Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations

1970 of U235 and U238 using a monochromator James Edison Hall Iowa State University

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Recommended Citation Hall, James Edison, "Photofission of U235 and U238 using a Compton scattering monochromator " (1970). Retrospective Theses and Dissertations. 4230. https://lib.dr.iastate.edu/rtd/4230

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Iowa State University, Ph.D., 1970 Physics, nuclear

University Microfilms, A XEROX Company, Ann Arbor, Michigan




James Edison Haï 1

An Abstract of

A Dissertation Submitted to the

Graduate Faculty in Partial Fulfillment of

The Requirements for the Degree of



Signature was redacted for privacy.

f Major Work

Signature was redacted for privacy.

or Department

Signature was redacted for privacy.

Iowa State University Of Science and Technology Ames, Iowa




A. Theory 1

B. Purpose 8

C. Literature Survey 9


A. Introduction 12

1. Discrete sources 12 2. Variable energy sources 13 3. Comparison of source intensities 16

B. Compton Scattering Facility 18

1. -capture source 18 2. Scattering platd 24 3. Target chamber and shielding 31 4. Direct (n,y) beam 35 5. Scattered beam 45 a. Energy spectrum 45 b. Intensity 50


A. Fragment detection apparatus 66

B. Targets 67

C. Calibration 70


A. Relative Yield from 74

B. Relative Yield from U^^^ 75

C. Absolute Yield from U^^® 77 V. INTERPRETATION AND CONCLUSIONS 80

A. Photofission Yield Equation 80

B. Present Approach 81

C. Interpretation 83

D. Concluding Remarks 86




A. Theory

A striking characteristic of the very heavy nuclei (Z s 90) is

their ability to undergo fission whenever they are excited with sufficient energy to overcome a fission energy barrier. The mechanism by which fission occurs at different excitation is in many ways very similar. First, the stably deformed target nucleus is excited by a to an excitation energy E, forming a compound nucleus. This is a complex state in which the excitation energy is

distributed among all the degrees of freedom of the nucleus, including

the surface deformation. As the process moves towards fission, an

increasing amount of the energy becomes potential energy of deformation

and the nucleus enters what is called the transition state. At some

finite distortion of the transition state nucleus, known as the saddle-

point deformation, the increase in energy due to nuclear forces (surface

tension) is equal to the decrease in the energy. If the nucleus

is slightly elongated beyond the saddle shape, the Coulomb forces drive

the nucleus to fission. However, if the deformation is slightly

reduced, the surface forces predominate and the nucleus reverts back

to its original shape.

The lowest energy required to reach the saddle-point deformation

is defined as the . Bohr suggested in I955 that a

nucleus possessing this energy is in an almost "cold" state of internal

excitation since the energy is expended as deformation energy (1). 2

He proposed that the low-lying levels at the saddle point ought to resemble the spectra near the ground states of stably deformed nuclei.

This is shown in Fig. 1 for an even-even nucleus. The low-lying states of an even-even transition state nucleus are predicted to be collective levels, since intrinsic states are not expected until sufficient energy is available for breaking a nucléon pair (about 1.2 MeV). Bohr also postulated that the lowest group of levels should be rotational levels built on the 1^ = 0+, K = 0 level, where I is the angular , rr

is the parity, and K is the projection of the angular momentum onto the nuclear symmetry axis. The energies of the rotational states relative to the "ground state" are given by

E = ^ ^ 1(1+1)

where I is the moment of inertia of the system about an axis perpen­ dicular to the symmetry axis. Since at the saddle point the nucleus

is much more deformed, X will be much larger than for the stably 2 deformed nucleus, fi /2I has been calculated from liquid drop theory O "3 O (2) to be about 2 keV for U at the saddle point, whereas it has a

value of about 7 keV for the compound nucleus. Thus, the low-lying

rotational levels in the transition state nucleus are predicted to be

more closely spaced than in the compound nucleus.

We should mention at this point that although the constancy of I

and M (projection of ! on a space fixed Z axis) is guaranteed by the

law of conservation of angular momentum, there is no such restriction

on K. In going from the original compound nucleus to the transition 3

}l=2+,3+,4+.5+-. K=2

)l= i~ 2-,3-4—,K=I

= 3-,5—; K= 0 = 0+,2+,4+,-', K=0


1I = 2+,4+,6+, K=2 J I=2+,4+,6+, "; K = 0 }I = 1-, 3-, 5—•. K = 0 I=0+, 2+,4+,6+, 8+' ; K=0 Ej-Eo" 71(I + !) ksV COMPOUND NUCLEUS 1 L_ DEFORMATION

Fig. 1. Bohr's "fission channels" for the transition state of an even-even nucleus 4

state, the nucleus suffers many changes in shape and redistributes its energy and angular momentum in many ways. The K-values of the transition state nucleus are therefore unrelated to the initial K-values. The transition state then corresponds to a collection of channels, each having its own K-value, which are accessible from a given state of the compound nucleus specified by E, I, M, and parity. Once at or past the saddle point the nucleus has a highly deformed shape which is considered to be axially symmetric in the sense that K remains a good quantum number. The assumption that K is conserved upon entry into a fission channel is supported by angular distribution measurements.

It is useful to examine the predictions of what other bands of levels should be present in the transition state. Above the rotational band a sequence of collective vibrations is expected. A K = 0, 1^ = 1 ^

3,5,... band is expected and attributed to a pear-shaped vibration in which material sloshes back and forth from one end of the deformed nucleus to the other. Also expected are low-lying levels built on a bending vibration like the bending vibration of a linear molecule. The bending vibrational channel will couple with the collective rotation to give of states with K = 1 and I^ = 1", 2", 3", 4", . . .

The energy spectra of normal even-even heavy nuclei contain a level designated as "y-vibrationa1" which involves a periodic collective deformation about axial symmetry. Collective rotations can be super­ imposed on the y-vibration giving a band with K = 2 and I^ = 2^, 3^,

4^, . . . The band built on the ^-vibrational level, which is well 5

known for normal heavy even-even nuclei, should not have a counterpart in the transition state since it corresponds to collective motion along the axis of symmetry. This is the principal feature of the act of fission. One could also consider the multiphonon states of these various modes which would produce bands at higher energies.

The low-lying levels in the transition state for an odd A nucleus will be very different from those in an even-even nucleus. In an odd A nucleus the lowest transition states are states of intrinsic excitation of a single nucléon, and their associated rotational bands with I = K,

K + I, K + 2, . . . and both parities. These bands of intrinsic excitations should be closely spaced (approximately every 250 keV).

Thus Bohr's fission channel theory can be summarized as follows.

The compound nucleus state has two constants of motion, total angular momentum I and parity. As the deformation of the nucleus in this state

increases, the nucleus makes transitions from one energy surface to another until it reaches the saddle point. By this time a large part of the energy of the system has been absorbed in deformation and, for

low excitation energies, the nucleus is "cold". It can be regarded as being in one of a few available transition states which have the same

total angular momentum and parity as the compound-nucleus state. The available transition states in low energy fission are also limited by

the available energy.

In the last few years there have been many attempts to calculate

the potential energy surface of the nucleus as a function of deformation.

Strutinsky has introduced a model where he incorporates shell effects 6

into the well-known liquid drop model (3, 4). In this, the shell- correction term, as a function of deformation, is calculated directly from summed Nilsson single-particle energies of the deformed shell- model potential. Strutinsky finds that the minima in the shell- correction term occur at deformations where a gap is left in the structure of unfilled single particle levels immediately above the

Fermi energy. Calculations show that many of the nuclei

(89 iZ i103) should have a second minimum roughly in the region of the liquid drop saddle point with a depth of about 2 or 3 MeV. This second minimum should tend to disappear towards the higher end of the actinide group of nuclei. A representation of these ideas is presented in Fig. 2.

It is interesting to consider the effect of the two barriers on

Bohr's fission channel model. If the second well is deep, the nucleus will stay there for a considerable time, therefore forgetting the K-value with which it passed over the first barrier. If the second barrier is about 2 MeV lower than the first, there will be a statistical distri­ bution of K-values, because many channels are open over the second barrier even for energies close to the first barrier. Thus, the possible absence of channel structure is a new feature which is related to the presence of an intermediate equilibrium state in fission.

The models presented above can be investigated in two ways:

(1) measurement of fission cross sections, and (2) measurement of the angular distribution of the fission fragments. According to the fission channel model, the , when measured as a function FISSION




Fig. 2. Stru:insky's double-humped potential 8

of energy, should show definite steps corresponding to new channels

opening as the energy increases.

The angular distribution of the fission fragments is determined

by the K-value of the transition state. At very low excitation

energies (just above the barrier) it should be possible to identify

the K-band by measuring the angular distributions. According to the

fission channel model, any anomaly in the angular distribution of the

fission fragments should coincide with a maximum in the fission cross

sect .

This will not be the case if a double-humped potential, with the

first barrier being the larger, is considered. In this case the

redistribution of K-values which takes place in the second well

determines the character of the angular distributions. However, this

should not affect the fission cross section since it should still

increase in steps associated with the "entrance" channels at the first

barrier. If the second barrier is the higher, the fission channel

picture should still be valid.

Thus, information aoout the relative heights of the barriers, the

depth of the second potential well, and the low-lying K-bands can be

obtained from experimental measurement of fission cross sections and

angular distribution of fission fragments.

B. Purpose

Bohr has pointed out that the case of fission following nuclear

absorption of electromagnetic energy (photofission) of even-even nuclei 9

presents some especially simple features (1) since the compound nucleus is always produced with I = 1 and M = ±1 (Z direction is taken as the direction of the beam), assuming electric dipole absorption. The lowest

I^ = 1" fission channel at the saddle point corresponds to the K = 0 sloshing mode vibrational band as discussed above. Thus, for energies close to the fission threshold, the majority of the nuclei are expected to pass through this particular channel. As the is increased, other channels of the I^ = 1" type become available and should be evident in the cross section.

The purpose of this research was to measure the cross section near threshold for photofission. An even-even , and an odd-A nuclide, were chosen in order to check the predictions of the models. The primary hindrance to accurate photofission cross section measurements has been the lack of a monochromatic photon source. In this thesis we will describe an attempt to design and build a suitable source of continuously variable energy gamma rays. The facility is described in detail in Chapter !1.

C. Literature Survey

The first experimental evidence of the photofission process was obtained in 19^1 by Haxby et ai. (5), by bombarding and with 6.1 MeV gamma rays produced by the reaction (p,0('y)o'^. The absence of a wide range of monochromatic sources forced experimentalists to use high-intensity beams produced by betatrons, synchrotrons, and linear accelerators. Several 10

investigators (6-9) made use of bremsstrahlung beams to obtain the shape of the photofission cross section curves near threshold prior to i960. In such measurements the cross section curves were obtained from the yield curves by the "photon difference" method, described by Penfold and Leiss (10). Unfortunately, large errors are inherent in cross sections extracted by this differential analysis. In particular, the measurement of photofission cross sections at low excitation energies requires the use of a thick-target bremsstrahlung spectrum, the exact shape of which is unknown.

The above measurements gave some evidence of a local maximum in the cross section curves at about 6 MeV for the even-even

Th and U ^ ^ but no corresponding bump was found for the odd-A nuclide 1^35 There was some question as to whether the bump resulted from errors and uncertainties in deriving cross sections by the photon difference method. For example, Katz et al. (9) showed that by con­ structing a number of differently smoothed yield curves consistent with the experimental data and then extracting cross section curves from them, the presence of the bump depended on the type of smoothing.

Strong evidence for the existence for this bump in some nuclides comes from the work of Clarke et al. (Il, 12). By using the mono- energetic gamma rays of energy 6.14, 6.91, and 7.11 MeV produced by the reaction (Ps

Realizing the large errors involved in the bremsstrahlung-induced 11

photofission cross section curves, De Carvalho and co-workers (13-16) have worked out a technique for measuring cross sections and fragment angular distributions using monochromatic neutron-capture gamma rays.

Nuclear emulsions loaded with either or Th^^^ were exposed to characteristic neutron-capture gamma rays from suitable sources placed in a reactor. This method has the disadvantage that it allows observation of photofission at only a few discrete gamma ray energies.

Since the energy spread of the incident gamma rays is very narrow

(«8 eV), the exact structure of the cross section curves cannot be obta ined. 12


A. Introduction

During the past two decades extensive research has been conducted

in an attempt to obtain better sources of gamma rays for photonuclear research. An ideal gamma ray source would be one producing a monochromatic beam of continuously variable energy. Gamma ray sources for photonuclear research will be discussed in the following sections.

I. Discrete energy sources

The first sources to be used for photonuclear experiments were radioactive which decay by gamma ray emission. In the early

1950's, these were used extensively in nuclear measurements, and are still used in Mossbauer experiments. Gamma rays

from suitable radioactive isotopes are limited in energy to less than about 3.5 MeV.

Another source is the characteristic gamma ray emission following reactions in nuclei. One of the most widely used reactions of

this type is (p,«y)0^^, which yields 6.14, 6.9', and 7.12 MeV gamma

rays for a bombarding energy of 3.645 MeV.

In the past ten years many photonuclear experiments have used the characteristic neutron-capture gamma rays emitted by materials placed

in a reactor. These gamma rays are limited to a usable energy range

from 3 to II MeV. A good discussion of this source is given by

Jarczyk et al. (17).

All of the above sources produce gaimia rays whose energy resolution 13

is limited only by the Doppler-broadened line width of the nuclear levels. The use of characteristic is limited in its application because of this narrow energy spread (approximately 1 eV).

Since the energy of each such gamma ray is related to discrete nuclear levels, only certain well defined energies may be obtained. Each of the above sources yields not one but several discrete energy gamma rays.

Thus, a photonuclear experiment utilizing these sources must involve an unfolding of the contribution of each of the energies present.

2. Variable energy sources

A large portion of all photonuclear experiments use electron- produced bremsstrahlung as their source of . of E may, in passing through a thin absorber, give rise

in each radiative collision to a bremsstrahlung x ray of any energy between 0 and E. Thus, the difficulty of finding a source of appro­ priate energy for an experiment has been overcome by successful use of a continuous bremsstrahlung spectrum. However, utilization of this necessitates an accurate knowledge of the energy dependence of the beam intensity. A measurement of this is not easily obtainable and

is not accurately known, particularly near the maximum energy E.

In 1954, Cormack (18) suggested that by allowing monoenergetic

gamma rays to undergo Compton scattering, a monoenergetic beam of

variable energy could be obtained. A gamma ray of energy EQ, after

Compton scattering at an angle 0 from a free electron has energy E,

given by (19) 14

1= 1+ (' - cos8 ) (1)

E c'

2 where mew 0.511 MeV is the electron rest . Thus, in the o scattering of monoenergetic gamma rays, the energy of the scattered radiation is defined by the scattering angle. The energy spread of the scattered beam depends on the finite angular interval used and on the velocity and binding of the electrons in the scatterer. Since this method involves the use of a small portion of a monoenergetic gamma ray beam after it has Compton scattered, the method is very inefficient.

The practical difficulty in the application of this method is one of beam intensity.

It was not until 1963, as multiCurie sources of various radioactive elements became available, that successful photonuclear experiments using

Compton-scattered gamma rays were reported (20). Shortly afterwards, more versatile facilities, using a suitably shaped scatterer to increase the intensity and a circular geometry to improve resolution, were reported (21, 22). The focusing property of these facilities is shown in Fig. 3. The gamma ray source, the scattering material, and the target are all made to lie on the same focal circle. From plane geometry one can see that all of the gamma rays coming from the source which hit the target after scattering from the curved scatterer must have been scattered through the same angleQ , Thus, from the properties of the Compton effect (Equation 1), all of the gamma rays of energy E^, after being scattered through the angle fl, will have the same energy E.

By moving the target along the focal circle, the scattering angle, and 15



Fig. 3. Focusing properties of Compton scattering method 16

hence the energy of the gamma rays striking the target, can be varied,

Mclntyre and Tandon (>2, 23) used a 1600 Co^^ source (gamma ray energies of 1.33 and 1.17 MeV), an aluminum scatterer, and a 2 meter radius focal circle to produce a gamma ray beam having an energy resolution of 2.5% (ful1-width-at-half-maximum).

Knowles (24) extended the energy range of this type of facility by using neutron-capture gamma rays as his source, in his facility, characteristic from a composite source of and were Compton scattered from a series of aluminum plates. This series of four plates (maximum total length of 17 ft) was arranged to approxi­ mate an arc of the focal circle. The energy range was 0.5 to 8.5 MeV and the energy selection I - 3%. At 7 MeV the intensity of the beam -I -2 "1 incident on the target was approximately 1 gamma ray eV cm sec .

The problem of obtaining a gamma ray source of only one energy, whether from a radioactive or a neutron-capture source, complicates the Compton scattering technique. However, if appropriate sources are chosen, the most intense gamma ray peaks in the scattered beam will be at the highest energy, in this case, the analysis of photonuclear yield data is much simpler than in the case of bremsstrahlung-induced reactions.

3. Comparison of source intensities

-1 -2 -1 A comparison of the beam intensities (gamma rays MeV cm sec )

for the different methods of generating gamma ray beams suitable for photonuclear experiments is given in Table I. The values for the Tabic 1. Comparison of Gamma Ray Source Intensities

Sou rce Energy Energy 1ntensity/peak energy Source Reference Class!fication (MeV) Resolution (ev~'cm" sec"')

Radi oact ive Co^^, 1.0 Curie 1.17, 1.33 1% 22.0 at I m 1sotope Ti^(n,Y) 6.75, 6.14 r/o 29.0^ (25-27) Neutron Pb207(n,Y) 7.38 1.2 Capture Mi^®(n,T) 8.99, 8.53 12.0

Proton F'9(p,ay) 7.12, 6.91, 6.14 17o 2'10"^ m Capture Li^(p,y) 17:6, 14:8 6.10-4

Bremsstrahlung Bremsstrahlung 6-40 0.6% 0.6'lO"^ (24f monochromator \ 0 f 0 o L

Compton 1 Ni58(n,Y) 5 2% 1.0 (2%;; Scattered

^Intensity 4m from the source; for a thermal neutron flux of 3 x lo'^ cm ^ sec

''intensity .3m from the target; for 1mA proton current.

^For experimental details see Phys. Rev. 126, 228 (1962). 18

neutron-capture sources were calculated for a 1 kg sample located in the 6 in. diameter tangential tube of the Ames Laboratory Research 10 _2 «I Reactor (thermal neutron flux=3*10 cm sec ) and represent the intensity at 4 meters from the source. The intensity of the bremsstrahlung beam is limited by pile up caused by the high counting rate of low energy gamma rays.

B. Compton Scattering Facility

The best gamma ray source for photonuclear measurements in the energy range 1 - 10 MeV, with regard to beam intensity, energy variation, and resolution, appears from the table presented to be a Compton scattering facility with a neutron-capture gamma ray source. This type of installation has been designed and constructed for use at the Ames

Laboratory Research Reactor. In the following sections the details of this facility will be presented.

I. Neutron-capture source

Certain criteria must be met in the selection of a neutron-capture gamma ray source. An ideal source would fulfill the following require­ ments; (1) emit a simple spectrum of gamma rays of high absolute

intensity, (2) have the most intense gamma rays of its spectrum at the highest energies, and (3) be available in a form which can withstand

the gamma ray heating near the reactor core. A list of possible sources

is given in Table II. The values given in columns k, 5» and 6 were

obtained from recent compilations of Bartholomew et al. (25-27). Fig. 4

shows bar graphs of the most intense lines in the neutron-capture gamma Table II. Neutron-Capture Gamma Ray Sources

1 2 3 4 5 6 7

1 ntensi ty Gamma Flux Target Melting Gamma Ray E1ement Per 100 Compound Point (°C) Energy (MeV) (oarn) at V _2 _] Captu res (106cm sec )

Be9 metal 1278 6.814 75 9.5*10"3 1.47 c'2 graphi te 3550 4.948 70 3.4-I0~3 0.455 SîjN^ 1900 10.83 14 7.5°10~2 .105 metal 651 3.918 47 3.4-10"^ 0.930 u> metal 660 7.724 17 0.235 4.09 Si 28 metal 1420 4.936 61 8.0-10'^ 3.99 solid I19 5.425 57 0.510 17.3 Ca^O meta 1 842 6.421 44 0.430 7.28 7,48 metal 1800 6.753 41 8.30 197 Cr53 metal 1890 8.881 14 18.2 31.4 r7.643 FeSS metaI 1535 43 2.70 136 ^7.629 N;58 metal 1455 8.996 26 4.40 104 ySg pOxide 1490 6.080 73 1.28 58.0 powder metal 327 7.368 95 0.709 8.58 20


î 4 « ( iiS ( 4 « • 10 4 • « 10 INIRtY (MlV) [NE*OY|N«V| eNïm(M

Mg Al

J l_ L_li 2 4 t a 10 2 4 e • 10 I 4 « 8 10 CNERtY (M«V) ENERCY (MlVI ENERGY (MtV)

Co T( «2

III I .1 II 4 • I 10 4 • • 10 4 e • 10 ENIRdY tM«V) ENER8Y (MlV) ENEROY(M«V)

Cr Ft NI

III II I» I Jailli. •! S S 10 « 0 10 ZKZMY (HeV) £NERGY(MeV)


14 8 8 S 4 S 9 10 ENERfV (MV) ENSR«VtMaV)

Fig. 4. Neutron-capture gamma ray spectra showing the relative intensity of the characteristic lines for each nuclide 21

ray spectra of the sources listed in Table 11. Because of its high energy gamma rays, and relatively high cross section, nickel was chosen as the source for our facility.

The source consists of a 1023 gram, 4 x 4 x .5 in. piece of natural nickel held in a spring-loaded mount as shown in Fig. 5. The mount was designed so that the source may easily be removed for replace­ ment. Because of the high radioactivity of the source assembly after removal from the reactor, handling must be done in a "hot cell" assembly. The source mounts are seated in bearings so that the orientation of the source may be varied.

The source assembly was placed in the center of the 247 in. long,

6 in. diameter tangential tube at the 5 MW Ames Laboratory Research

Reactor. At this position, the thermal neutron flux is 3 x lo'^

-2 _ 1 neutrons cm sec and the gamma heating is approximately .2 watts per gram. Thus, it was desirable to provide some cooling for the nickel source assembly. A cylindrical shell through which cooling water is pumped Vv3S wttachcd to the rsc" of the source holder, This aSScmbly is mounted inside a 5 7/8 in. diameter aluminum tube. These assemblies, along with the source orientation control which was mounted on the reactor face, are shown in Fig. 6. Between the source and the reactor face containing the orientation control, shielding necessary to prevent the intense gamma ray beams from emerging from that end of the facility was positioned. This half of the facility is shown in the top portion of Fig. 7.

The other half of the 6 in. diameter tangential tube contains the Fig. 5. Nickel source and mount

Fig. 6. Source assembly and rotation control COLLIGATION ASSEMBLY



Fig. 7. Beam tube assemblies 24

neutron shielding and the gamma ray beam . As shown in

Fig. 7, there are 29 in. of neutron moderator in the beam tube. At first, an additional 12 in. of moderator was included in the tube, but this was subsequently removed to increase the gamma ray intensity.

A large percentage of the neutrons emerging from the reactor are produced by the (y,n) interaction of the nickel gamma rays with the col limating materials.

2. Scattering plate

A high energy gamma ray may interact with by the nuclear, photoelectric, Compton scattering, or interaction.

The material and thickness of the scattering plate were chosen to make the Compton scattering interaction dominant over the energy range to be used. Not only was it necessary to consider the Compton interaction, but also the interaction of the Compton scattered gamma rays with the plate before emerging from it.

An estimate of the "efficiency" of different materials was made for

the following average conditions: Compton scattering of 8.0 MeV gamma

rays from the pivot point of the scattering plate through an angle of

12 degrees. Fig. 8 shows the geometrical arrangement being described.

The incident gamma ray strikes the plate at an angle Qi and the

scattered gamma ray emerges at an angle y . The effective thickness of

the plate as seen by the incident gamma ray Is given by =t/s in,


" " arctan 1 9 ' ' 25



TAN a= SIN 9 r/c + COS B


Fig. 8. Geometrical arrangement considered for scattering efficiency calculations, (a) complete facility, (b) beam interaction with scattering plate 26

As the gamma ray beam passes through a distance dx of the plate, its intensity is decreased due to Compton scattering through an angleg into a unit solid angle by the amount

di = -I ^ (0)• N dx ,

where ^ is the differential Compton scattering cross section and

N is the number of electrons per cm^. The intensity of the beam after it has traveled a distance x into the material is

1 = 1^ . where ji is the linear absorption coefficient for the material for a gamma ray energy of 8.0 MeV. The Compton scattered beam is then attenuated as it travels a distance y before emerging from the plate.


M = 1 N + ^y) dx odn where 6 is the linear absorption coefficient for the scattered gamma ray in the material. Expressing y in terms of x and integrating over values of x from zero to x , we obtain o

' (M+ B6) where B = s in 9 /tany - cos 9 . If ^ and Ô are in units of cm ', then

N = Z P "o A where Z, p , and A are the , density, and atomic weight of 27

the scattering plate material respectively and is Avogadro's number.

Equation 2, which gives a measure of the efficiency of the scattering plate, was evaluated for several materials and different values of x^. The linear absorption coefficients were taken from the compilation by Plechaty and Terrai 1 (28). The differential Compton scattering cross section was obtained by evaluating the Klein-Nishina formula (29)

da (0) _ [1 + cos^9 +60^(1 - cos9 )^]

2m^c^ [I +00 (I - cos 9)]^ [1 + W ( I - cosO)]

2 where CO is the energy of the incident gamma ray divided by mc . The results of these calculations are plotted in Fig. 9.

The limitation on the thickness of the scattering plate was that it had to be thin enough to be bent into an arc of a circle by applying a force to each end. The dimensions of our facility set an upper limit of about 0.375 in. on the plate thickness. This thickness corresponds to an effective thickness of 14.0 cm at a scattering angle of 6 degrees,

7.15 cm at 12 degrees, and 2.84 cm at 30 degrees. As seen from Fig. 9, aluminum is the most efficient scattering material for small scattering angles (i.e., largest effective thickness), while is better for the larger angles. Two different scattering plates were constructed for our facility: a 0.375 in. thick aluminum plate and a 0.250 in. thick

iron plate. Since in the photofission measurements we were interested

in the higher energies, hence smaller scattering angles, only the aluminum plate was used in the research reported in this thesis. 28



Fig. 9. Scattering efficiency of different materials for an incident 8.0 MeV gaftmia ray; the atomic number of each material is indicated at the right 29

The shape of the scattering plate was calculated so that upon application of a "column loading"-type force to each end, a uniform stress will be distributed along the entire length of the plate. This insures that the plate will bend into an arc of a circle. At its center the plate is 15 in. high and its total length is 89 in. As shown in Fig. 10, the ends of the plate are mounted in moveable supports which are connected by two O.5O in. diameter rods. One end of each of the rods is threaded and passes through a ball bearing screw assembly mounted in the plate end support nearer the reactor face. The ball bearing screws are rotated by a chain drive from a motor mounted on the plate end support. As the screw assemblies are rotated in the forward direction, the end support moves along the threaded end of the connecting rods, thus applying a force to each end of the scattering plate and causing it to bend.

The change in the curvature of the plate can be directly related

to the change in the length of the connecting rods, since they form a chord of the circle. !n order to indicate the amount of curvature of

the plate, a 10 turn, 10,000 ohm helipot potentiometer was attached to one end of the motor drive shaft. As the chord length, and hence the

curvature, is changed by the drive motor, the potentiometer's

resistance is measured and displayed by a digital ohmmeter.

The scattering plate is attached to a vertical post mounted in a

ball bearing. Another drive motor and potentiometer combination is used

to rotate this pivot and indicate its position. At each scattering

angle, the focal circle is defined by the nickel source, this pivot post, I#' HIS

Fig, 10, Scattering plate assembly 31

and the center of the target chamber. The scattering plate is then made

to lie along this circle by adjusting its curvature and rotation.

As the scattering angle increases, the area of the plate in the

gamma ray beam decreases. The projection of the beam from the nickel

source onto the plate is shown in Fig. 11 for several scattering

angles. The projections would normally be ellipses; however, horizontal

collimat ion in the beam tube causes them to be cut off on each end.

3. Target chamber and shielding

The portion of the Compton scattering facility external to the

reactor is shown in Fig. 12. A 10-in. thick block is moved (by

means of an air cylinder) along rails attached to the reactor face.

When the scattering plate is rotated out of the way, this gate may be

moved in front of the beam port to block the gamma ray beam. Limit

switches have been included in the facility so that it is impossible

to move the gate while the plate is in the way.

The shielding along the sides of the facility is a wall.

The end shielding consists of concrete up to a height of 24 in. and

lead the rest of the way. A removable lead plug is located in the end

shielding at the position which corresponds to zero degree scattering

angle. This is for the purpose of obtaining an energy calibration from

the unscattered beam. By means of a series of 10 lead-filled gates,

the scattered beam is allowed to pass through the end shielding and into

the target chamber at the desired angle. These gates may be raised

singly or two at a time by means of two air cylinders mounted on a 32







Fig. 11. Beam projection onto the scattering plate Fig. 12. External shielding SCATTERING PLATE


support which can move along grooves in the top shielding.

The target chamber has an inner diameter of 22 in. and height of

24 in. Access to the chamber is through a door on each side or by removing the top. The chamber is moved along a curved track by means of a drive motor. Since the center of the target chamber rotates about the scattering plate pivot at a radius of 84 in., the positioning of the chamber at the different scattering angle is relatively simple.

For a given scattering angle 9, a line joining the target and the plate pivot must make an angle 8 with the line joining the pivot and the nickel source. A calibrated scale is inscribed along the target chamber track to indicate the scattering angle corresponding to the target's pos it ion.

Thus, for each scattering angle, one must adjust the scattering plate's curvature and rotation and the target chamber's position.

Through the use of drive motors and readout devices previously discussed, these adjustments take only a few minutes.

Fig. 13 shows a top view of the Compton scattering facility with the top shielding removed. A complete view of the facility is shown in

Fig. 14.

4. D!rect (n, y) beam

in order to analyze the components in the scattered gamma ray beam,

the direct (n,y) beam emerging from the reactor had to be considered.

The energy distribution of the direct beam was measured with a high- resolution -drifted germanium detector, Ge(Li). This detector Fig. 13. Top view of facility with top shielding removed

Fig. 14. Complete view of facility 37

(purchased from Nuclear Corp.) had an active cylindrical volume of 65 cc and an energy resolution of 3.2 keV at i.33 MeV and 5.5 keV at 9.0 MeV. With the target chamber placed at the zero scattering angle position, the Ge(Li) detector was placed at its center. Because of the intensity of the direct beam, it was necessary to leave the 12 in. thick lead plug in place between the beam and the detector. A Nuclear Data

Corp. model 2200 pulse height analyzer with a 4092 channel memory was used, its analog-to-digital converter operates at a 100 MHz rate with a maximum conversion gain of 8192 channels. The energy distribution above 4.6 MeV as obtained in this manner is shown in Fig. 15.

For each characteristic energy present, three peaks were recorded, since the gamma ray energies are above the pair production threshold of

1.02 MeV. These correspond to the full energy peak and the single and double escape of the gamma rays. In order to analyze more easily the components of the direct beam, a pair spectrometer system was set up in the target chamber. Two 3x3 in. sodium iodide scintillation crystals were used to detect the 511 keV anni1ihation quanta. A diagram of the pair spectrometer system is shown in Fig. I6.

Since a pulse from the Ge(Li) detector must be accompanied by detection of a 511 keV gamma ray by each of the NaI detectors, only double escape peaks are stored in the analyzer. Fig. 17 shows the results of a pair spectrometer measurement of the direct beam. As expected, the 8996, 8525, and 6835 keV gamma rays from

in nickel are the most intense. However, several intense lines are present which can be attributed to elements other than nickel. Very § §

s s-

s 5- I Ï ; ; LU Z is uK- (C iis * 1: ! = Î : c:: s : 5

% AIAJH WUWs^wUU^ 8 2-


S 1— - r • p " I 1 1 1 1 1 1 1 1 1 > 0 00 1.00 2.00 3.30 y.oo 5.00 6.00 7.DO 8.00 9.00 ID.DO 11.00 12.00 13.00 m.DO CHANNELS i*io* J Fig. 15. Ge(Li) spectrum of the direct beam (DE and SE indicate the double escape and single escape peaks of the indicated energy) -n 0.00 7.00 arE^.'a' ' ID 6579 SE 6)03 6644 SE (Cr] O

7177 Dl (F.)

o_ M)S tE

75)5 DE

7693 DE



7535 SE

14 Dl

7693 SE

7929 SE (Cr)

8499 DE (Cr) 852S DE 7535

Si —1 n— 1 I —! 25.00 27.00 2B.00 29.CO 30.03 31.00 32.00 33.00 35.00 36.00 37.00 39.00 MI.00 CHANNELS IxlQ* 1 Fig. 15 (Continued) HIGH HIGH NAI VOLTAGE NAI GE VOLTAGE








Fig. 16, Block diagram of electronics for pair spectrometer -p- hO

l»*0^ X

Fig. 17. Pair spectrometer spectrum of the direct beam f-


Fig. 17 (Continued) f -P-


Fig. 17 (Continued) 45

prominent are the 7629 and 7643 keV lines from neutron capture in iron and the 7724 keV line characteristic of aluminum. Also visible is the

8884 keV line from . The aluminum line was expected since the tangential reactor tube and for the most part the inserted assemblies were constructed of aluminum.

The surprising foreign lines are those due to neutron capture in iron and chromium, thus indicating the presence of a large quantity of stainless steel. It was learned that the tangential tube passes through an 8 in. thick stainless steel shield at 3 ft on either side of the nickel source location. Thus, gamma rays from the shield are emerging from the reactor port in directions that are not necessarily parallel with the beam tube axis. To illustrate this, a measurement of the beam was taken with the Ge(Li) detector while the target chamber was at a position of 0,60 degree. The results are shown in Fig. 18. At this angle, the most intense iron and aluminum lines are more intense than the 8.99 MeV nickel line.

Thus, in order to determine the relative intensity of the neutron- capture gamma rays incident on the scattering plate, the scattered beam must be considered.

5. Scattered beam

a. Energy spectrum In order to estimate the energy spread in the scattered gamma ray lines, a calculation was made based on the spread of the scattered beam due to the finite dimensions of the source,

scattering plate, and target. Following the procedure of Tandon and 8 s-

8 a 1 I S : 8 s-

i g w i. & h J-




8 -0 00 1.00 z.tn 3.an «.oa s.oo s.oo j.w b.oo 9.oa lo.oo n.oo iz.oo u.sd i«.ao CHANNELS U10« i

Fig. 18. Ge(Li) spectrum of the direct beam measured at 0.6 degree (De and SE indicate the double and single escape peaks of the indicated energy) 0.00 >4.00 1,00 • M.oo M.00 (O

00 WW tl (cr)

o o Z) 7111 61 (Ft)

3 un " Ca> CL

?»I4 01

7fl9 01 (Cr)

IIU Bt > " I")

m» B1 (Cr)

Z+7 5s ê

Fig. 18 (Continued) 49

Mclntyre (23), the width of the target can be shown to be the dominant factor in the energy spread. The angular spread due to it is given by

A9 J. = AR/r (4)

where A0^ is the angular spread of the beam, AR is the width of the target, and r is the distance from the scattering plate pivot to the target. For AR = .75 in. and r = 84 in., A0^ = 0.009 radians. By differentiating Equation 1 with respect to 6, one obtains

AE (E ^/m c^) sin 8

A9 [I + E^(l - cos0)/m^c ]

For = 9 MeV and 6=6 degrees, this gives 200 keV per degree. Using the calculated value of A9^, one finds that the scattered lines should have a width of approximately 170 keV, which corresponds to an energy resolution of 2.1%. At 9= 30 degrees the scattered 9 MeV line should have a width of 105 keV, which corresponds to an energy resolution of


If the width of each of the lines in Fig. 15 is increased to

170 keV and the lines are moved closer together due to Compton scattering, a smeared out spectrum would result from the overlap of the lines. Thus, it was expected that the structure of the scattered beam could not be adequately studied by the use of a single gamma ray detector, since the pulse-height spectrum from it would contain not only the full-energy peak, but also the single and double escape peaks for 50

each gamma ray energy present. This was confirmed by viewing the 10

degree scattered beam with a Ge(Li) detector. The result of this measurement is shown in Fig. 19.

In order to obtain an accurate scattered beam spectrum, a pair

spectrometer must be used. A measurement of the 10 degree scattered

beam taken with the pair spectrometer described in section B.4. of this

chapter is shown in Fig. 20. As expected, the scattered lines due to

iron and aluminum are very intense. The width of the scattered 8996

keV line is approximately I80 keV.

The separation of the peaks in the scattered beam decreases as

the scattering angle increases. This is seen by plotting the energy

of the scattered photons as a function of scattering angle for some of

the more intense direct beam energies as shown in Fig. 21. Experimen­

tally, this is verified by measuring the scattered beam spectrum with a

pair spectrometer. As shown in Fig. 22, the scattered peaks not only

decrease in energy with scattering angle but also gradually lose their

separation. Thus, at the larger angles, the scattered beam consists

primarily of a single peak. The scattered peaks in Fig. 22 are wider

than those in Fig. 20 because the width of the beam entrance port of

the target chamber was increased for this measurement.

b. 1ntensity Not only must the energy spectrum of the

scattered beam be known for each scattering angle but the intensity of

each of the components of the beam must also be known. It was necessary

to measure accurately the number of photons in the scattered beam at

the target position as a function of scattering angle. In order to 10 DEGREE COMPTON SCATTERED BEAM


0.00 1. 15 2.30 6.90 B.05 10.35 II.SO IS.65 CHANNEL NO.

Fig. 19. 10 degree Compton scattered beam measured with a Ge(Li) detector 10 DEGREE COMf'TON SCATTERED BEAM (PAIR SPECTROMETER) o_

00 to


UOO 1 15 2 .10 5 .7S 6.90 8.05 9 20 CHANNEL NO.

Fig. 20. 10 degree Compton scattered beam measured with a pair spectrometer. The energies (keV) of the direct beam lines yielding the scattered peaks are ind icatecl 8996 8&I 8525


72J0— 7635 6835



48X3 — w


OJO 2X) 40 60 ao 10.0 14X1 16,0 18,0 20.0 22.0 24X) 26J0 28.0 SCATTERING ANGLE (DEGREES)

Fig. 21. Variation of the energy of Compton scattered gamma rays with scattering angle 54



15 degrees



281 3 32 383 4 34 485 5 36 5.87 6 38 6 84 7 40 791 8 42 8 93 944 9 95 ENERGY (MeV) Fig. 22. Pair spectrometer measurement of the scattered beam at several angles 55

relate the number of counts in a peak of a pulse height spectrum from a gamma ray detector to the number of photons of that energy incident

on the detector, the efficiency and peak-to-total ratios must be known

for the detector. Sodium iodide crystals have been used for intensity measurements of high energy gamma rays (30), since peak-to-total ratios are generally unknown for Ge(Li) detectors. Both the efficiency and

peak-to-total ratios have been measured experimentally (31-33) and

calculated by the Monte Carlo method (3^-36) for sodium iodide crystals.

For these reasons, a NaI crystal was used to measure the intensity of

the scattered beam.

The following procedure was used in obtaining the energy spectrum

and intensity variation of the beam as a function of scattering angle:

(1) measurement of the intensity variation of a single peak in the

scattered beam, (2) absolute intensity measurement of this peak at one

scattering angle, and (3) pair spectrometer measurement of the scattered

beam at all scattering angles.

The use of a Na i crystal to detect nigh eiieryy gamiria rays

necessitates the careful design of collimation and shielding surrounding

the crystal as discussed by Greenwood and Reed (30). Fig. 23 shows the

shielding and collimation configuration used in the intensity measure­

ments. The NaI assembly consisted of a 3 x 3 in. crystal directly

attached to a photo-multiplier tube and hermetically encapsulated in an

aluminum light-tight housing. The assembly was positioned so that the

center of the crystal was located at the focal point in the target

chamber. The collimation was tapered to a rectangular area 2 in, high Fig. 23. Co]limât ion and shielding used in the beam intensity measurements ^^"••v; «-A ^3vR. mV X

W/ ##%

NaI assembly




by 0.75 in. wide at the face of the crystal. This allowed the crystal

to view the entire scattering plate at each scattering angle. As

shown in Fig. 23, the first in the assembly (left side)

consisted of lead encased in brass. This piece was positioned in the

beam entrance port of the target chamber. After this collimator was

constructed, it was used as a mold to form beam attenuators. Molten

lead was poured into the rectangular slot through this collimator,

allowed to harden, and then carefully removed. Attenuators were then

machined from this lead plug for the purpose of reducing the beam

intensity incident on the Nal crystal to a tolerable level.

In order to correct the intensity measurements for variations in

the reactor power level, it was necessary to monitor the direct beam

emerging from the reactor port. This was accomplished by using a

lithium-drifted silicon detector to view a small portion of the direct

beam. Being very inefficient for detecting high energy gamma rays,

this detector was ideally suited for monitoring the intense direct beam.

Only gamma rays with energy greater than 2 MeV are counted. Fig. 2k is

a diagram of the monitor and Nal electronics used in the intensity


The intensity of the gamma ray peak due to Compton scattering of

the 8996 keV neutron-capture gamma ray was measured as a function of

scattering angle. Since the direct beam gamma rays with energy above

8996 keV have negligible intensity, it was possible to sum the counts

in the photopeak of the corresponding scattered line. This would not

be possible for the lower energy lines because of the contribution of 59








Fig. 24. Diagram of electronics for beam intensity measurements 60

nearby peaks. Actually, at the larger scattering angles (where the scattered peaks are closer together), there was a slight contribution to the low energy side of this photopeak due to the scattered 8525 keV

line. For this reason, only the counts above the centroid of the photopeak were summed, and this integrated total was doubled (a symmetric scattered peak was assumed).

The duration of each measurement was controlled by the monitor

counts. The pre-set scaler used to record the monitor counts shut off when a total of 10^ was reached. This caused the gate pulse from the

scaler to drop to zero thus shutting off the multichannel analyzer.

The clock time of each measurement was also recorded in order that the monitor counts per unit time at each angular position could be

calculated. The monitor count rate varied slightly as the scattering angle was changed because a portion of the monitor counts was due to

gamma rays which were scattered by the scattering plate.

The corrected integrated counts in the photopeak at each angular

position was obtained from

2N e-WX N = — R

where is the integrated total obtained from the pulse height

spectrum, R is the photopeak efficiency of the Nal detector, and JU

is the linear for lead at the incident energy.

The value of R is the product of the interaction ratio and the

photofraction of the crystal. The interaction ratio is the ratio of

the number of gamma rays that interact at least once to the number 61

that strike the crystal face. For the case of a parallel beam of gamma

rays of energy E incident along the direction of the crystal's axis of

length L, the interaction ratio is given by


where ^•(E) is the absorption coefficient for gamma rays of energy E in

the crystal. The photofraction is the fraction of the interacting

gamma rays that is completely absorbed in the crystal (including all

secondary radiation).

The photofraction for a 3 x 3 in. Nal crystal has been measured by

Jarczyk et al. using neutron-capture gamma rays (31). Snyder obtained

good agreement with these experimental values in his Monte Carlo

calculation (36). The values given in these references were used in the

present calculations. Miller and Snow have tabulated the values of the

interaction ratio for various crystal sizes and gamma ray energies (35).

The photopeak efficiency, R, varies from .084-3 at 4.5 MeV to .0465

at 8.0 Mev.

Fig. 25 shows the variation of the intensity of the scattered

8996 keV line with angle. The intensities are normalized to the value

at 13.45 degrees. As expected, the relative intensity decreases as the

scattering angle increases. This is due to the change in the Compton

scattering cross section and in the scattering geometry with angle. To

illustrate this, the differential cross section per unit solid angle for

Compton scattering was calculated from Equation 3 for the most intense

lines in the direct beam. These values (relative to the value at zero 10 II 12 13 14 15


Fig. 25. Variation of the intensity of the scattered 8996 keV gamma ray with angl 63

degrees) are shown in Fig. 26. As the scattering angle increases, the effective thickness of the scattering plate is reduced.

The absolute intensity of the scattered 8996 keV line was determined by measuring its intensity at a scattering angle of 13.45 degrees as a function of attenuator thickness. As before, the counts in the pulse height distribution above the centroid of the photopeak were summed. The intensity of the beam after passing through the absorbers of total thickness x is given by

1 = 1 e"^^ o

Taking the logarithm (base e) of this equation, we obtain

In I = In 1^ - |ix

Thus, the logarithm of the corrected integrated counts is a straight line function of the attenuator thickness. A linear least-squares fit was made to the data. The incident absolute intensity of the scattered line was the intercept ot this straight line fit. A value of 0.996 x

10^/sec. was obtained by this method. The above procedure has the advantage that it is not necessary to know the value of the absorption coefficient ^ . However, is just given by the slope of the straight

line fit. A value of 0.489 cm ^ was obtained for U in this manner.

This is very close to the value of 0.495 given by Plechaty and

Terrai 1 (28).

Several of the relative and absolute intensity measurements were

repeated in order to check their reproducibility. In each case the loo





050- 8996



OJO OX) 4.0 6J0 8.0 12.0 14.0 16.0 I8X) 20.0 22.0 24.0 26.0 28.0 SCATTERING ANGLE (DEGREES)

Fig. 26. Variation of differential Compton scattering cross section with angle 65

integrated count total for the measurement was reproducible to within a few percent. Each measurement yielded an integrated total count of approximately 10^. Thus the statistical error was very small. The major source of error in the absolute intensity lies in the precision of the absolute photopeak efficiencies. The quoted values of the efficiencies could deviate from the actual efficiency of our detector by as much as 15 percent.

Thus knowing the absolute intensity variation of one of the lines

in the scattered beam by these measurements and the energy spectrum of

the scattered beam at all scattering angles through the pair spectro­ meter measurements, completely defines the incident beam. 66


A. Fragment detection apparatus

Fission fragments are easily detectable because they are highly ionizing particles. Almost all of the photofission research prior to

1962 was conducted using gas-filled chambers as fragment detectors. A typical chamber was described by Katz et al. (9).

Excellent detection geometry was obtainable from this type of detection system. However, care was necessary in distinguishing between the pulses produced by fragments and those due to the photon beam or the natural alpha activity of the target.

In recent years solid state track detectors have been used in the detection of fission fragments. Materials such as mica, Makrofol, cellulose acetate, and Lexan have been used for detectors.

The tracks produced in such materials by fission fragments are observable with the aid of a microscope. This type of detector is

insensitive to the photon beam and allows discrimination between fission fragments and alpha pulses. However, since there is no way to turn these detectors off, one must correct the total number for back­ ground tracks.

Silicon semiconductor detectors have also been used for fission

fragment detection. A guide to the evaluation of these detectors has been given by Schmitt and Pleasonton (37). Excellent energy resolution

(thus easy discrimination between fragments and alpha particles) is

obtainable. Semiconductor detectors cannot be used with targets with 67

high natural activity due to . This damage is usually indicated by an increase in the bias leakage current 13 after an integrated dose of approximately 10 alpha particles. However, these detectors also have the advantage that they are completely insensitive to photon beams.

Since the target nuclides used in this research do not have high natural alpha particle activities, silicon semiconductor detectors were used for fission fragment detection. decays by alpha particle 2 235 3 emission at a rate of 7.34-10 /min/mg, and U at a rate of 4.74"10 /min/ mg (38). The detectors were 70 M thick, totally depleted, surface barrier detectors purchased from Nuclear Diodes Corp. Their active area was

50 X 10 mm.

Since the range of heavy in air is very short, it was necessary

to design and construct a target chamber which could be evacuated. A drawing of this chamber is shown in Fig. 27. The inside diameter of

this aluminum chamber is 6.125 in. and its height is 5.5 in. The detectors are mounted on moveable arms which pivot about the central

target position. A vacuum of less than 10 ^ Torr is maintained in the

chamber during operation. The beam entrance window is 0.05 in. thick aluminum, thus attenuating the incident photon beam a negligible

amount. This chamber was rigidly mounted inside the target chamber of

the Compton scattering facility. It was positioned so that its target

position coincided with the geometrical center of the larger chamber.

B. Targets

All of the targets had an area 0.75 in. wide by 2.00 in. high, llciFiCSEETT f^olL. f'"* " - -ï ^ ' < ? '



Fig. 27. Photofission target chamber 69

corresponding to the coilimated area used in the beam intensity measurements. Relative photofission yield measurements were made using

targets in the oxide form (U^Og) approximately 0.02 in, thick. These

targets, U^^^(99.27%) and U^^^(93.23%), were coated on the surface of

thin aluminum foils. The foils were mounted on aluminum frames which

could be rigidly mounted accurately at the target position in the


Segre and Wiegand have calculated the end point of the absorption

2 curve for fission fragments in U^Og to be 10.0 mg/cm (39). Thus there

is nothing to be gained by having targets thicker than this. Since

the fission fragment energy is independent of the gamma ray energy, it

is not necessary to correct relative yield measurements for target

thi ckness.

Absolute photofission yield and detection efficiency measurements

were made using a 1.6 mg/cm^ coating of on a thin nickel foil. This

target was produced by vacuum evaporation by the Isotope Division, Oak

Ridqe National Laboratory. The uniformity of this target was checked by

measuring the alpha particle activity at different positions on the foil.

This was accomplished by using a calibrated gas

system (Sharp model LB-100) and a moveable baffle with a 1.00 cm hole

in it. These measurements indicated that the deposit of varied

less than 5% over the foil. Removing the baffle, the total alpha

activity of the foil was measured. From this measurement it was deter- o «2 Q mined that the total U deposit was 13.81 mg. This nickel foil was

also mounted on an aluminum frame for mounting in the target chamber. 70

C. Calibration

Before measuring the photofission yields, two calibration measure­ ments had to be made: (1) experimental determination of the optimum setting of the counting system discriminator level, and (2) determination of the absolute efficiency of the fission fragment detector system.

Since the fragments are each formed with approximately 90 MeV of kinetic energy, they are easily distinguishable from the natural alpha activity («^5 MeV) of the target through the use of semiconductor detectors. It is necessary to set the discriminator level of the counting system low enough so that all of the fragments are counted, but high enough so that pulses due to alpha pulse pile-up are not counted. The system was calibrated by replacing the target foil with a

252 Cf source which was prepared by L. E. Glendenin and K. F. Flynn at

Argonne National Laboratory. The pulse height distribution from the detector, as seen in Fig. 28, shows the distribution of fission fragment energies from the of the source along with the 6.1 ncV alpha particle peak. The discriminator level for the phctofission measurements was set at a level of approximately 30 MeV.

Measurements indicated that maximum detection efficiency was obtained by using a single detector placed as close as possible to the target foil. A target-to-detector spacing of 0.23 in. was used. A block diagram of the complete phctofission measuring system is shown

in Fig. 29. The fission counts, beam monitor counts, and time for each counting interval were printed by the parallel printer. The counting

interval length was 10 min. After the information was printed at the 3 i- 6.) Mev 3 ALPHA 5Ï-


i- W d - is > Sg «5 Ï8 < E- m a: Is 0 55 z 2 8 cc

c3 8 »- \ X500 . ' . 8 J 1 d 1 » CO.00 is.aa im.OD KT.i.On 110.00 115.00 120.00 18.00 130.00 133.00 1*0.00 1*5.00 ISO.00 IS.OO ChHNNELS uio' I

252 Fig. 28. Pulse height distribution of fission fragments and alpha particles from Cf 72









Fig. 29. Block diagram of photofission measuring system 73

end of each interval, the system was automatically recycled. A large number of intervals (>100) was used for each scattering angle.

The absolute efficiency of the detection system was measured using O op the thin U target foil. The discriminator level of the counting O op system was reduced so that the U.19 MeV alpha particles from the U were recorded. Since the absolute rate of this target foil was known to be 10,140/min, the measured average alpha count of

1565/min yielded an absolute efficiency of 15.4%. 74


A. Relative Yield from

Using the thick natural uranium target, the fission fragment yield was measured for Compton scattering angles between 6.5 and 17.0 degrees.

At first measurements were made at approximately half-degree increments

(corresponding to a change of 150 keV in the energy of the scattered

8996 keV gamma ray peak). Then, smaller increment measurements were made where there was an indication of structure in the yield curve. At each angular position, fragment and monitor counts were recorded at

10 min. intervals, as described in the previous chapter. The use of short intervals allowed the removal of unusable data with a minimum loss of the good data. The data were considered unusable if the reactor became subcritical during the counting interval.

A fission background was observed even when lead absorbers were placed in front of the target in order to attenuate the gamma ray beam.

Neutron shielding was placed around the target chamber, but no decrease

in the background was observed. Subsequent measurements indicated that

the background was constant and independent of the operation of the

reactor. At first the background was believed to be due to the

spontaneous fission of the uranium target. However, since U^^^ has a

half-life of 7 * lo'^ years for spontaneous fission, the expected count

rate would be approximately 2 • 10 /min. This negligible contribution

was confirmed by removing the target and remeasuring the background.

Since there was no change in the background, this left only one 75

252 alternative. A portion of the Cf calibration source had self- transferred to the face of the detector. Since this background remained constant during the measurements, no attempt was made to obtain a replacement detector.

The average fission fragment count rate per time interval wao calculated for each angular position. The background-subtracted values are plotted in Fig. 30 as a function of scattering angle. The error bars indicate the standard deviation in the background subtracted values. The error associated with the angular positioning was estimated by checking the reproducibility of the scattered beam spectrum. As mentioned in Chapter II, this was accomplished by repeating the pair spectrometer measurements of the scattered beam at a few positions. In each case the scattered beam spectrum was reproducible within statis­ tical error. This should be expected since the angular positioning depends only upon mechanical adjustments.

Since the structure observed in the yield curve is very significant, these portions of the yield curve were rcmeasured several times. Two measurements of the complete yield curve were made four months apart.

The shape of the curve remained constant within statistical errors.

B. Relative Yield from

The measurements described in the previous section were repeated 235 using the U target. The fission background was higher in this case.

The increase in background was found to be dependent upon the presence of the target in the chamber and the reactor being in operation. PHOTOFISSION YIELD

{ o\


ii 5i { I i^M ' ^ ^ ^ Oi i Î Î

17 16 15 14 13 12 11 10 9 8 SCATTERING ANGLE(DEGREES)

Fig. 30. Photofission yield from 77

Subsequent measurements indicated that this was due to neutron-induced fission in the target. The (n,f) cross section for U is 580 barns, which is approximately 10^ times that of Surrounding the photo- fission target chamber with a cover of Cd and paraffin helped reduce this background, but did not eliminate it. For this reason, it was necessary to measure the background at each angular position. These measurements were made by placing a lead attenuator in the incident

gamma ray beam.

The average gamma ray induced and background fission fragment

count rate per time interval were calculated for each angular position.

The background-subtracted values are plotted in Fig. 31. In contrast to o o Q the case of U , no structure is seen in the photofission yield from u235.

C. Absolute Yield from

In an attempt to obtain values for the absolute photofission cross

sections for the target nuclides, careful yield measurements were made

at a few angular positions using the thin target. The use of the 2 thin (1.6mg/cm ) target insured that the fission fragments would not be

absorbed in the target. This, however, considerably reduced the count

rate. It was necessary to make many measurements (>200 time intervals)

at each angular position. The corrected fragment counting rates at the

three angular positions selected are presented in Table 111. 15



Q _J

Ul / > CO m 5 i {


Oî J i i l l i i

17 16 15 M 13 12 II 10 9 8 SCATTERING ANGLE (DEGREES)

235 Fig. 3'. Photofission yield from U 79

9 *^8 Table III. Absolute Fragment Yields from U

Scattering Angle Corrected Yield (degrees) (fissions/interval)

8.0 10.24 ± .78

11.5 1.69 ± .65

12.5 1,20 ± .43 80


A. Photofission Yield Equation

The photofission yield Y(9) at a Compton scattering angle 0 is related to the photofission cross section cr (E) by the yield equation

Eo Y( 0) = A J N(E,9 ) a (E) dE , (6) Eth where E^^ is the threshold energy for photofission in the nuclide studied, is the maximum energy of photons in the scattered beam

(E^^ and E^ are determined by the limits of 0), and N(E, 0)dE is the number of incident photons between energy E and E + dE. A is the constant of proportionality involving such factors as the number of in the target and the detection efficiency of the counting system.

This type of equation is known as a Fredholm intergral equation of the first kind, which can be written in general as

b J^K(x,y)f(y)dy = g(x) (a Sx sb)

There is very little literature on these equations other than proposals for numerical solutions (40-43). Phillips (40) points out that no

Miethùd oT nuiVier'icdl boJuLiûri hdS been very successful for dibiti a ry kernels K(x,y) when the function g(x) is known with only modest accuracy.

The reason is that only an infinitesimal change in g(x) causes a finite change in f(x), hence the equation is unstable. Phillips concludes that the success in solving this type of equation depends to a large extent on the accuracy of g(x) and the shape of K(x,y). 81

A yield equation of the same form as Equation 6 is also encountered

in photonuclear experiments using a bremsstrahlung beam. A general method used to obtain a numerical solution is to replace the integral equation by a set of linear equations. In this approach the energy

range is divided into energy intervals, and the spectrum N is replaced by a constant in each such interval. This step-wise approximation to

the spectrum to the matrix equation

Y = N • (T , (7)

where CT and V are column matrices and N is an n-th order square matrix. Equation 7 has the solution

-* •*-- ] (7 = N • Y

The solutions depend very strongly on the accuracy of the yields and

oscillate violently as a function of photon energy in regions where the

yields are known only to moderate precision. The problem is ill-

conditioned in the sense that there are many solutions which satisfy

exactly an integral equation slightly different from the original.

Thus, one might try to seek a "smooth" solution rather than an exact

solution. One of the most successful applications of this idea to the

solution of the yield equation for bremsstrahlung-induced photonuclear

reactions has been by Cook in his "least structure analysis" method (44).

B. Present Approach

The method used in attempting to unfold the photofission cross

sections was that of matrix approximation (i.e., Equation 7). The N 82

matrix was a square matrix of order 4l. The columns represent the division of the scattered beam spectra into 70.5 keV wide bins. The rows represent the different scattering angles (A05»O.25 degree between adjacent rows). The actual increment between rows was determined by requiring that the energy of the scattered 8996 keV line be incremented by 70.5 keV. Rows of the N matrix were constructed from the pair spectrometer spectra and normalized to the intensity variation of the beam with scattering angle.

An attempt was made to use Cook's "least structure analysis" method in order to obtain the photofission cross sections. The computer program for this method was modified for use with our N matrix.

It was necessary to perform all operations in double precision (16 decimal digits) because of round-off errors in the computer. At first

it was not possible to obtain a smoothed solution using this method.

The resulting cross section values oscillated wildly as a function of energy. More physically believable solutions were obtained by first multiplying both sides of Equation 7 by a diagonal normal i^iny nidLrix before using the smoothing technique. This normalizing matrix was

chosen so that it reduced the numerical variation in the N matrix as much as possible. The reason that this technique works much better

for the case of bremsstrahlung above 10 MeV is that the N matrix is

known analytically and is a smoothly varying function of energy. Also,

photonuclear yields at these energies obtained using bremsstrahlung

typically have much higher counting rates and thus less error in the

yields. 83

Since there was no a priori knowledge of the detailed shape of the photofission cross section, there was no reason for accepting or rejecting any smoothed solution, oscillatory or otherwise. For this reason, test cases were investigated. Cross sections consisting of one or more Gaussian peaks were constructed analytically. Each test cross section was represented by a column matrix which could be multiplied by the N matrix to produce the test yield matrix. Then a statistical error (b /"(yield value), where b is a random number between

-1 and +1) was added to each element in the yield matrix. This yield matrix was then put into the least structure computer program (CLSR).

These test cases led to the following conclusions: 1) CLSR was able to unfold the peaks in the cross sections but tended to give an oscillatory solution away from the peaks; 2) peaks in the photofission yield always indicate corresponding peaks in the cross section.

Conclusion 2) indicates the major advantage of using a Compton scattered photon beam rather than a bremsstrahlung beam for photofission measure­ ments in this energy range. in the present case, the maximum intensity

is near the highest energy for each Compton scattering angle. Thus, the

leading edge of our incident beam picks out the structure in the cross section. In the case of bremsstrahlung, the beam intensity decreases with energy for a given end-point energy. Thus, peaks in the cross

section are observable only as "breaks" in the curvature of the yield


C. Interpretation

Even though we were unable to obtain exact phctofission cross 84

238 235 sections from the U and U yield curves, the knowledge gained from the work with the test cases allows us to make some definite statements about the structure in the cross sections. Our measurements indicate

the following; 1) there is no structure in the photofission cross section of U observable with our resolution up to 8.2 MeV; 2) there are three peaks in the photofission cross section of U from threshold

to 8.2 MeV; 3) these peaks occur at approximately 5.5, 6.3, and 7.1 MeV and have widths of less than 350 keV; and k) the magnitudes of the

9 oft O Q c photofission cross sections of U and U are approximately equal up

235 to about 6.5 MeV, at which point the U cross section begins increasing more rapidly.

Conclusion 1) agrees with the predictions of Bohr's fission channel

theory for an odd A nucleus. Since the low lying bands would be those

of intrinsic excitations, they would be closely spaced and unobservable

with our resolution. Our conclusion agrees with the bremsstrahlung-

induced photofission measurements of Bowman et al. (45).

n o Q The structure observed in the U cross section is very significant

since it has been questioned since the measurements of Katz et al. in

1957. The present information about the photofission cross section of

up to 8.0 MeV is presented in Fig. 32. The two curves given by

Katz represent differently smoothed solutions obtained from the same

experimental yield data. Only the positions of the peaks observed in

the present research are indicated. The two higher energy peaks are

somewhat in agreement with the few points measured by Manfredini

et al. using neutron-capture gamma rays. 238 PHOTOFISSION • MANFREDINI (15)


KATZ (9)


o UJ m


2 Fig. 32. Photofission cross section of U 86

The structure observed in the photofission cross section of this even-even nucleus also supports the idea of fission channels near threshold. It would be necessary to measure the angular distribution of fragments at the energies of these peaks in order to be certain that they are due to I bands and do not contain a 2^ (quadrupole) component. 9 ? A We can also conclude from the observed structure that if U has a second barrier, its height must be greater than that of the first.

Conclusion k) agrees with the results obtained by Winhold and

Halpern (6) and Huizenga et al. (12).

D. Concluding Remarks

In the process of this research, a facility has been developed for the production of a variable energy photon beam. This facility operates very nicely; however, some improvements are desirable. More shielding and collimation in the beam tube in front of the nickel target should cut down the intensity of the background lines due to neutron capture in iron and aluminum. This would tend to give the scattered beam a more triangular shape, with the maximum intensity at the position of the scattered 8996 keV line. Our experience has shown that a triangular

N matrix makes the unfolding problem easier.

Hopefully, a better technique will be developed for numerical solution of the yield equation in the near future. This is the only hindrance to performing photonuclear experiments below 9 MeV using the present faci1i ty.

Photofission experiments below the classical threshold would yield 87

much information about states in the second well. In most cases this energy region cannot be studied by the neutron-induced fission. If adequate count rates could be obtained, the present technique would be ideally suited for such investigations. 88


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I wish to express my sincere appreciation to Dr. D. J. Zaffarano for his encourgemént, guidance, and patience during the course of this investigation and throughout my graduate program at Iowa State University.

His ability to approach problems from basic principles helped keep this research headed in the right direction.

I am especially grateful to Mr. Michael Yester and Mr. Robert Anderl for not only their invaluable assistance in the data analysis and computer programming, but also their friendship and encouragement.

The guidance and suggestions of Dr. E. N. Hatch during the design, construction, and testing of the Compton scattering facility are gratefully acknowledged; and his continuing interest in the project is appreciated.

Special thanks are due Mr. Roland Struss and the reactor mechanical engineering personnel for their valuable assistance in the design and construction of the Compton Scattering facility.

I would like to thank the following people for their help:

Mr. Chris Weber for the design of much of the electronic instrumentation,

Mr. Ken Johnson and Mr. Harlan Warden for help in constructing much of the equipment. Dr. A. B. Tucker, Dr. R. C. Morrison, and Dr. W. L.

Talbert, Jr., for many helpful discussions.

Words fail to express my gratitude to my wife, Martha, for not only her care in typing the thesis, but also her endless patience and constant encouragement; and to my son, Michael James, for understanding 92

why Daddy could not always be home to play with him.

I wish to dedicate this work to my mother, whose encouragement and sacrifices have greatly aided my education.

This thesis would be incomplete if the generous help of Dr. J. W.

Knowles was not acknowledged. His experience and suggestions greatly aided the completion of this research.