „ ^2^07 2 Designating = r^^^lx]-^) dUg. J r r n /2Vx2| -, 2mV J^(ln J. = C ^ in(u-) jdU^ = In— -1 2Vx ...(12) = (m / = 0 U " 1/3 s ^2^0^ ^2^0- = (Inri 5 dU Eq.(2) (b) and f , — > V 2Vx . n 2 \ 2 o \ 2 o Sinceo x^l,\ —2 p 2 "2 becomes / / one needs to consider all the three inte- grals. In the case of Jn , for a given V dE 27.^2 e^n ^^h^ the term Ini^^) would be negative ( + "^3' s dx 1,2 Y J-]_ ^2 -1 mV for all values of Ug lying between 2Vx and 2.2^ Hence one must use Ug'= 2Vx~-'- ...(9) 145 V and get For x<(l, becomes superfluous, t.tk-;t^ t- t ^v„«^jjjg / while J]_ and become identical.identical, _2o 2mV_ = ln(§X)2 = 4VX-1 ...(13) J,=J2=j-ln(§I)2 ^^^^ ,_,(^g^ I s J s Since 2Vx~''"<^ ^'^^^ ^2^o ^2^o' "^2 (b) include all possible values of . Hencej, J-. _-]_ ,. In this case or J„ requires an 2Vx appropriate upper cut-off value for U which makes the logarithmic term zero.Q = |ln(^)^jdUg = 4Vx~-'-(l+lnx) Thus, ) ..(14) In the case of J . one finds that Jt=Jo= f |ln(^)^[dU =4V ...(20) 7.-V ^1/3 J-^yC u^^s U„"= Z2V„ if V = ^2"^o 0 Comparison Hence with Experimental ' Stopping-power Data U "=Z V s^ 2 0 = \ 3 -ll ^^'^ convenience, the various (^TT •••^5;Mr') 2V I'^ s'^^J s stopping-power equations obtained by putting the values of J^, J 2 and in T-.v. Eq.(9) are shown below: In the actualJ.T evaluationT4.- ofj.T-4.-it is m. convenient to consider separately the A. xy 1 contribution of the two K-shell electrons from that of other electrons with Z^V^x """" ^ ^-^ ^^^^2''^^/i^„2^4^v„ 2mV^ velocrtles"usy2fx-r"^Thu;7 (a) V_) || = In- (Z2-2)V o , • ... (21) J,= ^ln(P)VlldU^ Z.V^x, ^^Z,V^xl/5 ^r^2 . -1 2Vx~ ^t:. o 2 4 f(Z,) '^''^ ^ - i'r2V_s3 -ll = ^ L3(Z,-2)+3(Z„-2) In \ 01 ' "-^^2 ,, /i o + 21n<( )^x ...(16) dx ' 2 Vo(^2~^ ^ y J ^^2 ^ 2 0 2f ( Z ) where the velocity of the (Zg - 2)th 6ln(Z,V )-Z„ Inx 1 -f^Z^ ln(2V)j electron, co\mting the outermost electron ' 2 0' 2 V^x^ ^2 as the first one, is given by U„ = ( 00) (Z2-2)Vo , ^/ „ v— as obtained from Eq. (5). 7 v 9 a r( 7 ) ^^^2' 4Tiz^e^n ' dj ( 2 0 , _ .tl^21 . ^'^^r.) Z2VQ 2 • dx ~mV^ (c) V<( - (3x-l/5^x-l) In this case both and would require upper cut-off values for U and ^ ...(17) has been considered by Mukherji ana Srivastava:2 A. x<^l dE _ ilEzVn f{Z2± (3x-l/5^x-l) , , Vo . dE 4uz^e4n 2mV^ , , 2 V/ V 2 • dx~ j^y2 ^2 J ° ...(17) ^2^0 " . ...(23) . 1. x 146 11 . dE 16 z en (b) V< fiz^) ...(24; where I„ is the mean ionization poten- dx ^Tr2 V m V o ^2 tial of a medium of atomic niimber Z2 The term z which figures in these equations explicitly as also implicitly through the Table I shows a comparison between parameter x stands for the "effective the experimental values of the stopping charge" Z^ff if the ion is partially- powers of 19f ions in Al from Northcliffe^ stripped and equals Zn if the ion is along with the corresponding calculated completely stripped If has been shown values using Eqs.(21), (22) and (23) in that appropriate cases. A similar comparison is shown in Table II with the experimental ^O^g Z^^^ = f(Zi) (25) data for ion in Al from Northcliffe5 f and calculated values using Eq.(21). Further, it is found that the energy-loss where fCZ^) = 0.28 z2/3 for Z-l_^45.5 and data of Hower and Fairhall" for comple- tely stripped ^Be ion in Au and Al foils = fCZn) Zi^/^ for Zi>45.5. Thus, the are in good agreement with our calculated criterion for complete stripping is values, as also Northcliff e 's5 values for 14n and ^°0 ions in Al. The experi- ,efi = Zi = f(Zi) (26; mental stopping-power data of Kelley . et al ' are also in good agreement with the corresponding calculated values of from which it follows that the velocity ours in the case of 12c, 1% and loO V above which the ion remains completely ions in 94.6 \im thick silicon. stripped is ZlVo Table I V = ...(27) m fTz]! Calculated and Experimental Stopping powers for ^^F Ions in Al Hence, at ion velocities above Vm z in the above equations and in Eq.(3c) (dE) must be replaced by Zi^ while below this (dE) Z^ff as given Ion Energy Mx' exp, it should be replaced by '•dx'calc Appropri- by Sq^(25). Eqs(2l) and (23) contain the (MeV/amu) /MeV cm f(Z,) ff(Zp)(Zp) , . 2 2) [ |ln(|mu/jdU3 Table II 5 Calculated and Expej'imental Stopping powers for %e in Al + 2 ln(13.6 Z,"^)] ...(28) (dEs Ion Energy Mx' exp (^) Further, it is found that the values of (MeV/amu) Mx'calc Appropri- I calculated from Eq.(23) are well .MeV cn^ /MeV cue ate represented by the expressions mg ' mg equation 9.92 3.51 3.46 Eq. (21) = (28 Z2^^^-6), for Z2<45.5 9.23 3.86 3.65 1 ^ ...(29) 8.13 4.00 3.98 II = (323+10. 33(Z-45) )for Z^^ 45.5 7.19 4.21 4.32 II 6 .20 II ^ ...(30) 4.86 5.02 5.38 5.04 5.22 1 3.50 6.51 6.74 Tl 147 References 1. Bethe, H.A, Ann. Phys. , ^, 325 (1930). 2. Mukherji, S, and Srivastava, B.K., Phys. Rev., B^, 3708 (1974). 3. Bohr, N. , K. Danske Vidensk. Selsk. Mat. Fys. Medd., 18, 8 (1948). 4. Mukherji, S., Phys. Rev. B12, 3530 (1975). 5. Northcliffe, L.C., Phys. Rev., 120 . 1744 (I960). 6. Hower, CO. and Fairhall, A.W., Phys. Rev., 128, 1163 (1962). 7. Kelley, J.G., Sellers, B. and Hanser, P. A. Phys. Rev., B8, 103 (1973). i48 NEUOEON THERMAIIZATION IN HTDROG-EKOUS MODERAIORS L.S. Kothari Department of Physics and Astrophysics University of Delhi, Delhi-110007 , India Ihe mechanism of neutron scattering from various moderators is a poorly understood subject. Ezact calculations of neutron scattering properties of commonly used moderators namely light and heavy water and graphite are extermely difficult. Calcula- tions of neutron scattering from light and heavy water are complicated because of our imperfect understanding of liquid structiores. Therefore one has to depend on various approxima- tions or models for such calculations. This paper first stresses on investigations carried out in this field for hydrogenous moderators. A scattering kernel for light and heavy water and its mixtures developed by us considering the low-frequency collective oscillations in the quasicrystalline approximation using Debye distribution has then been described. The total scattering cross section, diffusion coefficient and various other physical parameters calculated on the basis of this kernel has been presented and compared with the available experimental and theoretical results. (Cross section, diffusion, kernel, lattice vibration, model, moderator, neutron, scattering, thermalization) Introduction Gas Model Light and heavy water, along with This model for solids and liquids graphite are the three important modera- was first developed by Wigner and tors. As it happens, neutron scattering Wilkins Jr. around 1944, and has been from all these three is poorly under- very widely used. This model implies stood. Graphite has a layer structure the complete neglect of chemical and its lattice dynamics is quite diffe- binding. Radkowsky5 suggested that one rent from that of more isotropic solids. could partially take accoiint of the Because of this, considerable difficul- chemical binding in liquids by treating ties arise when one wants to calculate the mass of the scattering unit as a neutron scattering cross section of free parameter, and fixing its value by this material, and the problem is still adjusting the calculated values of the far from being closed-^. For light and total scattering cross section to agree heavy water, or mixtures, it is again with the observed data. Nelkin4 deve- difficult to calculate neutron scatte- loped another scattering kernel in which ring cross section precisely, because he included the contributions of of our imperfect understanding of the hindered rotation and intramolecular liquid state. However, a number of vibrational modes of the water molecules models have been developed to explain in the harmonic approximation. The neutron scattering from these materials translational motion was treated on the and we will consider them first. Later basis of gas model. To obtain an agree- we will consider some other hydrogenous ment between the calculated values of moderators. the total scattering cross section and the observed data, he had to divide the To study neutron thermalization, energy range into three regions and one needs information about the scatte- choose different numerical values for ring kernel, i.e. the scattering cross the parameters involved in each energy section for a neutron of energy E being region. This kernel, which is now scattered into a unit energy interval referred to as the Nelkin kernel, has about some other energy S ' . Calc\ilating been very widely used for thermalization this is a major problem in itself. For and diffusion studies in water and is water three different approaches have able to explain the results of pulsed been adopted: (i) gas model, (ii) sca- neutron experiments very satisfactorily. ttering kernel based on experimental data of the scattering law and (iii) Recent pulsed neutron experiments quasicrystalline model. by Fujino and his co-worker s^ in water 149 poisoned with non-l/v absorbers and the made to study neutron thermalization and measurements of temperature^coefficient diffusion using a scattering kernel of water moderated thermal reactors has based on this model. brought out the inadequacy of the Nelkin 20-22 kernel^ . It is now generally recognized We have recently developed that Nelkin kernel works satisfactorily scattering kernels for light and heavy in cases where equilibrium neutron water and mixtxires. We treat the low spectrum does not differ appreciably from frequency collective oscillations in the a Maxwellian - but in such cases the cal- quasi-crystalline approximation using a culated results are insensitive to the Debye distribution function. The rota- scattering kernel, provided of course tional and intramolecular vibrational that it satisfies the detailed balance modes are taken as discrete levels and condition. are treated in the harmonic approximati- on. Using these kernels we have cal- Many modifications of the Nelkin ciilated the total scattering cross kernel have been suggested, among others section and have studied the pulsed by Kosaly and Valko', Ardent e and neutron problem in H2O, D2O and in H2O GallusS, Esch et al9, Gotoh and Taka- poisoned with non-l/v absorbers. hashil'-'. Using an approach very similar to that of Nelkin, Hone ckll worked out a The total neutron scattering cross scattering kernel for heavy water wha ch section for H2O and D2O are shown in has also been very widely used for ther- Figs. 1 and 2 respectively. Also shown malization and diffusion studies. for comparision are cross sections based on a pure Debye model with = 200 Z ScatteriniS: kernel based on Experimental (case A) and Q-q = 250 K (case B) and ex- Data perimental results due to Hughes and Schwartz23, Neill et al24 and McReynolds Egelstaff and Schof ield"*"^ were et al25. amongest the first to develop a scatte- ring kernel for water based on the experimental data on scattering law. Koppel-^5 and also Haywood-'-^ have done considerable work in the direction. However, scattering kernels generated by this method depend strongly upon the accuracy of the experimental data and have only been rarely used for therma- lization or diffusion studies. Quasi-crystalline Model Quasi-crystalline model for water was proposed as early as 1933 by Bernal and Fowlerl5. Such a model is based on the idea that liquids behave as disor- dered crystals for times shorter than the diffusive time. In the early 60s considerable work, both theoretical and experimental, was done which lent this model. Larsson and support to 0 0004 OCOl 001 01 OS Energy Dahlborg-^^ found that the frequency £ CeV) I spectrum of water at - 3°C was very similar to that of water at +20C. Some Fig. 1. Total neutron scattering cross "5 dif f erenipeJ have later been reported by section for water at T=200C. Burgmann-'-' others-'-" '-LS. Curves (i), (ii) and (iii) re- and j present respectively the resiilts of present calculations based on j Following these and similar other , studies, a number of workers have tried our model and cases A and B. Cur- to explain neutron scattering in H2O and ve (iv) represents the values DoO, particularly the quasi-elastic sca- obtained using the gas model with ttering, on the basis of quasi-crysta- mass 18. • , X denote the experi- , lline model for these liquids. Total mental values of Hughes and Schwartz23 and Neill et al24 res- neutron scattering cross section as well j^, as the average cosine of the scattering pectively. For comparison, the angle in the laboratory frame of refer- experimental values ( ^ ) of till Whittemore and McReynolds25 for j ence has been calculated. However, j recently no attempt seems to have been . , 5*^C are also shown. 150 . coefficient and G is the diffusion coo- ling coefficient. The value of A^can be calculated by solving the integro-differential equation^"* 30 [2) where ^3 is the macroscopic scattering cross section, D(E) is the diffusion coefficient for neutrons of energy E, >- OOOOl O.Ol SgCE'-^E) is the scattering kernel and Energy, E (ev) fir ,E) is the neutron fliix at "T corres ponding to energy E. As an example we report in Fig. 3» Fig. Total neutron scattering cross calculated values of (curve i) as a section for heavy water at T= function of B^ in at 20°C. along 20°C. Curves , with the experimental data51~33. Curve represent (iv) represents calculations based on respectively the results of pre- Honeck kernel whereas curves (ii) and sent calculations based on our (iii) are based on pure Debye model with kernel and cases A and B. Curve e-Q = 200 (case A) and 250 K (case B) res . . , represent the pectively values obtained using the gas model with mass 20. • denote the experimental values of Hughes and Schwartzes. For comparison the experimental values ( -A ) of Whittemore and McReynolds^S at 9°C are also shown. P-ulsed Neutron Problem The pulsed technique for measuring neutron diffusion parameters in modera- ting materials was first introduced by von Dardel^o around 1954. Because of its simplicity, it is still very widely used. The experiment consists in intro- ducing a burst of high energy neutrons inside a medium and studying how it de- cays in time. If one waits for a suffi- ciently long time, the decay becomes exponential and one can determine the asymptotic decay constant for the pulse. (For small assemblies the problem is more complicated and we will not go into those details here^''^^. This decay 015 constant K.a is measured for assemblies of different sizes and the results are usually analysed in terms of a series Fig. 3. Dependence of Aoon buckling, B^ expansion^^ '^'-^ for heavy water at 20°G ( isZ^ = 19 sec"-'-). Curve (i) is based on (i; OUT kernel. Curves (ii) and (iii) are for cases A and B respectively, where B^, called the buckling of the Experimental data are due to assembly, is a measure of its size. Kussmaul and Meister^:r( O )jJones'2 = 0 corresponds to infinity assembly (^ ) and Parks et al53(A). Theo- and larger values of b2 correspond to retical results using the Honeck smaller sizes, ^(v) is the macroscopic kernel ( curve ( jv) ) are also shown absorbtion cross section for neutrons of for comparison. velocity v. It is assumed to vary as 1/v with velocity. Dq is the diffusion 151 j . ^ By fitting a polynomial in (eq. 1) 2.5 to the calculated or the experimental data on , one can determine the values 2.* - of Dq and C. In figure 4a are given the experimental values of Dq at various tem- peratures measured by different groups, along with our calculated temperature variation of Dq. It will be observed that the temperature variation of Dq cal- culated on the basis of the Nelkin kernel can not satisfactorily account for the experimental results. In general the values based on the Nelkin kernel are larger than the measured values. On the other hand, the calculated values of C that are based on the Nelkin kernel are smaller than the measured values in fig- ure 4b. ' I .8 i L_ \ I I L ] O 10 to 20 30 SO 60 . 70 60 T(°C) Fig. 5. Temperature variation of diffusion- coefficient DqI (i) present model} (ii) Honeck kernel (Honeck and Michael^'). In this figure the ex- perimental results shown are of the following workers: \ Ganguly et al48j5Parks et al33.^ Salaita and Robeson44. J Westfall and Waltner49. ^ Mala viya and Profidj if Kussmaxil and Meister^lj ^ Raiavski and Horowitz-* •, z Silk and Wade52. ^ Daughtry and Walt- ner55 20 40 60 eo ^BaosowsowToeoM Tcmperoture 7"("C3 Pig. 4. Temperature variation of (a) the diffusion coefficient Dq and (b) the diffusion cooling coefficient 8 - C for water: (i) present model; (ii) Nelkin kernel Clendenin54. X von Dardel and Sjostrand^S a Kuchle^O; Antonov et al^'; o Meadows and Whalen^S, « Lopez and Beyster^9. X DlQughy and Kvitek^'-'; A Dio and Schopper^-'-j ooEobayashi et al^^. a Paiano and Paiano43| ar Salaita and Robeson44, x Jones32, Williams and Munno^S, 8 Bret scherzo. The temperature variation of Dq and C for heavy water is shown in figures 5 and 6 respectively. Cvirves (ii) are based on kernel whereas solid Honeck 1 2L 1 1 1 1 I I I curves are results based on our kernel. O 10 20 30 40 50 60 70 80 T(°c) It will be observed that the variation in the measured values of C is very Pig. 6. Temperature variation of the diff- large. This is because, to determine usion cooling coefficient C for accurately the value of C one must heavy water: (i) present model; extend measurements to large values of (ii) Honeck kernel (Honeck and b2, taut 29,30 in such assemblies inter- Michael'^')' In this figure the ex- pretation of results becomes difficult. perimental points are of the follo- wing workers! i Ganguly et al4°; ^g20,21 Y^-^Q also calculated neu- Parks et al^^j ^ Salaita and Sg^®" tron spectra at different times follo- son44, I Westfall and Waltner4y} wing a bvirst of fast neutrons in various io^O Malaviya and, Prof ; ^ Kussmaul H2O and D2O assemblies at different and Meister-^ . 152 temperatures. Some typical results for are shown in figure 9. Our calculated are shown in figures 7 and 8 for results are also shown for comparison. DoQ^in figures 9 and 10. Ishmaev et In fig. 10 are shown the results in D2O ax^^, measured time-dependent spectra assembly at 43.3°C for a 50 cm cube in water assembly (30x30x45 cm^) at assembly (B^ = 0.0108 cm~^) and experi- 350c. In figure 7 is plotted the time mental results of Kryter et al^°. In evolution of the neutron flux at a few puilsed neutron experiments, the effect typical energies. The calculated of adding l/v poison to the medium is results account fairly well for the only to increase the decay constant by a approach to equilibrium of the neutron constant amount f'UJIa,* However, if the pulse. The experimental results of assembly is poisoned by a non-l/v Menzel and his group55 in water assem- absorber, then the asymptotic neutron bly(7.l6 X 25.02 X 25.4 cm^) at 37.8°G energy spectrum is modified and one has are shown in figure 8 along with the to solve the Boltzmann equation for calculated results. The agreement each poison concentration separately. between the two sets of data is good. Fujino and his coworkersw) have measured, as a function of time the Menzel et al^^ found that the reaction rate R(t) in water poisoned neutron spectrum after 23 M-S of the with various concentrations of cadmium: introduction of the pulse inside the where assembly was a I'laxwellian at 37.8°G. From this they concluded that the (E)t(e,i)ciE thermalization was complete in 23 \xs. "R{t)= \ Y However, as our study shows for this large buckling that they have used, the asymptotic spectrum is not a Max- well ian at the temperature of the medium and it takes about 60 ^s for the The experimental data along with equilibrium to be established. our calculated results are shown in Fig. 11. As is to be expected, for Time-dependent spectra in D2O ass- larger concentration the Nelkin kernel embly with b2 = 5.78 X 10"^ cm""^ at gives results which are markedly 20°C were measured by Poole and different from the experimental data. Wydler5° and Wydler57 and their results tfr 1 'lO 203O4O5OtO70 8O Time (ps) = Pig. 7. Neutron„spectra cp (E,t) for = Fig. 8. Neutron spectra 9(E,t) for B 0.0256 cm"^ for water at 35 C as a 0.2238 cm-2 for water at 37.80C function of time: present model and at different times. The ex- calculations; case B calcula- perimental data of Menzel et al-^ tions. The experimental results of ( • ) are also shown for compa- , Ishmaev et al^^for various energy rison. Curves , . — . . , groups are also shown for com- respectively represent re- sults on our model, case parison: ( A. ) 0.010 ev} ( + ) 0.015 based A and B. Curve is Maxwe- ev, (« ) 0.025 ev} (X) 0.100 ev. (The normalization is arbitrary llian at 37.8^0. Curve X- and is different for different X is the asymptotic energy groups.) spectrum corresponding to B'^ = 0.2238 cm~^. (The normalization at different times is arbitrary). 153 . ' 20 - / " 30 - - 60 r -_ - / - 1OO - \* 1 L 1 1 \ 1 E(ev, Fig.' 9. Neutron spectra (p(E,t) for = Fig. 10. Neutron spectra (p(E,t) for B = 5.78xl0~3 cm~^ for heavy water 0.0102 cm for heavy water at at 20°C and at different times. T = 43.3°C and at different ( • ) the experimental data of times. (• ) the J- experimental data Poole and Wydler5°. Curve is of Eryter et al-' . Curve based on our kernel. (The norma- present kernel. (The normaliza- lization at different times is tion at different times is arbi- arbitrary) trary) . In Fig. 12 we have plotted (X{^)-Xoo) /vqN as a function of cadmiixm concentra- tion, N, at various times, where Xoo is the fundamental mode decay constant for the unpoisoned assembly and Vq is the neutron velocity corresponding to an energy kgT. Experimental resl^lts of Meadows and Whalen-^ and Larsson and Moller°*^ are also shown. For comparison resuilts based on Nelkin kernel are also given. In almost the entire concentra- tion range studied, the agreement bet- »feen our calculations and the experiment- al results is very satisfactory, whereas Nelkin kernel gives rather low values Hh)- 18 I for ( Xoo)7voN. N =200 ' 10 aloms ctTJ I Ice Recently there has been increased interest in studying neutron thermali- zation in cold moderators, with a view of producing large flux of cold neutrons. Moderators like graphite or berylli\im are completely useless for this purpose 20 since they are almost transparent to low I ( )J5) energy neutrons more so at low tempera- tures. Hence one has to rely only on Fig. 11. Reaction rate R(t) as a function hydrogenous moderators. Lot of work, of time for water assembly (B"^ = both experimental and theoretical, has 0) for various concentrations of been done to study neutron thermali- cadmium. Experimental data of zation in HpO, ice and also liquid Fujino et al^^', .. . Hp and Because of possible hazards free gas kernel (mass = 1); . 01 explosion, some countries do not _ . , Nelkin kernel} , permit the use of liquid H2 in or near present kernel. 154 . reactor cores. Further in many ways, Using the Debye model for lattice H2O + D2O ice is almost as good as vibrations of ice with suitably chosen liquid H2 (D2 or mixtures), and the Debye temperature we"-'- have studied study of neutTon thermalization in ice, neutron thermalization in ice down to 4" K. which had been neglected for sometime, The results of pulsed neutron experiments is again gaining importance. at 268° Z are shown in fig. 13 . In fig. 3600 14 is shown the calculated temperature variation of the diffusion coefficient in icev along with some experimental valuesD2-66. Time -dependent spectra in ice ass- -3400 emblies at 77 and 21° K were measured by Reichardt°5 and these are shown in figures 15 and 16 respectively. Our calculated spectra are also shown. The equilibrium spectrum at 77° K is slightly 3200 - cooler than Maxwellian at 77° E. Further, equilibrium is established in around 450 [iS. When ice temperature is below about 50° Z, it takes unusally long for the equilibrium to be reached. At 21° K, 3000 even after 2 ms equilibrium is not rea- ched . Of particular interest is the equi- Fig. 12. ( X(t) -Xoo)/voN as a function librium spectrujn of neutrons in the of cadmium concentration, at presence of a l/E source. This, the so various times. Experimental re- called, steady state spectrum is what one sults, 5 Meadows and Whalen^^j would observe in a moderator block placed $ Larsson and Moller"^. Theo- near a reactor core. We have calculated 66-68 retical results, curve , steady state spectra in ice (H2O, present kernel calculations-, D2O and mixtures) at various temperatiares curve . . , Nelkin down to 4° K and in assemblies of various kernel, curves marked A repre- dimensions. Results for ice assemblies sent asymptotic values. at 77; 21° and 4° Z of b2 = 0.1113 cm-2 26 T > 266 K 22 (uag). 4X85 X 10^ sec 197 ^ 16 - (a) 0^ /OK Z 1* o 9* . o 10 o 1 1 t 1 1 o Experimental pointsjSiWcr o 173* K 193* K 213* K 233*K 253* K 273* K (11,(111,4(111) Present calculations^' o 1 1 ' ' 1 T 0-1 02 03 OA as 06 07 2 -2 ^^-"^^0.) Fig. 13. ( vS for ice at Fig. 14. Comparison of the experimental T=2680K ( u 2o, =4. 485x10^8 ) and theoretical results of the for different frequency distri- diffusion coefficient Dq for butions: curve (i)— 'Debye fre- ice as a ^'unction of temperature. quency (one phonon kernel): 6 Silvero2. O Antonqv et alo3, curve (ill— ..Larsson and XDloughy and Kvitek^O? Dablborgl^ which includes ro- Salaita^^, • Reichardt^S, A tational modes (one-phonon Ohanian° , — present calculations. kernel): curve (iii) Debye frequency distribution (one- phonon plus two-phonon kernel) 155 . » 0» 17 1 6 To ti ti Fig. 15. Comparison of experimental and Fig. 16. Comparison of experimental and theoretical spectra at differ- theoretical neutron spectra at ent times in ice at temperatvire different times in ice at T=2£k 77°EandB4= 0.1548 cm-2. Experi- and b2=0.1548 cm-2. Experiment mental points are from Reichar- tal points are from Reichardt°5, (a cube of nearly 17 cm side) are shown in fig. 17. The experimental results are those of Whittemore and McReynolds"° It will be observed that both experimen- tally as well as theoretically one gets the same steady-state spectnim at 21° K and 4''K. It was also observed as early as 1961 by these authors'^ that the effective temperature of the neutron dis- tribution does not go below 40° K, however much one may reduce the temperature of ice. We'-'- have shown that this arises because of diffusion hardening. To some extent the situation can be changed by adding some D2O to H2O. If we consider a pure D2O assembly even then thermali- zation is incomplete in fairly large assemblies. The values of effective temperature. NEUTRON ENERGY (Ev) — 2 E (E is mean energy of the eff - TIT, Fig. 17. Comparison of the calciilated distribution and kg is the Boltzmann steady state neutron spectra in constant) in D2O ice at various tempera- ice bl6ck with b2=0.1113 cm"2 tures and in assemblies of various kept at 77, 21 and 4°K with the bucklings are given in Table I. We note spectra measured by Whittemore that, unlike in H2O ice, here there is a et al'O. Experimental points strong dependence of Tg^^ on buckling. are reported by crosses. 156 ( Table 1 (These curves are all normalized at 0.0168 eV. ) Both for lower as well as Tgf-f(°K) of Steady-State Neutron Spectra higher D2O contents, the fraction of cold in D2O Ice at Various Temperatures neutrons decreases. The optimum mixture depends upon the size of the assembly. This is borne out by figures 20 and 21, Temperature of D2O Ice i°K) where steady-state-spectra in an assembly of B^ = 0.0158 cm"'^ (cube of ^ 45 cm side) at 21 K are shown. For this assembly the 2 cm«m-2 ^ 77 V ) optimum mixture is 30% H2O + 70/ D2O. 0.0 77.2 24.1 16.9 The variation of Tgf-f with change in 0.005 96.5 54.5 53.9 C2O concentration, in assemblies of va- rious bucklings, is shown in Fig, 22. It 0.01 112.5 69.5 69.3 will be observed that in an infinite ass- 0.0158 128.6 82.1 82.1 embly Tp^^ decreases steadily with incre- ase in BpU concentration, but it fails to 0.02 138.8 89.4 89.5 attain the temperature of the medium even 0.03 159.9 103.3 103.4 in 100? D2O. In H2O assemblies, the effective temperature hardly changes, as one goes from an infinite assembly down Figs 18 and 19 show steady-state to a cube of almost 20 cm side. On the spectra in a 17 cube at 21* K for diff- other hand, for D2O, Tg^^ increases erent HoO, DpO proportions. The vertical rapidly as B^ increases. lines at 0.0017 eV and 0.005 eV corres- pond to Bragg cut-off energies in graphite For a given buckling, there is a and beryllium. For this buckling (0.1113 range of optimum D2O concentration. For cm~2) we find that the proportion of cold large B^ values, about 20'/. D2O is expected neutron flux is mazimum in case of a to give the best resiilts, whereas for mixture with 70X H2O + 307 D2O (by weight). small B^ values 90'/. D2O and 10/. H2O would Pig. 18. Steady State neutron spectra in Pig. 19. Steady state neutron spectra in mixtures with 0, 5, 10, 20 and mixtures with 30,40,60,70 and 30X DoQ s-"*^ 21°K in^an assembly 90/. D2O at 21 iCin an assembly 32=0.1113 cm~^. All the with with 2. All the cut 0.1113 cm cxxrves are normalized at the curves are normalized at the off energy Also drawn in the cut off energy, Eq . Also drawn figure are lines corresponding in the figure are lines corres- to energies of 20 and 60 kg. ponding to energies of 20 and 60 kg. 157 . . —U 1 I I I I I I I 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 E I eV) — E ( eV 1 — Fig. 20. Steady state neutron spectra in Pig. 21. Steady state neutron spectra in mixtures with 0, 20, 50 and 70^ mixtures with 70, 80, 90 and DpO at 21° K in an assembly with 1007. DpQ at 21 K in an assembly with B'=^=0.0158 B^= 0.0158 cm~^. All the curves cm'^. All the curves are normalized at are normalized at the cut off the cut off Eg. energy, E^. Also drawn in the energy. Also drawn figure are lines corresponding in the figure are lines corres- ponding to energies of to energies of 20 and 60 kg. 20 and 601^ give the lowest Tg^^ values. We also cross section is almost 30 times that of note that for certain buckling values, para-hydrogen. At high energies both here '^0.05 cm~^, Tgff remains almost cross sections tend to the free atom value constant for changes in DpO concentration of 20 b. from almost 20/. to 707. . liquid Dp ^•'^^ mixtures have been widely used as cold neutron sources in European reactors'-'-. Considerable theo- retical work has also been done on the thermalization of neutrons in H2 and D2. One has to take account of the existence of the ortho-and para-spin states of the homopolar molecules, each of which has markedly different scattering properties. A further complication Hp, D2 mixture would be the formation or HD molecules. At room temperature the para:ortho ratio is nearly 1:3, whereas at 20 K ortho reverts to para and the equili- brium mixture contains nearly 99. 7X para-hydrogen Ntolror ersrty (tV) Neutron scattering cross section"^"^ Pig. 22. Comparison of predictions by the for H2 is shown in Pig. 22, alongwith Young-Koppel scattering model s''' 3 available experimental result -7 5 with measurements of neutron The scattering cross section for para total cross sections in normal hydrogen increases hy almost a factor ortho and para hydrogen at various of 10 around neutron energy 0.015 eV. temperatures: A Seiffert'^ (para This is because of the excitation of the at 14 K, normal at 16 Kit Mc- J=l rotational level. At neutron Reynolds and Whittemore ' ^( 21 K); energies below the threshold of any rota- O McReynolds and Whittemore'''^ tional excitations, the ortho-hydrogen (higher resolution measurements)} + Squires and St ewart^^( 20. .4 K) I (ref. Moon and Beynon'-'-). . 158 Since the spin- flip interaction from observe close similarity between these ortho to para (J=l to J=0) will result in results and our calciilated results for energy gain for the neutron, it might ice, presented in Fig. 23. Here too we appear that para-hydrogen is a better find that in H2 assembly the effective moderator at low temperatures. In actual temperature hardly changes as the thick- practice this is not so, since the scatt- ness of the assembly is changed from 1 to ering cross section of para-hydrogen at 15 cm, and its value is almost the same low energies is very much smaller than as that in the case of H2O ice at 21 K. that of ortho-hydrogen. In the case of D2, in larger assemblies the effective temperature is lower than Jacrot'^5 studied neutron moderation in H2 and also shows some dependence on in H2, D2 mixttires and found, the optimum assembly size. In the case of mixtures mixture to be i H2 + £ ^2 weight (50'/ inside small assemblies (2 cm thickness), Tgff increases with increase in H2 concen- 1 ortho-hydrogen ) . On the other hand Davi- tration but in the intermediate assembly es et al'° reported the optimim mixture the temperatiire remains nearly to be i H2 + Dp by weight. This diff- (5 cm) 1 constant over a very wide range of H2 4 4 erence in optimum mixtures is attributed concentration (25/. to 74'/). This is very to different sizes of cold neutron similar to otir results for ice with b2 = soiirces used by the two groups. More 0.05 cm-2 (Fig. 23). In large size, recently Carter and Jones' ' at Harwell results are available only for low H2 con- have studied neutron moderation in H2, D2 centrations and here again T^ff shows and mixtures at 20.4 K inside a cylinde- some dependence on H2 concentration. rical assembly of internal diameter 20 cm and thickness varying from 1 to 15 cm. The effective temperatures measured by them are reported in Table II. One will Table II 50 T = 21 °K Effective Temperature in Various Assemb- 55 lies of E2, 1*2 I'iixtures at 20.4 K ^ 50 Chamber Moderator Effective Thickness Tempera- (cm) ture (E) » « / 0 / 1 H2 38 °- iO 2 H2 38 35 5 H2 37 10 37 30 ^2 ^ oV 15 H2 37 25 1 D2 1 20 11 1 1 1 1 1 1 2 D2 Content in of Mixture I %l 5 D2 10 D2 29 Fig. 23. Variation of Tgff with content 15 D2 24 of D2O in the mixture for ass- emblies at 21" E with different H2)* 39 2 H2/D2(33X values of B^. 2 H2/D2(58/. H2)* 46 Inoue et al78 have studied neutron 5 H2/D2(25*/ H2)* 39 thermalization in methane at low tempera- 5 H2/D2(467. E2)* 39 tures. They find that because of the near free rotational modes of this mole- H2)* 39 5 H2/D2(74X cule, it is able to thermalize neutrons 15 H2/D2(8.5X H2)* 30 to lower temperatures than H2 + ^2 This is a very promising material 32.5 tures. 15 H2/D2(18.6/. H2)* and more studies may be made on this in coming years79. * Atomic percent 159 . . . ^ Neutron thermal izat ion has also been 10. Got oh, Y. and Takahashi, H.,Nucl. studied in a nimber of other hydrogenous Sci. Eng. 126 (1971). materials, including zirconium hydride, 11. Honeck, H.C, Trans. Am. Nucl. Soc. benzene polyethylene and some organic i, 47 (1962). material So Zirconium hydride has been 12. Egelstaff, P. A. and Schofield, P., used as a moderator in a number of experi- Nucl. Sci. Eng. 12, 260 (1962). mental reactors. In this material hydro- 13. Koppel, J. U., Report GA - 7055, Gulf gen acts essentially as an Einstein General Atomic (1966). oscillator, with a fairly well defined 14. Haywood, B.C., J. Nucl. Energy 21, frequency. Once the neutron energy gets 249 (1967). below the energy of the oscillator, ther- 15. Bernal, J.D. and Fowler, R.M.,J. Ghem malization will essentially stop. Phys. 1, 515 (1933). 16. Larsson, K.E. and Dahlborg, U., Rea- Lattice dynamics of polyethylene ctor Sci. Technol. 16, 81 (1962). corresponds to that of a chain structure. 17. 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IAEA) pp. 425, (1965). 81. Swaminathan, K. Tewari, S.P. and 57. Wydler, P., Nucl. Energy 20, 981 Kothari, L.S., Phys. Letters (sub- (1966) mitted for publication) 58. Zryter, R.C., Calame, G.P., Fullwood, R.R. and Gaerttner, E.R., Pulsed Neu- tron Research , Vol. I (Vi enna: IAEA) pp. 465 (1965). 59. Meadows, J . and Whalen, J. F., Nucl. Sci. Eng. 2» 132 (1961). 161 Discussion M.P. Navalkar I have done a lot of experiments and analysis in pulse neutron technique using moderators such as H2O, BeO, Pb etc. In BeO we have come to the conclusion that it is not possible to measure diffusion coefficient because asymptotic decay constant dose not exist below a certain size. What is your conclusion regarding this aspect for BeO? L.S. Kothari In pulsed neutron experiments one may not observe an asymptotic decay if the buckling exceeds the critical buck- ling. But I did not go into that aspect of the problem since it would have taken one away from the line I wanted to develop. I agree that in doing pulsed neutron experiments, particularly in D2O assemblies, one must be careful to choose assemblies so that B^-^ Bq . 162 6 UEUTEON TRANSPORT STUDIES IN PAST REACTOR SHIELDS R. Vaidyanathan, Z.P.N. Murty and R. Shankar Singh Reactor Research Centre, Kalpakkam India The present study alms at evaluating the relative accui^acies ivith which the different approximations to the transport theory represent the spatial and spectral distribution of neutrons in a typical fast reactor shield. Diffusion, removal diffusion and discrete ordinate transport calculations, with and without the inclusion of anisotropic scattering effects, have been performed for the lateral and axial shield configurations of the French fast reactor Rapsodie. The resiilts have been compared, with the measurements made in Rapsodie and the WIOBE calculations made earlier. (Approximations; diffusion; neutron; NIOBE; Rapsodie; • " reactor; shielding; transport calculation) i Introduction Scope of Calculations The prediction of the spatial and The investigations ^ere carried out spectral distribution of neutrons with the following specifications; through the reactor shield is a vital requirement for shield design. In fast a) The calculations were performed reactors, due to the small size of the for the axial and radial shield confi- core and the absence of a moderator, gurations of Rapsodie, which is a 40 MW there is a high leakage flux from the fast reactor at Cadara.:he, Prance. Both core with long migration lengths in the axial and radial cor figurations were surrounding material. Clearly, the studied as spherical systems with the , diffusion theory can not adequately specifications given in Table-1 with represent the asymptotic neutron angular 12 energy groups- flux, which exhibits severe anisotropy, especially near boundaries. Further, Table-la the major fraction of neutrons leaking into the reflector of a fast reactor is Axial Configuration of Rapsodie in the intermediate energy range ( ^ .5 I'leV) . V/ith such scarce spectrum and the pooily moderating materials like Zone Radius (Cms) sodium and steel as penetrating media, the virgin beam should principally Core (Driver Zone) 16 .00 I consist of intermediate neutrons. Thus, Expansion chamber 32.60 one expects that the removal treatment Transition Zone-5 36.95 of fast Blanket 64.60 1 which gives the penetration Axial neutrons to normal diffusion Transition Zone. 67.10 ; would reduce j'. theory. All the same, it has been found-L Sodium 258.80 that the diffusion theory would yield Berated Graphite •278.40 ,t accurate resiilts with an empirically Steel Virgo 14 SB 288.40 optimised energy group structure. But a Borated Graphite 376.40 I practical limitation of this procedure Steel A- 42 386 .40 ) very Borated Graphite 436.40 I is that the predictions are sensitive to the group structure in Steel X C-18S - 481.40 regions of short slowing down lengths. Another aspect of the neutron b) The transport equation was solved ttenuation problems in fast reactor with S/ approximation using DTF IV. To -'ields is the marked variation in see the effect of anisotropic scattering r.eutron spectrum with propagation considerations, the axial calculations through the shield. Earlier studies'^ were again performed with the sodium cross sections represented in 3 Legendre ; indicate that this effect is so severe that few-group calculations would not moments. The diffusion calculations yield desired accuracy. were performed v;ith ONEDX and a program 163 . . . was developed here to solve the removal Results and Conclusions diffusion scheme. A 70-group S4 calcula- tion was performed to estimate the Pig.l gives the spatial profile of variation of spectrum due to spatial the integral parameters mentioned in traverse in the radial shield. The Section 2, in the axial shield confi- 70-group cross sections were taken from guration. DTP IV is seen to agree with JAERI fast reactor group constants^. the measurements within a factor of two to three. The diffusion theory under- Table-lb estimates the high energy fluxes by several orders of magnitude at deep Radial configuration of Rapsodie penetration. It is better in predicting the thermal equivalent dose and hence the slow flux. The removal diffusion Zone Radius (Cms) procedure is seen to make a feeble attempt to improve upon the diffusion Test Zone theory resxilts. Anisotropic scattering 7.07 considerations Driver Zone 25.0 give rise to substantial UOp Blanket-I 28.0 deviations in the neutron spectrum, though the differences UO2 Blanket-II 63.5 are less pro- noiinced S.S. reflector in the integral parameters used 75-5 for comparison Thermal shield 117.5 here. The neutron Stainless steel 121.5 2/. borated concrete 181.5 O.5X borated structural 396.5 concrete c) V/e choose to compare here, the different methods with measurements made in the axial configuration of Rapsodie^ with respect to the following integral paramet ers i) Thermal equivalent dose in Mn: \ 1 Bmax , „ (r)/ = -i- a(B) ii) Fission equivalent dose in Si: Bmax 1 D„. (r) a(E)9(r,E)dE. lis . eq. CT J Bmax where a = f a(B) X(E)dE o«' X(B) - U-235 fission spectrum Fig. 1. Comparison of the calculated (r(E) - Activation cross section integral parameters in the axial a., - Activation cross section at c onfigurat ion. ^ 2200 ms/sec. spectra at selective points, obtained by The following approximations were the 70-group calculation are given in made in the investigations: Fig. 2. It is seen that the spectrum within a shield zone in the present a) Only coarse group fluxes (12 configuration does not vary so markedly, groups) were available at the core- as to give rise to difficulties in per- reflector boundary. A white boimdary forming few group calculations. The condition was used to specify the source present investigations indicate that - for the 70-group calculations. a) The diffusion scheme can not b) The argon cover gas between adequately represent the neutron dis- liquid sodium surface and the rotating tributions in the fast reactor shield. plug was ignored in the axial calculaticris 164 . c) Many group calculations should be carried out if the shield regions are so thick that the spectral variation with space traverse is sharp. Acknowledgement The authors are thankful to M.S. Erishnan for lively discussions during the analysis of numerical results. Ref erenc es 1. Avery, A. P. et.al., Neutron Attenuaticn studies in fast reactor shields, s # i> i< U AERE(R) 5773, (1967). HCUTRON EHER6V IH «« 2. Sumar Sahin, Comparison of Transport Theory and Diffusion Theory for Past Reactor Shielding Calculations, Fig. 2. Spatial variation of neutron Atomkernenergie - Sep. 1973- spectrum in the radial shield. 3. Eatsuragi et al. JAERI Past Reactor Group Constants Systems Part I - JAERI b) The removal treatment is not very - 1195, Aug. (1970) effective and almost reduces to straight- 4. Chaplet, M. et al.. Etude experimentale forward diffusion scheme. des protections de Rapsodie, CEA-R-3626. 165 SHIELDING FOR THE VARIABLE ENERGY CYCLOTRON AT CALCUTTA *G. Muthukrishnan, Hari Singh and *R. Mukherjee Health Physics Division, Bhabha Atomic Research Centre, Trombay Bombay-400085 India Shielding calculations are done for the AVF Cyclotron under construction at Calcutta. Concrete shields are designed to reduce the fast neutron flux to less than the maximum permissible levels outside the shields. Earth shields are designed to reduce the fast neutron flux outside the building to less than the maximum permissible levels for public exposure. Experimentally measured values of half-value layer thickness are used in the calculations. Neutron source strengths are obtained by extrapolation to higher energies from published values at lower energies. Total neutron spectra consisting of both cascade and evaporation neutrons are computed for the bombardment of 60 MeV protons on a Li target, using semi empirical relations. In order to calculate the roof shield thicknesses calculated total neutron emission spectrum due to the bombardment of 60 MeV deuterons on a Be target is considered. Shield thicknesses thus obtained, are comparable with values cal- culated for a similar cyclotron at Texas A M. University. The cal- culated neutron dose outside the shield agrees well with the values predicted by Monte Carlo calculations. (Calculation; concrete; cyclotron; design; earth shield; neutron spectra; shield thickness; shielding) Introduction Neutron Production The AVF cyclotron, under construction Neutron production, due to the at Calcutta, is based on the design of bombardment of Protons on a Li target, the 88 inch AVF cyclotron at the Lawrence is calculated using the semi empirical Radiation Laboratory Berkeley^. The relationship, developed by Yucker^. The design specifications are as follows: program "CASCAD" calculates the total neutron spectrum and the differential Protons 6-60 MeV spectra at various angles. The total Deuterons 12 - 65 MeV cascade neutron spectr^lm is shown in Alphas 25 - 130 MeV Figure 2. Figures 3 and 4 show the Internal beam current 1.0 mA differential spectra at various angles. External beam current 100 iiA. The evaporation spectrum is shovm in Figure 5. Netitron yields at higher Facilities include two high inten- energies due to the bombardment of sity caves with three beam ports and two deuterons and alpha particles are high resolution caves with six beam extrapolated from published values at ports. Figure 1 shows the proposed lay- lower energies. Table 1 gives the out of the experimental facilities. fast neutron yields due to the bomb- ardment of alphas on Ta and deuterons The shields consist of concrete on Be3»4,5,6. shields outside the experimental caves and earth shields outside the building. The angular distribution of The philosophy behind adequate shielding neutrons due to the bombardment of 135 is to limit the radiation intensity in MeV alphas on Ta is assumed to be the occupational areas to a dose rate of same as that due to 80 MeV alphas. This 5 Rem/ Year and in public areas to 0.5 is justified because there is no observed Rem/Year. Shielding calculations are change in the angular distribution of done for the maximum operating conditions neutrons due to the bombardment of 40 of the Cyclotron. and 80 MeV alphas on Ta^. The same was Permanent address: VBC Project, Bidhan Nagar, Calcutta-700064. 166 167 . - Table-1 Neutron yields from (a,n) and (d,n) reactions. ALPHAS ON Ta Energy Yield Energy Yield MeV ns/ sec-|iA MeY ns/sec-|iA 10 30 1.00 X 10, ^ 10 3.23 X 10 40 1.96 X lolO 20 6.60 X 10-'10 50 6.00 X lOlO 30 1.23 X lOll 80 3.00 X lOll 60 1.30 X 1012 120 8.00 X 10^1 65 2.06 X 1012 135 1.08 X IOI2 Extrapolated values. extrapolated to 120 MeV alphas on Ta by Wadman^ I While considering the skyshine effect, the total emission spectrum, due to the bombardment of deuterons on a thid target, Moyer^l Be Calculated by using 1, Berber theory is taken as the source of neutrons. Fig. 4. Differential cascade neutron Shields spectrum at 90^ , 120° and 150°, Concrete and earth shields are used inside and outside the laboratory res- pectively. The concrete used is ordinarjlj density concrete (density 2.4 gm/c.c). Experimentally measured values of half value layer thickness of concrete are used in the calculations. The same was extended to other shield materials, taking into account the density effect.8 Table 2 gives the fast neutron fluxes at 15 cms from the target and the corresponding values of the half value layer thickness. From experimental studiesl3, it is observed that it is ] only the higher energy component of the J incident neutron spectrum that determine£|! the half value layer thickness of the . shield material. Using these values, th(; shield thickness are calculated. Calculations are carried out to determine the neutron fluxes outside the; existing shields. These results are published elsewhere^. Table 3 shows shield thickness recommended to reduce Fig. 5. Differential evaporation the fast neutron fluxes to the maximum neutron spectrum. permissible level of 17 ns/cm^ sec. 168 . 2 . , Table- level of 2'D/cm2 _ qqq at a distance of 100 meters from the source. Fast neutron fluxes at 15 cms from the target and the corresponding values Using the transmitted dose obtained of the half value layer thickness for the by the Monte Carlo Calculations^^ ,15 for concrete shield. different neutron energies and shield thicknesses the transmitted dose rate due Particles Ener- Tar- Angle Fast Half to neutrons produced by the bombardment gy get from neutron value of 60 MeV deuterons on a thick Be target Tar- flux at layer was computed for a concrete shield of get 100 \iA thick- thickness 2.58 meters. The dose rate ns/cm2 ness thus calculated is 1.55 mrem/hr against sec. cms. our computed value of 2.5 mrem/hr. Deuteron 65 Be 0° 6.0x10^0 12.70 References Deut eron 65 Be 90° 6 .246x10^ 10.16 Alphas 135 Ta 0° 1 .45x1011 18.54 1. Phadke, D.Y. "Project Report on Alphas 135 Ta 90° 4 .028x1010 10.16 Variable Energy Cyclotron for Inter University Centre" April, 1967. 2. Tucker, V/.R. "Empirical Formulae for Table -3 secondary Nucleon Production cross sections". Proceedings of the special Recommended Conor et e shield thick- sessions on Accelerator shielding nesses to reduce the fast neutron flux presented at the 1965 winter meeting to the maximum permissible level at 7.2 of the American Nuclear Society. meters from the target for 100 iiA beam ANS-SD-3 (1965). current 3. Allen, N.J., Necha j , J.F., Sun, K.H. and Jennings, B. "Thick Target Past Particle Energy Tar- Angle Shield thick- Neutron yield from 15 Mev deuteron get from ness (in and MeV Alpha Bombardment". Phys. the meters) Rev. 81 (1951) 536. , target 4. Wadman, William W. "Angular Distri- bution of Neutrons Produced by 40 and 80-MeV alpha particles on Alpha 135 Ta 0° 3.90 a Thick Tantalum Target'*. Health Physics Alpha 135 Ta 90° 2.18 11 659. Deuteron 65 Be 2.58 (1965) On Smith, L.W. and Gerald Kruger, P. Deuteron 65 Be 90° 1.92 5. "Thick Target Yields from the (D,n) Distance from target is 3.90 m. reaction at 10 MeV", Phys. Rev. 82 (1951) 1137. 6. William W. "Summary of Earth shields are provided outside Wadman, , the building adjacent to experimental and shielding calc\ilations based on Texas vault areas. Measured values of half A and M University 88. inch cyclotron value layer thickness of concrete are specifications" UCID 2437 (1964). extended^ for this shield, by taking 7. Tochilin, E., Ross, S.W., Shumway, B. into account the density effect of the W., Kohler, G.D. and Golden, R. shield material. (density 1.76 gms/cc) "Cyclotron Neutron and Gamma-ray A value of 25.3 cms is taken for the dosimetry for animal irradiation half-value layer thickness of the earth studies". Radiation Research 4 shield. The shield thickness is calcula- (1956) 158. ted to be 12.5 meters of earth. 8. Wilson, Richard . "A Revision of shielding calculations". CEA-73(1959). Sky shine Calculations 9. Muthukrishnan, G. and Hari Singh. "Summary of shielding calculations Skyshine calculations have been for the Proposed Variable Energy Cyclotron at Calcutta. BARC./I-81- carried out by LindenbaumlO . Based on this, skyshine calculations are, done, (1970) 10. Lindenbaum, S.J., "Conference on considering the bombardment of 100 \iA shielding of High Energy Accelerators, deuterons (energy 60 MeV) on a thick Be Oak Ridge". TID-7545, 101 (1957). target. The total emission neutron MoyerU, taken 11. Moyer, B.J., Some observations on spectrum, calculated by Cyclotron Shielding, Unpublished. as the source. 12. Case, K.M., De Hoffman, F. and Placzek, G. "Introduction to the The attenuation properties of the Theory of Neutron Diffusion". roof shield are taken into account in Volume I. Los Alamos Science the calculation. A roof shield of 1.65 Laboratory (1953). meters thick concrete is found adequate 13. Stephens, L.D. and Miller, A.J. to reduce the fast neutron flux to a Radiation Studies at a 169 Medium Energy Accelerator". UCRL - 19386 (1969). 14, Roussin, R.W. and Schmidt, F.A.R., Nucl. Eng. & Design 15, 319 (1971). 15. Roussin, R.W,, Alsmlller, Jr, , R.G. and Barlsh, J., ORNL-TM-3689 (Rev.) 1972. 170 COMPUTER CODES AND DATA AVAILABLE FROM THE RADIATION SHIELDING INFORMATION CENTER * D.K. Trubey, Betty F. Maskewitz, R.W. Roussin Radiation Shielding Information Center Oak Ridge National Laboratory Oak Ridge, Tennessee .- 37830, USA The Radiation Shielding Information Center (RSIC)-^'"^ is a technical institute serving the international shielding community. It acquires, selects, stores, retrieves, evaluates, analyzes, synthesizes, and disseminates information on shielding and ionizing radiation transport. The major activities include: (1) operating a computer-based information system and answering inquiries on radiation analysis, (2) collecting, checking out, packaging, and distributing large computer codes and evaluated and processed data libraries. The data packages include multigroup coupled neutron-gamma- ray cross sections and kerma coefficients, other nuclear data, and radiation transport benchmark problem results. (Computer code} data library} information; RSIC} radiation} radiation analysis,- shielding) As an integral part of its infor- interdependent codes which constitute a mation collection and processing activi- complete analysis system making use of a ties, RSIC collects, makes operable, number of techniques. packages, and distributes computer code packages to nuclear scientists and The radiation treated by the engineers engaged in shielding research majority of the codes is either neutron or design5~5. The various codes are or gamma radiation or both, but some designed for calculations related to codes treat charged particles. The radiation from fission and fusion types of geometry treated vary widely, reactors, radioisotopes, weapons and with many codes allowing a general three- accelerators and to radiation occurring dimensional geometry. in space. The Center uses the word "package" to mean all the items needed to For convenience, the available codes utilize a code effectively. The package are grouped into two classes: (1) those normally includes documentation des- which treat radiation transport and cribing the theory and code operation identified by Computer Code Collection (contributor's report plus RSIC abstract (CCC) numbers and (2) those performing and notes) and one or more reels of tape auxiliary data processing usefiil for on which is written the source program, other radiation analysis purposes and operating (binary or hex) program, input identified by Peripheral Shielding and output for a sample problem, data Routine (PSR) numbers. The numerical libraries, and auxiliary routines. methods applied in the CCC codes are primarily discrete ordinates (1- and Most of the codes are written in 2-dimension) , Monte Carlo (up to 3- FORTRAN IV, which makes them nearly dimension) , and kernel integration machine independent. Several of the (generally 3-dimension) . The remaining packages actually represent coding include removal-diffusion (Spinney), systems. These are represented in the moments, spherical harmonics, and collection by prototypes, which are not invariant embedding transport theory necessarily usef\il in themselves, but codes and miscellaneous codes to which achieve generality in that they calculate fission product buildup, are designed to be easily changed. Such release and resulting dose, stepping code systems are most useful to the power, optimization, sensitivity research worker who will invest a great analysis, and others. deal of effort in learning to use the system. Other packages are groups of * Research sponsored jointly by the U.S. Atomic Energy Commission and the Defense Nuclear Agency under contract with Union Carbide Corporation. 171 . . . The PSR codes include multigroup 20 MeV and on secondary gamma-ray pro- cross section generation and handling, duction. Evaluations which are not being nuclear models, experimental energy modified frequently are found in the spectra unfolding, optimization, plotting, ENDF/B library, which is available in coupling discrete ordinate results to the USA from NNCSC at Brookhaven Monte Carlo, random number generation, and National Laboratory. others For workaday problem solving, it has As an adjunct to the computer code been found useful to generate and exchange, RSIC is involved in many data collect multigroup cross section sets, activities, with most emphasis being and package, document, and distribute placed on nuclear cross section data. them in a format suitable as input to Through cooperation with various agencies, the most-used computer codes. Bach RSIC assists in improving the adequacy of data set, packaged as a unit, carries basic evaluated cross section data and a Data Library Collection (DLC) number. packages and distributes various types As with the code packages, a particular of data libraries useful in radiation data package does not remain static but transport analysis. The emphasis of is subject to revision, updating, and the effort is on the improvement of expansion as required. Such changes are calculational tools available to the announced in the RSIC Newsletter. Other shielding analyst. data in the collection include gamma-ray interaction cross sections, neutron This work involves collaboration with induced gamma-ray production spectra, the National Neutron Cross Section Center fluence-to-kerma coefficients, radio- (NNCSC) at Brookhaven National Laboratory, active decay spectra and decay schemes, the Shielding Subcommittee of the Cross and detailed output from transport Section Evaluation Working Group (CSBWG), calculations Atomic Energy Commission Controlled Thermonuclear Research Division, the U.S. A continuing project, in cooperation Nuclear Data Committee, especially the CTR with the American Nuclear Society, is to subcommittee, and the Defense Nuclear collect, edit, and publish reference Agency (DNA). data in the form of "benchmark problems"^ The objective is to compile in conve- The Center's role in the Evaluated nient form a limited number of well- Nuclear Data File (ENDF) development is documented problems in radiation to assist in the acquisition, checkout, transport which will be useful in testing and review of "shielding" cross sections computational methods used in shielding in ENDF format which may ultimately be analysis. The problem solutions, having placed in the ENDP/B file. In this been determined by several methods, context, "shielding" cross sections are should be representative of the state evaluations performed in the shielding, of the art. The problem descriptions radiation effects, or weapons radiation are published in looseleaf form so transport communities which are likely that revisions and additions can be to have an emphasis on gamma-ray pro- easily made. In conjunction with duction cross sections, gamma-ray benchmark work, data sets are packaged interaction cross sections, and neutron which allow the recalculation, with a. cross sections in the energy range of particular calculational method, of interest for shielding with detailed already published results. energy and angular distribution resolu- tion. RSIC maintains and distributes Lists of selected codes and data the Defense Nuclear Agency (DNA) evaluated packages are given in the following cross-section library. This is working table. These are typical of the most library in ENDF format whose content can used but not necessarily the best for be modified and revised as often as the any particxilar application. Further evaluator deems such changes to be information on these or any other codes necessary. The key to this approach is or data are available from RSIC upon a selected evaluator, the person res- request ponsible for making the original evaluation for a particular nuclide or element. He is then responsible for authorizing changes in evaluations for that nuclide. The evaluated data are for those materials of interest to DNA, whose cross-section values were originally in a state of rapid change, and with emphasis placed on neutron energies up to 172 , , Table 1. Neutron/Gamma-Ray Transport 1-Dimension CCC-42/DTF IV Discrete Ordlnates CCC-82/ANISN Multigroup CCC-126/AS0P (optimization) CCC-130/DTF-69 (X-ray) CCC-204/SWANLAKE (sensitivity analysis) CCC-204/INAP (activation) 2-Dimensions CCC-222/TWOTRAN II CCC-209/DOT III CCC-230/ TRIPLET (triangular mesh) Monte Carlo 3-Dimen8ions CCC-230/MORSE-CG (multigroup) CCC-187/SAM-CE 2. Multigroup Cross Section Neutron PSR-I3/SUPERTOG PSR-52/MACK (kerma factors) Gamma Ray PSR-51/SMUG Coupled PSR-63/AMPX 3. Kernel Integration 3-Dimensions CCC-48/QAD CCC-94/KAP VI CCC-213/ACRA (radioactive cloud) 4. Spectra Unfolding PSR-17/FERDOR-COOLC PSR-4I/MAZE CCC-112/SAm) II CCC-233/CRYSTAL BALL 5. Fission Product Inventory CCC-217/ORIGEN CCC-225/REST CCC-237/BURP 2 6. Multigroup Data Libraries Neutron DLC-2/100G (lOO-group from ENDF/B) DLC-33/MONTAGE (lOO-group activation) Coupled DLC-23/CASK (22-n, 21-y) DLC-27/AMPX01 (104-n, 22-y) DLC-3l/FEWGl(37-n, 21-y ) References Maskewitz, Betty F. and Trubey, D.K. Computer Codes for Shielding Calcula- 1. Trubey, D.Z., The Radiation Shielding tions - 1970, Nucl. Eng. Des. 13 Information Center - A Technical In- (1970) 448-9. formation Service for Nuclear Maskewitz, Betty F., Clark, Francis H., Engineers, Nucl . Eng.Des . 2 (1969) 392-5 Trubey, D.K., Computer Codes for - 2. Maskewitz, B.F. , Trubey, D.Z., Roussin, Shielding and Related Calculations R.W. and Clark, F.H., The Radiation 1972, Nucl. Eng. Des. 22 (1972) 334-341. Shielding Information Center: A Roussin, R.W., Trubey, D.K. and Unifying Force in the International Maskewitz, Betty F. , Data Activities Shielding Community, Fourth Interna- of the Radiation Shielding Information tional Conference on Reactor Shielding, Center, Fourth International Conference Paris, France (Oct. 1972), CONF- on Reactor Shielding, Paris, France 721018, Vol. I, pp. 215-225. (October 1972), CONF-721018, Vol. 4, 3. Trubey, D.K. and Maskewitz, Betty F. pp. 1191-1201. Computer Codes for Shielding Calcula- Profio, A.E., Editor, Shielding tions - 1969, Nucl. Eng. Des. 10 Benchmark Problems, 0RNL-RSIC-25( ANS- (1969) 505-17. SD-9) (Sup.l, 1970, Sup. 2, 1974) Oak Ridge National Laboratory. 173 GI-AMMA RAY BUILD-IIP FACTORS FOR PIMITB MSDIA K.John and D.Y.Gopinath Health Physics Division Bhabha Atomic Research Centre Bombay-400085 Using the transport code ASFIT, energy build-up factors are calculated for various energies and different systems. The resijilts presented here are the energies O.O5, 0.1, 0.2, 0.4» 0.66, 0.8, 1.0, 1.25, 1.5, and 2.0 MeV. Media considered are air, aluminium, beryllium, calcium, carbon, hydrogen, iodine, iron, lead, magnesium, molybdenum, oxygen, silicon, sulphur, tin, uranium and water and their thicknesses are 1.0, 2.0, 4,0, 6.0, 8.0, 10.0, 15.0 and 20.0 mean free paths. Empirical formulae of the exponential polynomial type have been obtained for these finite region build-up factors. Dependence of the constants in the empirical formulae on the material property Z has been discussed. (ASFIT ; build-up factor ; empirical ; energy -, gamma ray ; mean free path) 1 Introduction in NSRD-NBS 29 . The media considered for the calculations are Air, Aluminium, The build-up factor defined as the Beryllium, Calcium, Carbon, Hydrogen, ratio of the total detector response to Iodine, Iron, Lead, Magnesium, Molybde- the virgin radiation' s response is a con- num, Oxygen, Silicon, Sulphur, Tin, Ura- venient concept in radiation attenuation nium and Water. The source energies calculations. In notation it can be considered are O.O5, 0.1, 0.2, 0.4,0.66, written as 0.8, 1.0, 1.25, 1.5 and 2.0 MeV and the thickness are 1.0, 2.0, 4.0, 6.0, 8.0, 10.0, 15.0 and 20.0 mean free paths. We analysed for empirical relations by fitting the data for each media and ener- where I = the total flux and gy as a function of thickness using the — LIX exponential polynomial'^. I e ^ = the uncollided flux o Results Any given build-up factor depends upon the material constituting the me- A very usef j.1 form for the build-up dium, the source energy or energies, the factors has been given by Taylor^ . He location in the medium and the source expressed the build-up factor as a sum geometry. An extensive study of build-up of the two exponentials, given by factors has been done by Goldstein and °^2^^^ Wilkinsl using the moments method. This B(^ix) = A e- °^1^^^ + (l-A)e- method assumes the medium as infinite and homogeneous. But in most of the shieldin; where A, o(-j^, and are constants. calculations one of the important para- meter is the transmitted flux. Due to the In our study we tried different types of assumption of the infinite medium moments exponential polynomials and saw that the method does not provide this. Another funct ion drawback of this method is that it is ^insuitable for the calculations of B(x) = A + A e~-^l^ (x in mean heterogeneous shields. free paths) is the simplest and the best fit to almost Present Work all the data from energies 1.0 MeV onwards. The constants are listed in In this paper we present the energy Table-1. Table-2 gives the media in which build-up factors in finite nledia for one the maximum error is above 6'/. . In all dimensional slabs obtained using the other cases the error is less than . Iteration 6/. ASFIT (Anisotropic Source Flux The constants obtained are given in Figs, Technique) 2 transport code which over- la to Id as a function of atomic number comes the above mentioned drawbacks of (zj for energies 1.0, 1.25, 1.50, 2.0. Below the moments method. The cross section 1.0 MeV we could not obtain a smootii data used for the computation is given curve for constants versus Z. 174 1 1 Table-1 C9nstant s of . the cui^-e ^ , , B( X} =^ Energy (MeV) z l.QO 2.00 AO 3.537+02 6.614+01 3.353+01 1 . 831+01 1.0 HYDROGEN Al -3.532+02 -6. 538 + 01 -3.259+01 -1.725+01 81 3.014-03 1 .363-02 2.361-02 3.635-02 AO 3.270+02 5 . 867 + 01 3.169+01 1 . 873 + 01 4.0 bERYLL lUM Al -3.265+02 -5.788+Ul -3.U63+01 -1 . 768 + 01 81 3 .232-03 1 .517-02 2 .484-02 3 . 543-02 AO 2.653+02 5.680+01 3.117+01 1.869+01 CARB'ON Al -2.648+C2 -5.599+01 -3.021+01 -1.763+01 81 3 .920-03 1.551-02 2.498-02 3.530-02 AO 3.044+02 5.807+01 3.150+01 1.900+01 AIR Al -3.039+02 -5.727+01 -3.054+01 -1.795+01 8 3.43 7-03 1.52 5-02 2 .482-02 3 . 486-02 AO 2.753+02 5.526+01 3.056+01 1 . 900+01 8.0 OXYGEN Al -2.748+C2 -5 .445+01 -2.959+01 -1.795+01 81 3 . 764-03 1 . 589-02 2 .542-02 3 .473-02 AO 3.034+02 5.689+01 3.099+01 1.891+01 10.0 WATER Al -3 .030 + 02 -5 .609 + 01 -3.002+01 -1.786+01 B 1 3 .448-03 1 .554-02 2 .520-02 3.5 0 3-02 AO 1. 787+02 5.031+01 2.937+01 1. 866+01 12.0 MAGNESIUM Al -1.781+02 -4.947+01 -2.839+01 -1.790+01 8 5 .533-03 1 .693-02 2 .589-02 3 .431-02 AO 1.625+02 4.908+01 2.918+01 1.900+01 13.0 ALUMINUM Al -1.619+02 -4.823+01 -2.820+01 -1 . 795 + 01 81 6.021-03 1 .723-02 2 . 594-02 3.41 5-02 AO 1.470+02 4.885+01 2 .932 + 01 1 .910+01 14.0 SIL ICON Al -1.464+02 -4.800+01 -2.834+01 -1 .805+01 D i A "7 1 — n a 1 "7 "5 n — n 9 AO 1.207+02 4.591+01 2.856+0 1.894+01 16.0 SUI.PHUR Al -1.201+02 -4.504+01 -2.757+01 -1.788+01 Bl 7.786-03 1 . 796-02 2.604-02 3.383-02 ...... • •••••••••• • • ••••«•••• ...... «• "ao" 9.243+01 4.167+01" " 2.729>01 1.904+01 20.0 CALCIUM Al -9. 172+01 -4.078+01 -2.630+01 -1.799+01 B 9 . 70 8-0 3 1 .917-02 2 .662-02 3.312-02 AU 5.92U+U1 3.510+01 2.520+Ul 1.878+01 26.0 IRON Al -5.837+01 -3 .417 + 01 -2 .420+01 -1.773+01 B 1.402-02 2 . 160-02 2.775-02 3.272-02 AO 2.186+01 1 .991 + 01 1 .796 + 01 1 .698+01 42.0 MOLYBDENUM Al -2.085+01 -1 .887 + 01 -1,691+01 -1.592+01 B 1 3.01 2-02 3 .208-02 3 .405-02 3.281-02 AO 1 .407+01 1 .469 + 01 1 .465 + 01 1. 543+01 50.0 TIN Al -1.301+01 -1 .363+01 -1 .359 + 01 -1.437+01 81 4 . 12 3-02 3 .919-02 3.834-02 3 . 376-02 AO 1 .264+01 1 .350 + 01 1.363+01 1.469+01 5 J.O IODINE Al -1.157+01 -1 .244 + 01 -1.256+01 -1.363+01 81 4 .389-02 4 . 105-02 3.983-02 3.443-02 AU 5.281+00 6 .453+uO 7.453+00 9.283+00 82.0 L~AD Al -4 .234+00 -5 .401+00 -6 .398+00 -8 . 229+00 Bl 6.285-02 5.456-02 4.836-02 3.836-02 AO 4.539+00 5 .600 + 00 6.607+00 8. 301+00 92.0 URANIUM Al -3.495+00 -4.551+00 -5.556+00 -7.250+00 81 6.023-02 5.271-02 4.646-02 3.736-02 175 • Table-2 ENEUV V50MM. Media Error {'/.) COKSTAKTS or THe FUNCTION SCI) . Ao»At t^X Hydrogen 13 A| .-Ao-rAA Beryllium 13 Carbon 12 Air 13 Oxygen 12 Wat er 13 Magnesium lU Aluminum 9 Silicon 9 Sulphur 8 1 mfp . In all other cases the error is less than 6'/.] 30 40 so so 70 X (ATOM/C NUMBEH) Fig. Ic ENERsy 100 Mav. COHSTAWTS OFTHf FUltCTIOK ENERiSY 2 00 Mev (I) - AO* A, CONSTANTS OF THE FUNCTION 8U) .Ao»A, X lU MEAN rni PATd A, .-Ao'^lA 4 2P0 10 30 30 40 50 60 70 z Catomic number) _4A_ Pig. la "W 10 20 30 « 50 60 70 JO W Z (ATOMIC NUMBER) Fig. Id References Goldstein, H. and V/ilkins, J.E. , Calcula- tion of the Penetration of Gamma rays, NYO 3075 (1954) V". Gopinath,!). and Santhanam,K. , Radia- tion Transport in one dimensional sys- tems-Part I, lJuc.Sci.e Engg. 43 186-196 (1971). Hubbell, J.H. , Photon Cross sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 JieV to 100 GeV 1969, ifSRDS-iJBS 29- Buckingham,R. A. , Numerical Methods, Sir Isaac Pitman e 5ons Ltd., London, p.329. z Catomic number ) Taylor, J. J., "Application of Gamma Ray I ENERGY ZSMeV. , CONSTANTS Cf THE FUNCTION Build-up Data to Shield Design" , V/APD BttJ = Ao»A, e'*'*, A, . -Ao ilA memo BM-217. Fig. lb 176 . PHYSICAL PRINCIPLES OF PHOTON DOSIMETRY* Walter S. Snyder** Health Physics Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 Estimation of dose absorbed in the human body is important from the point of view of health physics as well as because of the increased utilization of nuclear radiation in clinical and diagnostic medicine or therapy. An idealized mathematical model of the human body was developed and Monte Carlo calculation was applied to evaluate the photon dose. In this paper the attention is restricted to certain physical results or principles which are a by-product of such studies. These relate to evidence on the validity of the reciprocity theorem, use of the build-up factor for an infinite medium of tissue in calculating absorbed fractions, scaling absorbed fractions for the weight of the target organ, and the effects of non-homogeneity of the body on absorbed dose to the organs (Dose, dosimetry, Monte Carlo, organ, phantom, photon, reciprocity theorem, source, target, tissue.) Introduction respects the human body. In Figure 1 the exterior form of the phantom is shown and Estimation of dose is important for in Figure 2 some of the internal organs medical uses of x-rays and in nuclear medicine, whether for diagnostic uses or for therapy. Also it is of great impor- tance for health physics since use of nuclear energy requires careful control of sources so that no undue exposure of the occupational worker of the general public results. This paper is limited to consideration of dose from sources of photons within the body because the short range of electrons and alpha particles considerably reduces the complexity of estimation of the average dose to an organ, and it is this concept of average dose in an organ or tissue that is con- sidered throughout this paper. Although many of the principles given here can be applied to micro-dose or to the other concepts of dose these are not considered in this paper. Some ten years ago the author and his associates began to develop an model of the idealized mathematical Pig. 1. The adult human phantom. human body to use for Monte Carlo type calculations of photon dose. The story is lengthy and not without interest, but are shown, while Figure 3 displays a in this paper the attempt is to focus on sketch of a skeleton together with the what has been learned about dosimetry in idealization of it for the phantom. All a complex phantom resembling in some of these organs are described by rather Research sponsored by the U.S. Atomic Energy Commission imder contract with Union Carbide Corporation. **Consultant 177 r body organs in size, shape, composition and density. However, there has been no attempt to reproduce minor details of either the organs or of appendages, such as fingers, ears, etc. which are presumed to have a small effect on photon scattering. Some of the results of our studies have been published in MIRD Phamphlet No. 5 and more special results have been published in Health Physics2»3 and in ORNl report s'^~13. There have been sixteen organs used as a "source" organ and in each case twelve monoenergetic sources of photons were distributed liniformly in these organs. When a calculation is completed one has dose to all twenty-three "target" organs of the phantom from a uniformly distributed source provided the statistics are good. Frequently they are not, but this is discussed below. An extensive tabulation of results is in course of publication Fig. 2 as ORNL-5000 (in press )14 b^t here attention is restricted to certain physical results or principles which are OftNL-OWG T0-4810R a by-product of the studies. Variation of Dose with Organ Mass To a first approximation, the average dose to an organ from a source outside the organ and some distance away is independent of the organ mass or size. Strictly, the principle cannot be correct in all cases as is evident if the target organ increases so greatly that the solid angle subtended from the source is changed significantly or if the distance from soixrce to target is markedly changed. Except for these extremes the dose is relatively insensitive to the mass of the target Pig. 3- Idealized Model of the Skeleton for Computer Calculations (left) organs. As one example, in Figure 4 are plotted the dose per photon to three ... and a More Realistic Representa- different models tion (right) with Percentages of of the solid bladder Red Bone Marrow Found in the which is given three different weights. Shaded Portions of the Bones. Although the weights vary by a factor of two, the doses are so close they can simple mathematical formulae which are barely be distinguished on the figure. easily adapted to computation on a large The sources are in the ovaries and in the kidneys which are reasonably close scale digital computer. . to the bladder. This and similar The mass absorption coefficients are examples provide an answer to many chosen for three distinct types of questions medical people frequently ask; tissue; namely, bone plus bone marrow "Your calculations are for a standard which is homogeneous with a density of man, but my patient is not standard in about 1.5 g/cvP, lung tissue which has a many respects. What difference in dose will result if his liver is larger than density of about 0.5 g/cm^ and the remainder of the phantom which has usual?" From sources outside the liver ., the indicates difference density near 1 g/cmP. Each of these evidence little tissues has its own characteristic provided the average distance from to target about the same. composition and while each is homogene- source remains ous, the phantom as a whole has some of If the liver is both the source the diversity of the body. Thus the and target organ the answer; is rather organs of the phantom approximate actual different. If the source is uniformly 178 . . plotted for three shapes of thyroid which are sketched at the top of the figure and for masses ranging from 3.4 g to 19,6 g. One can scarcely distinguish the diffe- (4 rent points they lie so closely together and the curves do seem approximately constant for photon energies above 0.1 MeV. Below that, the curves are still close together but now the mean free path does not greatly exceed the diameter of the thyroid and so the curve is not flat . This is only one of many illus- trations which indicate the relative insensitivity of this quotient which is, however, only for sources distributed uniformly in the organ. Other illus- trations are given in Reference 15 The Reciprocity Theorem The interplay of theory and practice is illustrated by the reciprocity theorem first stated by Mayneord, (1945)16. PHOTON ENERCTT (M»v) This theorem states that if the same' activity is distributed uniformly in two Fig. 4. Dose for Three Bladder Sizes and subregions A and B of an infinite Two Source Organs. homogeneous scattering medium, the dose rates produced in the other regions are distributed in a sphere and if multiple equal. In symbols, D(A<—B) = D(B<—A) scattering is neglected (mean free path where A<— B indicates the source region much greater than the radius r) the B and the target region A. Now the body absorbed fraction of energy is 3t\x^I)/ A is neither infinite nor homogeneous and and this implies .that the dose vanes one may wonder whether the theorem is inversely as VT^' ^ . It is surprising how useful in practice. One of the by- well this formxala holds for target organs products of the Monte Carlo type of whose shape is not approximately calculation is that when A and B have spherical. In Figure 5. the absorbed each been used as a source organ one can fraction, AF, divided by ^^^'{^±q test to see whether the equation above holds—at least within the limits of ORNL-OWO 74-5131* statistical accuracy. In Figure 6 the resiilts of several hundred tests are recorded. The ratio D(A<—B)/D(B<—A) is calculated, where D(A<—-B) is the larger of the two dose rates for all choices of A and B such that the coefficient of variation (= 100 a/m) did not exceed 50^. The bar graph indicates the percentage of cases where the ratio did not exceed 1.2, 1.4, 1.6 etc. At the low photon 1 the 1 energies none of ratios exceeded two, THYROID <— THYROID but at higher energies there were a few exceptions and these are indicated. In all these cases about 60X or more of the ratios were below 1.2, while 95/. or greater were below 1.8. Moreover, a THYROID WEIGHT (g) part of this inaccuracy may be due to the 0 34 4 8.5 statistical scatter of the Monte Carlo » 11.4 the 1 13.4 data. In fact, as coefficient of . 15.9 variation is limited to 30X and then to • 19.6 20/. the exceptional cases where the ratio exceeds 2 tend to disappear. This is 1 1 1 ml 1 1 M 1 ml 1 1 1 M the basis for the claim- that the ratio PHOTON ENERGY (Mev) is, in most cases, below I.3, The data shown are only for organs composed of Fig. 5. Absorbed Fraction of Photons in soft tissue and when bone is one of the the Thyroid in Relation to Size organs the above result no longer holds and Shape of Organ. (Source in but an adjustment can be made which is Thyroid) given in reference 15. Thus, although 179 there is no doubt that the reciprocity factor has been tabiilated by Berger theorem is not exact for organs of the (1969)^' for an infinite space of water body, it can still be used if one is so that in effect the body is enlarged willing to accept a limited accuracy of to an infinite extent and is also 20-30/. . homogeneous. But this change has remar- kably small effect on the value of $ obtained for the body. In Figizres 7-9 the results are displayed, the value of $ obtained by the Monte Carlo calculation being the abscissa and the result of the evaluation of (1) the ordinate. When the two are equal the point should fall on the line bisecting the angle. It is foiAnd that for cases where the Monte Carlo results are reasonably exact, say with a coefficient of variation not exceeding 50/., the two results agree within a Fig. 6. Distribution of Reciprocity: Tissue Organ and Tissue Target. The Build-up Factor For many source and target organs the Monte Carlo estimates are statisti- cally uncertain and the authors have therefore sought other methods which, Fig. 7. Monte Carlo Estimates of Specific while less exact, would not involve Absorbed Fractions Compared with large errors. The specific absorbed Build-up Factor Estimates. that is fraction, the fraction of photon 0«NL-r)WG 7'r7£B,-R energy absorbed per gram of the target 2 organ, can be written as F PHOTOM ENERGY O.OE Me^' / / . (1) where the integral is of the product space AxB and \i and lig^j^ denote the mass attenuation and mass absorption coeffi- cients for photons of the required energy and A[ denotes the mass of organ A and I 1x-Y| the distance from point X to point SaF (MON~E CiMO ESTIW1T6S1 Y. Fig. 8. Monte Carlo Estimates of Specific Absorbed Fractions Compared with This expression can be integrated Build-up Factor Estimates. using statistical methods and when it is compared with the results obtained from factor of about 2 and usually are much the Monte Carlo technique a surprising closer than this. This agreement is not fact emerges. In effect, the build-up due to the lack of influence of the 180 — References - — 1 — ' . "O'^zz ' 1 , . . 1. Snyder, W.S., Ford, M.R., Warner, G.a. - I PHOTON EMERGY Vev and Fisher, H.L., "Estimates of Absorbed Fractions for Monoenergetic Photon Sources Uniformly Distributed in Various Organs of a Heterogeneous Phantom," MIRD Pamphlet No.2,J. Nucl. Med,, Suppl. No.l, 15 (1969)." 2. Cloutier, R.J., Smith, S.A., Watson, E.E., Snyder, W.S. and Warner, G.G., "Dose to the Fetus from Radionuclides in the Bladder", Health Physics, 26, No. 4 (1974). 3. Poston, J.W. and Snyder, W.S., "A COEFFICIENT Or viRlfiT.ON 1 / BETWEEN 20-30% Model for Exposure to a Semi- Infinite j Cloud of a Photon Emitter," Health , , I , i 10 Physics, 26, No. (1974). ' to"* ra""' 4 SflF {MONTE CaRLO ESTIMATES) 4. Snyder, W.S., Ford, Mary R. and Warner, G.G. , "Estimation of Dose and Dose Commitment to Bladder Wall from Fig. 9. Monte Carlo Estimates of Specific Absorbed Fractions Compared with Radionuclides Present in Urine',' Build-up Factor Estimates. Health Phys. Div . Ann . Prog .Rept . for Period Ending July 31, 1970, ORNL- build-up factor, for it has -values of the 4584, 206. order of 10^ at 20 mean free paths in many 5. Snyder, W.S., Cloutier, R.J. and cases. Only the results for photons of Smith, S., "Dose to a Developing Fetus energy 0.03, 0.05 and 1 MeV are shown here from a Gamma Emitter in the Bladder," but they are typical of the others. In Health Phys .Div. Ann. Prog. Rept . for particular, note the values with arrow Period Ending July 31, 1971, ORNL- attached on the two plots for the lower 4720, p. 119. energies. These represent the ratio where 6. Snyder, W.S. Ford, Mary R., Warner, bone is one of the organs and the arrow G.G. and Brindza, P., "Absorbed represents the displacement that would Fractions for Internal Emitters," occvir if one replaced p.^^ for soft tissue Health Phys .Div. Ann. Prog. Rept . for with for bone. Thus this method seems Period Ending July 31, 1971, ORNi- to afford a means of getting values of $ 4720, p. 121. which are sufficiently accurate to bring 7. Snyder, W.S., Ford, M.R. and Warner, one within a factor of 2 of the correct 6.G., "Estimates of Absorbed Fractions result and do not involve inordinately for Photon Emitters within the Body," i large sample sizes. Health Phys .Div. Ann. Prog. Rept . for Period Ending July 31, 1972, ORNL- Special Studies 4811, p. 86. 8. Hilyer, M.J.C., Snyder, W.S. and The Monte Carlo technique can be Warner, G.G., "Estimates of Dose to applied to a wide variety of expos^ure Infants and Children from a Photon situations, for example, dose to the Emitter in the Lungs}' Health Phys. fetus from a radionuclide in the body, Div. isjin. Prog. Rept . for period ending dose to an individual sujrrounded by a Jvily 31, 1972, ORNL-4811, p. 91. large cloud of radioactive material, and 9. Snyder, W.S., Poston, J.W. and for I also to children. It is particularly Dillman, L.T., "A Model Exposure instructive to note that preliminary to a Semi-Infinite Cloud of a Photon j phantoms have been designed for children Emitter," Health Phys .Div. Ann. Prog. j and the results obtained indicate that Rept. for Period Ending July 31, dose per photon increases by an order of 1973, ORNL-4903, P- HO. magnitude or more as the phantom becomes 10. Snyder, W.S. and Ford, M.R. , "Esti- j smaller. These phantoms are now in the mation of Dose and Dose Commitment Wall a photon . process of being refined at ORNL to to the Bladder from better the child. The study Emitter Present in Urine'," Health I represent of dose to the bladder, an organ for Phys .Div. Ann. Prog. Rept . for Period photon changes Ending July 31, 1973, ORNL-4903, j which the dose per greatly during the nrocess of filling, p. 115. G.S. ' has been publishedl5. No doubt these 11. Hilyer, M.J.C., Hill, and Warner, of the many uses G.G., "Dose from Photon Emitters I are only a few examples to which the Monte Carlo method of Distributed UniforniLy in the Total ' calculation can provide answers. Body as a Function of Age," Health 181 . . . Phys. Div. Ann. Prog. Rept . for Period Ending July 31, 1973, ORNL-4903, p. 119. 12. Snyder, W.S. and Ford, M.R. , "Esti- mates of Dose Rate to Gonads of Infants and Children from a Photon Emitter in Various Organs of the Body," Health Phys. Div. Ann. Prog. Rept for Period Ending July 31, 1973, ORNL-4903, P- 125. 13. Snyder, W.S., Poston, J.W., Warner, Gr.G. and Owen, L.W., "Dose to a Dynamic Bladder for Administered Radionuclides," Health Phys .Div. Ann Prog. Rept. for Period Ending July 31, 1974, p. 13. 14. Snyder, W.S., Ford, Mary R., Warner, G.G. and Watson, Sarah B., "A Tabulation of Dose Equivalent per Microcurie-Day for Source and Target Organs of an Adult for Various Radionuclides," ORNL-5000, ( in press ) 15. Snyder, W.S. "Estimation of Absorbed Fractions of Energy from Photon Sources in Body Organs," Medical Radionuclides ; Radiation Dose and Effec ts, USAEG report CONF-691212 (1970T7p.33-49. 16. Mayneord, W.V., "Energy Absorption: IV. The Mathematical Theory of Integral Dose in Radium Therapy',' Brit. J. Radiol. 18, 12 (1945). 17. Berger, M.J., "Energy Deposition in Water by Photons from Point Isotropic Sources," MIRD Pamphlet No. 2, J.Nucl. Med., Suppl. No.l, p. 15 (1968). 182 TRACE THEORY APPLIED TO PHYSICAL, CHEMICAL AND BIOLOGICAL SYSTEMS* S.C. Sharma and Robert Katz Behlen Laboratory of Physics University of Nebraska Lincoln, Nebraska 68508, U.S.A. The conceptual structure of the 6-ray model of track effects will be presented. Its universal applicability to a wide spectrum of radiation detectors and radiation environments will be shown. For 1-hit detectors, the response with LET variation is described by two parameters, the D-37 dose for gamma-rays and the size of the sensitive element. The role of 1-hit detectors in the measure- ment of radiation quality will be briefly outlined. A simple cellular model which applies to cells whose radiosensitivity para- meters have been determined experimentally yields the cellular survival, RBE, OER etc. for heavy ions, neutrons and pions. (Cell} delta ray; dose,- ions; LET; model; neutron; OER; one-hit detector; pion; radiation; track) Introduction bombardments as well as to mixed radiatian environments including stopping Studies of track effects in emulsion particles^. and other physical, chemical and biolo- gical media indicate that secondary Dose - Response Functions electrons are the principal agents coupling the track-forming particle to The transition from gamma-ray to the medium through which it passes. The heavy ions is achieved by using gamma-ray spatial distribution of ionization energy dose-response transfer functions. Most by the secondary electrons about the path of the detectors display a 1 - or - more of the particle determines the track hit response to dose. That is, the structure and is a relevant parameter to probability P that a detector is activa- describe radiation effects. Since gamma- ted at dose D may be expressed as: rays are also coupled to an irradiated medium through secondary electrons, P = 1 - e'^/^o (1) differences in the effects observed in these kinds of irradiations arise either where E^ (also called the D-37 dose) is from the time schedule with which the the dose of gamma-^rays at which 37% electrons are generated or from their of the detector's sensitive elements spatial distribution, or both. Track survive (or at which 63% are activated). effects may be correlated with effects At this dose there is an average of 1 hit observed from gamma-ray irradiation by per sensitive element. These are on-off assuming that the response of small sub- detectors. If they are not activated by volumes of the medium near the path of a passing particle their response to the an energetic particle is as if these next particle is as if there were no subvolumes are part of a larger system prior irradiation. Among the detectors, irradiated with gamma-rays to the same which are classified as 1-hit detectors, dose. Thus the knowledge of the dose- are photographic nuclear emulsions. response function of a medium to gamma- rays may be coupled with the spatial Biological cells display a different distribution of dose from secondary sort of response, described by the electrons to yield the spatial distri- mathematical form of a multi-target, bution of response about the path of a single-hit model, expressed as: charged particle. The theory has been applied to a variety of detectors of P = (1 - e-^^^o)^ (2) interest in dosimetry, including nuclear emulsion, scintillation where m is the multiplicity of the target counters, plastics, glass, thermoliimine- structure, and it is taken that each of scence, and chemical dosimeters, the m elements of the target must be enzymes, viruses, and biological cells. inactivated, by a single hit, for the It is applicable to track-segment cell to be killed. If some lesser number * Supported by the USAEC and the NSF (RANN) 183 . of elements than m have been affected by the radiation, it can be said that the cell has accumulated sub-lethal damage. Theory The size of a sensitive element plays an indirect role in determining the response of a detector to gamma- rays, as it affects the D-37 dose, but it plays a direct role in heavy ion irradiation. We take each sensitive element to act collectively, and find the radial distri- bution in energy density 1 deposited in sensitive elements of radius slq as a function of the elements' radial At distances where both t and ag Proiu Eqs. (1) and (3) we note that are substantially less than x, the the response of a 1-hit (m = 1) detector normalized curves of Eig. 1-lie atop one may be found_£rom the two detector another, with the essential result that parameters and aQ. We also note that sites for which t/aQ< 1 experience a ion "local dose" which varies as z^^~^aQ~ detector parameters and parameters , are not separable variables. Dosimeters while sites for which t/ao > 3 experi- we now identify as 1-hit detectors are ence a local dose which as varies shown in Table-I. In most cases the z^^~^t~^ 2. In both cases the local dose varies as z^/p^ characteristic target size is only poorly evaluated. The identification is 1 - hit Detectors based on gamma-ray, or heavy ion res- ponse or both. Having the parameters Eq When Eq. (1) is applied to Fig. 1, and ao we can calculate the response of with a suitable value of Eq and a.Q, we a detector to any radiation environment^ obtain the probability P for inactivation. In Fig. 2 we show the systematic varia- Since the radial integral of the tion of RBE with an increase in LET. probability is the cross-section a for In Fig. 3> we show the predictions that the ( in)activation of a sensitive were made and sent to Appleby' before element by a single passing ion, we may his measurements of the yield of the find the radiosensitivity of a detector Fricke dosimeter in the PPA nitrogen to this mode of inactivation. beam. Results are in quite good agree- 04 ment . a = j27ctP dt (3) 0 To summarize the features and Radiosensitivity k^ may be calcula- characteristics of 1-hit detectors, we ted from: note that when energy is deposited diffusely, it is most efficiently used ki = a/L (4) by a 1-hit detector because there is no 184 Table-I PROPERTIES OF l-HIT DETECTORS >. 6. K T erg/cm' A f/lOOeV BidUil Production Vtllne S.Oxlo' 1 5 2.0 610 1.8 15 6.0 210 85 0.05 110 Thysilne 1.3 g Glycine 7.7x10? 20 5.3 170 Cytosin* 3.0xlo' 150 0.4 320 ln«ctl»«t1oB (enzynes) lyio jyne 3.3xl0' 14 4.5 310 Tryps In 2.5 18 2.7 400 1.7 25 1.4 540 ONA-tse g a-9t1«ctosUise 3.1x10" Inictlvttlon (viruses) T-1 5.7x10' Fig. 3. Calculated values of the RBE of k-174 (243-252A) , 5-0 c T-7 (i A Model for Cellular Sijrvival When m = 1, the detector cannot accumulate sub-lethal damage. The pro- bability that it will survive irradia- tion by a beam of particles of fluence F is e"*^^. When m>l, the sensitive element can accumulate sub-lethal damage. We take the gamma-ray dose- response curve for biological cells to be of the form as given in Eq. (2). We follow the mathematical operations as outlined in 'Theory' and arrive at the delta ray theory of the inactivation of cells. Just as in the 1-hit detector, a cell can be inactivated by the passage of a single ion, which is called ion-kill mode, and they may be inactivated in a second mode, called gamma-kill , through the participation of many delta-rays from different ions. The surviving fraction of a biological species when a dose D of the radiation is deposited is given by Pig. 2. Radiation detectors. The niimeri- cal values of the detector para- l^/N,=e-^o?Ftl-(l-e-(l-^^^/^o)"'j (6) meters have been found in diffe- rent ways for the different detectors, must be regarded and (7) as somewhat tentative. P=a/ao = (1-e 185 where Oq, k, m and Eq constitute a set of four fitted parameters. T-1 HUMAN KIDNEY CELLS- ANOXIC -TODO-1966 D = PL (8) -125PZ-2/3 Z(l - e (9) (10) Y where D dose in gamma-kill mode. For biological materials there are two size parameters which we have called Fig. Oq and k. The first 4. Calculated values of the response of these is nomi- of nally the cross-sectional area of a cell alanine, the deaerated and the aerated nucleus. The second parameter k is Fricke dosimeters as a function of depth in a Bevalac formally the value of z^/ 4p2 a,t which beam plateau (or saturation cross-section) is irradiated phantom having the achieved when cells are bombarded with stopping power of water, after various heavy ion beams. Parameters Eq Irradiation with 220 MeV/nucleon and m are extracted from the x-ray oxygen beam. The predicted values of survival curve of a biological cell. the average RBE in plateau and One compact set of four parameters peak regions agree with recent describes the cell survival curves for measiirements of Appleby'. all 1 track-segment and stopping particles. 1 1 —I 1 1 1 r 1 1— The extension to the mixed radiation environments arising from heavy ion beams, T-1 KIDNEY CELLS (ROISMAN. 1973) OXYGEN BEAM neutrons and pions is straight forward 10° provided that we know the spectrum of - secondary charged particle distribution^. In Fig. 4 the parameters for T - 1 human kidney cells and the sirrvival curves they generate are shown in com- parison with the data to which the parameters were fitted^. A beam of heavy charged particles ENERGYj^l^lgl (MeV/nucleon) 228 can be approximated by a simple model 170 incorporating attenuation and straggling, but neglecting secondary particle pro- 6 8 10 duction, beam contamination, energy DEPTH (cm) inhomogeneity and focusing5 . Use of the heavy ion beam model yields cell survival Fig. 5. Survival data (Todd) for anoxica- as a function of depth in a MeV/amu 250 lly exposed T-1 human kidney cells oxygen beam to be compared with experi- are superimposed on a family of mental data of Roisman et al. (LBL-2016, theoretical curves from fitted 1973) • These results4»5 as shown in parameters^. Fig. 5 were predicted before the experi- ment was actually performed. value of the fraction of the dose With this model, we have designed delivered to kidney cells in the gamma- ridge filters (to obtain iso-survival kill mode (Eq. 10), for both aerobically regions of any desired width) , have and anoxically irradiated cells". This calculated survival, OER, RBE, dose as a demonstrates that the RBE of a 1-hit function of the depth in a phantom for detector must decline with an increase different cell lines and have compared with the 'LET' of the radiation. Both some of these calculations to the S and OER show a similar decline. Thus calculations of the response of different it is suggested that an alanine dosi- 1-hit detectors. In Pig. 6, we show the meter, or other suitable 1-hit detector, calculated response of an alanine can be used alongside a conventional dosimeter, here labelled as its RBE, in dosimeter in the measurement of radiatitm a cross-field irradiation with a neon quality, particularly in the case where beam, and compare it with the calciilated quality is changing". 186 . • . . . . DlBcusslon A.K. Ganguly I am intrigued by the track model you present. Can you extend the model to deal with tracks in individual high molecular weight systems, arising out of single or a few radioactive atoms in- corporated in them. S . C . Sharma The theory specifically avoids the assignment of the microscopic interacti- ons between radiation and matter which are ultimately responsible for the obser- ved effects. We understand the structure of the track common to all the detectors rather than the individual phenomena different in each detector. We have simulated tracks in different emulsions and work is in progress to understand the parameters of significance in track structtire. So the answer is 'no' at the present time. S. Mukher.ji Fig. 6. Experimental values of the sur- viving fraction of kidney cells 1. Is the theory on delta ray pro- irradiated aerobically and duction tested in the single case of ion- anoiically, at different depths pair formation in elemental gases ? in a " submarine" with a beam of 2. The energy-loss rate for heavy oxygen ions at an initial energy ions is not always given by Bethe's of 226 MeV/nucleon at the BEVALAC equation. (From Roisman et al., lBl-2016, 49, Sept. 1973) are compared with predictions of the delta-ray S.C. Sharma theory^ » 5 1. I believe there is good deal of Acknowledgement information on delta-ray production in elemental gases. We use simple delta- We thank Rose Ann Nelson for her ray distribution formula and are always assistance in the course of these interested in knowing more about the investigations, and in the preparation finer details of the variation of CO- of materials for publication. values in gases for various energies. References 2. I agree. For our computations, we use standard tables for energy-loss 1. Butts, J.J. and Katz, R., Radiat and range-energy values for heavy ions. Res. 10, 855 (1967) Although the stopping power information 2. Katz, R., Sharma, S.C. and is not very accurate for very low energy Homayoonfar, M., The Structure of and relativistic heavy ions, yet the Particle Tracks, in Topics in final results are not affected a great Radiation Dosimetry . F.H. Attix, ed.. deal Academic Press, New York (1972). 3. Katz, R., Sharma, S.C. and P.S. Nagara.ian Homayoonfar, M., Nucl. Instr. and Could your theory predict the RBE, Meth. 100, 13 (1972) OER etc. when the high LET and low LET 4. Katz, R. and Sharma, S.C, Nucl. are deliberately used, i.e. the syner- Instr. and Meth. Ill, 93 (1973). gestic effects ? 5. Katz, R. and Sharma, S.C, Phys. Med. Biol. 12, No. 4, 413 (1974). S.C Sharma 1-hit 6. Sharma, S.C and Katz, R., The The theory can predict the response Detector in the Measurement of of any detector to any mixed radiation Radiation Quality, in Proceedings of environment. For cells the high LET and the Fourth Symposium on Microdosime- low LET parts are apportioned In lon-klll try, Verbania-Pallanza (Italy), and gamma-kill modes respectively. For Euratom (1973) details, please refer to our paper in 7. Appleby, A., private communication. Physics in Medicine and Biology (1974). 187 SPECTRUM SHAPES OF LOV/-ENERGY PHOTON SOURCES R.C. Sharma, S. Somasiindaram, IL, Unnikrishnan and Shiv Datta Body Burden Measurement Section Health Physics Division Bhabha Atomic Research Centre Bombay-400 085 The spectrum shapes of low-energy photon (LEP) sources undergo interesting changes in the presence of scattering media of low atomic numbers. Two readily observed changes in the spectrum shape are (a) downward shift of the peak energy and (b) apparent deterio- ration of the energy resolution of the detector. A study of these changes is useful for in vivo assessment of LEP-emitters such as 24lAm, 239Pu, U, 210pb etc. A computer program, based on Monte Carlo principles, has been evolved to compute the magnitudes of these changes in piilse-height distribution. Calculations were performed for point sources of low-energy photons located on the axis of the detector and for different thicknesses of the scatte- ring medium interposed betvfeen the source and the detector. The variable parameters considered in these calculations are initial photon energy, thickness of the interposed material and type of detector. The magnitudes of both the above-mentioned changes in the pulse-height spectra of LEP sources embedded under media of low effective atomic number, such as water (Z = 7.42), tissue (Z = 7-33) and perspex (Z = 6.47), are found to be dependent to a great extent on the energy resolution of the detector employed, apart from the electron density and effective atomic number of the scattering medium. The theoretical results are presented and compared, wherever possible, with experimental values obtained with iNfal^(Tl) detector. (Detector; Monte Carlo; perspex; photon energy; pulse height; resolution; scattering media; tissue; water). Introduction point sources of LEP emitters embedded at various depths in a tissue- equivalent • It has been observed recently in material have also indicated the feasi- connection with in vivo detection of low- bility of correlating with depth the energy photon (LEP) emitters (Ey<100 observed peak-shift or the change in keV) with thin iTal(Tl) scintillation or resolution-'-"-^. On the basis of such ilal( Tl)-Csl(Tl) phoswich detectorsl-4 correlations, it would be possible to t that the presence of tissue produces derive effective soft tissue thicknesses appreciable changes in the original for individuals of differing body builds pulse-height spectrum which may be ex- to facilitate correction of the cali- ploited advantageously to estimate the bration factors. Besides, in the depth at which activity is located. Two literature the occurrence of these most readily observed changes in the phenomena has usually been explained spectrum of a mono energetic LEP soujrce qualitatively as being exclusively due to . located in a medium of low effective Compton scattering in the intervening = atomic number ( Z2 , such as tissue (Z mediiim.-'-~4 The present work describes a 7.33) or water (Z = 7.42), are (a) computer program evolved to compute the downward shift of the peak energy and changes in pulse-height spectra for a (b) apparent deterioration of the v/ide range of lovj energies and depths of energy resolution of the system. sovirce in tissue-like media. The cal- Experimental work in our laboratory has culations provide a better insight into indicated that the magnitudes of these the actual mechanisms leading to the effects are in general different for observed changes in p\ilse-height spectra different absorber-scatterers, which could of LEP sources. The results of calcula- be explained qualitatively on the basis tion are presented and compared with the of differences in the effective atomic experimental values. numbers and the electron densities (number of electrons/cm3) of the material4. Experimental studies with 188 — j Computer Program escape peaks would not affect the present calculations. It is therefore assumed Kathematically the problem is that the interaction of the exit photon specified by reierr ing to fig. 1 in spectrum with the detector could be which. C represents the Nal(Tl) detector adequately represented by the smearing of radius R and thi ckness T, on the axis of the former by the G-aussian resolution of which is placed a point source S at a function associated with the latter. distance t from the detector face. The Experimental measurements at four photon intervening space b etween S and C is energies below 100 keV show that the filled with water V/ also of radius R. standard deviation of the G-aussian peak It is desired to co nstruct the pulse- can be expressed as a function of energy height response of C due to monoenergetic by the relation photons emitted by 3. This is achieved in two steps: a(E) = A ;/¥ + B The constants A and B are determined from the experimental plot of a(E) vs. -fE. Smearing of the exit photon spectrum is then accomplished by computing the contributions from each channel to the others, using the Gaussian distribution function and is carried out as follows: The contribution from the kth channel of the exit photon spectrum to the jth channel of the smeared pulse- height spectrum is given by C(J) „ B(K,J) = exp[- i^=fi^%B ^ f C(J-l) where A(K) is the number of counts in the Pig. 1. Source detector geometry used in kth channel of the exit photon spectrum, comnutational scheme. E(k) is the mean energy corresponding to the kth channel of the exit photon First, the line spectrum incident spectrum, C(j) and C(3-l) are the upper on the detector face, hereafter referred and lower limits of the jth channel of to as the "exit photon spectrum", is the smeared pulse-height spectrum and cr^ determined by the I-Ionte Carlo technique. is the standard deviation of the Gaussian Scattering from the surroiindings is not peak in the pulse-height spectrum at taken into account. This idealization energy E(k). Expressed in terms of is quite justified since only low- energy normal probability function P(x), photons are involved. The Monte Carlo simulation of (a) is achieved by B(K,J) = A(K)L?(X2) - P(Xi) following the sampling techniques des- „ G(J-l) - E(K) 2 wnere Xn = —^ j- ^ and iLa^ cribed by Cashv:ell and Sverett5. Fig. 2 aj^ shows the flow chart of the computer program schematic used in the present Thus, using the normal probability studies to compute the exit photon function values and experimentally spectrum. The relevant cross sections obtained o^'s, the contribution from all = ;;'or water are taken from reference^. the k channels (k 1 .... n') of the exit photon spectrum to every jth channel The second step req.uired is the (j =1 ... n) is calculated to get the derivation of the pulse-neight spectrum smeared pulse-height distribution. The resiilting from the interaction between location of the peak is found by using the exit photon spectrum and the NalCTl) the technique of "linearization of the detector. A rigorous derivation would peak" . In practice five channels on require that each photon of the exit either side of the peak were used for spectrum be follov/ed individually into this purpose. the detector in order to compute the actual energy deposited in C. However, Experimental Setup And Calculations extension of our calculations for thin Kal(Tl) detectors'? to a detector of A Harshavj integral assembly (10.16 thickness 5 rom confirmed that below cm dia x 5 mm thick Nal(Tl) having 1 mm 100 keV, most of the photons incident Be as radiation entrance window) is on the face of the crystal are comple- currently in use in our laboratory for tely absorbed. The presence of iodine detection of Pu/Aim in vivo. The Nal(Tl) 189 No I »,V,Z.U' 0 Yts X-XtU.S' E- Eo Y'Ytv:S Xw,Yw At Z-Tw I Upt) ColcutaW e' CalculoK Nfw U.V.W 90 100 110 ' No IS Torn NUMBER OF HISTORIES TO BE TRACED. Channel NO. Iw IS THE THICKNESS OF WATER r IS A RANDOM NUMBER BETWEEN I 0 AND . Fig. '5- The exit spectrum (histogram) of E IS THE ENEROY OF COMPTON SCATTERED PHOTON photons for initial energy 60 Ndti iS THE NUMBER OF COUNTS IN THE CHANNEL CORRE SF-ONOING KeV and v/ater thickness 6.3 cm IC ENEROY E OF THE EXIT PHOTON SPECTRUM and the resultant peak in the pulse-height spectrum (continuous line) from a of Fig. 2. Flow chart for computing exit- Nal(Tl) detector photon spectrum. dimensions 10.15cm x 5 mm. The points indicate the corresponding experimental data. scintillation crystal is coupled to a 2.54 cm thick quartz light pipe and mounted on a RCA 8055 phototube. The Nal(Tl) scintillator as described above output from the phototube is routed and a point source of initial photon ^ through a FET pre-araplifier to a 400 energy 60 K.eV is used, the thickness of channel pulse-height analyser. In order the interposed water scatterer being to have a meaningful comparison between 6.3 cm. The exit photon spectmjim and the theory and experiment, the computations theoretical peak are for 20,000 source were performed for point sources of low- photon histories. The figure illustrates energy photons located on the axis of a how the peak-shift is introduced. The Nal(Tl) detector of the available size exit photon spectrum does not show any and for different thicknesses of the shift in the maximum photon energy and scattering material interposed between the number of counts in the original peak the source and the detector. The variable channel is still overwhelmingly large. parameters considered are (a) initial This would be representative of the case photon energy (from 20 keV to 100 KeV at of an ideal detector having an infinitely intervals of 10 lleV), (b) thickness of fine resolution, introducing no line interposed scattering material varying broadening. In actual practice, however, from 1 cm to 12 cm and (c) type of the exit photon spectrum would be dis- detector - the energy resolution dis- torted due to the finite energy resolu- tinguishing each type. The experimental tion of the detector and its variation results were obtained with a point source with energy (fwhm vs. photon energy of 241 Am (60 KeV) with different thick- relation) . Since the peak-shift appears nesses of distilled water in a thin only after the smearing of the exit perspex container interposed between the photon spectrum vrith the experimentally source and the detector. Another determined values of fwhm, it may be scatterer employed was perspex. concluded that it is the energy resolu- tion of the Nal(Tl) detector which ' Results and Discussion introduces the peak- shift in the pulse- height spectrum. Different exit photon In fig. 3 are shown a typical exit- spectra, incident on the same detector, photon spectrum as a histogram, the would also indicate different values of resulting peak in the smeared pulse- peak-shift (AE). The smeared spectrum height spectrum as a smooth curve and in fig. 3 has a peak at 58.07 KeV, i.e. the experimental values (normalized to ^E = 1.93 KeV. 'Ifter smoothing, the the smeared spectrum at the new peak peak-shift in the experimental pulse- channel) as circles. The detector is a height spectrum for the same case is 190 to be 1.97 KeY. Eig. 5 shows the variations of AE and fwhm with depth of a point isotropic V/e may next consider some hypothe- source of 60 KeV photons under water tical detectors having the same f\-fhm vs. when Ilal(Tl) detector described earlier peak energy relation as the iTal(Tl) is used. The continuous curve shows the detector but having different energy computed values and the experimentally resolutions; i.e. we consider detectors measured values are shown by the points. with The experimental values of -a E fall close to those predicted by calculations. otE) = Ka(S) The experimental fwhm values are slightly higher than the predicted values where aXll) is the standard deviation of probably due to very little back scatter normal distribution centred at energy from 1 mm thick perspex source container. E for a hypothetical detector, a(S) is The srrall difference between the fwhm the standard deviation of normal distri- values does not seem to introduce bution centred at energy E for the ilal(Tl) significant difference in AE values. detector and E is a constant. Therefore AC (KeV) 171 u« So 11 , 1 , ,— ' "--^ , and fwhm = 2.355cr^ 1 The exit photon spectrum in fig. 3 is smeared using several values of a' and the peak-shifts (•^E) are observed. Fig. 4 depicts this dependence; -^E is as of Z. It is plotted a function seen - A-o that when the sane exit photon spectrum * / is incident on detectors having different energy resolutions, the peak- shifts observed are different. In the typical case given, the peak-shift could vary from 0 KeV to 3-09 KeV, depending upon the energy resolution of the detector. appears to satiirate for a detector 1 > 1 1 . r having an energy resolution twice as bad as that of our detector. Fig. 5. Theoretical variations (conti- nuous curves) of peak shift, F¥HI^ and ?/T ratio of the number of photons in the 60 EeV channel to the total number of photons * in the exit spectrum) with depth = . of a point source of photons of energy 60 KeV under water. Ex- perimentally measured values are indicated by maxked points. Fig. 6 illustrates the variation of AE with the initial energy of source photons when the source is located at a constant depth of 3> 5 and 7 cm of water. These results are obtained from our program by treating the initial photon energy as a variable parameter . Since fwhm is a function of the incident photon energy and increases with energy, AE would increase. In the initial stages this increase will be Fig. 4. •• Theoretical predictions of peak- augmented by the rapid decrease of P/T shift (AE in II eV) for hypotheti- (the ratio of the number of photons in cal detectors having standard the 60 KeV channel to the total number deviation of Gaussion peak in the exit-photon spectrum) which in Ea,- a being the parameter for turn is caused by the predominance of - ITal(Tl) detector and K a constant. the photoelectric effect in this region. The results are for a point source Beyond this, P/T increases slowly in of initial photon energy 60 keV accordance with the decrease in mass iinder v.'ater depth of 6.3 cms. absorption coefficient which works 191 against the increase in AE. The com- low-energy photon soirrces embedded in bined effect of all is that AE first media of low effective atomic numbers. increases steeply with E and then falls The role of the detector in introducing to a lower value. such cnanges has been delineated. : Wl— — . , 2 - 1 1 1 1 1 I I I 1 I •'01 2 3 « 5 6 7 8 9 10111 Fig. 7. Computed FV/Hiu as a function of VE for the cases of point source Energy (KeV) under water thickness of 0,3,5 and 7 cms. Pig. 6. Theoretical peak-shift ( AE) as a function of initial photon Acknowledgement energy for point isotropic sources under constant water depths of The authors wish to express their 3, 5 and 7 cm as continuous sincere thanks to Shri T.K. Haridasan curves. Broken curves are for for his assistance in the present work. perspex. References The dotted curves in fig. 6 are for the same detector and perspex scatterer. 1. Morsy, S.ll., El-Assaly, E.M. and The calculations yield AE values less Aloush, A. A., Assessment of radioactire than those for water, whereas the experi- contamination in man, IAEA (1972) mental values are higher than those for p. 115. water (fig. 5). We have used the cross 2. ilundo, J., Keane, A.T. and May, fl.A. section data in ref. 8 for perspex ibid, p. 579. (density taken as 1.0 g/cc) and in ref. 6 3. V/renn, M.E., Rosen, J.G. and Cohen, IT. for water, '.'/e have not used the cross ibid, p. 595. section data from any other reference to 4. Sharma, R.G., Somasundaram, S., resolve this difference. Surendran, T., Kapur, D.K. and 3arg, S.P., BilRC report Ho.BARC-748 (1974). Fig. 7 shows fwhm plotted as a 5. Cashwell, E.D. and Everett, C.V. function of /E, E being the observed A practical manual on the Honte Carlo 'peak' energy. Deviations from the method for random walk problem, approximately linear relation observed Pergam.on Press, London (1959). when no scatterer-absorber is present 6. Sieg^bahn, K., Alpha, Beta and Gamma- are evident. This deviation increases ray spectrometry, Elsevier, Amsterdam with the thickness of the scatterer (1955) . . (water) and there seems to be no signi- 7 . Sharma , R G . , Garg , 3 . P . and ficant departure from linearity below Somasundaram, 3. iiucl. Instr. i-Ietnods, an energy of 25 lieV. 101 (1972) 413. 8. Hubbell, J .H. , US National Bureau of Conclusion Standards report iTo. HSRDS-HBS 29. A computer program using Monte Carlo techniques has been described to calcu- late changes in the pulse-height spectra obtained from detectors exposed to 192 DOSE FUNCTION FOR BETA DOSIMETRY S.J, Supe and Shiv Datta Division of Radiological Protection Modular Laboratories, Bhabha Atomic Research Centre, Trombay Bombay-400085 , INDIA The feasibility of using various shapes and sizes of field limiting devices and collimators with beta ray eye applicators has necessitated the study of dosimetry for these fields. A method of obtaining dosimetry for any shaped field from the data for circular fields is presented. The method is based on a similar procedure for X and gamma rays. The surface dose compu- tation is done based on Clarkson's method but without splitting the surface dose into air dose and back-scatter dose. The depth dose evaluation is based on depth dose function which is defined as the dose rate at a particular depth for particular circular field. The usual method of splitting depth dose into primary and scatter doses was not found necessary. The evaluated values for the surface and depth dose were compared with experimentally obtained values for three non circular fields. The good agreement in these data indicates the practicability of the method suggested. (Air dose; arbitrary shaped field; back-scatter factor; Clarks ' method; dosimetry; depth dose; surface dose) Introduction method for roentgen and gamma radiations for such estimation. This method con- The early cases of lesions of eye sists of measurement of air dose, use of were treated by X-radiation and have re- back scatter factor and scatter functions sulted in radiation cataract. With the for estimation of this data. The air use of P-ray emitters like radium D + E dose is to be actually measured for the and radon, the eye lense dose was appre- field size under consideration. However, ciably reduced. IvTien a pure for the estimation of surface dose the beta emitter, was available for use as eye small variation of air dose with field applicators, the gamma component of eye size is neglected and air dose assumed lense dose was eliminated. This reduced to be a constant. The non-circular field the frequency of incidence of radiation size is divided in a large number of cataract and no further attempts were segments of circles with different radii reported to reduce the eye lense dose. drawn at equal angles. The back scatter These applicators were usually used factors for these are averaged to give without any field limiting or collimating the effective back scatter factor for the devices regardless of size of the lesion field under consideration. resulting in much larger doses to the lens of the eye. Recently, use of field To obtain the dose at any depth the limiting devices-*- as well as collimators'^'- dose is divided into its two components, has been investigated and shown to be the primary dose and the scatter dose. possible for almost all cases. The fea- The primary dose is obtained by extra- sibility of matching the field shape to polating the central axis depth dose for that of lesion size has raised new various field sizes to zero field size. problems of dosimetry. As various lesion The scatter dose is evaluated by obtai- shapes are encountered the present dosi- ning the average scatter function for the metric data of circuJLar fields4-7 ±s field under consideration by the same insufficient for the treatment of widely method as used for back scatter factor. varying shapes of the lesions. Further, The data so obtained are used for getting it is virtually impossible to carry out the central axis as well as off axis dosimetric studies for the numerous field depth doses for the field under consi- shaping devices of variety of sizes and deration. Further interpolation of this shapes. In this work a method of esti- data yields complete isodose curves. mation of surface and depth dose for any shaped field from the available data for Air Dose for Beta Rays circular fields on the same lines as X and Gamma fields was tried. Adoption of this procedure in case of beta rays is handicapped by difficul- Clarkson® Meredith and Neary^ and ties. The measurement of air dose for Johns and CunninghamlO described the betas is rather diffiCT^t-'-'-. Air dose 193 I . with beta rays is possible only if the experimentally obtained ones. collecting electrode of an extrapolation chamber or a flat ionization chamber is Depth Doses equally thin as the upper or polarizing electrode. If a thicker plate is used the A further difficulty was observed i contribution due to back scatter from the calculating the dose at any point in plate will not permit the measurement of tissue on similar lines as those for X the air dose. and gamma rays. In the case of beta rayS; obtaining the value of the primary com- Further, the increase in air dose is ponent of dose was found to be rather going to be very rapid with increasing difficult. The central axis depth dose field size as a large active area would data for beta rays are available from the be contributing to the dose. A constant maximum field size of about 8 mm down to dose output is not possible with the beta about 2.00 mm and would not yield by ray sources when used with the field extrapolation the primary dose with the limiting diaphragms and hence it was required accuracy. Any attempt to decided to try and find out whether dosi- measure doses for field sizes smaller metry at surface and in tissue could be than about 2 mm diameter is handicapped developed on similar lines as that of X with inaccuracies introduced in making and gamma rays but without the help of a electrodes of extrapolation chamber constant air dose. smaller than this diameter^^ and the primary component of beta dose at various —Surface— ——Dose^— depths cannot be obtained with sufficient . , I accuracy The variation of surface dose was studied with the field size splitting it Close scrutiny of the procedures for into air dose and the back scatter dose. calculating the dose at any point within For this purpose using an extrapolation the field and at any depth revealed that chamber, doses were measured for a RA- such separation of scatter dose from (tracerlab) type eye applicator with primary component is not necessary. It increasing field limiting diaphragm was noted whether primary dose is deter- diameters. Measurements were also mined separately and added to the average repeated for 450 mCi ^^Sr- ^Oy source value of scatter function or whether the with a collimator of 1.05 cm length. average of the total dose is estimated, The surface dose rates for rectangular the same results are obtained. Thus it shaped field sizes have been evaluated was decided to use dose function for beta from the dose rate for circular fields rays rather than scatter functions. The by using Clarksonl2 method. These are dose function is defined as the dose rate presented in Table I. In addition, at the particular depth on the central surface dose measurements for the appli- axis of a circular field. The dose fun- cator with the corresponding shapes of ctions were evaluated in the following field limiting devices have been carried manner. The surface dose rate for a out with an extrapolation chamber and particular field size was multiplied by the results 'thus obtained are presented the percentage depth doses at different in column 4 of Table I. The evaluated depths for the same field. These dose values agree well within + 5/- with the functions for various field sizes and TABLE- ' ' , SmFACE DOSE RATES FOR VARIOUS FIELD LIMITING DEVICES & COLLIMATORS Sr. Collimator/ Source to Dooe rate(rad/8) | Doee rateCrad/s) j No. field limiting I surface Extrapolation ; evaluated valuea ' device aiEe(iixm) ! dlstanoe(oa8) cbflBber neasurfflnents V 1 1. 6x6 0 117.0 116.2 ! I 2. 6 x4 0 77.5 81.2 i , 1 62.1 3. 6 X 3 0 65 4. 6.6 X 6.2 1.05 19.2 18.7 i 5. 6x8 1.05 20.1 19.5 6. 6x6 1,05 14.5 13.8 194 I . Using the surface dose rates and the dose functions for circular fields as basic data for Clarkson's method, com- putation of depth dose in the space around the source could be easily carried out. This has been done for three fields and the depth dose data thus ob- tained are presented in Table I and II. Non-circiilar field limiting dia- phragms were constructed and using the experimental method already described dose data were obtained for these fields which are also presented in the same tables. It can be seen that the depth dose data obtained by the computation and those obtained experimentally are in fairly agreement for the three shapes. This agreement indicates that the pro- cedure suggested here is practicable enough for therapeutic purpose. The computation can be carried out within a period of a few hours with some practice. A computer programme can also be easily written for this purpose. Acknowledgements We are indebted to Shri G. Subrah- manian for his keen interest in these investigations. Gratefiil thanks are also due to Shri S.M. r.ao for his help in experimental measi^rements a) RA-1 applicator with field limiting devices. b) 450 mCi source with colli- mators. TABLE- I EXPERIMENTAL AMD EVALUATED DEPTH DOSE DATA RA-1 Applicator with field shaping devices . D«ptb F»re«nta«* depth dose data toe oollinatora sizes of ' 6x8 6 X 6 6 X 3 £ixp«rlsental Syaluattd ExperljB*ntal Evaluated Experlaeatal Evaluated 0. 100 100 100 100 100 100 100. 49.0 45.3 46.5 44.9 46.0 45.7 200 26,5 22o7 24.5 21 .7 23.5 20,6 300 13.3 11.3 12.2 10.2 11 ,0 9.0 m m mmm mm mmmaamm^i 1 wM mm »mmm^ naa wKfli mmm mmmm mm mm mmm mm «a»aia«a 450 mCi Soureewlth oolllaatcars 8 X t) mm 6 X 6 ssn 0 100 100 100 100 100 100 100 64.9 71.7 66.6 73.0 64.9 69.0 200 40.9 41 .8 46.7 43«0 38.7 38.7 300 26,1 25.1 29.0 26.0 24.4 22,3 1^ 195 . , , , . References H.A., and Collins, V.P., Radiology, 76, 278 (1961) . Supe, S.J. and Cunningham, J.R., Am. Sinclair, W.K. and Trott, N.C., Brit J. Roentgenol, and Rad. Therapy , 79 . J. Radiol. 15 (1956). 570 (1965). Clarkson, J R., Brit. J. Radiol, 14, Supe, S.J., Am. J. Roentgenol, and Rad. 265 (1941). Therapy , 11^, 24 (1972) Meredith, W J. and Neary, G.J, Brit, Supe, S.J. and Rao, S.M., Brit. J. J. Radiol., 12, 75 (1944). Radiol., 786 (1974). 10, Johns , H.E. and Cunningham, J.R., 4. Krolimer, J.S., Am. J. Roentgenol and Springfield, Illinois, Chas. C. Rad. Therapy, 66, 791 (1951). Thomas (1969). The Physics of Radioloar. Jones, C.H., and Dermentzoglou, F. 11, Sheppard, C.W., and Abele, R.K., Brit. J. Radiol. 203 (1971). AECU-655, (ORUl-265) (1949). Mc Taggart, W.G., West, W.D., Claypool, 12, Supe, S.J., Int. J. Appl. Radiat Isotopes, 24, 545 (1972). 196 ACTUAL PROBIEMS IN PHOTON DOSIJ-ISTRY* D. F. Regulla and G. Drexler G-esellscliaft fiir Strahlen-und Umweltforschung mbH Hiinchen D-8042 Neuherberg, Ingolstadter Landstrasse I Germany, F.R. A brief review of the evolution of quantities and units in dosimetry is given, and the relevance of the dosimetry concept to applications in medicine, technique and health physics is pointed out. IVhile radiation dosimetry seems to have, from a phj'-sical point of view, achieved an adequate status, handling of the physical fundamentals as well as practical app- lication of quantities, units and measurement methods to operational dosimetry appears to be limited mainly to the level of highly competent authorities in dosimetry, such as IGRU or, on a national basis, to primary standard laboratories. This consequence is based on the authors' experience, that there is hardly a country, in which the numerical value of a dosimetrical quantity can be determined reproducibly through the different institutions engaged with practical dosimetry. WHO and IAEA, for this reason, started to establish a net-work of secondary standard laboratories, recently, with the aim of an improvement of dosimetry in medicine, radiation protection and radiation research. Details of this joint international effort on standar- dization are given, results already evident in some countries are presented. Recent advances, particularly in solid state dosimetry, are discussed together with the scientific aspects of physics in diagnostic radiology. To the authors' opinion almost every effort in the field of diagnostic radiology is worthy and promising for reasons of reduction of population dose and amelio- ration of information but also due to the broad interdisciplinary possibilities, the immediate output of applied research and, last not least, the benefit to mankind. Some examples on new results of medical physics as well as an outlook to future developments are given. Introduction From literature study we found key- microdosimetry , calculation of stopping note addresses to be often characterized by power, solid state dosimetry etc. two formalities: On the one side, the Doubtlessly, at this place a keynote speaker wishes to express his gratitude address could exceptionally be presented to the responsibles of the conference for on the basic physical aspects of the honour of invitation - which practice dosimetry. we should like to join - and, on the other side, he searches for a concept of However, to the authors' opinion it the lecture by interpretation of the term should be pointed out, that dosimetry keynote. Following this example we found even after its physical definition and the term keynote defined in the dictionary interpretation in terms of the respective as "fundamental tone of a scale". quantities and units is gaining importance Seeking for a relationship between this and justification only by imbedding it definition and the subject of the present into the matrix of the manifold appli- session "Radiation Dosimetry and cations. Thus, dosimetry is loosing the Instrumentation" one is inclined to character of ending in itself and correlate the term fundamental tone merely becomes a tool for a relevant qualitative v/ith the physical basis of dosimetry and quantitative description of the vfhich could function as a connecting link radiation field and its interaction with between the diverging topics, such as the absorber medium. On the basis of *bedicated to Professor Dr. F. Wachsmann on the occasion of his 70th birthday. 197 .. this approach one has - by returning to radiation quantity of which "roentgen" the dictionary definition of the keynote was said to be the imit^. As a conse- - to see the fundamental tone of dosi- quence of this ommission the roentgen metric physics in connection with the had gradually acquired a double role: scale of applications, at least, in The use of this name for the unit had biology, medicine industry, agriculture, become recognized as a way of specifying health physics and research. not only the magnitude but also the nature of the quantity measured. This The dosimetric procedure self- practice conflicts with the general evidently practiced today by starting usage in physics, which permits, within from the the physical fundamentals and same field, the use of a particular I adapting them to the respective field of unit for all quantities having the same application has not been common as far dimensions as to the beginning of the sixties. For a long time, any quantification of the A number of dosimetric quantities * radiation effect was performed by and units have been introduced in course description of type and intensity of the of time, but only those that are of effect under consideration. The early importance in the framework of the ;i biological dosimetry methods to be dosimetry concepts discussed here, will designated as "analog technio^ues" such be reviewed. ' as the erythema dosimetry, the epilation dosimetry or even mouse-dead dosimetry Ob.jectives of Dosimetry become understandable by the lack of a relevant dosimetric philosophy and The term "dose" is biologically -\ physical concept of measurement . Time oriented and originating from the early was not yet ripe for a detailed appli- medical use of X-rays. In order to cation to photon fields of the funda- reproduce medical and biological '| mental concepts of particle fluence, radiation effects, compare different flux density and energy spectra - radiation effects among each other and familiar from the kinetic theories of estimate the amount of ionizing radia- gases— because theories of the dual tion for any application one needs an corpuscular and wave nature of photons effect caused by and related to the were still evolving. It was the dose, which can well be defined, application of ionization as a physical measured and quantified along a scale. pre-condition for a dosimetric digita- This, however, is no more a medical or lization of the measuring procedure biological problem but a physical one. that first made a definition of physical Therefore, dose has at least been quantities possible in dosimetry and defined in terms of physically measurable established a connection to the exact quantities natural sciences by introducing well- defined and reproducible units. The ideal unit of dose from the Nevertheless, the concepts of exposure standpoint of radiation protection and and fluence are philosophically rather biophysics would be the one which would close: They both attempt to define the produce the same biological effect radiation field independently of its independent of the kind and energy of interaction with matter. radiation. Such an ideal is, parti- ^ cularly on biological basis, probably f The importance of, and the state unattainable because of the extreme of art achieved in modern dosimetry complexity of radiation-induced damage ' may be measured against the fact, that in living systems. For realization, a ^ dosimetry and its aspects are discussed physical dose unit is applied which ' within the frame of physical symposia gives nearly the same biological effect ^ and conferences, today. Nevertheless, independent of the energy of a given ' there has up to recently been much kind of radiation. i discussion of the fundamental concepts and quantities employed in radiation Thus, it is the aim of dosimetry to J dosimetry. This has arisen partly from determine a physical quantity to which » the rapid increase in the number of the chemical, biological and medical individuals using these concepts in the effects can be related. In this conne- expanding field of science and techno- ction particularly those quantities will logy, partly because of certain be of importance, v^hich describe the 1 obscurities in the existing formulation physical interaction of radiation with i of the quantities and units themselves. matter. ' I For instance, a serious source of confusion has been the failure to define adequate, and that in time, the 198 . . . . Radiation Quantities and Units (DE) = D(QP).(DF) Prom results of radiobiology it is The dose equivalent is a rather obvious that local radiation effects can hybrid quantity compounded of three well be correlated with local energy den- elements, the first consisting of physical sity. Therefore, it appears logical to data, the second concerning factors choose the energy absorbed (or alternati- derived from radio-biology and the third vely imparted to) a mass of matter for consisting of administrative factors. dose description. The energy imparted by Thus, dose equivalent is by definition ionizing radiation to the matter (AWp) immeasurable in a volume is the difference between the sum of the energies of all the directly The unit of dose equivalent is the and indirectly ionizing particles which "rem". The dose equivalent is numerically have entered the volume (AW-g) and the sum equal to the dose in rads multiplied by of the energies of all those which have the appropriate modifying factors. left it (AWj^), minus the energy equiva- lent ( A W^) of any increase in the mass ii) Recently defined is the quantity that took place in nuclear or elementary "kerma" which represents the kinetic particle reactions within the volume energy transferred to charged particles by the uncharged particles per unit mass of the irradiated medium. This is the same common interpretations On the basis of "energy imparted to as one of the of 'first collision dose', that matter", the concept of absorbed dose D a concept- has ol great value in fast has been defined and recommended by ICRU proved to be neutron dosimetry. The concept is also ll'^ as "the quotient of dWj) by dm', where closely related to the energy equivalent dWj) is the energy imparted to the matter of exposure in an X-ray beam. by the ionizing radiation in a volume element dV, and dm = pdV is the mass of Per definition, the "kerma" (K) is the matter with the density p in that quotient of dV/ by dm, where dV/r^ is the volume, the sum of the initial kinetic energies of all dWg 1 dW^ indi- ^ _ ^ the charged particles liberated by dm p* dV rectly ionizing particles in a volume element of the specified material, dm is By this definition the absorbed dose has the mass .of the matter in that volume the dimension energy per mass which in el enent dV terms of the SI units refers to J kg~^. The special unit of the absorbed dose is ^ dWj. 1 dWg. ' the rad. . " ^ dm" p ' dV" 1 rad = 0.01 J kg"""", formerly g""'" Kerma can be a useful quantity in 1 rad = 100 erg dosimetry when charged particle equili- brium exists at the point and in the The definition of absorbed dose is material of interest and bremsstrahlung valuable for all types of radiation and losses are negligible. It is then equal radiation energies in all kinds of matter. to the absorbed dose at that point. Prom However, the of indication absorbed dose the more specific definition K = "^-^^^/p is only useful if conditions of the irra- (v7here = energy fluence of the photons; diation and the material, in which the Y [io-jo = mass energy transport coefficient) absorbed dose has been determined, are io becomes evident that it allies the reported. Moreover, the definition primary and secondary components of the appears incomplete without specification radiation field for mathematical treat- of the size of the volxme element3. ment of dosimetrical problems. The unit of kerma is equal to that one of absorbed Apart from the absorbed dose, addi- dose tional quantities and units common in dosimetry should be mentioned here: ,iii)V/hile for photons, the reduction of fluence or energy fluence is primarily i) For protection pxirposes it is by a reduction of particles, the useful to define a quantity which will be caused energy fluence in case of charged parti- termed the "dose equivalent", (DE) . (DE) cles decreases mostly by energy losses is defined as the product of absorbed dose, of the particles with practically con- D, quality factor, (QF), dose distri- stant particle flux density. For charac- bution factor, (DF) ,and other necessary these energy losses, the mass modifying factors. terizing stopping power S has been introduced. 199 . The mass stopping power of a mate- V/e shall distinguish betvreen the rial with the density p for charged two basic approaches to radiation dose particles with the energy E is the determination at a specific point of quotient of dE and the product of p and interest in matter: dl a) The first approach gives primary attention to the radiation field itself; ^ - p.dl in concept, measurements of energy-angle distributions of particles in the field where dE is the mean energy loss i^ithin are carried out to specify the radiation the path length dl in material v/ith the at each point in terms of physical density p. quantities, giving rise to direct absorbed dose calculations. iv) A quantity closely allied to stopp- ing power is the linear energy transfer, b) The second approach characterizes abbreviated LET. This is defined as the the field primarily in terms of its linear-rate of loss of energy (locally interaction with matter in local vicinity absorbed) by an ionizing particle of the point of dosimetric interest, by traversing a medium and may conveniently appropriate measurements. This approach be expressed in keV/fj,. The use of the is of great practical value and has concept of LET concentrates attention in formed the basis of almost all radiation the transfer of energy to the material, dosimetry rather than on the loss by the particle as does mass stopping power. The distinction between the two approaches is somewhat arbitrary in that Physical Concept of Radiatiori Dosimetry we know the radiation field only through" its interaction with matter. So far, the concepts of some dosi- metric quantities and units and their Calculation of Absorbed Dose from Field definitions have been revievzed; it is Parameters pertinent to examine physical concepts I, and practical techniques currently used The calculation of absorbed dose in operational dosimetry. provides the term energy imparted to ( matter, W-^. The concept of energy Implied in the term radiation dosi- imparted will be considered from the metry is the central problem of the point of view of a macroscopic field radiation field characterized by theory. specific field parameters. V/ithin the radiation field there are interactions A complete specification of the between the ionizing particles and the field can be made in terms of (i) the atoms or molecules of matter. The nature of particles, (ii) the spatial absorbed dose refers to such interactions. density of particles, (iii) the energy Though absorbed dose does not give a of the particles and (iv) the direction final answer on the kind of expected of the particles. This can conveniently biological effect, it is that dose be expressed by n (r, E.iX, t) d"^r i quantity which corresponds with the dEdH, which is the number of particles observed biological reaction in the at time t in the volume element d"^r most promising way. It seems important around r with the energies between E and to point out this fact, in particiilar, E + dE and v/ith the velocity vectors in as the opinion can be heard that it is the solid aiigle element of dO-around the sufficient to refer chemical or biolo- unit vector-ft.. Other parameters, such gical radiation effects solely to, for as polarization"' v;ill not be regarded. instance, particle fluence. Nevertheless, field quantities such as particle flux In the present case of a field of density, particle fluence, energy flux photons and electrons, '.1-^ on the basis density and energy fluence are reDated of ICRU definition is given by the to dose quantities by physical laws via general expression, in which the the interaction coefficients dependent temporal variations are neglected. on radiation energy and matter for the different types of radiation, for Wj, = jK(r) pdV-]"dVj"dri .diV[A instance, the attenuation coefficient, .Je®I® the energy absorption coefficient, stopping povrer as well as capture and (r,^E®) dE®J scattering cross sections. 200 : where: The absorbed dose D in the point r is then calculated by u (eP' P (?,^,eP) d^ I . lim D V-»0 The indices p, e refer to the photon or JpdV electron component the radiation field. Calculati on alone is rarely sufficient l(r,A, E)dBdX^- the fluence of the res- for dose determination but will provide pective radiation compo- a limited number of measurements. In nent in the energy and principle the determination of field angle range under consi- paramet er s such as particle fluence and deration energy sp ectra are well-established physical concepts and permit quant ifi- E the energy of electrons cation of unperturbed radiation fields or Dhotons by utiliz ing highly sophisticated technique dV the volume element From this, any absorbed dose may be dXI the solid angle element calculated using the fluence (r,^,Ej distribution for each kind of radiation mass energy transfer incident on the medium. However, to coefficient make thorough determination of field parameters in, as is normal, an imknown radiation jKpdV the total kinetic field is complicated and time- initial consuming; most energy of electrons of in cases it may even be impossible and, moreover, not the volume dV, V7hich all input data concerning interaction have been released by the with matter will be knovm with photons through photo and sufficient accuracy. Compton effect Particularly, the respective interaction coefficients for a certain material change with the particle For the calculation of the electron energy thus providing knov/ledge in its fluence I® of the first generation of spectral distribution. This distribution photo or Compton electrons one can proceed may change v/ith penetration as follows depth for reasons of interaction with matter, and that both Ej)dDjdXl = lJ.jP(?^,ri^,EP). for photons and secondaries. Moreover, the consistency of most absorbers is normally not homogeneous causing serious discontinuities in the field parameters and requiring differentiation of the — dH dUdEPdE? . interaction coefficients. After this short analysis of the more theoretical approach of absorbed In this equation is dose some actual problems in photon dosimetry shall be pointed out. At 11 the number of electrons first, basic field parameters, such as per unit volume of the low energy photon spectral distributions, absorber still look for an intensive investigation. The evident output of those investiga- direction of primary tions influences the largest field of photons X-ray application, the X-ray diagnosis. As a high proportion of the ionizing da/dS^dil^ differential cross radiation received by the population is section for the genera- due to medical X-ray diagnosis it is tion of photo or Compton essential that the necessary diagnostic electrons information shoiild be obtained v/ith the least possible amount of radiation. direction of photo or Compton electrons of trie In the range where the energy first generation r_^lative dependence on the mutual effect of to the direction jQ.^ patient and detector systems is great, as is the case with the usual poly- energy of photo or cliromatic X-ray spectrum. X-ray spectro- Compton electrons metry is indispensible in answering the 201 v questions which arise. From the spectra of a diagnostic X-ray tube (operating at 120 kV) monitored in front of and behind -f— a phantom it can distinctly be seen, that the low-energy component of the primary radiation merely contributes to the exposure of the patient but is hardly noticeable any more in the image forming radiation (Fig. 1). Different filtration / \ at the tube strongly affects the spectral / distribution of the primary radiation whereas the spectrum of the image forming 1 radiation is mainly influenced by the object and the tube voltage. Hence, the Photon energy (keV) necessity for higher filtration to reduce radiation dose to the patient is evident. Fig. 2. Comparison of an attenuated pri- mary radiation ( , measured) no to the integral scattered 0) b) radiation( , calculated) at an K — 2mmAI — 2mmAl image point. Phantom thickness 1 — immAI 20 cm HgO, tube voltage 120 kV, 60 — immAt* — £ mmAt* / field size 10 x 10 cm*^. | QlnvnCu VmmCa \ fj i to the widely used scintillation spectro- /'/ [i] A IY|I meter with limited resolution depending 1- on energy would yield serious problems in ^f unfolding the pulse height spectra. 1 1 Fig. 3 shows the deterioratim of an assu- Photon Entfgy med but typical test spectrum by the inherent qualities of two spectrometric systems (ciystem I : fwhm=const. System Fig. 1. Primary radiation (a) in front of II: fwhm=f(E)). Thus considering the and (b) attenuated by a 20 cm exposure of patient quantitatively the water phantom for different tube determination of fluer.ce together with filtration. Tube voltage 120 kV. geometric data must only be regarded as the first step for solving the above However, comparison of the spectra introduced fundamental integral equation. of the image forming, attenuated primary radiation, and the scattered radiation both incident at an image point clearly showLS the limits of scatter elimination (Fig. 2). The spectrum of scattered radiation includes a large portion of the same energy range as the primary radia- tion spectrum thus hardly rendering feasible an energy-selective filtration of the scatter component behind the patient. Furthermore, a strong increase in scatter proportional to the increase in volume irradiated can be recognized. Problems of adaptation of the spectral sensitivity of the image recording system to the available radiation quali- ties as well as those relating to the Fig. 3- Influence of energy resolution improvement of grids can also be solved of a detector on the pulse by spectrometric methods. height spectrum. For measurements of the spectrosco- I'lany attempts have been carried pic field quantities, semiconductor out to determine a ttenuated photon and detectors represent state of art since electron spectra w itnin organs of inter- the interpretation of their pulse height est together with the interaction and spectra into polychromatic spectral energy absorption coefficients. Since fluence is feasible with the well-known a considerable lac k of information of characteristics of the detectors. In those data exists, approximations by particular, the constant resolution over Konte-Carlo transp ort codes together the areas of interest simplifies the with an appropriat e mathematical descri- calculation of true spectra. By contrast. ntion of the human body's shape and of 202 . . . . its dimensions have been carried out . The special unit of exposure is the Problems arise from considering all roentgen (R) ; 1 H = 2.58 x 10"^ C kg"-"-. interactions possible as well as their With present techniques it is difficult mathematical treatment. From results to measure exposure when the photon already available agreement vfithin a energies involved lie above a few MeV or factor of 2 is supposed to justify those below a few keV. The principal quantity extensive calculations, in principle. in the relationship betv/een exposure and absorbed dose is the average energy Determination of Absorbed Dose by required to produce an ion pair (w-value). Measurements The "exposure" is measured v/ith ionization chambers which in dimensions and wall Absorbed dose evaluation and cal- material must fulfill the conditions of culations are generally verified by an CPE or Bragg-Grray experimentally determined description of the field parameters in terms of its CPE is achieved v/ith chambers walls interactions with matter. The objective consisting of air equivalent materials of this approach of absorbed dose is to so that avoid the complete field characterization by taking into account that the dose en _en quantities are integral quantities pro- ] S /wall S viding integration over the different air spectral field components. Thus, instead of using integration procedures on a and a linear extension d>R max of the calculative basis and the application of secondaries more or less knovm coefficients, one can alternatively apply selected measuring The BRAGG-GRAY principle describee techniques which are able to appro xima- the possibility to express the absorbed tively perform the intended integration dose Dm in a material by the specific experimentally ionization J in a small air filled cavity imbedded in the material by use of the In order to perform such a measure- equation ment, one must use an effect caused by irradiation which is easy to measure (S/p) (S/p; M = W.J and, moreover, in magnitude proportional air (S/p) (S/p) to absorbed dose. Since the medium to air air which the radiation dose is applied does, in general, not yield a proper measurable effect, a radiation sensitive detector provided the following pre-conditions are is brought to the point of dosimetrical fulfilled: (i) the cavity dimension must interest. It is the detector material be such that particle flux density is not = (ii) in which the dose-proportional effect is changed, i.e. ^^^y. ^jvj* for non- measured. For certain pre-conditions, ionizing radiation the ionization in the i.e. charged particle equilibri\im, CPE, cavity must be small against the secon- or the fulfillment of the Bragg-Gray daries of the material, i.e. (M-en)M'^ conditions, one can - by means of the ) . , (iii) the cavity wall d^^-^R, measured dose effect - perform the vj-hich^ii the range of secondaries, or is determination of absorbed dose generated made of tissue equivalent materia.l in in the irradiated medium as if it were case of biological measurements. there instead of the substituting detector. A suitable measuring effect Determination of absorbed dose (Dj^j) is the ionization of gases. As pertinent in an arbitrary material from exposure dose qiiantity the "exposure" (X) has (X) measured in air by means of the been introduced, for air as a detector BRAGG-GEAY principle is characterized, as material mentioned above, by The "exposure" is defined as the (S/p)^ Quotient of dQ by dm, where dQ is the air Sum of the electrical charges on all ^^(S/P? air the ions of one sign produced in air vrhen all the electrons liberated in a volume element of air with the mass dV, For conditions of CPE, defined by the equation = are completely stopped in air. conditional WqJ^)^^ (^^en'^^kr one obtains with ' _ dQ _ 1 da ~ ' (s/p)h ^ ~ dm p dV rSTpT^air 203 : the special form of the BRAG-G—G-RAY-pri- approximately equivalent materials this nciple for X and y-rays: ratio will change much less with the spectrum than the single coefficient. Therefore, the radiation spectrum does " air not affect the dose determination so ^^^en/P^air significantly as in case of dose cal- culations from the field parameters. By using [rdj = 0.869. X [r] which is the absorbed dose in air one receiv es The concept, as well as the methods the .^reneral formula: and tecliniques in dose measurements are well established, thus meeting the requirements of a high accuracy standard Dj,.[rdJ = 0.869 y . Z[Rj-f.XLRj \ '/'J But problems may arise from field en application and control of procedures and equipment. This is shown at the The f-fact or implying measurements determination of a basic property of a of exposure under conditions of CPE radiation detector as is the energy converts exposure values to absorbed dependence of its signal response dose} another conversion factor, g, in Fig. 4. Even for the same detector implies measureuents of ionization under different energy calibration factors may Bragg-Gray conditions. Usually, the be achieved at different labs for factors f and g are calculated from the reasons of differing calibration spectra ratios of the mean values of the mass applied. It is obvious that these energy absorption coefficients and tue discrepancies refer to different approa- mass stopping pov^er of the tv;o media, ches of effective energy with non-compa- respect ively tible spectra since monochromatic X-rays are, up to now, not common in the range , da ,„p -In dii-^ of low energy photons. In other terms, , „Pn — ^en^^^P hi dE^ it appears possible to produce any f = 0.869 response curve which you are asked for, f/ /-,Pn -In i® even a flat response, by use of an adequately filtered bremsstrahlung. The resulting serious problem may only be solved sufficiently by standardization -1. of calibration procedures. This was M lirgently called for at the IAEA- 0.869 dE^ Symposium on Advances in Physical and da — dBj-ne Biological Radiation Detectors in fall I(S(2')P~')air ^ 1970, however, without leaving a sound effect. It can be shown that the dose conversion factors f and g are not dependent on geometrical factors, such as depth in water or the field size, i'urther detai- led parameters of interest can be taken ' / from the respective ICRIJ-Reports / / ^ " / \ / > /' f-T^ ^ ;sue rrgelK ^ \ For soft tissue 1.1 =30 •/. air approximately energy independent between O.i and 10 MeV; the resulting absorbed dose D, . [rdj = 0.97. X tissue^ [rJ. Fig. 4. Response of a dosimeter for Obviously, also the above shown different qualities of calibration way of dose determination is dependent radiations (The curves are fitted;, on interaction coefficients which to unit sensitivity a 120 keV) provide prior knowledge of the quality 1. Assumed response to monoener- of radiation or making assumptions as to getic sources its composition. However, it is the 2. Calculated response to cali- ratio of interaction coefficients for bration set v;ith AE/Emax = 30j- the medium of interest and air as 3- Calculated response to a cali-= detector material v;hich influences the bration set with AE/Emai = 60*/f calculation. Particularly, in case of 204 Operational Dosimetry and Problems From a recent directory published by the International Atomic Energy Agency one can find that the high energy radiotherapy eqiiipments are concentrated in advanced centres of preferably deve- loped nations. This inequity certainly has created a separation of the level of dosimetry as practiced by the countries involved. The need for constant develop- ment and improvement of new, reliable dosimetric techniques has no doubt thrust Fig. 5. Spectral distribution of two the advanced institutions into the front X-ray qualities of the same HVI line in the field of radiation dosimetry. (0.75 mmCu) achieved with diffe- Radiotherapy centres in some of the rent tube voltages and filtrations. developiftg nations certainly cannot afford to catch up with this trend due to As a result, one has really to be in the lack of both equipment and trained doubt, if the problem of the establish- personnel. Moreover, facilities in such ment of absorbed dose or exposure measure- parts of the world have frequently ex- ments with an ideal uncertainty of around perienced neither the \irge nor the need + 4/. is further on of exclusive priority. for new techniques while other pressing Eventually it should be of preference to problems claim higher priority. direct main effort to the proper defini- tion and application of radiation fields In general, the most observable in terms of the respective parameters. deficiency in these centres is the lack A IAEA panel on the activities of of some of the equipment considered Secondary Standard Dosimetry Laboratories essential for basic dosimetry work. This (S3DL), taking place at Rio de Janeiro includes various types of ionization still at the end of this year will try dosemeters but, equally, education and to balance both the aspects of calibration dosimetric joining to reference labs. and education in order to overcome those problems, world-wide. The installation The necessity for transferring ra- of SSDL's by '.ffiO/LlEA has already encou- diation quantities between different raged improvement at many institutions labs has become evident bv multinational and thus, in turn, has increased the surveys for cobalt-60 radiation therapy standard of medical dosimetry practices. dosimetry, by means of a postal dose Standardization of procedures and intercomparison service. These surveys, techniques in these regions, however, based on a joint V^HO/lAEA^ project, seems to be a difficult task at the pointed out that more than 40X of the present tine. participating institutes exceeded by partly significantly more than + 5/. the A useful tool in the field of reference dosimetry value. applied dosimetry, supplying standard ionization techniques can be the solid These findings for cobalt-60 gamma state dosimetry, which is based on dosimetry which dosimetry somehow is meas\rrable changes of, at least, one simple to proceed, give a certain imagi- property of the solid body as a fimction nation upon the dosimetric problems in of interaction with radiation. Some that practice where X-rays are applied and newer solid state dosemeters, for where, in addition, the accuracy of dose instance thermoluminescent or photolumi- distributions is of interest. In this nescent dosimetry, have proved particu- case all uncertainties of an X-ray gene- larly suitable for special problems such rator application must be taken into as storage of dose information, use in acco\int. In this connection one again very confined spaces or measurements of laust point out the need of establishing extremely low or extremely high doses. characteristic field parameters, i.e., at Further, for certain detector materials least, the penetrability or the HVl of there is a relatively small to negle- the X-ray quality imder consideration. gible energy dependence of the relative However, as can be seen from Fig. 5 v/hich mass stopping power compared v;ith water or shows the spectra of two calibration soft tissue. The geometrical and me- qualities with the same HVL, even this chanical features of the detectors are first approximation to the radiation outstanding together with a reasonably energy by its penetrability characteris- good reproducibility of the radiation tics, is a doubtful value. induced signal, whicn has just again been 205 . , . . roven for thermoliiminescent dosimetry However, there are still fundamental TLD) on the occasion of an I.nternatio- monitoring problems due to discrepancies nal Buratom Intercomparison on Nov, 11 between the objectives of radiological to Nov. 15, 1974 at Bologna, Italy. protection measurements and its physical The results of that meeting, clearly practicability. As a common basis of point out the necessity for a new gene- understanding, the principal objectives ration of read-out devices to achieve of personnel monitoring are the demons- higher precision and that more reliably. tration that the level of radiological The new readers shoiild be automated in safety meets appropriate standards, and cycliig \:±th a multi-step temperature the provision of information that allows program and diminish the influence of improvements of working conditions if planchet reflectance on the signal, f.i. necessary. In more specific terms, the by using hot gaz heating. Nevertheless, objectives are to achieve compliance with, TLD is worthwhile to be shortly reviewed the recommendations of ICRP as reflected on its possibilities and the problems to national legislation. These specific still to be solved. Multiprobe TLD objectives can only be met if measure- measurements in medical physics can be ments of the personnel dose allow esti- recommended as routine procedure for the mation of the mean dose in various determination of dose distributions, organs, since this is the basis of ICRP surveys of radiation burden in critical recommendations. In practice, however, organs during radiation treatment as the radiation field will neither be well as for equipment checks . Problems locally nor temporally constant for of sterilisation or handling of the simple straight-f orwar_d I measurements, detectors can be overcome. i.e. each point of the body surface will be exposed to a radiation field different In the large field of radioecology in intensity, spectral distribution and a number of surveys and an equal number incident direction. For these reasons, of different results due to inadequate the relationship between measured dose assessments can be found in lite- personnel dose at the surface and requi- rature. These surveys involve investi- red organ dose is rather complex and gations of radiation burden from natural ambiguous sources ( t errestrial and cosmic radiation, radiation resulting from building Because of the lack of physical materials) and sources caused bjr civi- realization of the measurement of organ lization and technical progress (medical doses an appropriate philosophy has been diagnosis, nuclear power plants). Of installed declaring the surface dose particiilar interest will be exact data measured at a representative place of on the medical radiation burden causing the trunk to be equal to the respective around 95/. of the artificial radiation body dose. This philosophy is valid for burden as well as routine dosimetry in external radiation coming from directions the popula,ted environment of nuclear predominantly within one hemisphere, i.e. povjer stations for permanent control of the direction towards which the individual the radiation level. The importance of is facing. quant it itative information on the effect of radiation on human beings justifies In order to meet the requirements any effort of this philosophy, the dosimeter should be approximately tissue-equivalent In all these application fields of between photon energies from 10 keY to radioecology TLD could be of major im- 3 PleV. For discrimination between the portance. However, sensitivity and radiation burden of the skin, due to p's energy dependence are still lacking and low-energy photons and of organs in improvement. Basic features of the the depth due to higher energy photons a detectors would be a lower limit of simple dosimeter system should be suffi- detection of jirad and particularly, an cient consisting out of two detectors energy independent response down to differently shielded - in compliance with around 10 keV. At the moment, there is, recommendations of ICRP publication-^^ ,15 to the authors' knowledge, no detector In this dosimeter-system one detector material fulfilling both requirements. behind 10 - 20 mg/cm^ filtration would differentiate the non-penetrating radia- In occupational monitoring the tion, the second detector behind 0.5 - 1 possibilities of dose assessment with g/cm^ tissue equivalent filtration would TLD meet, in general, the requirements give a measure of radiation of higher of modern health physics trends for penetrability vihich could be set equal higher possible accuracy and that to to the organ dose. better respect the I'-IPD values and determine also lov/ doses for an amelio- TLD is able to meet the requirements ration of the working conditions. of this philosophy, within the error 206 . I . limits acceptable of a factor 1.5 in Modern solid state dosimetry techni- Fig. 6. However, there still remains ques eventually matching the require- the problem of more specific data inter- ments of microdosimetry, such as thermally pretation in case of doses in the stimulated exoelectron emission (TSEB), vicinity or in excess of i-EPD's. are still under elaboration. TSE3 promises a detector depth around some V/hile personnel dosimetry is well loci ngstroem. Hov/ever, at the moment, installed in developed nations, using the investigations deal still with the partly highly sophisticated dosimeters interpretation of the TSEE mechanism and discussing problems of philosophy as prior to dosimetry application. Results mentioned above^^, more than 30X of of unexpected high exoelectron energies occupationally exposed personnel in in Fig. 7 are first steps of betjer developing coimtries is not monitored. understanding of the phenomenon-^ ^ 2ven in countries vrith monitoring Particularly for measurements in vacuo, ser^rices which I got to know as an IAEA- high reproducibility and linearity has expert, this service was partly done been foimd for TSEE output versus alpha quite unsufficiently. For instance, one or gamma fluence for different grades of service applying a four-filter badge, ceramic beryllium oxide in Fig. 8. evaluated only the open-window field for all kinds of radiation vrorkers. Further, the calibration has been done only v/ith a 70 kV radiation X-ray quality using no additional filtration to the inherent filter. It is obvious, that energy independent TLD introduced to personnel monitoring in these countries will be of major help and effectiveness in radiation prot ection. o < KhfVi I •c^i I. >iao kiV ' 1 1 III 1 1 1 iiJi 1 1 1 1 Mil 1 1 1 Mill 1 1 M "r J Relarding potential IV A Fig. 7. Integral exoelectron energy dis- . c • a tributions 1 o for ceramic BeO (Bery- llium Consolidated) during the > » heating and cooling cycle. Para- meter glow temperature. /-fiuence fcm-^J ^ a tffl660i-ev ft 1 1 1 1 IIJI I 1 I It 111 1 1 1 1 III! 1 1 1 1 >iii B 100 xm UOOD atlSXfi ' Expcsura X,,fTiR Fig. 6. Reading of TL dosimeter shielded with 300 mg/cm in dependence of the dose applied (Parameter: photon energy) For the understanding of radiation mechanisms in radiobiology and radio- chemistry it is important to intruduce further parameters for field description in addition to the absorbed dose. Particular interest is given to the a - fluence lan-'l density of energy imparted along the path of a particle (LET concept), to the Fig. 8. Integral TSEE output of different energy deposed in a certain object size ceramic BeO versus a- and y- fluence. ' or to the statistical distributions of these energy amounts deposed in certain object sizes. The quantities and .methods important for the studies of reaction nechanisms and describing microdosimetry shall not be further discussed, here. 207 . . Conclusion 2. ICRU-Report 11, 1968, Radiation Quantities and Units. illthough the concept of energy 3. Rossi, n.H., Mcroscopic Energy absorption in matter represented a phi- Distribution in Irradiated tiatter, losophical departure from the idea of Radiation Dosimetry, Vol. I, Acad. quantifying the radiation field per se, Press, New York (1968) . the absorbed dose probably is, at pre- 4. Rindi, A. and Thomas, R.K. Health sent, the central physical dose quantity, Phys. 23, 715 (1972). while other dose quantities are auxiliary 5. Fano, U., Spencer, L.V. and Berger, quantities supporting, for instance, the K.J. Penetration and Diffusion of determination procedure of absorbed dose X-Rays, Handbuch der Physik 38/2, (exposure) or requirements of health 660 (1959). physics (dose equivalent). But, review- 6. Jones, T.D., Auxier, J. A. and Snyder, ing all the dose quantities existing and v/.S. Health Physics 2±, 241 (1973). having in mind, that even the main 7. ICRU-Report 10 a, 1962, Radiation quantity, the absorbed dose, cannot be Quantities and Units. measured simply in practice^ ^one is 8. ICRU-Report 14, 1969, Radiation inclined to think of DENNIS exclaiming: Dosimetry: X-Rays and G-ainma Rays with Once upon a time we had the Roentgen, Maximum Photon Energies between 0.6 which we could measure but didn't want,- and 50 HeV. then we had the rad which we wanted but 9. ICRU-Report 17, 1970, Radiation couldn't measure; and now we have got Dosimetry: X-Rays generated at the kerma which we don't want and can't Potentials of 5 to 50 kV. measure" 10. ICRU-Report 19, 1971, Radiation Quantities and Units. Both the approaches of absorbed dose 11. ICRU-Report 23, 1973, Measurement of pointed out above, i.e. starting indire- Absorbed Dose in a Phantom Irradiated ctly, from the determination of field by Single Beam of X- or Gamma-Rays. parameters or from direct measurements 12. Moos, V/.3,, Balamutov, V.G. and of the radiation interaction with matter, Abedin-Zahed, R., National and are still lacking further and more exact International Radiation Dose Inter- data concerning basic parameters of comparisons, IAEA-PL-479/18. interaction. For instance, there are 13. ICRP-Report 12, General Principles serious doubts as to the adequacy of of Monitoring for Radiation Prote- %if-values, there is a need for stopping ction of V/orkers. power data and spectroscopy of secon- 14. Dunster, H.S., Symposium Radiation daries in matter-, further there are Protection - Philosophy and problems in measuring compatible chara- Implementation, Aviemore / Scotland, cteristics of field instruments for June, 1974. bremsstrahlung due to the absence of 15. Ecker, E.H., Wittmaack, K., Regulla, standardization of calibration conditions. D.F. and Schulz, F., Proc. 4th Int. Thus, care has to be given to the Conf. on Luminescence Dosimetry, correlation between the measurement Krakow (1974) output and the absorbed dose. In applied 16. Dennis, J. A., Personnel Dosimetry dosimetry there is the further problem Techniques for External Radiation, of data interpretation which often are p. 207, EiiTopean Nuclear Agency, measured at a point different from the i'ladrid (1963) . one of dosimetric interest. Further, absorbed dose cannot be seen isolated from considerations of LET and micro- dosimetry in the fields of radiobiology and radiotherapy. However, emphasis should be given to the importance of ensuring that the Inevitable imprecision of data measiirement , estimation and transfer is not reflected in a corresponding imprecision of concept. References 1. Franz, H. and Kobner, V/. Proc. 2nd Int. Conf. on the Peaceful Uses of Atomic Energy, Geneva 1958,P/971 21, p. 101. 208 , . NEUTRON DOSIMETRY BY TJEERMOLUMINESCENCE DOSIMETER Yutaka Furuta and Shun-ichi Tanaka Japan Atomic Energy Research Institute Tokai Research. Establishment Tokai-mura , Naka-gun Ibaraki-Ken, Japan In this report, a historical survey of neutron dosimetry by thermoluminescence dosimeter (TLD) is made to begin with and then, as the basic problems for neutron dosimetry, the energy response to neutrons, gamma-ray discrimination perfor- mance in gamma neutron mixed fields, and sensitivity improve- ment are described. Furthermore, two types of conversion efficiencies are introduced to obtain the integral glow value of TLD from its kerma value. These efficiencies are given for any charged particle and may serve not only to estimate neutron energy response of any TLD but also to study the energy transfer to material from charged particles. As applications of these studies, the possibility of development of a rem response TLD or absorbed dose measurements for neutrons by TLD are also described. (Charged particle, dosimeter, dosimetry, efficiency, gamma ray, kerma, neutron). Introduction (TL) phenomena including radiation dosi- metry as a research tool. In early days, Because of its many superior chara- studies were mainly made for X or gamma cteristics, studies of the thermolumi- rays, but in later 1950s considerable nescence dosimeter (TLD) have rapidly effort was concentrated on the practical increased during the past ten years. means of measuring neutrons with TL Especially, some of TLD's have an materials effective atomic number similar to that of air and most of the studies have been Haring and Schoen^ tried to detect devoted to gamma-ray exposure measure- neutrons by a CaF2 film with or °Li ments. Therefore, the studies of TLD as film held in front of the CaF2 film. a gamma-ray dosimeter are considered to The CaF2 TLD responds to alpha particles have proceeded fairly well at present. produced by (n,a) reaction of ^^B or °Li with neutrons of a high reaction cross On the contrary, investigations on section. These materials serve as the neutron dosimetry can not be considered radiator of alpha particles. They as sufficient and there are many problems described that the lower limit of neutron yet to solve. detection in the case of using -'•^B film was 3 X 10^ neutrons, and besides, °LiF In the present report, the authors film was more energetic and found to be will survey the historical development more suitable and 5 x 10^ neutrons could of neutron dosimetry by TLD and v;ill still be detected. Furthermore, they show the approaches to develop a new used simultaneously a second GaF2 film dosimeter or dosimetry to neutrons. without the radiator film in order to eliminate the contribution of gamma rays Historical Survey to the TLD. In their report, it was also suggested that the utilization of protons The discovery of radiation-induced recoiled by neutrons in radiator was a thermoluminescence goes back to the disadvantage because of their rather small beginning of the present century. It energies, but the utilization of neutrons vfas reported recently that Mme. Curie to be moderate, which could possibly be wrote in her thesis her discovery of the done by the human body, was promising. phenomena in the course of studying the We see in their report many fundamental various physical and chemical effects concepts for neutron dosimetry by TLD produced by exposing various substances used in these days. to radium^. Rapid development of the studies, however, may be considered to A neutron dosimeter using TLD in have started in 1950. conjunction with a fast neutron moderator and a radiator was reported by Surjadi^. 2 Daniel et al had introduced wide His dosimeter consisted of a layer of feasibility of the thermol-uninescence CaF2 '^-^^ enveloped by a LiF film and a 209 . . , paraffin ball surrounding the detector thermal neutron fluence similarly to the device. He studied the relation between case of Wingate et al.'. the sensitivity and the ball radius from 4 to 12 cm and the energy response to mono- 3. Endres^ reported a pair of energetic neutrons of 1,2 and 14 MeV. capsules of LiF TLD's used at Hanford as a neutron dosimeter, of which one was The sensitivity to fast neutrons filled with a phosphor alone for measure- can be considerably increased by suspen- ment of gamma-ray exposure and the other sion of LiF TLD in alcohol, and the filled with the same phosphor and alcohol method was practiced by Karzmark et al^. (or other hydrogenous material) for In this case, alcohol serves both as the measurement of the gamma-ray plus neutron moderator for fast neutrons and as the exposvire. radiator of recoil protons. Furthermore, it is convenient to use a volatile 4. At Brookhaven National Laboratory, liquid like alcohol because it is readily a neutron dosimeter system has been evaporated at room temperature prior to developed by using LiF TLD within a read-out Bonner sphere. In the report by Disten- feld et al. a 12" diameter polyethylene At that time, Harshaw Chemical sphere modifies the neutron response Company (Cleveland, Ohio, U.S.A.) had characteristics of the LiF TLD to reaso- developed activated LiF crystals speci- nably resemble the dose equivalent fically for TLD in cooperation with the response characteristics of neutrons in University of Wisconsin. These materials tissue from thermal energies to approxi- were identified as TLD-100 (natural Li matelj'' 20 KeY . Evaluation of the gamma- containing LiP TLD) and TLD-700 (^Li ray response is made by using "LiF TLD enriched LiF TLD) . Cameron et al° of the (°Li enriched LiF TLD) and ^L±F TID ('Li university studied the characteristics enriched LiF TLD) pair simultaneously in of these TLD's and showed that thermal the system. neutron dose in gamma neutron mixed fields may be estimated by subtracting To evaluate experimentally the neu--, the light output of TLD-700 from that tron shielding performance, Gayton et al. of TLD-100, because of the response of reported several methods using LiF TLD. TLD-700 to thermal neutrons was less than One of them was a new type of spectro- 0.5/. of TLD-100. meter, the DELTA spectrometer, which used LiF TLD's along the axis of a The 1st International Conference on cylindrical moderator irradiated on one Luminescence Dosimetry was held in 1965 face. The spectral information was at Stanford and many papers were sub- obtained from the thermal neutron ! mitted. In this conference, the major fluence distribution by an iterative reports concerning neutron dosimetry were solution to a matrix equation. The as follows: report described that the device covered nine decades of energy and was suffici- [ 7 ; 1. Wingate et al. reported the TL ently^sensitive to measure fluence levels j response of TLD-700 to thermal and fast of 10° neutrons/cm^ neutrons at energies from 0.26 to 14 MeV. From the results, they concluded that Kuz'min et al. studied the relation TLD—700 made a convenient gamma-ray between sensitivity and phosphor layer dosimeter in mixed gamma neutron fields thickness of TLD with recoiled proton because of its low neutron sensitivity. radiator, and obtained a flat response Furthermore, they indicated that the dosimeter to neutrons having energies of thermal neutron fluence may be conveni- 0.2 to 4.5 MeV. ently measured witii normal LiF( TLD-100) with linear relationship between light Stolterfoht and Jacobi^^ also obtai- output and neutron fluence up to about ned energy response of ^LiF TLD with and 10-'-^ neutrons/ cm^ , and also pointed out without alcohol using two kinds of from their results of glow curve that a capsule made of teflon and polyethylene higher read-out temperature was required to fast neutrons of 3 to 15 MeV. than gamma-dose measurements. In 1968, the 2nd International 2. A pair use of TLD-100 and TLD-700 Conference on Luminescence Dosimetry was was proposed by Simpson to obtain held at G-atlinburg. In this conference, gaimna-ray dose in gamma neutron mixed energj' responses were reported by Endres fields of a reactor environment utilizing and Kocher-^ • to neutrons of several the characteristic of the same response types of TLD's (TLD-lOO, TLD-600 (^Li to gamma rays and different response to enriched LiF TLD made by Karshaw neutrons. He also obtained the linear Chemical Co.), Li2B40Y, CaF2, and BeO) relationship between light output and placed on a polyethylene phantom with and 210 , without Cd or shield. a new idea was reported by Mayhugh et al.2-^. They tried to apply the activa- Use of a TLD with neutron activation tion of TLD composite material for material was proposed by Kocher and thermal neutron dosimetry. That is, Endres-^5 as a personnel neutron dosimeter, after exposure of a TLD in gamma neutron of which TL is induced by radiations (thermal) mixed fields the TLD is anne- emitted from the material activated by aled. When a constituent nucleus has neutrons. In their dosimeter, Rh was an activity by thermal neutrons, the TLD used as a neutron activation material. landergoes self-irradiation (self dose) from the internal radioactive nucleus. A pair of ceramic BeO discs, of A period of time after, the TL is read. which one was covered with a non- The read corresponds to the neutron hydrogenous material (graphite) and the exposure, independent of the gamma-ray other with a hydrogenous material contribution during exposure in the mixed (polyethylene) was reported by Becker fields. They suggested 44Ca or ^ Dy as and Crase-'-". For read-out, thermally suitable isotopes contained in the TLD. stimulated exoelectron emission (TSEE) technique was used. In November of the same year (1971) a 17 Symposi-um on New Development in Busuoli et al. showed that the Physical and Biological Radiation Dete- ratio of the main peak (210°C) and the ctors was held by IAEA in Vienna. In the high temperature peaks (250 - 300°C) of symposium, Attix^^ discussed the neutron the glow curve of TlD-100 is 24.5 for Ixminescent dosimetry problem and pro- gamma rays and 2.4 for slow neutrons, and posed a TLD system to obtain the suggested that this characteristic makes neutron tissue dose by BeO TLD for ther- it possible to use LiF TLD for measuring mal neutrons, for intermediate neutrons neutron dose in gamma neutron mixed by a mixture of some TLD-lOO powder with fields. TLD-700, and for fast neutrons by TLD-600 and TLD-700 combination. Falk-'-^ reported a personnel neutron dosimetry system consisting of three Neutron dosimetry technique utili- pairs of LiF TLD's (TLD-600, -700) shiel- zing TLD self dose proposed by Mayhugh^-^ ded with Cd. In his system, one of the for thermal neutrons was extended for pairs is shielded from the front, one fast neutrons by Pearson et al'^^. They pair from the back, and the third pair is used phosphors such as MgFp TLD which shielded from both front and back. contain two activating nuclei with different threshold energies and diffe- An application of the LiF-teflon rent decay times, and suggested some discs using °LiP and 'LiF TLD's pair neutron spectrum analysis. laminated between the plastic layers of an identification card was reported by Efforts to utilize TLD's for per- Nash and Attiz^S as accident dosimeters. sonnel neutron monitoring are continuing at several major laboratories. At the In July 1971, the 2nd AEC Workshop Savannah River Laboratory a prototype on Personnel Neutron Dosimetry was held badge had already been developed'^'^, and in New York^*^. In this meeting, many further development have been made by researchers participated from main esta- Hoy^^. The newly developed dosimeter blishments in the United States. It was consists of a 2" diameter polyethylene then reported that most of the establi- hemisphere which is divided into two shments employed the albedo type TLD parts at I/4" from the roiinded end, and neutron dosimeter, and the following was only a large part is covered with Cd concluded at the meeting. plate. Both parts have recesses for a pair of ^LiF and .'LiP TLD's and the 1. Neutron dosimeters utilizing the whole placed in a stainless steel albedo neutrons require a fixed or well housing and attached to a belt. The known spacing between the dosimeter and report concluded that it has limitations the body of the individual. in certain energy regions of the spect- rum, but the dosimeter provides a reaso- 2. Energy dependence is still an nably acciirate method of integrating important problem, but the dosimeters personnel exposures from unknown spectra can give good results when properly worn at installations where neutron sources and when calibrated with neutron spectra are contained or sufficient scatter is will present . . approximating those to which they . be exposed. The response of LiF and Li2B40Y TLD The 3rd International Conference on to thermal neutrons has been investi- Luminescence Dosimetry was held in gated by Ma j born et al.^° primarily with October 1971 in Riso. In the conference, a view to using them for personnel moni- 211 toring in areas with mixed gamma neutron Basic Problems fields. The investigations include: 1) measurements of TL response vs. thermal If we wish to use TLD for neutron neutron fluence, 2) measurements of TL dosimetry, some basic properties must be response vs. dosimeter thickness, 3) taken into consideration. These are the measurements of TL response vs. isotopic energy response, gamma-ray discrimination, abixndance of °Li and -'-^B, and 4) measure- and sensitivity. We will describe about ments of backscattering and gamma-ray these problems. contribution from a phantom in a colli- mated-beam geometry. Energy Response Blum et al.^'^ reported a usage of a In any case, one of the most basic mixture of highly sensitive CaSO^ TLD requirements for radiation detection is (CaS04(a/]V28) ^nd glucose (3 parts of to know the energy response of the glucose and 1 part of CaSO^CTm) powder) detector to objective radiations. for fast neutron dosimetry. The same authors'^" also reported the results of Figures 1 and 2 show the energy res- fast neutron dosimetry by CaFp TLB in ponse of typical TLD's to neutrons. Ex- pair use with hydrogenous (polythene) and perimental results were obtained to mono- with non-hydrogenous (lead) screens. energetic neutrons produced by Van de They concluded that lead was a convenient G-raaff accelerator. In the same figures material for the latter and recommend the energy responses obtained by calcula- microrod type TLD rather than disk type tions are also shown. These were obtained because of the directional dependence of as follows: the former dosimeter. I I 1 1 I I I 1 1 I I M| i 1 1| I , , T1lll| I If Attix et al.-^*^ reported that an "1 attempt was made to determine the gamma- ®LiF(Mg)' ray dose component in the neutron beam from a cyclotron by CaFp and 'LiF TLD 6 icV (TLD-700) at U.S. Naval Research Labora- S V tory. Kocher et al.^"'" reported a five- element TLD using LiP blocks for beta 1C5" S 8 particles, photons^ and neutrons used at eKp.(F irut« & Tanaka) Hanford, of which 'LiF block is shielded to provide interpretation of the 1 cm tissue depth dose, and a second '''liP 1 1 I I I" • ' ' ill 'I'll block is xmshielded to provide the kerma 1 icT* id"' I 10 to' dose interpretation, and two "LiF and neutron energy (MeV) one 7LiF blocks are used for fast and thermal neutron dose interpretation. Calculated response of several albedo neutron dosimeters using °LiF TLD was reported by Alsmiller and Barish52 a { l/IO) - for neutron energies lower than 400 MeV. K They obtained the results for each of the dosimeter geometry considered, which were presented for both mono-energetic and continuous incident neutron spectra and and isotropically for both normally ^ i exp. (Wlngate et al.) j^j- ' incident neutron fluences. a ' (Goldatoln et "l-jl^, o " (Furuta i TanaXaCj. cal. ( " ) The 4th International Conference on Dosimetry was held in 10' Luminescence Kf« tcr' I )o Xrakdw this summer (1974). The present nautron energy (MeV) authors have not acquired yet the pro- ceedings except manuscripts of a few Fig. 1. Energy responses of ^LiF and "^LiF papers. In these, there is a paper on therraoluminescence dosimeters. composite dosimeters using CaS04 and BeO phosphors for x-ray, gamma-ray, When the TLD is calibrated by ^"^Co beta-ray, and neutron dosimetry reported gamma rays, the integral glow value to by Iga et al.33 in their dosimeter. neutrons is obtained by the kerma CaSO.(Tm) powder and Won-TL °Li or 'Li calculation compound mixtures in a weight ratio of (i; 1 : 1 are used. = ?^(i)-^(i) 212 , , , . , I = C.e(.).(E^ K(i) + Q(i)).cr(.)(E^) " 1 r- I ' ' m il III I II'll'l'T ' iii|"^f 111! I— .$(Ej,),N^^ (2) CoSG4(Tm) where integral glow value (R i I Co equivalence/neutron. 9 8 g cin-2) , . S > incident neutron energy (HeV), I 1 1-1 *^ ^(i) mean conversion effici- 8 ency for i-th particle I I I I I << I"' produced or recoiled by 10' Hill f I I I I mil incident neutron to Kf' icf 1 . 10 obtain integral glow neutron energy (MeV) value from kerma value of the particle (R "^Co I I llllj I 1 I Mil g~-^ equival enc e/ erg . ) K kerma value of i-th par- (i) ticle (erg-g"-*^), ( X I/IO) conversion factor to obtain erg unit from MeV unit fraction of energy trans- (i) fer to i-th particle from incident neutron, V -!xp. (Goldstein at al.)?^' _ A " (Tochilin et a'.r*"* Q-value of nuclear rea- ' (Taraka t Furuto)-"' '(i) O ction concerning i-th —.cal. (FuT'ita' 4 Ta.iakaJ''^' particle production (MeV), I I I I I I I I , ,1. I .1 I ml mil reaction cross section ^ mill 1 III (i) n' with neutrons of energy JO 1 10 E concerning i-th parti- neutron energy (MeV) cle (cm ) Fig. 2. Energy responses of CaSO^ and BeO flu enc e of neutrons thermoliiminescence dosimeters. having energy E^ (neutron. cm~2 ) Q-amma-ray Discrimination number of atom concerning '(i) In most cases, neutron fields are i-th particle in unit accompanied by gamma rays, and to obtain weight of TLB {g~^) the neutron dose in these gamma-neutron mixed fields gamma-ray discrimination If we know the value of the mean must be taken into consideration. As conversion efficiency for each particle seen in the historical survey, the follo- produced or recoiled by incident neutrons, wing methods have generally been used. we may estimate the energy response of any TLD to by the above calculations. neutrons i) Utilizing a pair-use of two types conversion Therefore, it is clear that the of TLD which show the same responses to efficiency is also very important in gamma rays but different responses to developing a new TLD, and we will describe neutrons; for example, °LiF and 'LiF the efficiency further in a later section. TLD's. We may also estimate the energy res- ii) Utilizing the difference of glow ponse of the moderator type or the albe- cuirve shape; for example, °LiF TLD. do type dosimeter by this method in conjunction with the calculations, such iii) Utilizing the reaction caused as the I-Ionte Carlo calculation, of only by neutrons; for example, the self neutron spectmim at the TLD set position. dose induced by neutron- activated nucleus. 213 These methods are also usefiil for the mean conversion efficiency and the future development of a new TLB's. differential conversion efficiency. The mean (conversion) efficiency is defined as "the ratio of the integral glow value, Care must be taken in the facts say the whole luminescence, Gq to the that any TLD has non-negligible response initial energy Eq of a charged particle to the fast neutrons as seen from the which induce the TL (Gq/Eq)." The energy responses to neutrons, and that differential (conversion) efficiency is ^LiF TLD is sensitive to thermal neutrons defined as "the ratio of the partial because of large cross section of ^Li(n,a)T glow value dG to the differential energy reaction to thermal neutrons inspite of loss dE by which the partial glow is small contents of ^Li in '''liF TLD. There- induced (dG/dB)." In general, both the fore, as described in the literature, it efficiencies are not necessarily equi- valent. is not suitable to use TLD in fast neu- tron fields. The response of TL material to neutrons provides much information with Sensitivity many applications for radiation physics including health physics and reactor As seen from the energy responses of physics, which could not be obtained from TLB's, the sensitivity of TLD to neutrons the investigation for gamma rays. The generally is not so large except for some reason is the response resulting from TLD's containing elements of high reaction the migration of many kinds of charged cross section with neutrons. On the particle composing TL material, which is whole, it is about lO'lO r dOcq eguiva- considered as a fundamental phenomena in lence for 1 MeV and about lO"? R °°Co radiation physics. The differential equivalence for 10 MeV to unit neutron efficiency may serve to theoretical fluence in rough estimation. For the treatment of these phenomena and the mean moderator type or the albedo type dosi- efficiency may serve to practical use for meter, incitement of the sensitivity by estimating the energy response of TLD several digits may be expected. The to charged particles or neutrons. sensitivity of them, however, shoiild be changed by geometrical conditions of the The mean efficiency (relative to moderator, and the energy response must that for electrons) as a function of the be obtained for each geometry. mass stopping power for the initial energy of charged particles is shovm in The development of new phosphors of Fig. 5 (upper), and the differential high sensitivity or new method to read- efficiency (relative to that for electrons] out the luminescence should be expected. as a function of the mass stopping power i The photon counting or the TSEE method of a charged particle for the energy at is considered to be promising. each instant during energy loss in materia^j is shown in the figiire (bottom). 3!hese Recently, new phenomena were found were obtained for a chain of particles by Podgorsak and Moran.59 phenomena one after another from experimental data concern the electrical polarization of electron (for LiF and other TLD), phenomena in dielectic solids which can proton (for LiF TLD), triton (for °LiF be induced by ionizing radiation. TLD), alpha (for LiF and CaF2 TLD), According to their report, radiation- berylliim (for BeO TLD), oxygen (for induced thermally activated depolari- CaSO^ TLD) and so on. The story of zation (RITAD) effects are quite different obtaining the efficiencies should be from radioelectret effects, and for interesting. It is describedju however, normally pure CaF2 sample, the RITAD more fuUy in another report. 55 signals showed a signal-to-noise power advantage of 40 decibels. They suggested In Fig. 3, the ranges of the mass that the phenomena will be a great stopping power which must be considered potential for use as a dosimetry technique. to reactor neutrons are shown for several types of particles. Conversion Efficiency New Approach for Neutron Dosimetry by TLD To develop a new TLD having desired response to neutrons, its energy response Dose Equivalent Measurements must be estimated. As seen in the pre- ceding section, it may be done by calcu- As seen in the historical survey, lation if we know the mean conversion the TLD dosimeters already developed may efficiencies for all charged particles be mainly classified as follows or a produced or recoiled by neutrons. We may combination of the following: consider two types of conversion effici- encies for the TL phenomena. They are 1) moderator type, 214 1 2) albedo type, from the TLD is too simple. If we can 3) self dose type. make, however, a new TLD which shows a neutron response similar to that of dose At present, all of them do not equivalent, the defect becomes no longora necessarily satisfy the desired condi- problem and it may be applied to neutrons tions for neutron dosimetry. Especially, having any spectrum. Hence, we will call it is difficult to obtain a significant hereafter the TLD having such property as value by moderator type dosimeter to the rem response TLD, and will introduce neutrons because neutron spectrum is not our approach to develop the TLD. well known usually. The same thing may be said for albedo type dosimeter. The As described in the preceding section, self dose method is rather hopeful in we already obtained the conversion effi- estimating neutron spectrum reasonably ciency for any charged particles and the using many types of TID as threshold energy response to neutrons of any TLD detectors. It is unsuitable for perso- may be estimated by calculation. nnel monitoring, but, though only rough estimation of fast neutron dose can be The rem response TLD now considered obtained, it may serve an accident is consisted by a pair of two types of neutron personnel monitor even if single TLD having almost the same response to TLD is used. For example, CaSO^ TLD, gamma rays and one type sensitive to which is usually used as a gamma-ray neutrons while the other is not. Fig. 4 personnel dosimeter, can be used as a shows an estimated neutron response of fast neutron monitor utilizing ^'^S(n,p) the TLD. It was obtained by subtraction 32p reaction. of the integral glow value of the neutron insensitive TLD from that of the neutron sensitive TLD. In the same figure, the maximum dose equivalent for mono- energetic neutron of unit fluence inci- dent normally on a 30 cm thick tissue equivalent phantom43 is also shown. From the figure, a fairly good agreement is seen between both responses. O p(Lll I 7 5 (CaFj/ Lucas t Ralnbolt^l) O o(LiF) Harvey I Townsend*2) A a(LiF) J»hnert<0) X 0(CaSO,) Furuta t Tanaka35) I I "III _l _i I I I mil Iff' 10 for initial energy (MaV/mg • on'^) I I I I II I 1 I I I 1 I n ii| —I I I I 1 ii| o 'Cor • 1 o p(LiP) - J»hnert<0) V a(CaFj) - Lucaa ( Rainbolt*'.' a a(LlFT - Harvey t TcJmaend*^' H a(LlF) - Jlhnurt<0) _ x OCCaso )- Furuta t Tanaka^o) Fig. 4. Energy response of a newly deve- loped rem response thermolumi- nescence dosimeter. to 10 0 C3X Absorbed Dose Measurements Fig. 3. Mean conversion efficiency and In reactor physics or engineering, differential conversion effici- including fusion reactor, we often en- the necessity to obtain the ency . counter absorbed dose or energy deposition by One of the reasons for the diffi- neutrons for any material. Estimation culty in obtaining the significant value of radiation heating in shield materials by moderator type or albedo type dosi- or damage of structural materials are meter is that the information obtained considered as the example. These problems 215 . are very important in reactor physics or engineering, even at present, and the importance will rapidly increase in the near future especially in fusion reactor. Recently, applications of TLD in gamma- ray. heating estimation have been reported. por neutrons, however, applications, in absorbed dose or energy deposition measurements are not reported yet. In this report, we will offer a suggestion of the feasibility of TLD in neutron absorbed dose or energy deposi- tion measurements. As described previously, . we had obtained experimentally the energy res- ponses of several TLD's. From the results it was seen that the responses of some TLD's very much resembled the Mutxu «iur9y (MeV) calculated kerma of some material. We will show two examples from the results in the present report. Fig. 5 is a comparison between the energy Fig. 6. Energy response of UD137N ther- response of 'LiF TLD to neutrons obtained moluminescence dosimeter and by experiment and the calculated kerma kerma of iron. of aluminujn, and Fig. 6 is also the energy response of UD137N TLD (made by At present, the following combi- Matsushita Electric Industrial Cq., Ltd.) nations are considered as giving good (CaS04(Tm) and non-TL '^LiP TLD) 53 and results the kerma of iron. Good agreement may be seen from the figures. material TLD f Aluminum '''LiF 1.0 X 102 CM Sodium UD137N 2.7 X 102 I -« a 'Of o Iron UD157W 5.0 X 10 The value of f shows a fitting factor to obtain the kerma of a material Kjjj in erg. g"-'-/ unit neutron fluence from the integral glow value Gmj^-Q of the corresponding TLD in R "'^Co equivalence/ unit neutron fluence for each neutron energy E^ i that is Conclusion Recently, the necessity of a neu- neutron energy (MeV) tron dosimeter having high sensitivity and accuracy is increasing at rapid rate in health physics and in reactor physics and engineering. Fig. 5- Energy response of ^LiF thermo- luminescence dosimeter and kerma As may readily be seen from the of aluminum. historical survey, personnel neutron dosimeters practically used at present if the It may be concluded that are not necessarily sufficient to the disturbed by neutron field is not purposes. For neutron absorbed dose or positioning a TLD, and if the contri- energy deposition measurements the same bution of gamma rays to the integral may also be the case. The thermolumi- glow value of the TLD may be estimated, nescence dosimeter, however, has many dose of some material may the absorbed superior characteristics CQJOgajced with TLD. be estimated by other dosimeters, and it should be 216 . , . • . . . . . • . . , ,. . . utilized in various fields. The authors 18. Falk,B., RFP-1581,18p (1971). believe it has the ability, and they 19. Nash, A. E. and Attix,F.H., Health feel honoured if some suggestions des- Phys., 21, 435-439 (1971). cribed in this report might be of service 20. Second ASC Workshop on Personnel to the development of new neutron dosi- Neutron Dosimetry, BNWL-1616 , 109p meters or dosimetry. (New York, 1971) 21. Mayhugh,M.R. , Watanabe, S. and MuccdUo, Acknowledgement R., Proc. 3rd Intern. Conf .Luminesce- nce Dosimetry , Riso' Report No. 249, The authors express their thanks 1040-1050 (Risc), 1971). to the Organising Committee of this sym- 22. Attix,F.H., Proc. of a Symp. on New posium and to Professor G-hose for their Developments in Physical and Biolo- kind offer of a chance to deliver this gical Radiation Detectors, lAEA-SM- Key-note address in this symposium. 143/25,3-15 (Vienna, 1971). One of the authors, Y.Puruta, is 23. Pearson, , Wagner, J ., Moran, P. R. and also indebted to IA3A for making his D. Cameron, J. COO-1105-175 , ( 1972 ) attendance to this symposium possible. R., 8p 24. Korba,A. and Hoy,J.S., Health Phys., 581-584 References 11, (1970). 25. Hoy,J.S., Health Phys . ,2^, 385-389 (1972) 1. Eisenbud, M., Health Phys.,26, 110 26. Ma jborn,B . ,B;z{tter-Jensen, L. and (1974). Christensen, P. , Proc . Symposium Dosi- 2. Daniels, F. and Saunders, D,F., The metry Techniques Applied to Agricul- thermoluninescence of crystals; ture, Industry , Biology, and Medicine, report, A3CU-1583 , 26lp Pinal (1951). 169-177 (Vienna, 1972) 3. Hiring, and Schoen, M. , Proc. Symp. 27. Blum, E. ,Bewley, D.K. and Heather, J. Selected Topics in Radiation Dosi- Q, Phys. Med. Biol. ,17, 661-662 (1972). metry, 541-548 (Vienna, I960). 28. Yamashita, T. , Nada, N. , Onishi, H. , and 4. Sur jadi, A. J. , Atomkernenergie , 8, Kitamura, , Proc . 2nd Intern. Conf 435-437 (1953). S. Luminescence Dosimetry, pp 4-17 5. Karzmark, C . J. , White , J- and Fowler, ( Gatlinburg, 1968) J.F.,Phys. Med. Biol. , 9, 273-286 29. Blum, 3. ,Bewley, D.K. and Heather, (1964) J.D. Phys, ATed. Biol. ,18, 226-234(1973). 6. Cameron, J.R., Zimmerman, D., Kinney, , 30. Attix, F.H. , Theus,R.B . , Shapiro, P. G., Buch,R. , Bland, R. and Grant, R., Surratt , R. E. , Nash, A.S. and Gorbics, Health Phys., 10, 25-29 (1964). S.G. , Phys. Med. Biol. ,18,4 97- 5 07(1973). 7. Wingate,C.L.,Tochilin,S. and Gold- 31. Kocher, L.F. , Nichols , L. L. , Endres, G. stein, N., Proc. Intern. Conf. Lumi- W.R. , Shipler,D.B. and Haverfield, A. nescence Dosimetry, 421-434 (Stan- J., Health Phys., 25, 567-573 (1973). ford, 1965). 32. Alsmiller, R. G. , Jr. and Barish,J., , . Intern. Conf . Lumi- 8. Simpson, R.E. Proc Health Phys.,26, 13-28 (1974). nescence Dosimetry, 444-456 (Stan- 33. Iga,K. , Yamashita, T. , Takenaga, M. ford, 1965) . Ohta,T. and Oonishi, H. , Composite G.V/.R., Proc. Intern. Conf. 9. Sndres, dosimeters based on CaSO^:Tm and Luminescence Dosimetry, 435-443 X-ray y -ray p-ray BeO phosphors for , , (Stanford, 1965). and neutron dosimetry presented in 10. Distenfeld,C. Bishop, W. and Colvett, , , the 4th Intern. Conf .Luminescence D., Proc. Intern. Conf. Luminescence Dosimetry (Krakow, 1974 ) Dosimetry, 457-466 ( Stanford, 1965 ) 34. Funata,Y, and Tanaka, 3 , Nucl . 11. Gayton, F.M. ,Hall, J.A. and Webb, G. A. . Instr and Meth. ,10^,365-374(1972) M., Proc. Intern. Conf . Radiation Measurements in Nuclear Power, 152- 35. Furuta,Y.and Tanaka, S The relation 161 (Berkeley, 1966). between light conversion efficiency and stopping . power of charged par- 12. Kuz' min, V. V. , Lushchik, Ch.B , Savikhin, ticles in thermoluminescence F.A. , Sokolov, A.D. and Yaek, I . V. dosi- meter, presented the 4th Intern. Atomnaya Snergiya, 22 , 482-488 (1967). Conf. luminescence Dosimetry (Krakow, 13. Stolterfoht, N. and Jacobi, W. , Strah- lentherapie, 111,536-544 (1967). 1974) 36. Goldstein, N. , Miller, W.G. and Rago, 14. Sndres, G.W.R. and Kocher, L.F. , Proc P. F., Health Phys. 18,157-158(1970). 2nd Intern. Conf . Luminescence Dosi- metry, 486-500 (Gatlinburg, 1968). 37. Tanaka, S. and Pututa, Y. , Neutron 15. Kocher, L.F. and Sndres, G. W.R. ,BMWL responses of thermoluminescence dosimeters, BeO (Na) CaS04^(Tm) , SA 1831 Rev.,17p (1968). , and 16. Becker, K. and Crase,K.W., Nucl.Instr. mixture with "^LiF or '^LiF, presen- and Meth. ,82, 297-298 (1970). ted the 4th Intern. Conf. Lumines- cence Dosimetry (Krakow, ) 17. Busuoli, G. , Gavallini, A. , Fasso, A. and 1974 38. Tochilin,E. , Goldstein,. N. and Miller, Rimondi, 0. , Phy s. Med. Biol. ,1^, 673- 681 (1970). W.G. , Health Phys, 16,1-7(1969). 217 . . . . . 39. Podgorsak,i^.B. and Moran,P.R., Y. Furuta Science, 179, 380-382 (1973). 40. Jahnert.B., Proc.3rd Intern. Conf. Our rem response TLD introduced in Luminescence Dosimetry, 1031-1039 this symposium has a neutron response (xRiso', 1971) similar to that of the maximum dose equi- 41. Lucas, A, C. and Kainbolt , C . , Proc . 2nd valent when it was used in a free space. Intern. Conf. Luminescence Dosimetry, We are also considering now another TLD 4 56-463 (aatlinburg,1968) which shows similar response to the maxi- 42. Harvey, J. R. and Townsend, S. , Proc mum dose equivalent when put in front of 3rd Intern. Conf. Luminescence Dosi- a human body. metry, 1015-1030 (RisoM971). 43- Radiation protection instrumenta- S.Makra tion and its application, ICRU Report Adding a small-size polyethylene N"o.20 (1971). moderator to a paired TLD detector which J. , T. , . 44. Simons, G. and Yule J , N"ucl Sci is located on the body improves the res- 3ng.,^, 162-175 (1974). ponse very slightly . I think there is Simons, G.G. and Olson, A. P , Nucl. Sci 45. . very little point in doing so. 3ng.,51, 176-197 (1974). 46. Tanaka, 3 . , TakeuchijK. and Furuta,Y., I feel that the delta-spectrometer in preparation. has a poor resolution thus the practical importance of this instrument is limited. Discussion Hydrogeneous radiator - TLD combina- tion is a very promising device, I hope A.K. Ganguly it will be used more widely. What is the highest energy of neu- Y. Furuta tron upto which you feel you can use the TL dosimetry? In our rem response TLD, hydrogeneous material only use for the purpose to sli- Y Furuta ght compensate the slope for 10" 1 MeV region neutron energies to the MADE res- It may be considered that the prob- ponse . lem depends on the size of TLD used. Vi'hen most of the lost energy of the pro- I also think so, but for some purpose duced or recoiled particles is absorbed it may be useful. in the TLD, good results may be expected. I also think so. W. S. Snyder Are the comparisons with dose based on the "air-dose", that is the dose to a small dosimeter, or are they based on the maximum dose within the body? 218 . EFFECT OF HEAT TREATMENTS ON THEEMOLUMINESCBNCB OF PURE Al20^ A.S. Basu and A.K. Ganguly Health, Physics Division Bhabha Atomic Research Centre Bombay-400085 Six TL glow-peaks at the temperatures 100°C, 150°C, 200"C, 275°C, 310^C and 415°C are observed in pure AI2O3 after gamma irradiation. For higher exposures ( > 1000 R) the 275°C TL glow-peak is masked by the lower temperature peaks and is not seen. Thermoluminescence of this pure AI2O, is investigated after different thermal treatments. The overall sensitivity increases with annealing tempera- tures and reaches a maximum at about 1200°C. The results are explained in terms of the structural change in alumina during these heat treatments. (Aluminium oxide; glow; heat treatment; impurity; temperature; thermoluminescence) Introduction 700°C to 1400°C. The heating is done for two hours in air at any given temperature Rieke and Daniels-'- have shown that and cooled in the switched off furnace. gamma ray induced thermoluminescence of The sample so prepared are referred to as aluminium oxides depends on the extent treated AlpO^ at that temperature and are of hydration and the crystal form stored in light tight containers. produced by different calcining treat- ments. A peak at 236°C depends on TL G-low Curve Recording sodiujn impurity. They have used differ- ent samples of AI2O3 with varying For studying the TL output , the impurity contents and prepared with samples Here given gamma exposure of different calcining treatments. In the 3.3 X 10^ R from a "^Co gamma irradiation present paper thermoluminescence of facility. The glow curves were then A120-J is studied with one sample of spec recorded at a linear heating rate of pure quality alumina (with impurity 25°C/mln using 2 mg of irradiated powder, contents in ppm level) after different in the temperature range of 25°C to thermal treatments. 500°C. The details of the TL Reader set up used is fully described elsewhere . Experimental Results Phosphor Characteristics and Preparations Fig. 1 shows the TL glow curves of The starting material of spec pure AlpO^ treated at temperatures as indica- AI2O3 used in the present investigation ted and also of untreated AI2O3 (virgin contains the following impurities (data sample without giving any heat treatment) supplied by the manufacturer) after gamma irradiation. Chloride - 0.05/. From the figure it can be seen that Sulphide - 0.01/ AI2O3 exhibits six peaks in its TL glow Fe - 0.01/. curve at temperatures of 100°C, 150°C, Loss on ignition - 1/ 275°C, 310°C and 415°C. The 275°C and 310°C peaks are not easily discernible The general method of preparing AI2O3 from a visual inspection of the TL glow consists of precipitating A1(0H)3 which curves but can be distinctly seen by after repeated washing is fired at partial bleaching techniques. If an llOQOC to remove the last trace of H2O. irradiated powder is heated at 220°C for Hence it can be presumed that the above half an hour, the TL recorded, it sample had been fired at about 1100°C exhibits clearly the 275°C peak. Similarly TL glow curve of irradiated For studying the effect of thermal powder after heating at 280°G for half treatment on alumina, the sample is an hour exhibits clearly the 310°C peak. heated at temperatures ranging from 219 Figure 3 shows the glow curves of AI2O3 when " the sample is quenched i.e. when it I400*C is removed directly from the indicated temperature to the room temperature from lOOOOC onwards. The TL glow curve of quenched as well as fxjrnace cooled AI2O5 1300'C is the same for treatment temperatures upto 900°C. Figure 4 shows the glow curves of A120-5 when it is heated under vacuum (atmospheric pressure of (1-I.5)xl0~'^ Torr) at a few indicated temperatures. Table 1 gives a compara- tive study of the relative TL outputs of AI2O2 when it is heated under these three conditions. From the above table is is \ iioo'c clearly seen that the TL output of \ quenched AlpO^ is less than that of furnace coolea AI2O5 from treatment tem- 80O°C,9OO''C, lOOO'C peratures of lOOQOC onwards. The TL output reduces still more when it is heated \inder vaccum. 700*C t- I i- UMTREATEB 50 100 150 200 ;5? 310 330 400 450 500 TE),fP£«ATUP5 (°C) Fig. TL glow curve of AI2O5 heated at different temperatures for two hours and cooled in the furnace. The total thermoluminescence output (area under the TL glow curves) increases KPOO'C as we go from untreated KL20-z^ to 1200°C 3 2. As the treated samples as in fig. 2 treatment temperature is increased from 1 "» 700°C to 12000c, the area goes to a maxi- , . mum and then falls for any further 200 250 300 350 increase in the treatment temperature. TEMPERATURE IN "C Fig. 3. TL glow curves of AI2O3 when at different temperatures for two hoiirs and quenched. 4 1400*C 3 2 2 2 1 1300*C ^2 no 200 210 300 TOO 800 900 uoa noo taw 1300 TEMPERATURE IN 'C TEMPERATURE OF lEAT TMATMENT X Fig. 2. Relative TL sensitivity of AI2O5 Fig. 4. TL of AI2O3 samples heated at at different temperatures and different temperatures in vacuum cooled in the furnace. for two hovirs. 99n . Table-1 It is known from Low Energy Electron Diffraction^ that a alumina undergoes a Comparative study of relative TL sensi- change of surface structure upon hea.t tivity of AI2O5 when heated under diffe- treatment under vacuum above 1250°C rent conditions. accompanied by a change in the chemical composition of the surface by the loss of oxygen. This structural change is reversible and can be changed back to the Temp, of Relave TL Relative Relative initial stage by heating at 1200°C in treatment output TL out- TL presence of oxygen ( 10"^ Torr of oxygen for two when cooled put when output hours in the the when pressxire) . furnace sample is heated in In the light of the above discussi- C) quenched vacuum ( ons, our TL results can be interpreted to indicate that a alumina is the most 700 33.2 33.2 sensitive TL emitter among various forms 800 42.5 42.5 of alumina and presence of oxygen during 900 42.5 42.5 any heat treatments to aliimina helps to 1000 21.5 42.5 preserve the TL sensitivity. For tem- 1100 43.2 21.9 perature of treatments higher than about 1200 .2 50.5 25 1000°C, fast cooling of the sample 26.17 1300 17.6 7.32 reduces the TL sensitivity perhaps 1400 21.4 3.3 because the s\irface structural changes oc curing in a alumina get frozen. Relative TL output for untreated sample - 30.65 References Discussions 1. Ricke, James K. and Daniels, Farrengton, J .Phys .Chem. , 61, 629 The different modification of AI2O5 (1957) obtained on annealing^ at different 2. Sunta, CM., Ph.D. Thesis, Agra temperatures are University, 1970. 150OC 300°C 3. Holzapfel, G. and Chrysson, E. , Third AI2O3 3H2O ^Al20j- AT n IH2Onn n > Internat .Conf . Luminescence Dosimetry, Riso, Oct. 11 - Oct. 14, 1971. °Q°°> Y AI2O3 - a AI2OJ 4. French, T.M. and Somorjai, G-.A., J. Phys. Chem. , 74, 2489 (1970). Y-AI2O3 is a face centred close packed oxygen lattice which transforms into a hexagonal close packing - the a form on heating at 1000°C. This transformation Y to a is complete when heated at 1200°C in air. Annealing temperatures below 1200°C is likely to produce a mixture of y/a. 221 . . ' THERKOLUMIIIESCENCE MBCHATTISMS IN LITHIUM FLUORIDE ; r 1 S.P.Kathuria,V.N.Bapat,C.I'I.Sunta and V.K.Jain Health. Physics Division Bhabha Atomic Research Centre ,.„;,. ' ' ' , Trombay, Bombay-400085 , India Five glovj- peaks upto 200°C are well known in lithium fluoride after gamina irradiation. Seven new glow peaks above 200°C are reported in the present work. They are designated as I to XII in the ascending order of temperature of appearance. Activation energies are determined by initial rise method for five glow peaks, which coiold be well isolated by partial annealing from the lovier teiiiperature glow peaks. TL emission from the prominent glov/ peaks is similar and contains four bands with maxima at 370nm, 390 nm, 415 nm and 470 nm approximately. The ispectral distribution of the total TL emission and emission from glow peaks V (195°G) and ZII (400°C) are obtained also by plotting the integrated intensities of individual glow curves recorded at every 5 nm interval from 250 nm to 800 nm. The TL emission spectra obtained in this way are corrected for the instrument response. Optical absorption spectrum of lithiiAjn fluoride crystal is recorded after garmaa. irradiation. Distinct absorption bands are observed at 225 nn, 250 nm, 310 nm and 380 nm. Absorption spectra are recorded also after various thermal annealing treatments. The spectral similarity of individual glow peaks and the continuous bleaching of F band (250 nm) with the annealing of individual peaks, shows that F centre takes part in recombination process at each stage of glow peak emission. The thern^ly released carrier at individual glow peaks is therefore of hole type. (Irradiation; gamma rays,- LiF; optical absorption; spectral distribution; tiiermoluminescence) Introduction respective trap centres are liberated and captirred at V3 centres containing tvro Thermoluminescence of lithium fluo- trapped holes 12, This would result in ride has been studied extensively by a a single hole centre (V^j- centre) which number of worker sk"-' Five glow peaks upto is unstable at room temperature. The 200°C have been observed by all workers indirectly produced mobile hole then but observation of TL emission at tem- undergoes recombination at an impurity peratures higher than 200°C has varied site with electron from F centre result- from worker to worker. Sunta et al°» ing in light emission. In the present observed ten glow peaks upto 400°C. work, a study of optical absorption spectra and TL emission spectra in LiF There are conflicting opinions after gamma irradiation is undertaken to regarding the natvxe of charge carriers identify the luminescence centres and released on heating and also about the nature of charge carriers released on > thermoluminescence mechanism^ ' heating. Christy et al8 proposed the recombination Experimental the absorbing . centre as impurity centre 1 at 196 nm. TL emission occurs when a hole freed by thermal heating is Lithium fluoride samples used are captured by this centre. The crystal is (i) LiF (T) powder (I40 to 200 mesh) from grov/n restored to its initial state by an . crystal in the Technical Physics electron tunneling from a nearby F Division of this centre and (ii) TLD-100 centre, to the impurity ion v;ith the of Harshaw Chemical Co., USA. Before use emission of a second photon. However, the povfders were annealed at 400°C for Claffy-^-^ observed thermoluminescence in 1 hour and cooled to- room temperature by the absence of 196 nm absorption band leaving in air on a block of aluminium. also Irradiation was carried out in °^Co gamma cells having dose rates of 2.3 I-Iayhugh et al-^^ found that trapped ICR/min and 7.0 KR/min. TL measurements charge carriers responsible for TL are were carried out using 5 mg of powder electrons. On heating the irradiated at a linear heatirg rate of 25°C/min with LiF phosphor, electrons from their a reader system described by Sunta-'-^. 222 . . . Experimental arrangements for recording and then quenched to room temperature. optical absorption spectra and TL emission The glov; curve recorded after this spectra have been described elsev/iiere-^4 annealing treatment shov/s a clear glov; peak at 220°C which was not seen before Res^olts and Discussion the annealing treatment. (Fig. 2 curve b) . This peak was obviously submerged G-low Curves below the 195°G glow peak. Aliquots of the irradiated sample were then successi- TL glow curves of five LiF samples vely annealed at higher temperatures. are shown in Fig. 1. Qualitatively all These annealing temperatures and tirae are the five glov; curves are similar. It is chosen in such a way that the glow peaks also evident from the figure that while preceding the one under examinations are the general structujre of the glow curves completely eliminated during each anneal. remains the same, the relative peak The glow CLirves recorded after each such heights may vary from sample to sample, thermal annealing are given in fig. 2 -he TL of LiF obtained from whatever (cujrve b to h) . Following this procedure, source, does not seen to depend, critica- seven more TL glow peaks above 200°C lly on the impurities so far as the glow which v/ere not obvious (curve a) are curve structure is concerned Kovrever, observed at 220°C, 237°G, 260°G, 295°G, it does depend upon the impiarity and 312°G, 337 C and 405°C. Following the preparation parameters if one looks at similar procedure, these new peaks the sensitivity, relative peak heights clearly shov/ed up in other samples also. and response characteristics of various Thus, a total of twelve glov; peaks are peaks. In the sample TLD-7C0 (Batch 48 observed in all the Li? samples studied. DZ) there are ten distinct glow peaks They are designed as I to XII in the seen at the temperature 62°C , 102°C', ascending order of the temperature of • 142°G, 175°C, 195°C, 215°G, 232°C, 257°C, appearance. • 287°G and 403°C . In other four samples, glow peaks at the temperature 215°G, 232°G, Thermal activation energy of glow and 287°C are not clearly seen but there peaks II, V, VIII, XI and XII are deter- exists a mined by initial rise methods for LiF (T) presence and TLD-lOO samples and are given in Table-1. : Table-1 Thermal activation energies of glow peaks II. V. YIII, IX and XII deter- mined using initial rise method Glow peak Thermal activa- G-low Temperature ( G) tion Energy (eV) peak IIo. LiF(T; TLD-lOO LiF(T) TLD-100 II 102 103 1.36 1.25 V 195 195 1.63 1.5 VIII 257 260 2.10 2.08 XI 332 337 1.97 1.97 ZII 402 405 1.54 1.37 TL Emission Spectra The annealed TLD-lOO samples are irradiated to lO^H and 10°R and the glow curves with 10 mgm of each of these Fig. 1. Til 31ovr curves of iiiF samples for samples are recorded at intervals of 5 nm the gamma exr)osure 7.05 x 105r from 250 nm to 800 nm. The area under (aj TLD-lOO (48 LV/) (b) TLD-lOO each glow curve is determined and (IJL; (c) TLD-6C0 (26 EAD) (d) TLD- plotted against the respective wavelength 700 (48 DZ) (e) LiF (T) after correcting for the system response ( curves a of figs . 3 and 4} . Gurves b To ascertain the exact number of of figs 3 and 4 show the Tij emission glow peaks beyond 200'-'G one of the LiF spectra of glov; peaks V and XII respecti- samples (TLD-lOO) was annealed at 160°C vely recorded in a similar v;ay with 105r for 30 minutes after gamma irradiation and 10°Pl irradiated TLD-lOO samples. It so as to erase the first 5 glow peaks is seen from these figures that there 223 are four emission bands appearing at 370 nm, 390 nm, 415 nm and 470 nm and qualitatively all the TL enission spectra are siiuilar. However, there is variation in relative intensity of emission bands. 5 - 4 - a »100 3 - 2 - 0 / JTig. 3. TL emission spectra of TLD-100 (IJL) after lO^il gamma irradia- tion (a) Total TL emission (b) TL emission from glow peak V. 100 200 300 400 TEMPERATURE °C Pig. 2 . TL glov; cijirves of TLD--100 (IJL) (a) After 7.05xlO'^'-R of gani-ia irradia tion (b) •a followed by 30 rain amiealing at 150°C (c) •a followed by 20 min annealing at 180°C (d) •a followed by 10 rain annealing at 22C°C (e) 'a f ollovred by 20 min annealing at 240OC (f) •a follovred by 30 min annealing at 260OC (g) 'a f ollovfed by 10 min annealing at 300°C (h) •a followed by 2 hrs annealing 250 300 350 400 4 50 500 550 600 at 330°C WAVELENGTH (nm) Similar results were obtained when Pig. 4. TL emission spectra of TLL-100 emission spectra were recorded at the (idL) after 10 R gaima irradia- temperatures 85°G, 135°C, 180°C and tion (a) Total TL emission (b) TL 380°C^ . At these t emperatiires promi- emission from glovf peak XII. nent glow peaks II, III, V and XII are emitted respectively. This shows that Optical Absorption Spectra the same luminescence centres are involved in the therraoluminescence Fig. 5 shows the absorption spectra process at all temperatures. The change of LiI''(T) crystal after gamma irradia- in the relative intensity of TL emission tion and annealing at 100°C, 150°C, bands is possibly because of the change 200°C, 250°G and 350°G for 30 minutes in the configuration of the luminescence each. After gamma irradiation three centres with temperature. absorption bands at 250 nm, 310 nm and 224 .. . . • , . 380 run are seen clearly and. there is a the holes which are being captured by the suggestion of another absorption band at trapping sites corresponding to lower 225 nm. 250 nm absorption band is a well temperature glow peaks. knov/n ?-band and is due to the electrons trapped at the negative ion vacancies. The progressive decrease in F-band optical density after different M, thermal annealings (fig. 5 curves f) I a to shows that F-centres take part in the recombi- nation process. The exact configuration of the luminescence centre is not identi- fied in the present work. Thus on heat- ing the gamma irradiated LiF sample, holes are released from traps of differ- ent thermal stability which recombine with electrons of the F-centrea - part of the luminescence centres. Energy is supplied to the luminescence centre by the recombination of the hole with an electron which appears as light. The Fig. 5. Optical absorption spectra of emitted TL emission bands correspond to LiP(T) crystal after the energy states of the luminescence centre modified by the crystal field. (a) 7. 05x10^3 gamma irradiation (b) 'a' followed by 30 min annealing at Acknowl edgement s 100°C (c) 'b ' followed by 30 min annealing at Autho^rs are grateful to Dr. A.K. 150°C Ganguly, Director, Chemical Group for his (d) ' c ' f ollov/ed by 30 min annealing at keen interest in tne v;ork and many helpful 200°C discussions (e) •d' followed by 30 ain annealing at 250°C References (f) 'e' follov7ed by 30 ain annealing at 350°C. 1. Daniels, F. , Boyd, C.A. and Saunders, D.F., Science 117, 343 (1953). The F-band decreases progressively 2. Daniels, F. , Lum. Dosimetry, AEG Symp after each thermal annealing (curves a Ser. Vol. 8, G05fF-650637 , Stanford to f ) . After annealing the crystal at (1965) 350°C , the absorption at 225 nm and a 3. Claffy, B.v/., Lum. Dosimetry, AEG part of the F-band only are left (curve Symp. Ser. Vol. 8, GOUF-650637 f) and in the corresponding glow curve Stanford (1965). there is only one glow peak present at 4. Cameron, J.R. and Daniels, F. Science, 402°C. Both the absorption bands, 225 n:n 134 . 333 (1961). and F-band disappear together with the 5. Cameron, J.R., Zimmerman, D.V.'., Kennqy, 4C2°C glovf peak after annealing the G. , TJuch, R., Bland, i1. and Grant, R. , crystal at 400°C for 1 hour. If it is Health Physics, 10, 25 (1964). assumed that an electron and hole centre 6. Sunta, CI-I. and Kathuria, S.P. Advan- are required for TL emission, it would ces in Pnysical and Biological Radia- appear that the 225 nm absorption is due tion Detectors, SM-143/24, IAEA, to hole centres and is correlated with^ Vienna (1971) 402°C TL glow peak (XII). FJLick et al^ 7. Sunta, G.I-I., Bapat , V.H. and Kathuria, have suggested that the absorption at S.P. Proc. 3rd Int. Conf. Lum. Dosi- 225 nm arises from a centre v/hich traps metry, Oct. 11-14, Riso (DAEC and two holes. Such a centre has been iden- IAEA), (1971). tified in KCltCa^'. 8. Christy, R.V/., Johnson, iJ.H. and i/ilbarg, R . R . , JJlppl . Phys . J^, 2099 All the glov/ peaks are regenerated (1967) by irradiating the LiF sample, having 9. laick, CO., Claffy, E.V/., Gorbies, glov7 'oeak ZII as residual to Hg lamp UY S.G., Attix, F.ii., Schulman, J.H. and light^^. UV light photons release the Allard, J.G., J. Appl. Phys. 28,3867 charge carriers from the peak XII traps (1967) R.V/. which are captured by the trapping sites 10. Kayhugh, M.k. , Christy, and corresponding to lower temperature glow Johnson, K.I-i., J. Appl. Phys. 41 , peaks, emptied during thermal annealing. 2968 (1970) 11. Claffy, E.W., Phys . Stat . Sol . 22, 71 The glow peak XII has been correla- (1967). S.i'i. V/olfe, D.ft. ted v;ith the optical absorption found at 12. Viinter, , and 225 nm vrhich is due to hole centres. Christy, R.V/., Phys. Rev. 186, 949 Therefore charge carrier involved in the (1969) transfer process from peak XII traps are 13. Sunta, C.il. Ph.D. Thesis, Agra Univ. (1971). 225 14. Kathuria, S.P., M.Sc. Thesis, Bombay University (1974). 15- Jones, D.S. and Burt, A.K., Lum. Dosimetry, ASC Symp . Ser. Vol. 8, COiJF-650637, Stanford (1965). 16. Kathuria, 3. P., Indo-Soviet Conferen- ce on oolid State Material, Dec. 11- 16, Bangalore (1972). 17. Crawford, J. H. Jr. and Nelson, CM., Phys. fiev. Letters ^, 314 (i960). 18. Kathuria, S.P., Bapat , V.N. and Jain, V.K., Presented at the Fourth Int. Conf. Lum. Dosimetry, Aug. 27- 31, 1974, Krakow, Poland. THERMOLUMINESCENGE RESPONSE OP LiF TO GAMMA RAYS V.K. Jain and S.P. Zathiiria Health Physics Division Bhabha Atonic Research Centre Trombay, Bombay 400085 India The thermoluminesc enc e of lithium fluoride shov?s twelve peaks, of which II (lOOOQ), III (135°G) and V (190°G) grow linearly first and then become nonlinear, eventually saturate and finally show decreased response or damage. Peaks beyond the Vth peak on the other hand seen to grow supralinearly right from the beginniiig. None of the available explanations for the supralinearity of the dosimetry peak (V) is entirely satisfactory. Similarly damage too is not understood. In this paper it has been shovm that the radiation induced sensitisation is linked with the Xllth peak (400°C). It is postulated that this peak is created as a result of irradiation and hence is supralinear right from the beginning. The other high temperature peaks, though supralinear, are not found to be responsible for radiation induced increaf^e in sensitivity of lower temperature peaks. It is shown that the trap centres (TC's) responsible for the Xllth peak are generated as a resiilt of the break up of complex centres TCLC's on irradiation. This break also causes the addition of luminescence centres (LC's) which leads to increase in sensitivity. The complex centres (TCLC's) themselves are formed due to the 400^0 annealing. Decreased response or damage after saturation is the result of loss of lumines- cence centres v^hile the traps remain unaffected. (Dose; gaEima rays,- LiF; response; sensitivity, supralinear; thermoluminescence) Introduction one hour and cooled to room temperature by leaving in air on a block of aluminium. Many aspects of TL response to X- Irradiation was carried out in Co-60 and gamma rays of LiF dosimetry phosphor gamma cells having dose rates of 2.3 'i^B./ are vaguely understood. For example, the min and 7.0 feU/min. TL measurements complicated annealing behaviour-'- » 2 and \iere carried out using 5 mg of powder at radiation sensitization^ » 4, 5 are not a linear heating rate of 25°C/min with a satisfactorily explained. Similarly, reader system described by Sunta°. radiation damage in LiF is quite critical and needs investigation. Results and Discussion The glow curve of LiF has many more Thermoluminescent Response of Some Peaks peaks than are generally reported in I j' literature". In this paper the TL res- Fig. 1 shows the glow curves of ! ponse of some of these peaks is reported. lithium fluoride after gamma irradiation. ' The model proposed earlier^, to explain There are total of tvrelve glow peaks radiation sensitization and supralineari- present in the glow curves of LiF ty in LiF is elaborated. Some aspects of samples^. But for the first peak v;hich the lowering of response, due to radiation decays rapidly and Xlth peak which is peak, be 1 damage are reported and the involvement hidden under Xth ten peaks can of luminescence centres in this is clearly seen. In Fig. 2 the response liscussed. of some of the peaks viz. II, III, V, VIII, and XII is sho\m. From .the growth Experimental pattern it appears that the TL peaks in LiF fall into two groups: one group Lithium fluoride samples used were comprises peaks upto the Vth (dosimetry (i) LiF (T) powder (140 to 200 mesh) from peak) and the other of peaks beyond the ! crystal grown in the Technical Physics Vth. The first -group peaks initially Division of this Centre and (ii) TLD-100 rise linearly and become supralinear at of Harshaw Chemical Co., USA. Before use higher exposures. The second-group the powders were annealed at 400°G for peaks seem to respond supralinearly right 227 from tne beginning (VIII and XII in fig. 2). 2\lso snovm in this figure is sensitization by gamu.a irradiation and annealing at 350°C for 15 niin for peaks V and VIII. The well known sensitization procedure enliances the response of not only the Vth (dosimetry) peak but also of the VIII peak as shov/n and other peaks, not shov^n. Sensitization is shown for two ganna pre-exposures and it can be seen that when the sensitization is incomplete the phosphor still responds supralinearly though at a higher exposure. iT Pig. 2. Response of peaks II, III, V, VIII and XII in LiP(T). Peak V and VIII (1) LiF(T) annealed at 400^0 for 1 hour (2) 1 followed by 1.15x10% of sensitization exposure and annealing at 350°C for 15 min (3) J L- I "XL 1 followed by b.gxlO^R of sensi- tization exposure and annealing '- Fig. 1. TL glow curves of LiF TLD-100 as in 2. Peak XII as in above. exposed to 2.3xlO''R and LiP(T) exposed to o.gxlO^R and 2.3x105r. One of the reasons for the therrno- exposure and subsequent annealing gives lurainescence peaks to be supralinear the residual theraiolumine sconce (RTL) . throughout could be that they are created How S/So varies with RTL remaining as a by irradiation as has been suggested by result of annealing at different tem- Ilason and Linsely^*^. The Vlllth peak peratures for various periods is shown and the Xllth peak both are supralinear in Fig. 3- From these curves it is but v;ith a difference. Tne Vlllth peak apparent that S/bo does not depend is radiation sensitized but not the criticalljf on RTL except when the latter Xllth. In fact radiation sensitization has decreased to a negligible proportion is dependent on the Xllth peak vfhich is which corresponds to peak XII. Sunta 'created' (see next section). If the et al concluded tliat glow peak XII Vlllth peak were due to traps whicii alone is responsible for sensitization. captured more than one charge carrier, A model was proposed earlier" to explain its grovjth would be supralinear*. supralinearity and sensitization. The model postulated the formation of a !iupralinearity and Sensitization complex centre (TCLG) consisting of a trap centre (TG) and a luminescence The ratio of the response to 100 R centrelO. Initially the number of such of gamma rays of TLL-100 sensitized by complexes is s.aall. .By annealing at 4.0x104r of gamma rays and subsequent high temperatures (400 C), trap centres annealing ( S ) and that of the unsensiti- and luminescence centres are brought zed TLD-lOO ( So) gives the sensitization togetuer to form more complexes'^. On factor (S/So). Also the area of the irradiation this complex breaks up into glow curve remaining after the gaimna its constituents (TO and LO) . As irra- * The fact that for densely ionizing radiations like alpha rays the relative response of the high tem- perature peaks is more, suggests this. 228 diation progresses, more and more lumine- The TL response of the powder is therefore scence centres are added which, cause that enhanced by radiation (radiation increase in TL response leading to supra- sensitization) . At 400°G however, the linearity. Annealing the irradiated "created trap", TG and the added lumine- po'.^der at a lov/er temperature say 35C°G scence centre, LG , combine to form the does not reform the complex and the added complex (TCLG). The increased sensitivLty l-jiiinescence centres continue to be is thus removed. available resulting in sensitization. Radiation Damage The response curves of fig. 2 show decrease beyond the saturation point. The decrease depends upon the total exposure given to the phosphor (order of graphs 1,2 and 3 reverse to 3>2 and 1 beyond saturation) . This decrease in response is due to damage effects (13) and is a general feature of LiF thermo- luminescence. This is presented in fig. 4. Prom these graphs as well as those of fig. 2 it appears at least for the first group of peaks, that even after dainage the saturation exposure does not alter indicating no change in trap population. This has been verified for various initial exposixres. The thermo- luminescence output, however, decreases tfiroughout indicating less recombinations. Thus damage to TL in LiF can be attributed to loss of recombination or luminescence centres. This is also indicated by the change in tne TL emission spectrum of LiF after damage-'-'^. 8 S/So .ig. 3. Change in sensitization factor with annealing at different tem- perat'ores for different times. As has been indicated by Zimmerman , v;e postulate further an association between the TL trap and the luminescence centre. Thus when the luminescence centres increase on irradiation as a result of break up of TCLG, they get spatially associated with the nearest trap available. I'ow on release of the charge carrier from the trap there is greater probability of recombination with :-e luminescence centre. I'hen this mxTiber has increased sufficiently, as l.appens after an exposure of about 5xio4il for glow peak V, there is no -urther increase in the probability of recombination and maximum response is reached. iJiaiilarly after a pre-exposure of the 3a_'.e order followed by 230°C annealing for 1 hour, though the trap responsible for lower temperature peaks -.ave been enptied, the recombination Fig. 4. Damage effect in LiF (T) for centres continue to be associated with 8.3xlO°R. For each peak (Wot upper curve is without the respective traps. The 280°G annea- marked) , ling does not destroy this association. damage and lower with damage. 229 . . . . • Conclusion eds.J.A. Auxier et al . (CONF-6S0920, WBS, Springfield, Virginia, USA (1968) The main characteristic required to 6. Kathuria, S.P., M.Sc. Thesis. Univer- be seen for LiF in dosimetry is sensi- sity of Bombay, Bombay (1974) tivity. The radiation sensitization in 7. Jain, V.K. , Kathuria, S.P., and LiF is due to the break up on irradiation Ganguly, A.K., J. Phys. C (Solid St. of a complex centre (TCLC) into TO and Physics) 8, (1974) LC which itself is formed while annealing 8. Sunta, CM., Ph.D. Thesis, Agra at 400°C. University, Agra, (1971). 9. Kathuria, S.P., Bapat , V.N., Sunta, References CM. and Jain, V.K., Paper in this conference 1. Cameron, J.H.., S\mtharalingam, N. and 10. Mason, IS.V/. and Linsley, G-.S., Proc. Keney, G.U., Tnerrnoluminescent Dosi- 3rd Int. Conf, on Luminescence metry, University of V/isconsin Press, Dosimetry, Riso, ed. V. Mejdahl, iladison, V/isconsin, U.S.A., (1968). (Riso Report i-lo. 249) (Riso: Danish 2. Zimmerman, D.V/., Rhyner, C.R. and ASC and IAEA) (1971) Cameron, J.R., Health Physics 12, 525, 11. Sunta, CM., Bapat, V.N. and (1966) Kathuria, S.P., Proc. 3rd Int. Conf. ' 3- Suntharalingam, N. and Cammeron, J.R. on Luminescence Dosimetry, Riso, ed. Phys. I'led. Biol. IJ-, 397 (1969). V. Mejdahl, (Riso Report No. 249) 4. Cameron, J.R. and Zimmerman, D.W., (Riso:DAEC and IAEA) (1971). Modifications of the Kathematical 12. Zimjnerman, J., J. Phys. C (Solid St. model reported in COO-1105-102' . and Physics) ±, 3277 (1971). Report COO-1105-113, (1966). 13- Marrone, M.J. and Attix, F.H., 5. Claffy, E.W., Klick, C.C. and Attix, Health Physics 10, 431, (1964). F.H., Proc. 2nd Int. Conf. on 14. Jain, V.K., Bapat, V.N. and Kathuria, | Luminescence Dosimetry, G-atlinburg, S.P., J. Phys. C (Solid St. Phys .) ~6,L343 (1973). E 230 . . CHANGE IN TL SENSITIVITY OP QUiRTZ DUE TO STRESS M. David and A.K. Ganguly Health Physics Division Bhabha Atomic Research Centre Bombay-400085 Stress and strain caused by progressive and impact pressure loading can change the TL sensitivity of natural quartz. Stress due to progressive loading enhances the TL sensitivity considerably. It is found that sensitisation increases as the amount_uf stress increases and reaches a maximum at about I4OO kg cm . The TL sensitisation obtained is correlated to 'strain hardening' by the dislocation nets produced by stress. In the case of stress caused by impact loading, TL sensitivity is reduced. This may be due to the conversion of quartz to a glassy state at a high stress. (Quartz; sensitivity; stress; thermoluminisum) Introduction Results TL of quartz has been observed to be Effect of Stress by Progressive Loading affected by the stress to which the crystal is subjected prior to irradiation. The crystals were subjected to The effects of stress on the TL output of stresses of different peak loadings. The quartz have significance in both desired stresses were developed on the understanding and applications of TL sample by loading at rate of 500 kg/min. phenomenon in (i) archaeological and The sample was kept in the state of peak geological datings^"-^ and (ii) radiation stress for three minutes and then the dosimetry^. stress was released at the same rate as loading. The stresses given to different This paper reports the results plates were 308 kg.cm~2. visible obtained in the studies carried out on deformation was found in the samples for the effect of stress on TL of natural stresses upto I4OO kg.cm~2. por stresses quart z above 1400 kg.cm~2 extensive cracks developed in the crystal. Experimental Methods Natural thermoluminescence (NTL, the Thin plates (0.5 cm thickness) were TL signal naturally present inside the cut from naturally available transparent sample prior to any ajrtificial irradia- single crystal of quartz along the tion) glow curves were recorded using 5 directions perpendicular to c-axis. mg of the samples. A linear heating These plates were then polished very rate of 25°C/min was employed over a carefully to obtain flat s-urfaces to temperature range of 25°C-500°C. ensure uniformity of stress all over the Figure 1 shows the NTL glow curves crystal obtained from all the five samples. Two TL peaks were observed, one at 260°C and An Instron Universal Tensile Testing Machine was used to give various stresses to the samples. Two kinds of stresses were applied to the crystal plates: (i) stress by progressive loading along the c-axis and (ii) stress by impact loading along the c-axis. These quartz plates were then powdered using agate mortar to sizes '1 1 less than 0.151 and were used for TL 1 1 studies. All the irradiations to gamma-rays Pig. 1. TL glow curves of unirradiated were done in ice bath at a rate of quartz samples after giving 6.9 X 103 R/min. different amounts of stress by progressive loading. 231 . . . e . another at about 350°C. No significant Table-1 difference in TL output was observed between the stressed and unstressed Effect of stress on thermal activation samples energy of different TL glow peaks of transparent quartz The stressed samples were subjected to a heat treatment of 400°C for 90 mins. energy along with an unstressed sample so as to Activation (eV) remove the NTL completely. These samples Peak Natural Sample after stress were then given an artificial irradiation t emp . sampl 308 1436 2873 (test dose) of 2.4 x lO^R from a Co-60 gamma source and the glow curves were 70°C .658 .658 .732 .621 recorded. There were mainly five glow 110°C .298 .653 .675 .582 peaks present in all the samples viz: at 180°C .718 .784 .843 .814 75°C, 110°C, 180°C, 235°C and 320°C 255°C .873 .906 .829 Areas under glow ciirves are plotted 320°C .831 .865 .911 .878 against stresses in Figure 2. 1 - 70 C Pt«» 2 - 1'0'c PtAR 3-180*0 PEAR 4 - ZWC PtAK 5 - 320* C PEAK I 9M 1436 len 1000 2000 3000 STRESS CKj Cm') STRESS iKg.Cn?) Fig. 2. Effect of stress (by progressive Fig. 3. Effect of stress on Thermal Acti- loading) on Thermoluminescence of vation Energy of different glow Transparent quartz. peaks of transparent quartz. TL output is enhanced very slowly Effect of Stress by Impact Loading with the increase in stress till 600 kg cm~ beyond which it goes through a stress Stress by impact loading was done developing maximum sensitivity in the by dropping a load of 200 kg from a crystal and falling back to almost the height of 20 cm on a (10 x 8 x 5 mm) value obtained with the unstressed plate. The sample got crushed and was crystal at 2875 kg.cm"'^. The fall in the further crushed to a standard mesh size TL output beyond 1400 kg.cm~2 appears to (0.151 mcs) . This sample was heated at be associated with plastic deformations 400°C for 90 minutes and thpn given a occurring to the samples at heavy loads. test gamma dose of 2.4 x lO-'R and the TL was measured. It was found that the The sensitisation produced is by sensitivity was reduced considerably. overall enhancement of the entire glow The glow curves of the stressed and curve. Even though the change in sensi- Tinstressed samples are given in Figure 4. tisation is observed no change in behaviour in respect of linearity of response to gamma dose was observed. The glow peaks of the samples subjected to stress, saturate at the same dose as that of unstressed sample. Activation energies of the glow peaks of the stressed samples were ^ calculated using the initial rise method'' (see Table-l). Average activation energies of the glow peaks of the samples are plotted against the stresses in figure 3. It is seen that the activation energies increases in the cases of all TEMPERATURE 'C the peaks and reaches a maximum at 1435 Fig. 4. Effect of stress by impact kg.cm" . It is to be remembered that TL transparent emission also was maximum around this loading on TL of stress quartz 232 . • . . . The activation energies of the TL 2. Aitken, M.J. TL Dating in Archaeology, glow peaks of the sample subjected to in TL of Geological Materials (Mc impact loading were also found to have Dougall, D.J.J Ed) Academic Press, reduced considerably. London and New York, p. 369 (1968). 3. Zeller, E.J. Geological Age Discussion and Conclusion Determination by TL, in TL of Geological Materials (Mc Dougall D.J.j ' Mc Dougall^ explained the effect of Ed) . Academic Press, London and New stress on the TL output of quartz as due York (1968) to variation in free energy associated ^. Mc Dougall, D.J.; Some TL Properties with trapped electrons of the crystal, of quartz and its potential as which in turn is related to the formation accident radiation dosimeter. Paper and annihilation of lattice dislocations. presented in 3rd International Gonf. on TL (1971) The initial increase in the observed 5. Randall, J.T. and Wilkins, M.H.F. TL (cf. fig. 2) after giving different Proc. Roy. Soc . , A-184 . 366 (1945). stresses can be correlated to the strain 6. Short, M.N.; J. Geology, Jd 705 hardening due to the development of (1970) dislocation nets in the crystal. If the argument is valid, the stress induced sensitisation should be initiated at the Discussion elastic limit of the crystal and should reach a maximum during the early stage of permanent deformations. The sensiti- D.V. Gopinath sation of the sample starts around a stress of 600 kg cm" . This means that the 'hardening' due to the development Does this enhanced sensitivity of dislocations starts at about this change with time or is it permanent ? stress. It is possible that the TL sensitisation by stress is associated If permanent, does it mean that by with 'strain hardening' in quartz pounding it in different ways, one can crystals and that the elastic limit for obtain different sensitivities? this sample is at about 1400 kg.cm~2, beyond which the crystal damage occurs. The fall in sensitisation may be due to M. David the plastic deformations in the lattice and annihilation of dislocations during the recovery from strain hardening. Yes, it is a permanent sensitisation in the sense, it will not be de- The reduction observed in TL output sensitised by itself with time. The after impact loading of the crystal may sensitisation produced is not dependent be due to the conversion of quartz to a on the method of powdering,- it depends glassy state at a high stress. Short" on the amount of stress to which the gives data showing the conversion of sample was subjected. quartz to a glassy state at a load of 300 K.bars. It is to be noted that in our studies the stress given to the crystal by impact loading was also well above the suggested pressure for the conversion In archaeological and geological dating of the samples, natural TL and its calibration against artificial TL is very important. The present investigations bring out that in these types of appli- cations of TL, the geological stress that the sample might have received, should be taken into consideration. References 1. Ichikava, Y. and Higashimura, T. Application of TL of quartz, paper presented in conference on TL at Tennessee (1969) 233 . ESR-TL CORRELATIOIT STUDIES IN Cab04(RE) PHOSPHORS K.S.V. Nambi "' Health Physics Division * ' Bhabha Atomic Research Centre ' Bombay-400085, INDIA ' - • ESR and TL glow curve measurements were done after gamma irradiation at room temperature of CaS04 samples doped indivi- dually with all the lanthanide series rare earth (RE) elements, an yttrium doped sample and a few undoped samples of different origins. Samples were prepared in the laboratory using standardized techniques and concentration of the dopant in individual doped samples was maintained at a typical value of O.iy. by weight in CaS04. ESR as well as the TL glow curve patterns of all the sixteen samples were almost identical excepting for relative intensity differences. By observing the build up of these signals with increasing gamma dose and also by following the decay of these for storage at room tem- perature, it could be inferred that the nature of the trapping species indicated in the ESR ajid TL glow curve patterns are the same. The behaviour of these patterns for various thermal annealings at different temperatures have revealed that the trapping species might have configirrations like SO4, SO3, O3 etc. having different thermal stabilities and these are res- ponsible for the observation of the multi-peak TL glow curve structure involving a variety of thermal activation energies. The increased intensities observed in the ESR and TL signals of the differently doped samples indicate that presence of various RE impurities in CaS04 enhances to different extents the stabilities of these trapped species after gamma irradiation. (CaS04; correlation; dose; ESR; gamma ray; glow ciirve; irradiation; TL) Introduction A varian dual cavity X-Band ESR spectrometer employing 100 KG/sec field In thermoluminescence, trapped modulation was used to record the ESR electrons and holes either at an impurity spectra of gamma irradiated samples at ion or at a host lattice ion or at a room temperature. The TL recorder used complex involving both, play the key role has been described in detail elsewhere^. and if any of these are paramagnetic in nature, it is evident that ESR technique Results and Discussions can be effectively applied to determine the structure of these trapping TL Glow Curves of Gamma Irradiated CaS0 4 centres. This paper presents the (RE) Phosphors results obtained in an attempt to correlate ESR-TL characteristics of All the CaS04 samples (doped and rare-earth doped calcium sulphate undoped) exhibited varying TL outputs [CaS04(RE)J phosphors after gamma irra- but their TL glow curves were characteri diation at room temperature (RT) sed by the appearance of glow peaks at more or less the same temperatures; the Experiments " relative intensities of the various glow peaks were also varying from sample to CaS04 (polycrystalline) samples sample-^. Actually about twelve glow doped individually with all the rare peaks could be resolved in each glow earths of the lanthanide series and an curve by 'partial bleaching technique' yttrium doped sample were prepared in and fig. 1 gives TL glow curve obtained the laboratory by the simple technique from gamma irradiated CaS04(Dy) phosphor of coprecipitation and evaporation. with all the glow peaks labelled from I The dopant concentration chosen was to XII. about 0.1'/. by weight. A blank CaS04 sample without addition of any dopant It is known that TL glow curves are was also prepared. characteristic of the various traps exis 234 . . 1 1 ting in a phosphor which are thermally construed to demonstrate that the deactivated as the temperature is pro- different traps are the basic nature of gressively increased. From the similarity the host material and the dopants of the glow peak temperatures obtained influenee only the relative populations for the sixteen samples it is amply in the various traps. Whether the trapp- demonstrated that the dopants have not ing species shown in the ESR spectra are altered the basic nature of the traps the same which are involved in the TL already existing in the base matrix^ they glow curves was verified by ESR-TL result only in different Imninescence correlation studies the result of which efficiencies. In fact the activation are shown in the next section. energies of these traps have been found to be directly proportional to the peak ESR-TL Correlations temperatures independent of the dopant added. That the impurities already Gamma Dose vs. ESR-TL Signals Build-up present in the starting material of CaS04 had no influence on the characteristic The ESR signal intensity obtained TL glow peak temperatures obtained in all for various gamma irradiations has been the doped specimens was confirmed by monitored and plotted in fig. 2 for the studying the TL glow curve pattern of case CaS04 (Tm). The ESR signal intensity pure CaaO^ samples of different origins increases with dose till about lO^R all of which gave the same glow peak beyond which saturation sets in. This temperatures-'- pattern is very much analogous to the TL intensity vs dose relationship shown in the same figure. A condition has thus been satisfied for a possible conclusion that the trapping species involved both in ESR and TL are the same. Fig. 1. TL glow curve of gamma irradiated CaS04(Dy) CaS04(RE) Irradiated I I I I 1 I ! 1 of I I 1 i I I Gamma I I I E3R Spectra voL n I I uL L ^ 10' I0» 10^ Phosphors ' GAMMA DOSE («) . None of the samples gave any ESR Fig. 2. Gamma dose build-up curves for signal prior to gamma Irradiation. The ESR and TL in GaS04 (Tm). ESR patterns show some remarkable similarities except for the cases of Room Temperature Decay Characteristics La, Lu, Od and Eu dopants in CaS04. The of ESR-TL Signals cause for this exception has not been analysed in the present work. In Further evidence for the nature of general, a six peak spectral pattern is the trapping species being the same both seen having the same set of g-values in the TL and ESR, has been provided by (2.001, 2.0022, 2.003, 2.004, 2.0057 and the parallel nature of the decay patterns 2.0113) and even the four exceptional of these signals for storage of the gamma cases exhibit peaks which could have irradiated sample at room temperature. enveloped the above generally observed Fig. 3 presents tne results obtained for six peak spectral patterns. the case of CaS04 (Tm). As the ESR of irradiated solids is Thermal Annealing Characteristics of due to the unpaired trapped charge ESR-TL Signals carriers in the material, the similarity of the ESR patterns obtained above can be The bleaching of the ESR signals of 235 dent of their environment in the crystal lattice, has been verified by many workers. Hariharan et al obtained isotropic lines with g-values of 2.0045 and 2.01 respectively for SO5 and anisotropic lines for SO4 and SO2 in irradiated Na2S04 crystals at room tem- perature; Gromov et alA obtained axially symmetric lines for SO3, O2 and 0 in K2SO4; Morton et al-' observed that SO4 could be observed even upto 300°K in Fig. 3. Decay of TL and ESR of gamma irradiated K2SO4 and SO3 is the more irradiated CaSO^CTm) for storage stable radical at higher temperatures; at RT. Spitsyn et al° detected SO4 in irradiated SrS04 350°C; Gupta et al' gamma irradiated CaSO^ phosphors corres- identified the complicated powder ponding to various stages of bleaching spectrum obtained at LNT for irradiated of the TL signal was studied after BaS04 ^1"*=^ radicals like SO4, SO-j, SO2, annealing the samples at different tem- SO2 and 0^. peratures successively. The temperatures chosen were 400°K, 500°K, 675°E and 800°E The range of g-values deducible for and samples were heated for half an hour the various signals in the six-peak each at these temperatures. These envelope obtained for the CaS04 powder treatments successively erased the TL in the present study compare well with signals in four stages of three peaks the range of g-values reported for many each: I-III, IV-VI, VIl-IX and IX- XII of the radicals mentioned above. It is, respectively. The ESR patterns were therefore, reasonable to expect that ESR almost identical for all the samples and signals obtained in the present study of fig. 4 presents the thermal annealing gamma irradiated GaS04 are mostly due to behaviour of the ESR signal for the case host lattice radicals like SO4, SO3, 0^ 'of gamma irradiated GaS04(Tm). etc and that the stability of these radicals has been affected by the indivi- dual RE dopants to different extents as indicated by the differences in the intensities of these signals. The individual indentification of the various radicals in the complicated six- peak ESR spectra obtained, is rather difficult as these have been obtained for powder samples and at a single frequency. However a careful examination of the spectrum and its annealing behaviour (fig. 4) does reveal that the various radicals are bleached effectively at different temperatures (the ESR spectrum does not bleach uniformly over its entire field range). The less complicated, nearly isotropic line (g 2.0040) seen in the penultimate stage of the annealing process, perhaps belongs to SO5 radical which has been observed at comparably high temperatures with more or less the same g-value in sodium ajad potassium sulfates. The line F is evidently composed of superimposed signals and the signal represented by the part which is completely bleached by annealing at 400°K is probably due to 0^ having a near isotropic g-value of about 2.012. In the Fig. 4- Typical thermal annealing chara- context of TL, these various radicals, cteristics of ESR signals of expecially SO4, 30^ and 0^ represent gamma irradiated CaSO^ powders. radicals with trapped holes characterised by different activation energies. The presence of isolated paramag- netic radicals like SO a, SO3 etc. in Conclusion gamma irradiated sulphate salts like K2SO4, Na2S04, BaS04 etc almost indepen- Prom the foregoing results and dis- 236 . . ' cussions, it can be concluded that hole ESR spectra. Thanks are also due to traps provided by the host lattice ions V.M. Bapat for the help he rendered having configiirations of SO^, SO^, 0^ during the course of this work. etc. give rise to the observed TL glow curve pattern in CabO^ and addition of References rare-earth ions seem to affect the stability of these various traps to 1. Nambi, K.S.V, Ph.D. Thesis, Gujarat different extents. Combined with our Univ., Ahmedabad (I974j. findings on the TL emission spectra it 2. Atkins, P.W. and Symons, M.G., 'The could be said that the TL process in Structure of Inorganic Radicals CaaO^ (RE) is perhaps similar to that in Elsvier Pub. (1967 ) Hariharan, N. and Sobhanadri, CaF2(RS) involving RS^t^^^^^^^^^^-RE^^ 3. Mol. Phys. 17, 507 (1969). reactions with simultaneous trapping and 4. G-romov, V.V. and Morton, J.R., Can. release of holes at the sxilphate sites J. Ghem. M. 527 (1966). during irradiation and heating respective- 5. Morton, J.R., Bishop, D.M. and ly- Randic, M. , J. Ghem. Phys. 1885 (1966). Acknowledgements 6. Spitsyn, V.I., G-romov, V.V. and Karaeva, G.G., Dokl. Akad. Nauk, 5. I am grateful to M.V. Krishnamurthy S.S.R., 1^, 178 (1964). and W.D. Sastry or Radiochemistry Divi- 7. Gupta, N.M., Luthra, J.M. and sion for their help in recording the Shankar, J., Rad. Eff. 21, 151 (1974). Discussion S . I'lakra I feel that heating the sample and detecting the emitted light is not the only possibility for TL evaluation. Efforts like yours besides theoretical importance are of practical importance too K.V.S. Nambi Thank you for your kind comments. 237 ) NBUTEON DOSE EVALUATION USING CALCULATED NEUTRON SPECTRA S. Makra Central Research Institute for Physics 1525 Budapest II4. P.O.B. 49 Hungary Measurements carried out at shielded neutron sources such as nuclear reactors and neutron generators showed the importance of intermediate energy neutrons not recorded by most of the commonly used monitors. Based on these measurements correction factors were established for scintillation survey instruments, track plates, activation detectors and other routinely used devices. Although this simple technique has proved to be very useful, the need for a more sophisticated evaluation method was evident. With this in mind we started with the calculation of neutron spectra transmitted through and reflected from shielding slabs. Calculations were performed by using the MUSPALB albedo code developed in our Institute as well as with the 05R code written in Oak Ridge, USA. Over the last four years spectra for different reactor and neutron generator sources with H2O, polythene, concrete, beryllium, aluminium, graphite, iron, boron loaded polythene and iron-concrete mixture shields were calculated for thicknesses ranging from 5 cm to 200 cm. Calculated spectra were used for personnel-, survey-, and nuclear accident dosimetry evaluation. International comparison measurements have shown the value of this evaluation method. For illustration several examples are given. (Computer code, dose, dosimetry, monitor, neutron, shielding, spectrum) Introduction Early measurements of the stray show how evaluation techniques can be neutron field carried out at shielded established to take into account the neutron sources showed, that the energy fraction of the neutron dose not recor- spectrum of the neutrons in such circum- ded by a given dosimeter. This stances is quite wide. The leakage spe- requires the knowledge of the spectrum ctrum of shielded nuclear reactors, in question. In the first part I shall radioactive neutron sources, or even 15 deal with investigations performed with MeV neutron generators span from the moderator devices, these bulky instru- source energy down to the eV range or ments are not used as personnel dosi- even to thermal energies. Dosimeters meters (it's somewhat difficult to wear used for personnel monitoring, on the a 20 lb sphere on top of your working other hand, in spite of the considerable clothes!) but the information yielded by progress achieved in the past decades, them is readily applicable to dosimetry do not cover this wide energy range evaluation. In the second part I shall in Fig. 1. In my lecture I intend to discuss problems concerning leakage spectrum calculations and their appli- cations in dosimetry evaluation. albedo dosimeter Dose Fraction Measurements boron -loaded detectors Theoretical considerations as well as monitoring results showed the impor- ! track plate tance of the intermediate energy neutro- ns not monitored by the commonly used scint. counter neutron dosimeters. gas- filled cou nter Nachtigall's measurements^ showed moderated counters that the contribution of the neutrons in the energy range 0.5 eV - 0.1 MeV to the total dose is quite high; sometimes I I I I I I I [ I U . exceeding 90 /. in the vicinity of 10^ 10^ 10* 10^ thermal 1 10 10* lo" 10* experimental and power reactors in Energy ( eV Fig. 2. Another important conclusion was that the intermediate dose fraction varies by more than an order of Pig. 1. Diagram showing the energy range magnitude depending on several para- of some commonly used neutron meters, which were not established monitors. 238 during the course of these investiga- mrem /h tions . 10 o point o — o o ( total neutron dose O 0 0 I > o o iJ 1 i 0-10 tl-» 21-30 31-« *viO SV-M 61-70 71-»0 «1-«> 91-«I0 "A X X gannnna X " ^ ^X X Fig, Dose percentage due to 0.5 eV - X 0.1 MeV neutrons averaged from 0.1 data for 135 measuring sites (Nachtigall, 1965). fast neutrons ° In Budapest in 1967, we commenced Slow 1 A i with the investigation of the stray neutrons radiation field of our experimental 1 1 1 1 1 1 1 1 T 1 1 1 1 reactors using a measurement technique aoi p 50 100 150 cm similar to that developed by Nachtigall: The neutron dose rate for the whole Fig. 3. Dose equivalent vs. height over energy spectrum in question was moni- the top shield of the WWR-S rea- tored by rem-counters, the dose resul- ctor for neutrons in the 10"^ _ ting from the slow and fast neutrons < 10' eV, E<0.5 eV and E>1 MeV being monitored by scintillation energy range (denoted as "total counters. Owing to the similarity in neutron dose", "slow neutrons", the responses of the slow neutron and "fast neutrons", respecti- survey and personnel monitors (boron- vely) as well as for gamma loaded scintillators and cadmium radiation. covered films) on the one hand, and those responses of the fast neutron survey and personnel monitors (proton % recoil scintillation counters and track 100 r plates) the results were applicable for personnel dose evaluation. Figures 3 and 4 illustrate typical monitoring results^. Based on several measure- 50 ments similar to the one shown here calibration factors were established. 6 For instance the multiplication 0 L S I t -f s i f factor of 9 - 32 was established as Slit s I f T f t top shield that applied to track in annular shield at hall plates order concrete to obtain the total neutron dose for iron shield biological irradiation the hall of our iVV/R-S type reactor. facility The introduction of this correction considerably improved the accirracy of Fig. 4. Percentage dose of our dose evaluation and at the same slow, inter- mediate and fast time emphasized the importance of the neutrons, as search for well as gamma rays at different dosimeters with a wider sites energy range. of the shield of the WWR-S reactor. Average Energy Determinations Average energy determinations of keV up to 15 MeV the shape of the dis- the radiation field yield information tribution is a measure of the source which is also applicable for dosimetry energy. The multisphere technique^ evaluation. For this pixrpose several makes use of the variation in the techniques were developed. One, deve- counting rate ratio of different dia- loped in the Lawrence Radiation meter Bonner-sphere counters when irra- Laboratory*^ is based on the determina- diated with different energy neutrons. tion of the spatial distribution of the In oiir laboratory both techniques were thermalized neutrons inside a moderator. investigated with the aim of developing For source energies from a few tens of a theory for average energy determina- 239 tions and for checking calculations and Although average energi es and dose measiirements . It was shown that both fractions obtained by measur ements proved techniques, owing to imavoidable instru- to be very useful in dosimet er evaluation, ment distortions, measure a quantity the need for a more sophisti cat ed evalua- differing from the mean energy" » 7, tion method was evident. Wi th this in mind we started with the cal culation of Mean energy and another widely used neutron spectra transmitted through and quantity the effective energy, are reflected from different shi elding slabs. defined as follows: Je.m dE Spectrum Calculations mean energy h (E) For the calculation of the spectrum modifying effect of different shields we effective energy ^^^^=Jf^^L^^^l^ used two computer codes ; one, the MUSPALAB code developed by Vertes^ makes use of the so called albedo formalism, where 9 (E) represents flux density and the other, the 05R5S, is a Monte Carlo the d(E) weight function is the flux-to- code. The original version of this code, dose conversion function. Both E and the 05R, was written in Oak Ridge9, and ^eff ii3-ve a practical significance. How- was adapted to our institute's IGL 1905 ever measjirement techniques determine a computer, and several modifications were quantity B which is defined as performed in order to reduce the running timelOjll, k(E).y (E) dE Both codes caxi handle neutron average energy E = sources J k(E).cp (E)dE with different energy and angular distributions. The shielding layers are taken where k(E) is a weight factor, character- as planar, calculations can be made for one-component slabs, for mixtures and istic for the^instrument , the quantity- for measured but S or is the one actua- laminated shields. Both transmitted lly used. "^Qff and reflected neutron spectra are calcu- lated. The energy range of the output A monitoring result is given in spectra spans from the maximum source energy down to thermal energies. Fig. 5 as an example showing the relationship between these quantities. These results not only show a good Using the computer codes MUSPALB and agreement between theory and measure- 05R5S spectrum calciilations were performed ment but emphasize the importance of for several different reactor and mono- using well-defined terms, as a discre- energetic sources and for several shield- ing layers. Fission, pancy of a factor of two may occur if light-water modera- ted instrument response is not correctly reactor, fast reactor escape and taken into account. monoenergetic neutrons were taken as source, the shielding layer composition was water, polyethylene, lucite, concrete, E^f,E (MeV) aluminium, beryllium, iron, and several mixtures of iron, concrete and boron. The 2.0 shield thickness ranged from 10 to 60 cm B bS in the 05R5S calculations, and from 5 upto 1.0 120 to 200 cm when using the MUSPALB code. 0.5 Some typical results are shown in spheres the following figures: Fig. 6 shows fission neutrons after passing through 20 cm and 100 cm thick boron-loaded con- crete; in Fig. 7 spectra of fission neu- 30 40 50 60 wt% Fe trons are plotted after passing through 100 cm thick iron-concrete shields of Calculated and measured effe- different mixing ratio-'-^,- for neutron ctive energies, and average generator survey evaluation, the spectra displayed energies behind a 100 cm thick in Fig. 8 were applied-'-^. iron-loaded concrete wall. Mea- sured and calculated effective Spectrum Comparison and Evaluation energies (open circles and hat- ched stripes, respectively) are In 1972 after calculating several presented for both the Block hundreds of leakage spectra we commenced evaliiation of and Shon, and the paired spheres the compilation and spectra technique. The horizontal range calculated by us or taken from the lite- of the hatched stripes corres- rature . The final purpose of this work ponds to the estimated iincerta- is to prepare a compendium of neutron inty in the fraction of the iron leakage spectra to facilitate dosimetry, aggregate (35-50 wt '/). primarily nuclear accident dosimetry 240 , ) a(ire) CONCRETi- . B TransrrifUed Ftsscfi Scectra &Dron coritefTl (\vt'/>' I I i 1 ; 10'' 1 -a Ki' \cf \& yc? io' Energy (eV Fig. 8. Spectra of monoenergetic neutrons transmitted through 60 cm concre- te. The flux density of thermal neutrons depends only slightly on source energy. evaluation, by making available spectra lOOlyV \0 ) to laboratories Energy involved in dosimetry, but lacking manpower and/or computers to develop their own computation techniques. In order to facilitate spectrum com- parison and evaluation several handling codes were written. SPEC TRANS- 2^4, for Fig. 6, Flux density vs. energy plots of instance, calculates the spectra for 48 fission neutrons after passing predetermined energy intervals, computes through 20 cm and 100 cm thick kerma and dose-equivalent spectra as well concrete with different boron as dose fra-ctions and a,verage energies. contents (in wt X). The calculated spectra are written on a magnetic tape and plotted in a variety of different formats. Another computer code used for spectrum hajidling is the TRESPASS-'--' Some representative results are presented in Figs. 9 and 10: Fig. 9 shows spectra of fast neutron sources transmi- tted through 50 cm thick iron as measured in the Soviet Union and calculated by us? Fig. 10 shows fission neutrons passed through 40 cm water slabs calculated by the 05R5S and the MUSPAIB code^°; Fig. 11 gives results for 5 MeV monoenergetic neutrons and a 10 cm berated Polythene slabl7,18. For the calculation, handling and application for evaluation of neutron Fig. 7. Effect of the concrete-iron spectra a computer code family has been mixing ratio on the shape of the developed, vfhich is shown schematically spectrujn and on the flux reduc- in Fig. 12. tion of fission neutrons after passing through a slab 100 cm thick. Parameter: Fe content in 241 rNPulS SPECTRUM SprcTBi*i Fig. 9. Spectra transmitted thxough 30 cm CAtCULATlNO COOES Data iron or steel slabs. The calcula- STonAOE tion for a fission spectrum and pure iron (solid line) is compa- red with two spectra measured at 05BSS IBtSPASS I LIBRARY the IBR fast reactor} the "Fe-Mn" j curve (dotted line) is for a o f err -manganese steel, while the formot "Fe alloy' curve (dashed line) is SPtCTRLM \ \ »o»c*'"u"» LIBRAffy I prfnloull for a steel containing Mn, Cr, Ni I and Co. r-,-r-r-^-,— 5PECtBANS-5 FITTING CODE 0(ne data Pig. 12. Scheme showing the computer code family used for spectrum calcu- lation and dosimetry evaluation. IH P- K Spectrum Applications for Dosimeter Evaluation Survey Results of Shielded Reactors N, /N 2 '^.4 30.0 L 1. I? MoV 1.02 ^'lfV M, /N, 16.9-'. 16.3% In the early sixties only fast and 26 .7 30. 7'/. slow neutron detectors (cadmium covered film, slow and fast neutron scintilla- tion counters, track plates) had been Itf' used in our institute for reactor sur- EHtHCTItVI veys and personnel monitoring. In 1966, inpMS. 10.0 CH unicR fission, cosine distr. Bonner sphere techniques were introduced. In order to improve the precision of the Fig. 10. Pission neutrons after passing neutron dose evaluations, calculations through 10 cm water calculated were performed for determining the rea- by the 05R5S and the MUSFALB dings of the devices mentioned above. codes. For comparison the follo- Calculated results-'-^ for two rem counters .' wing quantities are given: fra- are given in the following three figures ction of transmitted neutrons, (Figs. 13-15)-'- 9, and their response fun- . mean energy, percentages of alow ctions are shown in Fig. 16. Results and E>2.5 MeV neutrons in the show that, as a rule, Bonner sphere transmitted spectrum. survey results can be considered as quite 242 . \\ \\ \ \ -3r^ \ 0.6 \ 1 0.4 \ 0.2 X)^ 10' 1 10 10^ 10* 10^ 10^ 10^ Neutron energy (eV) Fig. 16. Relative deviations of the DN- f50 A-1 rem counter (dashed curve) and a 10-in. Bonner sphere (solid curve) from the ICRP Fig. 13^ Relative response of two rem response curve. counters for fission neutrons which have passed through con- acc\irate (there is little point in app- crete + iron layers of different lying a correction smaller than 10%), thickness es however for a 100 cm thick iron-shielded reactor a 30/. over-reading occurs which we consider to be significant. The evaluation of a proton recoil 25 cm sphere ^ scintillation survey instrument measure- 41 ment requires much sophistication, as the (0 C!9 c set of graphs shown in Fig. 17 proves it. o Q. Here, the instrument reading is plotted lO Oj against shield thickness for a light- water reactor. Parameters are shielded «< composition and detector discrimination level. The two upper graphs show that for iron-loaded concrete, independent of I. the mixing ratio as well as the discri- mination level, the relative reading is 0.4 - 0.5> i.e. an average correction factor ^2 can be applied. This is not so fOO true for iron shields where the detector reading happens to be one or even two Fig. 14. Relative response of two rem orders of magnitude lower than the actual counters for fission neutrons dose strongly depending both on shield which have passed through water thickness and discriminator setting. layers of different thicknesses. Dose percentages of intermediate energy neutrons (1 eV < E <1 MeV i.e. the energy range not monitored by t he, old- - 1 1.0 1 I 1 concrete fX fe, £t - OS concrete *30Xft. £^ « 10 c o - iOMtV a ~ f.2MeV ^ t^MiN . 1 1 1 1 1 two rem 1 1 1 1 1 1 1 1 Fig. 15. Relative response of 1 counters for fission neutrons 0 20 1,0 to iO fOO 120 t*0 d(cm) which have passed through iron Fig. 17. Relative response of fast neutron layers of different thicknesses, detector for various shield mate- rials and discrimination levels. 243 i I I I I I I I I I I I I I 1 I I 1 I [- fashioned slow and fast neutron survey ————I— ——————————————— instilments) are illustrated in Fig. 18 determined by measurement and calcula- REFLECTED REACTOR SPECTRA tion. It should be noted that the fairly good agreement between theory and experiment may be misleading, for in many cases complicated shield geometry, scatter, or other factors impossible to •••••• include into the calculation model may Mj,(o««J«f^ cause large discrepancies. >too : Fe leV < E c -1 MeV 50 4; 20 cm Fe concrete t30%Fe ii:25cm Al J a> oin xs V 40 1—1—1— —1—1—1—1 ...1 I 1 20 W 60 80 -100 d (cm) I i I I I I I ' I 1 I I i__i L .J_i Fig. 18, Dose fractions of intermediate energy neutrons behind the 10 10 10 shields of light-water reactor ENEflCY(Evl sources. Circles: measured values lines: calculated data. J Fig. 19. Spectrum from a light-water re- actor after being reflected from Evaluation for a Scattered Neutron Field slabs of different materials. The following results show an exam- By using these spectra correction ple of the application of backscattered factors for the nuclear emulsions and spectra in dosimetry evaluation for com- fast neutron scintillation monitors, as plex geometries. The ZR-6 critical well as for sulphur activation detectors assembly is a light-water moderated, routinely used for neutron monitoring enriched uraniiim fuel system, located in were obtained (Table 1). These results - a well some distance below floor level. which were proved by measurements for Neutron radiation in the reactor hall is some selected cases - show that average due mainly to scattering from walls and correction factors can be used with rea- other structures. The walls are of sonable accuracy: concrete, while aluminium and iron are the other structural materials. The K(E > 1 MeV) = 2.1 + 0.5 contribution to the dose of the radiation scattered from different materials for nuclear emulsion and scintillation varies from point to 'point in the hall. proton recoil detectors and Thus the dose at a given point can be expressed as the linear combination of the doses due to the scatter by concrete, K(B> 2.5 MeV) = 8o5 + 3 Al, and Fe: for sulphur activation detectors. D = kgDc + kpg^Fe + ^Al^Al Nuclear Accident Dosimeter Calibrations where D^, Dpg and D^^ denote the respective The two preceding examples were for doses resulting from the scattering by complex situations where simplifications concrete, iron and aluminium, and kj^-s are were unavoidable. Far more accurate the relevant weight factors. Owing to the evaluation was applied in the problems complexity of geometry the k factors discussed here. cannot be determined. Instead, we de- termined the maximum possible variation Highly sophisticated evaluation tech- in spectral shape, in Fig. 19 (Makra, niques can be used when the source 1973). spectrum and the irradiation geometry are 244 Table 1 «>,S MeV ( \ f-((E)(IE-1 ' OiA 1 Correction factors for detectors o.weV ;/ having 1 MeV and 2.5 MeV energy thresho- y // \ lds, irradiated with the radiation of the direct ,/ \i a3 ZR-6 critical assembly, scattered from '/ \l direct reflected // \\ the walls and from other structures. The 1 \\ spread of the values is caused by the z 1 \\ a. 02 ;/ 1 - spectrum changes of the assembly due to » // 1 bJ differences in water reflector thickness. '/ \ f \ '1 \ 0.1 Correction factor (fission - reactor) Reflecting 1 1 1 1 1 material 10'* 10"' E > 1 MeV E> 2.5 MeV K)* X)^ K)"* 10"' Kf 1o' NEUTRON ENERGY (MeV) concrete 1.7 - 2.2 5.6 - 7 iron 1.9 - 2.6 8.3 -11.5 Fig. 20. Steel filtered spectrum of the Oak Ridge Health Physics Resear- aluminium 1.6 - 2.1 5.9 - 8.0 ch Reactor (solid line) and the same as modified by the refle- ction of a water-filled human well known. This was the case when we phantom (dashed line). performed calibration r\ins at the Oak Ridge National Laboratory with the Dosar Conclusion facility^O or in Vinca near Belgrade, „^ Yugoslavia, with a heavy water assembly'^. As an example the dose evaluation proce- Spectra of neutrons passed through dure for NAD dosimeters positioned on or reflected from different slabs may be human phantoms will be discussed here. calculated and applied for dosimeter For the Dosar irradiations the following evaluation. As the use of such spectra calculation steps were used: 1) the lea- considerably improves evaluation techni- kage spectmm of the facility was deter- ques the application of spectrum calcula- mined by the ORNL staff using the DOT tions is being continued. One of the purposes of our work is to prepare a code ,• 2) we determined the modifying effect of the shields, by using the compendium of neutron spectra which makes MUSPALB code. 3) The backscattering available these spectra in a readily effect of the phantom was taken into applicable form to scientists involved account modelling the phantom with a in neutron dosimetry evaluation. water slab and determining the back- scattered spectriim with the MUSPALB code Acknowledgements using the spectrum obtained in the pre- vious step as input. 4) The summed Thank are due to my co-workers, direct + reflected spectra were used as J. Palfalvi, L. Koblinger and P. Zarand a model spectrum for fitting to flux for their contribution, as well as to values of the NJ^D activation detectors. Dr. P. Vertes for the development of the As an illustration, spectra for a 13 cm 14USPALB computer code and to Dr. H. Ing thick iron shield are shown in Fig. 20. (Chalk River Nuclear Laboratories, Canada) for the valuable discussions. The same procedure was applied for the evaluation of our measiirements per- formed at the Vinca heavy-water reactor. In this case the reactor escape spectrum was calculated at Chalk River using the 05R code^5, otherwise the procedure was identical with that discussed previously. 245 . . . . , . References Y.T. Song 1. Wachtigall, D. , Atompraxis 11 (1965) 1) Mixed use of average and mean 203. energy need clarification. 2. Nachtigall, D., Proc. Conf. Neutron 2) Calculating fast neutron spectra Monitoring for Radiological Prote- throxigh iron, what cross-section did you ction 329 IAEA Vienna 1967- use? 3. Makra, S., Toth, M., KFEI Kozl. 16 3) Direct + scattered and Direct (1968) 381. neutron spectra were compared. However, 4. Block, S., Shon, F.J,, Health direct and direct + scattered had exactly Physics 8 (1962) p. 533. same spectrum, though scattered were D. 5. Nachtigall, , Rohloff, P., Jul-213 about 20X need clarification. -ST report (1964) 4) You made comment on optimum 6. Makra, S., KPKI-70-6-HP report (1970) mixing ratio in connection of your spe- and lectiire No. 107, Second IRPA ctrum calculation. How coiild it be used? congress, May 3-7 1970, Brighton, England S. Makra 7. Attix, F.H. (editor). Topics in Radiation Dosimetry. Academic Press, 1) The terms I used are defined in New York, London, 1972 p. 433. some of my earlier papers (e.g. 1st IRPA 8. Vertes, P., Nukleonik 12 (1969) 67. Congress Lecture, Brighton, 1970) and in 9. Irving, D.C., Freestone. R.M., Kam, condensed form in Attix 's recent Radia- F.B.K., ORNL-3622 (1965). tion Dosimetry book. Mean energy is a 10. Lux, I., Koblinger, L. , KFKI-73-2 mean value without any weight factor; report (1973)- effective energy is weighted by kerma 11. Koblinger, L. , KFKI-74-47 report or dose-equivalent, effective energy is (1974) weighted by detector response. 12. Makra, S., Vertes, P., Kernenergie 2) The earlier calculations Abagian 16 (1973) p. 378. data were used, for recent calculations 13. Makra, S., Palfalvi, J., Vertes, P., the 05R library was obtained from RSIC Health Phys. 26 (1974) 29- 3) The direct and direct + reflected 14. Palfalvi, J., KFKI-73-57 report spectra displayed were flux per unit lethargy (1973) . (linear scale) _vs. energy (log scale) 15. Palfalvi, J., KFKI-74-48 report plots. The very similar shape in this (1974) . case actually means that the low energy 16. Palfalvi, J., Koblinger, L. , KFKI- neutron contribution for the upper curve 74-63 report (1974) is considerably higher than for the 17 . Makra , S . , Palfalvi , J . , Zarand , P . lower one. Proc. Conf. Neutron Monitoring for 4) We did not develop any code for Radiation Protection Purposes, 47, optimum mixing ratio determination. IAEA Vienna, 1973. However, comparison of results for 18. Allen, F.J., Futterer, A., Wright, several mixing ratios can be used for a W., Budka, A., BRL 1130 report general orientation. (1961). 19. l^lakra, S., Bekes, B., Proc. Conf. Advances in Physical and Biological Radiation Detectors p. 425 f IAEA, Vienna, 1971. 20. Makra, S., Zarand, P., KFKI-71-82 report (1971). 21. Palfalvi, J.. Makra, S., KFKI-74-68 report (1974). 22. Poston, J.W., Knight, J. P., Whitesides, G.E., Health Phys. 26 (1974) 217. 23. Ingf H., Private communication 1973- 246 UTILIZATION OF PLASTIC SCINTILLATOR IN THE MEASUREMENT OF UNCHARGED RADIATIONS P.K. Sarkar and K.N. Kirthi Health Physics Division Bhabha Atomic Research Centre Bonibay-400085 Uncharged radiations like neutrons and gamma rays produce scinti- llations in plastic scintillator through secondary charged particles. The energy distributions of these recoil particles are related to the energy distribution of the incident radiation. An attempt has been made in the present work to get back the original incident spectrum from the recoil distribution. The computer code UNFOLD designed for the purpose makes a minimiim-variance, maximum likelihood estimate of the incident spectrum by iterative least square technique. Neutron spectra from different Be(a,n) source and 252 Qf spontaneous fission have been measured. The results agree well with those published. Plastic scintillator proves to be more useful when the incident gamma spectrum is continuous in nature because the Compton continuum produced in the scintillator has a well defined integral relationship with the incident gamma spectrum. Continuous gamma spectrum in Apsara reactor beam hole has been estimated using the technique developed. (Apsaraj energy distribution; gamma ray; iterative; neutron; plastic; recoil; scintillator; UNFOLD) Introduction Plastic scintillator is one of the proton recoil detectors that can effici- Mixed radiation fields exist in many ently be used as a neutron spectrometer. nuclear environments of applied and basic It has a basic advantage over the liquid interest. An example of particular scintillators for its high detection importance is the incore radiation field efficiency and convenience of handling. of a reactor, consisting, mainly of Unlike anthracene or stilbene the pulse neutrons and gamma rays. In the measure- height produced in plastic scintillator ment of a radiative component of such does not depend on the direction of mixed fields the usual procedure is to neutron incidence nor it is sensitive to employ a certain detection system which thermal or mechanical shock. Kim-'- has responds only to that particular compo- pointed out that if the disadvantage of nent and discriminates against others. gamma response can be removed then Though it is well known that total dis- plastic scintillator promises to be a very crimination against background is simple neutron spectrometer with high impossible, the actual choice of efficiency and moderate energy resolution. detection system is often based primarily Young2 has shown that the resolution of a upon this very requirement. Existence of scintillator detector increases with the a non-zero sensitivity to background decrease in the thickness till proton implies an experimental interdependence escape from the scintillator tries to among the components of a mixed radiation affect resolution. Now, if proton escape field. Due to this complementary is also accounted for in estimating the relationship, an improved definition of neutron spectrum a thin plastic detector any given component automatically can give a high degree of resolution. provides more precise knowledge of the Apparently, it seems meaningless to use remaining ones. plastic scintillator in gamma spectrum analysis because of its comparatively The present effort is directed bad resolution and mainly because it towards the development of a general produces a smeared rectangular distri- method for measuring both the continuous bution rather than clear photopeaks for gamma and neutron component of a mixed mono energetic gammas. But when it radiation field. The technique applied becomes evident that it is the Compton is charged particle recoil, the recoil recoil spectrometers that only can be medium being a plastic scintillator. used in the precise determination of the Protons and electrons are the recoil continuous gammas ray spectra^, the particles produced when plastic scinti- plastic scintillator has the advantage llator is exposed to neutrons and gamma due to the fact that scintillations are rays respectively. mainly by the Compton electrons produced 247 in it due to the incident gamma radiation. being gaussian in nature. In the recoil detection technique the Monte Carlo technique, though it gives problem basically lies with the unfolding the desired accuracy, does not yield an of the incident distribution. The energy- analytical expression from which the spectrum of the recoil particles gets a incident spectrum can be deduced complicated smear in the observed pulse directly. It requires an unfolding ii height distribution due to multiple based on matrix con.figuration of scattering, non-linear light output and response function. photomultiplier statistics. Still, if the response of the detector to mono- Unfolding the Measured Distribution energetic incident radiation is known, the incident spectrum can be estimated When a measuring instrument is fed by inverting the equation that relates the with a distribution g(s), the output incident spectrum to the observed dis- obtained becomes y(t). Thus the tribution. But if straight forward function of the instrument can be looked matrix inversion or iterative techniques upon as an operator 0 and the situation are employed amplification of the can be expressed in mathematical terms fluctuations in the experimental pulse as height distribution or large oscillations are likely to occur. fO] g(S) = y{t) Calculation of the Response Function This equation can be written in matrix notations as K.G. = Y where K is In view of the practical difficulty the response matrix of n x m elements, associated with obtaining series of Y is the proton recoil distribution, and monoenergetic neutron or gamma sources, G is the spectrum to be evaluated. An the response of the scintillator to those easy solution to tais equation is radiations were calculated theoretically. It is not practicable to use an analytic G = E"-^ Y expression for the response function, since in general, the extremely compli- But this solution is not ixnique and cated analytic expressions which exist are also it can be shown^ that G will not be approximations not easily related to known accurately due to the statistics practical counter configurations. associated with the observed data, what Several attempts were made to calculate at the most can be obtained is the the response function in different ways. maximum likelihood estimate of 'G', based They have been discussed elsewhere^^. In on 'a priori' informations with error the present case Monte Carlo technique and variance minimised as far as has been employed to calculate the possible. Error minimisation is carried response functions. out by the usual least square techniques. Variance is minimised by using the Computer codes MECROS-N and weighting matrix and iterative techni- MECROS-G^ were developed to get the ques, resulting in a minimum variance response of the scintillator to neutrons maximmn lilellhood estimate of the and gamma rays respectively. The present spectrum. In order to remove spurious calculations follow the course of each fluctuations smoothing has been applied neutron or gamma photon inside the to the observed data, using time series scintillator, collision by collision, and and Fourier analyses. calculates the energy deposited by the charged particles produced due to Experiment and Results elastic scatterings and reactions. The light pulse produced by the incident For measuring the neutron spectrum radiation is obtained by summing up the different thicknesses of scintillator contributions of all the charged parti- were coupled to photomultipliers and cles after multiplying them with proper pulses were fed to a multichannel statistical weights and using proper analyser after a stage of conventional formulations for light output vs. amplifiers, Channel calibration was particle energy. Biased Monte Carlo done by a ^^Co gamma source. Neutron technique i.e. Russian roulette and spectrum from different Be(a,n) sources splitting is adopted. The statistical and from spontaneous fission of 252cf weight of the incident radiation after was estimated. Details of the experi- each collision is multiplied with the mental set up and results have already non-escape probability and is allowed been published4» 6 . Figs. 1,2,3 give to make further collisions inside the the estimated spectra of Pu-Be, Ra-Be scintillator. The finite resolving and 25'icf respectively. For measuring power of the spectrometer system has been gamma spectrum a single thickness of the considered by making a random fluctuation scintillator has been used. The 248 . / selection of the thickness has been made by optimising resolution of the detector miA FKOM * il J and electron escape from the scintillate: HANt) MOiM NO TM Continuous ganma background at Apsara beam hole number 3 was measured. The experiment was repeated with a lead shielding of 2.5 cms thickness. The observed and unfolded spectra are plotted in Figs. 4 and 5- LN£HGr ( Mt„ Fig. 1. Pu-Be Neutron . Spectrum. Fig. 3. Californiujn-252 Spontaneous (THE. THO amis ^R£ NOT NORM>(LIS£.P TO £(JyAi. -(,Rt/J, fission neutron spectrum. A - - — PR£5£WT tVORK. P/(TA f ROM THOMPSON et I Fig. 2. Ra-Be Neutron Spectrum. c - Fig. 4. Observed and Unfolded Gamma Spectrum taken with Plastic Scin tillator at Apsara Beam Hole No. (The Number of counts for the unfolded spectrum is plotted in an arbitrary scale. The areas under the curves are not normalised) 249 . . . . suggested in the present paper. Acknowledgements The authors are thankful to Dr. A.E. Ganguly for his constant encouragement and valuable guidance and also to Shri S. D. Soman for his keen interest in the work. We thank Dr. M.R. Iyer and Shri Hari Singh for their help. References 1. KIM, CM., A theoretical comparision of 4ii fast neutron spectrometers, UCRL- 9604 (I960) 2. Young, W.R., Neutron spectra from organic scintillators, UCRL-16149 (1965). 3. Gold, R. and Olson, I.K., Analysis of Compton continuum measurements, ANL- Pig. 5. Observed and Unfolded Gamma 7611 spectrum taken with Plastic 4. Sarkar, P.K.; Kirthi, Z.N. and Ganguly, scintillator at Apsara Beam Hole A.K., Response of plastic scintilla-.or No. 3 after 2.5 cms Lead shielding. to neutrons, gamma-rays and charged (The number of counts for the particles, BARC 756 (1974). unfolded spectrum is plotted in an 5. Burrus, W.R., Utilization of 'a arbitrary scale. The area^ under priori' information in the statistical the curves are not normalised) interpretation of measured distri- butions, ORNL-3743 (1964). Discussion 6. Sarkar, P.K., Kirthi, K.N. and Ganguly, A.K., A Technique of measxir- It is evident from the results shown ing neutron spectrum. Proc . 2nd that both the continuous gamma spectrum Symposium on neutron dosimetry in and the neutron spectrum in presence of biology and medicine, Munich, Sept. gamma field can be estimated by plastic 30 - Oct. 4 (1974) scintillator with fairly good accuracy. In order to separate out the two com- Discussion ponents of a mixed radiation field, first the neutron spectrum has to be estimated, K.V.S. Nambi then it has to be converted to the proton recoil distribution in the scintillator Have you attempted to measure the used to measure the gamma spectrum. The 'skyshine' spectinim from the gamma pulse height spectrum due to proton garden at BARC using a plastic scintilla- recoil distribution has to be subtracted tor and your unfolding technique? from the observed pulse height spectrum. The pulae height distribution thus P.K. Sarkar obtained can be used to unfold the gamma component Because of the experimental diffi- culties associated with such measurements Though plastic scintillator has poor so far no attempt has been made. We have resolution in case of discrete gamma a plan to do it in future. peaks, the high degree of Compton domi- nance makes it very useful where the H. Sanjeeviah spectrum is continuous. In the case of neutron spectrum estimation, the most 1. Can one use a plastic scintilla- important limitation lies in the tor te measure bremsstrsiiLung spectra? Judicious selection of number and energy range of thin scintillator employed to 2. Bremsstrahlung radiation (EB or resolve the spectrum. However, this IB) is generally of low intensity. So limitation becomes insignificant when we will not the low efficiency of the take into cognizance the fact that plastic scintillator hinder the measure- plastic scintillator can efficiently be ment ? used to determine both the neutron and gamma component of a mixed field. Work P.K. Sarkar is in progress in determining the two components sep&rately, using the method 1. The continuous nature of 250 . BremsBtrahlung spectra indicates that energy and obtained pulse height of plastic scintillator can be used to charged particles ? measvire such spectra. But care should be taken to have the response function P.K. Sarkar very precisely estimated. In fact experimental estimation will be more 1. The lowest energy which can be valuable than the theoretically calcula- discriminated against gamma backgrovind ted ones. is 1 MeV. 2. The efficiency factor can be 2. We have considered the formula- increased by increasing the thickness tion given by Lindstrom et al (Nucl. (or volume) of the scintillator. In fact Instr. and Methods ^8 (1972) 413) provisions can be made to arrest all the primarily. But we also have performed bi emsstrahlung radiations. But care experiments at a ?an-de-Graaff shovLLd be taken to optimise the thickness accelerator using our scintillator because of light attenuation In the to check the validity of the relation- scintillator. ship for the present scintillatoi' (supplied by Technical Physics Division, Y. Furuta . BAEC ) 1. What is the lowest detectable energy of neutrons ? 2. What data did you take from for the relation between charged particle 251 : NEUTRON SPECTROMETRY BY SANDWICH SURFACE BARRIER TECHNIQUE * O.P. Joneja Bhabha Atomic Research. Centre Tronibay, Bombay-400085 India A neutron spectrometer using silicon surface barrier detectors employing ^LiF as a radiating material is developed. An incident neutron interacts v;ith the radiating atom resulting in t\io charged particles, which are detected by sandwich, detector geometry and the corresponding sum pulses from both, the detectors shall uniquely define the incident neutron energy. This paper also presents results obtained by Konte Carlo simulation of all the correction factors for the detector head employed. A new concept for resolution correction is developed which brings dovm the lower energy li:.iit of the detector system. The spectrometer is employed for incore spectrum studies in case of a thermal reactor 'Kahter' and the results obtained exhibit a good agreement with that of calculations by GAl'I THERFiOS EXTERMINATOR Code. (Detector; energy Ifeakage; ^Li5'; iionte Carlo } neutron,- sandwich; spectrometry; surface barrier) , Introduct ion Experimental Set-up The study of neutron spectrum in Tvjo identical silicon surface reactors offerSan effective tool to check barrier detectors each having an area the validity of calculational methods, in 260 mm^ and a depletion depth of 500 addition, the damage suffered by cons- microns, enclosing 150iigm/cm2 of ^LIF truction material in high flux experimen- layer in a sandv/ich geometry and housed tal and power reactors requires the in a steel container forms a detecting knowledge of fast neutron spectrum. The head. For the purpose of calibration, neutron energy of interest in case of each leg, comprising a detector and a fast and epithermal reactors is considered set of amplifying unit S3 is adjusted to to extend from 10 keV to 10 HeV and exhibit identical pulses for a given uptil now the results from several experi- energy loss in the respective detectors. mental tecliniques are normalized to scan A fast coincidence along vfith a gate unit such a vfide energy region. The present ensures detection of coincidence events method, however provides the spectrum and elimination of single particle events. information for most of the energy region The calibration; is accomplished by of interest in a single shot. The tnermaliaing neutrons from an Am - a - Be spectrometer head consists of two silicon neutron source. surface barrier detectors sandwiching a ^LiF layer. Although charged particles i'l02ite Carlo l-iethod produced due to °Li (n, a)T reaction receive energy depending upon their angle It can be easily visualized that a of ejection, the suiq of their kinetic sandwich system operating in coincidence energy in principle remains constant and mode shall suffer from the following is equal to energy of the incident losses neutron plus Q value of the reaction. Thus, for a continuous incident neutron 1) V.'hen either one or both the par- spectrum there will be one to one ticles escape from the finite correspondence betv/een neutron energy and separation betv/een the detectors, sum,p\ilses but since the cross section i.e., gap leakage. of *^Li(n, a )T reaction depends on neutron coincidence response from 2) There is no energyj therefore spectrum unfolding when both the particles hit the shall require an pulse height information same detector, i.e., double res- correction. efficiency ponse leakage. *Tne work done at KFA-IRE, Juelich in V/est Germany 252 . 3) An event is also considered lost carrier belt forms core of the reactor. when tiie pulse height resulting The assembly is controlled with the from either detector falls below help of nine boron carbide rods. The the threshold setting, i.e., bias detector head in the present experiment leakage. is located in an aluminium channel situated a,t a distance of about 30 cms iTow, in case the failure of coinci- from the central absorber rod and about dence response due to above losses depends 140 cms from bottom of the core. upon neutron energy then spectriia unfol- ding without considering above effects -iesolution Correction and Comparison with shall results in a distarted spectrum. In Calculations order to evaluate all the leakages, a i-Ionte-Carlo Code 'CQIiJCIDE' is developed The subject of resolution correction in Fortran IVl . The leakage simulation in general nas been dealt by it. G-old2 is accomplished for an isotropic incident and the standard expression for numerical neutron flux assuming that the lighter solution can be ^^rritten as charge particle is ejected isotropically in the laboratory sj^stem. The output Y = RX Y = output reactor lists all the leakages per observed coincidence count for several neutron R = xiesponse matrix X = input energies and the results obtained for the reactor detector head employed are presented in Pig. 1. The input vector X can be determined by matrix inversion, however this method quite often is found to yield oscillatory solutions and that is why one finds nujaber of iterative schemes available in literature but unfortunately none of them can be recommended for a particular measurement. It is interesting to state that available iterative methods aim at correcting the experimental data for resolution vmereas in the present work correction is attempted through cross section. In this method one has to construct an advancing matrix from a detector response to thermal neutrons and then transform the cross section vector by matrix operation. The advancing response matrix and the cross section transformation for thermal 0 10 20 30 40 50 60 70 RO 90 100 response obtained at different power levels is presented in Eigs. 2 and 3- Pig. 1. Leakage factprs obtained by Monte The measured lethargy spectrum after all Carlo for a °Li system (a-2.D0, the corrections is shown in fig. 4 along s=C.C12? cm) X-axis -n. energy with fission spectrum and calculated (I'leV), y-axis leakage factors/ reactor spectrum. It can be seen tnat registered count: for bias=1.5 measured and calculated spectra agree HeV within +12/. over most of the energy region of interest. The larger dis- Description of Thermal Assembly 'Kahter ' crepancies belov; about 250 keV might result from non reproducibility of the The sj)ectromet er is used for incore response function and also lovfer spectrum studies in the case of a graphite moderation in experimental results might moderated assembly 'ilahter', at the be due to the fact that during experi- institute of reactor development at ment detector head was not coinpletely Juelich in V/est G-ermany. The fuel surrounded by fuel balls. IMso a (U-Th)02 is fabricated in the form of relatively larger error in one of the balls, each containing one gm of 235u higher energy bands is expected to resijlt and 5 gms of ^'^^Ta. A uniform mixture from the fact that tne code employed for of coated particles and graphite com- calculations was good for thermal pressed to a diameter of 5 cms forms the reactor calculations and moreover tne core of a fuel ball, which is further calculated spectra is averaged over a enclosea by a 5 rorn thick graphite large volume containing the site of jacket. A cylindrical graphite structure experiment . 40 cms thick having an inner diameter of 2.16 metres and height of 2.40 metres with a slanting base and an additional cylindrical passage leading to a 253 • Acknowledgement s 1-Jy sincere thanks are due to Dr, R. hacker for providing all the facilities and valuable suggestions. I shall also like to thank Dr. P. Cloth for the discussions. I would like to thank Dr. P.K. Iyengar for suggesting the problem and useful discussions. hlso , I v;ould like to thank Dr. i-I.P. Navalkar for his interest and suggestions. - '- • References 1. Joneja, O.P., Past bpectrum litudies with 3iie burface Barrier Sandwich Detector KPA, Internal report IRE - 25-73. 2. Gold, R. , Jin iterative unfolding method for response j.iatrices, iil'JL - 6984 (Dec. 1964) ?lg. 3. Plot detects the actual cross section data and the resolution, corrscted cross section data ^ 30, _ . . , j'';,Lg. 4. Comparison of neasnred : calcula- ted and fission 254 ; ROLE OP HIGH RESOLUTION Ge(Li) DETECTOR IN TRACE ELEMENT STUDY IN WATER ACTIVATED WITH THERMAL NEUTRONS J.M. Chatterjee (Das)*, E. Peeters and M.A. Castiauz Institut Royal des Sciences Naturelles de Belgique Rue Vautier 31» 1040 Bruxelles, Belgium While chemical analysis is limited in its application of element detection, gamma-ray spectrometry plays a big role in the nondestmictive element detection in the neutron activated samples with large volume high resolution Ge(Li) detector. The water samples from the volcanic region of the island SANTORINI (Greece) have been activated with thermal neutrons, and the gamma-rays emitted by the long-lived radioisotopes have been detected with high resolution Ge(Li) detector. The analyzed results show the high concentrations of alkaline and magnetic elements if compared with that of these elements in the normal sea water samples. The presence of some rare earth elements has been observed as well. (Activation; analysis; element; gamma rays; Ge(Li) detector; neutron; nondestructive; resolution; spectrometry; water) Introduction d) The local people are living on fishing in the Aegean Sea and the sea of The activation analysis has its Crete which surround the island. important role in the various fields of radio analytical chemistry. The procedure Seven places including the bays were is applied successfully to the trace chosen to cover the whole rim as well as element study in the samples of biology, the body of the volcano (fig. 1). The metallurgy, mineralogy, medicine, water, hot water sources under the huge rocks air (pollution study) and also for in- (steno source 1 and 2), the bays flowing dustrial process control in different to the sea (Erinia, St. Georgia, St. laboratories. The direct counting with Nicolas), the natural lake of the the high resolution large volume Ge(Li) volcano, the hot vapour coming out had detector has made possible the rapid and been considered the main reservoirs of precise determination of elements of different elements. The water from these mult i elemental samples. places and the vapour condensed were collected for sampling by sucking with The procedure has been used to study plastic syringe; 2 ml of sample was the trace elements of the water collected poured into the sterilized quartz vials from the region of living volcano precautions were taken not to contaminate Santorini (Nisos-Thira, Greece). them during collection. The vials are then sealed in the flame. Site Choice and Sample Collection SANTORINI (NISOSTHIRA') The region was chosen for several reasons, particularly a) Mere sight has been enough to realize the existence of some elements; the pronounced rusty red colour of iron oxide visible on the rocks of the volcano and the green sea water extending few km from the source show the presence of high. concentrations of iron. b) The information on this region Is very scanty; only some geological study has been report e dl. c) The place is very near to the residential area and considered one of the tourists' places in Greece. Eig.l. Shows the sites for sample colle- ction. Present address - E.S.C. Division, Saha Institute of Nuclear Physics, Galcutta-9 255 . . Experimental Procedure of Cs and Fe are found, the large quantity of iron is visible from the rusty With thermal neutrons of estimated red colour of the rocks. All other flux 3 X 10-'-2n/s/cm2, the samples were observed elements have their concentra- irradiated in the reactor of C.E.N. tions more than those present in the ( Saclay-France) for five days along with normal sea water. The absence of Sr, Cs standards prepared from Zn, Co, Br and and Rb in the sample taken by condensing Hg compounds. The standards are used the hot vapoixr from the outlet of orater as comparator and also for checking the inay be due to (1) some geochemical change neutron flux in the reactor canal. An in the molten part of the volcano and (2) empty quartz vial was irradiated to check the filtration by the various earth layers the impurity added to the sample from the inside the volcano. Two more elements wall of the container. Eu and Se have been detected in the sample of vapour condensed. The large The activated samples were then concentration of Se in this sample is cooled down for four weeks, the reason is, noticeable during the irradiation extremely large amounts of 24iTa, 38ci,4-22: and o^Br are The presence of sulphur is apparent produced and these short-lived nuclides from the yellow layer in the orater and present an initial radiation problem and from the smell of H2S in the water sample their gamma-ray spectra mask the spectra from hot sovocce. But this element could of other trace activation products. not be detected because of its very short half-life (5-07 m) . However, a gradual 1 ml of the activated sample was and careful activation analysis of sea inserted into the disc of plexiglass water and marine organisms will provide (internal diameter 19-9 mm and thickness much information about the geochemical 3.7 mm). Tvjo coxial right-angled Ge(Li) change and pollution of this region. detectors - ORTEC and PHILIPS - of active voltunes 31-4. and 64 cc respectively were Acknowl edgement s used In combination with 16 Z multichanjiel pulse height analyser ( Intertechnique The authors wish to express their BA 163) • The analyser has the provision heartiest thanks to Prof. A. Capart, for simultaneous accumulation of four Director of the I.R.S.N.B., Bruxelles for separ3.te spectra with proper analogue-to- his active help during the measurement digital converter ( Intertechnique CT 102). and participation in sample collection. The detectors were incorporated with One of the author J.M.C. is grateful to preamplifier and the signals were ampli- IAEA, Vienna for sponsoring the fied by CRTBC spectroscopy amplifiers; fellowship for the post-doctorate their resolution had been 2.2 keV for research during this period. ORTEC and 1.8 keV for Philips on 1,332 keV ga,mma-ray from 60Co. References 30-35 photopeaks of energy rsmges 1. Wikovich, D. and Heezen, B.C., 100-2,000 keV from each sample were Submarine Geology and G-eophysics; edited detected with the time interval of W.E. Whittard and R. Bradshaw, 14-15 vreeks. The coujiting time was Proceedings of the 17th Symposium of the adjusted according to the coimting Colston Research Society held in the statistics desired. The major isotopes University of Bristol, 1965. sea^rched had been of half-lives from few 2. Bowen, H.J.M. and Gibbons, D., Radio- days to several years. activation Analysis; Clarendon Press, Oxford (1963) Result s and Discussions The elements fo\ind are Ce, Hg> Cr, Sr, Cs, Rb, Zn, Co, Pe, Sc, Eu, Se and Br. Br is not observed in the measure- ments taken 18 weeks after irradiation. Y erv interesting observations are made in this region. Variable concentrations of most of the elements are observed. Ce and Gr are not found in all the samples, Hg content is very high (500/) in comparison with that in the normal sea water2, (14-20 mg/'l of Sr is foxind in the water samples but is totally absent in both the samples of condensed vapour) o Extremely large concentr3.tions 256 . . SUI-n-IIKG UP OP THE DELIBBRATIOUS OF THE INTERInTATIOHAL SYl^IPOSIUl'u ON RADIATION PHYSICS By A.K. Ganguly- Director, Chemical Group Bhabha Atomic Research Centre Trombay, Bombay-400085 INDIA At the near conclusion of this logy besides carrying out the basic Symposium, a very successful one at that, nuclear physics experiments with this thanks are due to the untiring efforts machine. Dr. Hubbell from the United of Professor A.l-i. Ghose and to his States presented to us the status of wonderful band of enthusiastic workers. photon cross-section data from 100 eV to 100 GeV range. Our interest at the Historically, a national symposium present moment is still towards lower on metrology of radio-nuclides was held energies of this range, say from 100 HeV in 1966 in Trombay which finally emerged to 100 eV. Workers are comfortable in from its deliberations as essentially a keV to a few MeV range. Radiation symposiiiin on Instrumentation in Radiation Physics in this country has to take Physics. This vj-as then appropriately better cognizance of the energies below renamed as National Symposiiim on Radia- few keV and above a few HeV. The tion Physics organised in 1970. Now, at tradition of radiation physics, which the end of 1974, we are witness to this in this country started with Sir J. G. International Symposium on Radiation Bose and Prof. M. N. Saha, as Physics. Papers, presented, and deli- emphasized at this Conference, in this berations in the Symposium have also been ooimtry and elsewhere has to expand the marked by progressive enlargement of domain of energies Indicated above. scope and enhancement of standards. My intention in this summing up effort is Dr. P. K. Iyengar in his talk on not to restate vrhat has been stated; in radiation physics and nuclear technology fact I find the summary of this Symposium eloquently emphasized the needs of R and has already appeared as a publication of D efforts that can readily be imdertaken this symposium as abstracts of papers. in this country using the nuclear Barring only a fevf all of them were reactors and the cyclotrons for the presented during these 4t days. V/hat development of material sciences. Using this publication does not contain, is radiation production machine as a tool free for discussion during these for Radiation Physics experiments, scientific sessions. research work has to come of age now in this country in the light of the pro- In view of the above, I should like gramme in technology and nuclear resear- only to re-state some of the high-lights ches. V/ork in this line has been going of the papers and discussions that on for some time with the coming of the appear to me as significant. So, I fast reactor technology and the high hope, you will excuse me since this energy accelerators. This line of talk will have some of my personal bias activity is bound to take a new enlarged built into it. I coxild not avoid this dimension inspite of myself. Professor A.M. Ghose emphasized The papers were excellently classi- new techniq_ues for measureiiient of fied under broad headings of the angular scattering and his ideas about scientific sessions as 'Basic Interaction the development of double scattered Cross-Sections', 'Radiation Transport neutron polarimeter are indications of Theory and Applications', 'Radiation some important developments. The Bose Scattering in Bulk Media', 'Radiation Institute shows great promise in the Shielding' and 'Radiation Dosimetry and future developments in these directions. Instrumentation ' Dr. P. Perey's talk on Gamma photon There had been at the back of the production programme at ORNL appeared minds of most of the Indian participants, particularly relevant in our context as the fact of the near completion of the well. It was stimulating to find re- big radiation production machine, the appearance of a great interest in the Variable Energy Cyclotron in this city. basic gamma spectrometry using sodium Right in the beginning of the symposium, iodide and development of the powerful the proceedings so\mded to me as an tecimique of spectrum unfolding. We, exercise in thinking aloud as to what of in this country, have still a sustained the many good things we can do in interest in sodium iodide crystal Radiation Physics and in Nuclear techno- spectrometry for very pragmatic reasons 257 . and simultaneously we have also been Dr. W.S. Snyder's talk on radiation sustaining an interest in high energy dosimetry of human organs used for neutron (60 MeV neutron) spectrometry computational purposes - the concept of using plastic scintillators. This work a Phantom of a Phantom and again the is going to receive a fresh impetus since computational techniques were based on mono-energetic neutrons of energy higher the iionte Carlo methods. than those available at Trombay, would be available in Variable Energy Cyclotron. S.C. Sharma presented a model based on the experimental track structure for Dr. D.V. Gopinath's presentation of computation of internal dose delivered a generalised formulation of radiation to an organ from an external source. transport problems that has the sphere On first hearing the approach developed to deal, in the onset, with photons, by Sharma and Katz, it appeared that the neutral and charged particles, woiild be model could be handled for micro dosi- a commendable attitude to maintain. In metric computation of internally deposi- covering the energy range, we are ted radio nuclides. talking about, it V70uld be necessary that v/e need further development in techniques Dr. D.P. Regulla, while discussing for precision measurement of cross the versatility of luminescent dosi- sections in the low and high energy meters, attracted attention to a ranges that have been indicated earlier. phenomenon in his experiment of TSEE. Because in the final analysis, this is an An irradiated phosphor gave indications essential input experimental data for of the emissions of exoelectrons of computational physics. A number of other about 300 eV. V/e are yet to understand papers related to computational physics what these mean. as presented, laid very great emphasis on the Monte Carlo techniques. Still we Dr. Y. Furuta emphasized the do not have precision data at the low present state of all-out development in energy end of the degraded high energy the field of neutron dosimptry by T.L. particles of photons. Dr. D.K. Trubey, Phosphors like^Li and 7Li?. The from a very good practical angle laid problems of dosi.aetrj'' of high energy emphasis on development of shielding neutrons in the tens of I-IeV range are standards. This is an activity which we still to be resolved for health and are yet to hatidle systematically. safety op erat i ons Professor T. Hyodo discussed the V.'e have listened to an extremely problems of gamma back-scattering and interesting lecture by Shri C. techniques of measurements. It appeared Ambasankaran , where the VEC machine was that the problems of low energy end of described in many of its constructional the back-scattered spectrometry are still details. It is heartening to note that to be handled coherently, specially when the various parts of the cyclotron, such the incident energy is comparable with as the main magnet, coil, resonator tank the K electron binding energy of heavy etc. are being fabricated indigenously. nuclides. When the machine is in operation, towards the end of 1975, it will fulfil Professor P.P. Kane produced an the long felt need in India to carry out evidence, during the discussion, indi- studies of high energy neutrons, gamma cative of the influence of the K electron rays and multiply charged heavy ions. binding energy on the scattering of low In his talk on solar energy, a topic energy photons. The difficulty of dealing apparently not directly associated with with the miiltiply charged heavy ions as the radiation physics. Dr. V.G-. Bhide pointed out by Dr. S. Kukherjee is a laid emphasis on the possibilities of problem in its own right. Researches on solar energy becoming a great hope for the stopping of multiply charged accele- the future energy requirements. rated heavy particles produced in tbe accelerators can be undertaken for Dr. S. I-Iakra in his talk on experimentation. Here I would like to "iJeutron Dose Evaluation using calculated mention that the possible future Neutron Spectra ", brought up very programme of VEC includes acceleration significantly the question of shield of multiply charged heavy ions. optimisation. Even at this stage of development of Codes and Techniques for Dr. D.K. Trubey 's talk giving com- radiation transport, practical shielding prehensive description of the ORNL problems are still being handled on Shielding Information Centre, naturally empirical or adhoc basis in great attracted attention for obtaining majority of situations. Dr. G-opinath information on the very topics on and Dr. Trubey brought to our attention, shielding enumerated in the talk. the existence of a code for optimisation 258 for a given sequential shield. It is Dr. Sharma dealt with the model of a felt that it is still v/orth looking for track structure and Professor G-hose prescription of shields both in regard indicated some indigenous methods for to thicknesses of the individual layer using the principles of geometrical of materials and their sequence for a optics: in the development of techniques given set of shield materials. for radiation measurements. While explaining the mechanism of Radiation \'le have been listening to a whole Damage, Dr. P.K. Iyengar mentioned series of excellent papers from Indian development of theoretical models for authors and the abstracts to which I made development in radiation physics. Dr. R a mention earlier gives an account of Ramanna, in his inaugural speech felt the present state of activitxes in radia- that this symposium will be able to give tion physics research. 'Ve missed lis- some indication as to where we ;,jO from tening to new efforts in radiation here in radiation physics. I feel that physics based on the recent developments in some later symposia we should also of theoretical principles. invite some of those theoreticians who are also interested in seeing hjome Professor L.S. Kothari dealt v/ith applications of their theory. the theory of neutron thermalization and 259 NBS-1 14A (REV. 7-73) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession 3. Recipient's Accession No. BIBLIOGRAPHIC DATA No. SHEET NBS SP-461 4. TITLE .'\ND SUBTITLE 5. Publication Date RADIATION PHYSICS - Proceedings of the International January 1977 Symposium on Radiation Physics, held at Bose Institute, 6. Performing Organization Code Calcutta, India, Nov. 30-Dec. 4, 1974 7. AUTHOR(S) Proceedings Editors: A. M. Ghose, D. V. Gopinath, 8. Performing Organ. Report No. J. H. Hubbell. S. C. Rov. 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. Proiect/Task/Work Unit No. NATIONAL BUREAU OF STANDARDS 2400105 DEPARTMENT OF COMMERCE 11. Contract/Grant No. WASHINGTON, D.C. 20234 12. Sponsoring Organization Name .ind Complete Address (Street, City, State, ZIP) lo. lype or Keport & Period Covered Organized by: Bose Institute, Calcutta, India final Co-sponsored by: Dept. of Atomic Energy (DAE), India Assistance from: International Atomic Energy Agency (IAEA) 14, Sponsoring Agency Code National Bureau of Standards 15. SUPPLEMENTARY NOTES Library of Congress Catalog Card Number: 76-6O8379 16. ABSl RACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) These proceedings contain invited and contributed papers presented at the International Symposium on Radiation Physics organized by and held at the Bose Institute, Calcutta, India Nov. 30-Dec. 4, 1974. The purpose of this symposium, recognizing radiation physics as the thread held in common by a variety of medical, engineering and scientific disciplines, was to bring together specialists from these disciplines to report on, exchange, and make available through these proceedings, information and experiences of common interest to workers in these diverse disciplines. Topics thus brought together in this symposium include new measurements, theoretical developments, compilations and applications of basic cross section and trans- port data for photon, electron, neutron and heavy ion beams interacting with matter. 17. KEY WORDS (six to twelve entries; alphabetical order: capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Cross sections; dosimetry; electrons; neutrons; photons, radiation physics; symposium. 19. 21. NO. 18. AVAILABILITY [X' Unlimited SECURITY CLASS OF PAGES (THIS REPORT) 1 For Official Distribution. 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