Louisiana State University LSU Digital Commons
LSU Historical Dissertations and Theses Graduate School
1962 A Study of the Reactions, Beryllium-9(helium-3,neutron)carbon-11, Lithium-7(helium-3,neutron)boron-9 and Carbon-13(helium-3,neutron)oxygen-15 by Time- Of-Flight Techniques. Jerome Lewis Duggan Louisiana State University and Agricultural & Mechanical College
Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses
Recommended Citation Duggan, Jerome Lewis, "A Study of the Reactions, Beryllium-9(helium-3,neutron)carbon-11, Lithium-7(helium-3,neutron)boron-9 and Carbon-13(helium-3,neutron)oxygen-15 by Time-Of-Flight Techniques." (1962). LSU Historical Dissertations and Theses. 718. https://digitalcommons.lsu.edu/gradschool_disstheses/718
This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected] This dissertation has been 62—3644 microfilmed exactly as received
DUGGAN, Jerome Lewis, 1933- A STUDY OF THE REACTIONS, Be9(He3,n)Cn , Li7(He3,n)B9 AND C13(He3,n)Ol5 , BY TIME-OF- FUGHT TECHNIQUES.
Louisiana State University, Ph.D., 1962 Physics, nuclear
University Microfilms, Inc., Ann Arbor, Michigan A STUDY OF THE REACTIONS, Be9(He3 ,n)C1;L, L i7(He3,n)B
AND C13(He3 ,n )0 15, BY TIME-OF-FLIGHT TECHNIQUES
A D issertation
Submitted to the Graduate Faculty of the Louisiana State University and A gricultural and Mechanical College in partial fulfillm ent of the requirements for the degree of Doctor of Philosophy
i n
The Department of Physics
by Jerome Lewis Duggan B. A., North Texas State College, 1955 M. A., North Texas State College, 1956 January, 1962 ACKNOWLEDGMENT
The author wishes to express his appreciation and gratitude to his research advisors, Dr. P. D. M iller and Dr. W. M. Good of the
Oak Ridge National Laboratory and Dr. V. E. Parker of Louisiana State
University, for their assistance and encouragement during the course
of this work.
In addition he wishes to thank Dr. R. F. Gabbard of the
University of Kentucky, Dr. J. H. Neiler, Dr. G. R. Satchler, Mr.
R. P. Cumby and Mr. M. C. Taylor of the Oak Ridge National Laboratory for their assistance in this project.
Also, appreciation is due Mrs. B. A. Denning for typing the manuscript of this thesis.
Finally, he would like to recognize the financial support of the Graduate Fellowship Program of the Oak Ridge Institute of Nuclear
Studies and the Physics Division of the Oak Ridge National Laboratory. TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENT...... i i
LIST OF TABLES...... v
LIST OF FIGURES ...... v i
ABSTRACT...... x l
CHAPTERS
I. INTRODUCTION...... 1
The Importance of He R eactions ...... 1
Reaction M echanisms ...... 3
The Levels in $ } , an d C ^ ...... 9
I I . EXPERIMENTAL APPARATUS AND PROCEDURE...... 15
Spectrometer Resolving Power ...... 15
Sources of Energy Spread ...... 18
Elapsed Time M easurement ...... 21
Refinements for (He ,n) R eactions ...... 23
Electronics ...... 33
I I I . PRESENTATION OF DATA...... 44
Plastic Scintillator Efficiency ...... 44
Pulse S pectra ...... 48
The Be^(He^Jn)C11 R eaction ...... 51
The C13(He3,n)015 Reaction ...... 53
The Li^(He3,n)B^ R eactio n ...... 65 CHAPTERS - ■ PAGE
Measured Q V alu es ...... 72
Discussion of Errors ...... j6
IV . CALCULATIONS AND RESULTS...... 80
Plane Wave C alculations ...... 80
Distorted Wave C alcu latio n s ...... 90
Discussion of Theoretical Calculations and Results . . 95
BIBLIOGRAPHY...... I l 6
APPENDIX...... 121 V
LIST OF TABLES
TABLE PAGE
I. Measured Q, V alues ...... 77
II. Spin and Parity Assignments ...... 96
III. Optical Model Param eters ...... 97 LIST OF FIGURES
FIGURE PAGE
1. Reciprocal Velocities for Neutron Groups
from Be'^(He3 ,n )C '^ ‘ ...... 20
2. Block Diagram of Post Acceleration Pulsing S ystem ...... 25
3. Average Target Current vs Reciprocal
Pulser V oltage...... 26
M easured 7 -Ray Duration vs Pulser V oltage ...... 27
5 . Electronics Used to Study Time Resolution
P a r a m e t e r s ...... 3°
6 . Time Converter ...... 3k
7 . Block Diagram for Time-of-Flight Spectrum...... 35
8 . Time-of-Flight Spectrum for Neutrons from
C1 3 (He3 ,n ) 0 15 at 0 ^ = 0°, E ^ ~ 2 Mev
and Flight Path 3 m...... * ...... 37
9. Time Spectrum for In7(He 3 ,n )B ? a t
ER 3 = 2 .3 5 Mev, 0=0° and Flight
P a th 6 m. . j f ...... 38
10. Time Spectrum for Be^(He3,n)C'*"*' a t Eg e 3 = 2 .5 Mev,
0 = 0° and Flight Path 6 m...... 39
11. Block Diagram for Pulse Spectrum ...... l)-0
12. Pulse Height Spectrum for 9*83 Mev Neutrons
from Be^(He3,n )C '1''*' ^1
13. Block Diagram for Pulse Spectrum with
Memory S p litte r ...... k2 v i i
FIGURE PAGE
14. Calculated Efficiency of ^ x 3 in. Plastic
Scintillator ...... 47
1 5 . Theoretical Pulse Spectra of 10-Mev Neutrons
for 4 x 3 in. Plastic S cin tillato r ...... 5 °
1 6 . Absolute Efficiency of 3 x 4-in. Plastic
Scintillator with Bias Level at 1.1 Mev ...... 52
1 7 . Angular Distribution for Ground State Neutrons
from Be^(He'^,n)C 11 a t ERe3 = 2 .1 Mev ...... 5^
18s. Angular D istribution of 1st Excited State
Neutrons from Be (He ,n)C at
EHe3 = 2 .1 Mev ...... 55
1 9 . Angular Distribution for 2nd Excited State
Neutrons from Be^(He^,n)C‘^ ‘ at
EHe3 = 2 .1 Mev ...... 56
20. Angular Distribution of 3rd Excited state
Neutrons from Be^He^nJC 11 a t
EHe3 = 2 .1 Mev ...... 57
21. Angular Distribution of 4th Excited State
Neutrons from Be^(He^,n)C^ at
ERe3 = 2 .1 Mev ...... ~ 58
22. Excitation Function for Be^(He^,n)C'^‘,
Ground State Neutrons ...... 59
2 3 . Excitation Function for Be^(He^,n)C^,
1st Excited State ...... 60 FIGURE 9 3 11 2b. Excitation Function for Be (He ,n)C ,
2nd Excited State ......
2 5 . Excitation Function of the 3rd Excited
S tate fo r Be'^(He^,n)C^‘*" ......
26. Excitation Function for l+th Excited State
of Be^He^nJC1 1 ......
2 7 . Total Excitation Functions for Be^(He^,n)C'1'"*' . .
28. Excitation Curve for C^(He^,n)0^,
Ground State Neutrons at 6 = 0° ......
2 9. Excitation Curve for C^(He^,n)0^,
3rd Excited State Neutrons at 9 = 0° ......
3 0 . Excitation Curve for C^He^nJO1^,
Ground State Neutrons at 0, , = 90° ...... l a b y 31. Excitation Curve for C^(He^,n)0*^, 3rd Excited
State Neutrons at 9. , = 90° ...... la b 32. Angular D istribution for Ground State Neutrons
from C1 ^(He^,n)01^ at E He3 =2.66 Mev,
F l i g h t P a th 3 m......
33- Angular Distribution for 3rd Excited State
Neutrons from C^(H e^,n)0^ at Ejj 3 =2.66 Mev,
Flight Path 3m ......
3b. Energy Spectrum for IdT(He^,n)B? at 9 = 0° . . .
3 5 . Li^(He^,n)B^ Excitation Function at 9 = 0°
for Ground State Neutrons ...... IX
FIGURE PAGE
3 6 . Angular D istribution of Ground State Neutrons
from Id7(He^,n)B? at E He3 =2.1 Mev ...... 75
3 7 . Calculated Angular D istribution for Ground
State Neutrons from Be (He ,n)C at
- 3 = 2 .1 M e v ...... 99 He-1 3 8. Calculated Angular Distribution for 1st Excited
State Neutrons from Be^(He^Jn)C''"1' at
ERe3 = 2 .1 Mev ...... 100
3 9. Calculated Angular Distributions for 2nd Excited 9 3 11 State Neutrons from Be (He ,n)C at
Efi 3 = 2.1 Mev - ...... 101
J+O. Calculated Angular D istribution of 3r State Neutrons from Be^(He^,n)C 11 a t EHe3 = 2 .1 Mev ...... 103 1+1. Calculated Angular Distributions for 1+th Excited State Neutrons from Be^(He^,n)C^ at EHe3 = 2 .1 Mev ...... 101+ 1+2. Calculated Excitation Function for Ground State Neutrons from C 1 ^(He^Jn)01^ for 0 = 0 ° ...... 105 1+3. Calculated Excitation Curve for C^(H e^,n)0^, Ground State Neutrons at 0n , = 9 0 ° ...... 106 l a b 1+1+. Calculated Angular D istribution for Ground State Neutrons from C 1 ^(He^,n)©1^ at EHe3 = 2.66 Mev ...... 107 X FIGURE PAGE k-J. Calculated Excitation Function for Ground State Neutrons from C'*'^(He^,n)0'^ ...... 108 k6. Calculated Angular D istribution for 3r State Neutrons for C^He^nJO1^ at EHe3 = 2‘^ MeV ...... 105 k'J. Calculated Excitation Function for Ground State Neutrons from Li^(He^,n)B^ at 0 = 0 ° ...... XU ^ 8 . Calculated Angular D istribution for Li^(He^,n)B?, Ground State Neutrons at E He3 = 2 .1 M e v ...... 112 k3. Calculated Angular D istribution for Ground State Neutrons from C^CHe^^nJO^ at ^ M ev ...... Hi*. ABSTRACT Angular distributions and excitation functions have been measured for the following reactions; Be'^(He^,n)C11, Li^(He^,n)B^ a n d C 1^(He’^n)01^, by tim e-of-flight techniques. These measurements were made with the Oak Ridge National Laboratory 3 Mev pulsed Van de Graaff accelerator which has been modified to give time resolution capabilities of 4 mp. sec for neutrons. Distorted and plane wave stripping calculations have been made in an attempt to fit the measured angular distributions. In the distorted wave calculations the distortion is introduced by scattering from both the Coulomb field and the nuclear optical potential,. The calculations show that the distorted wave angular distributions can be made to fit the data while the plane wave calculations fail except for those angular distributions which are peaked strongly in the for ward direction. For the Be^(He^,n)C^ reaction resolved neutron groups were seen for the ground state and the first four excited states (l- 9 9> XL 4.26, 4.75, and 6 . 5O Mev) in C . Excitation functions were measured a t 0 ° a n d 90° for He^ energies from .5 t o 2 .7 Mev a n d a n g u la r d i s t r i butions measured at 2.1 Mev. From the distorted wave calculations the following spin and parity assignments have been made; no(l/ 2 *" -> 7 /2 n ^ l / 2 " -» 7 / 2 - ) , n 2 ( l / 2 " -* 7 / 2 “ ) , an d ^ ( 3/ 2 "). For the Li^He^njB 9 reaction neutrons from the ground state were clearly resolved from the unresolved second and third excited x i i states. An excitation function -was measured from .5 t o 2 .7 Mev a t 0 ° and an angular distribution was taken at 2.1 Mev for the ground state group. Distorted wave calculations give a spin and parity assignment o f ( l / 2 - -» 7 / 2 ") for this group. F o r t h e C1 ^(He^,n)01^ reaction, resolved neutron groups were IK seen for the ground state and third excited state (6.15 Mev) in 0 . Excitation functions were measured from 1 to 2 .7 Mev a t 0 ° a n d 90°• The most outstanding feature of the excitation function is the resonance at a He center of mass energy of 1.55 Mev. This resonance corresponds to a new state in O1^ at an excitation of 24.01* Mev. This state has a laboratory width of ~ 100 kev. Angular distributions were measured for the ground and third excited states at 2.66 Mev. From the dis torted wave calculations the following spin and parity assignments have been made; nQ(l/ 2 ” ) a n d n^(^/2+ -» rj/2+). In summary it might be said that the angular distributions from the (He^,n) reactions studied, though complex in nature, can be fitted with distorted wave calculations, even at low energies. Furthermore O it appears that the (He ,n) reactions can be used to make spin and parity assignments to many of the proton rich nuclides which are virtually inaccessible by other reactions. CHAPTER I INTRODUCTION I . THE IMPORTANCE OF He3 REACTIONS 3 It has heen known for m any years that the investigation of He induced reactions might he a productive source of nuclear data. Because of the high mass excess of the He particle (15-8 Mev), reactions in duced by it are characterized by high Q values and therefore compound 3 systems which are highly excited. The median binding energy for HeJ in duced reactions with l)-0 < A is 17 Mev. As a result of this, relatively 3 low energy accelerators can be used with He to reach regions of exci tation which would be inaccessible with protons or deuterons and the same accelerator. It has also been pointed out (Br 5 8) t h a t t h e p ro b a bility of p-wave or higher angular momenta interactions relative to 3 s-wave should be greater for He than for protons or deuterons of the 3 same energy. This is true since the He particle has a larger radius and a greater mass than either protons or deuterons and therefore at the same energy it would have a larger relative orbital angular momentum. 3 From the point of view of studying reaction mechanisms He induced reactions are particularly interesting. It is expected that O (He ,n) reactions would proceed in a rather complicated fashion. This complexity is a direct consequence of the intermediate binding 3 energy of the HeJ particle. It is predicted that both "direct inter action" and "compound nucleus" would play important roles in describing these reactions. Of course at the higher He^ energies the direct process should be more predominant. However, even at the higher energies it would seem unlikely that the reactions would proceed by a purely direct process. Unfortunately there have been very few measurements made on (He ,n) reactions. In particular the excitation functions and angular distributions of individual levels in the residual nucleus have not been studied in any detail. Some measurements have been reported on the mirror reaction (He^,p), (Wo 59, Ho 5 6 , Ho 59, Sh 5 6 , Hi 59, Hi 59a). These measurements indicate that indeed the (He^,p) reactions do proceed in a rather complicated manner. There is evidence of both "compound nucleus" formation and "direct interaction." In addition to these there is the possibility of "heavy particle" stripping (Ow 57)- This model might become important in the description of both (He ,p) ■D and (He ,n) reactions. The available experimental data on both of these reactions below a He^ energy of k Mev, indicates that there are large back angle cross sections. In general "heavy particle stripping" amplitudes tend to show maxima at the back angles. In this model it is assumed that the observed particle comes from the nucleus of the target while the He particle interacts as a single configuration with the residual core. Of course this model would probably yield to "direct stripping" and some "compound nucleus" at the higher energies because of the difficulty of this model to predict the high momenta of the ob served particle which the kinematics of these reactions would demand. ■5 In summarizing the above description of He induced reactions and their importance it might be said that there are possibly two features of these reactions which makes them important. The first is the fact that it has recently become apparent that considerably more information can be obtained about the details of nuclear structure by carefully studying the reaction mechanisms which are involved (To 55* *3 Wi 5 5 , La 5 7 ). From this point of view He induced reactions qualify since they are known to proceed in a complicated manner. The second important feature of these reactions is their possible importance as a spectroscopic tool. If the reactions can be described in terms of the available models then spin and parity assignments can be made for many of the proton rich nuclides which are not readily accessible by other reactions. In the following sections a more detailed discussion w ill be given about the general features of the "compound nucleus" and "stripping reactions." I I . REACTION MECHANISMS Compound nucleus. Many of the ejiperimental observations on nuclear reactions have been successfully explained in terms of the so called "compound nucleus" model. In this model the incident particle is assumed to interact with the nucleus as a whole. During the reaction an intermediate state is assumed to form. Using a reaction equation * the process can be written as follows; A + a -»C -» B + b, where A is the target nucleus, a is the incident projectile, C is the inter mediate state, b is usually the observed particle, and B is the residual * nucleus. This_ state C is assumed to have a mean life and'a definite energy of excitation which is governed by the kinematics of the reaction. The mean life of the "compound nucleus" is assumed long compared to the transit time of the incident projectile across the radius of the * target nucleus. The method of decay of the state "C " is assumed in dependent of its method of formation. This means the possible decay channels are determined by the energetics and kinematics of the reaction. ■* Therefore several reactions can be used to observe the same C . In order to describe the features of the angular distributions and exci tation functions for this model it is necessary to look in detail at the region of excitation of the state C . At low energies of excitation the yield curves for the observed particle may show sharp resonances due to the individual states in the "compound nucleus." Angular distributions measured on the low side of the resonance w ill be similar to those on the high side. In general it can be said that the angular distributions for this region of excitation w ill exhibit a marked symmetry about 9°°* In the intermediate region of excitation where the average level density in the "compound system" is greater, the angular d istri butions may s till be symmetric about 90°• However if two or more levels interfere with each other the singular distributions might show marked asymmetry if the levels are of opposite parity. These angular d istri butions w ill in general change rapidly as a function of bombarding energy. In this region it is wise to measure the angular distributions at closely spaced increments of energy. At high energies of excitation the levels in the compound nucleus are closely spaced. In this region the statistical cancellation 5 of interference terms w ill in general give smooth excitation functions. Angular distributions w ill again tend to be symmetrical about 90°. Thus it can be seen that the formulation of a "compound nucleus" can predict a wide variety of shapes for the yield curves and the angular distributions. In the section to follow the general characteristics of the competing "direct interactions" or specifically "stripping" w ill be discussed. "Stripping." If the energy of the incident particle is fairly high then there is a high probability that the reaction w ill proceed in a "direct" fashion. These direct interactions are also enhanced if the low lying levels of the residual nucleus are the ones chiefly excited. More specifically it might be said that the direct inter actions are favored when the momenta of the incident and the observed particle are high. That is to say that the "compound nucleus" model might well explain the angular distributions and excitation functions of the more highly excited states even if the low lying levels seem to proceed by "direct interaction." It might be added here that this doesn’t seem to be the case for the (He ,n) reactions studied for this paper. Our results seem to show that at least in two cases (these w ill be discussed in detail later) the "stripping" calculations show better fits for the more highly excited states than for the ground states of the residual nuclei for these particular reactions. Never theless qualitative momenta arguments would be in favor of better fits for the ground state groups. In these direct reactions it is assumed that the passage from the in itial configuration (target + projectile) to the final configuration (observed particle + recoil nucleus) is instantaneous. Probably the most famous of these "direct interactions" is the so called "stripping" reaction. A theoretical treatment of deuteron-stripping reactions was first proposed by Serber (Se 47). However he was interested in very high deuteron energies and the to tal angular distributions of all the observed particles independent from which states they came. Butler (Bu 50 , 51)--developed the theory to explain the behaviour of groups from specific levels in the residual nucleus. It was through his work that the spectroscopic value of the calculations was realized. In this "stripping" model it is assumed that the incident particle (a deuteron for this discussion) fails to make-a head-on collision, which would result in the formation of a "compound nucleus," but instead only grazes the surface of the nucleus with one of its nucleons. If the passage is sufficiently close to the nucleus, the nucleon involved in the collision which is loosely bound to the deuteron (2.23 Mev) might be stripped off by the nuclear forces that it feels from the target. The other nucleon involved would pass forward as the observed particle. It can easily be seen that the reverse~process "pickup" is obviously very similar to stripping. In this case the deuteron would pass close to the nucleus and pick up a nucleon from the surface of the target nucleus. The first experimental evidence of this pickup reaction ((d , t ) in this case) was given by Newns (Ne 52). In order to quickly review the qualitative features of these stripping reactions it is helpful to look at the theoretical expression for a simple (d,p) stripping reaction (Bu 57)* la this simplified calculation the interactions of deuteron with the target nucleus as well as the proton with the final nucleus are ignored. With these assumptions the differential cross section is expressed by; .2 Srf r i i (r,JL(Qr), h ^ iK r)) ( 1 ) where L is the orbital angular momentum of the captured neutron, r is the radius of the interaction, is the so called "reduced width" for the reaction (it is the probability of finding the captured particle in its captured state at the nuclear surface (r Q) "^e effective range of the interaction, Q is the momentum taken into the nucleus by the neutron (see diagram), K K and K, are the momenta of the proton and deuteron, K an d 7 is determined by the deuteron binding energy. From the diagram it can be seen that the orbital angular momentum carried into the nucleus would be fiQr. The quantity r can be thought of as the classical impact parameter (o < r < r Q). From these considerations the maximum orbital angular momentum transfer would be fiQro« Now the main feature that equation (l) predicts is a rapid variation of differential cross- section as a function of 0. This is because of the rapid oscillation of the term (f) as a function of 0. In general the spherical Bessel (l) function JL(Qr) has its maximum where Qt q ~ L. The h£ '(iKr) a r e t h e spherical Hahkel functions which are generated from the Bessel functions by the relation; hJ^UKr) = JL(iKr) + inL(iKr) . (2) The n^'s are the spherical Neuman functions which are generated from the Bessel functions by; JL(x) S “l(x) - "l(x) S jl(x) = h ■ ( 3 > X The Bessel function contribution to the cross section is damped p by the term - - K2 + 7 2 K2 + | 2 This term is independent of the angular momentum transferred and de creases rapidly with angle. An increase in bombarding energy w ill shift the angular distribution peaks to the lower angles and f w ill cause the peaks to be steeper. The excitation function should be a smooth function of energy. The calculations made in the last chapter of this thesis are just a refinement of the picture presented above. The chief difference is that distorted "wave functions" were used instead of the plane waves above. In the calculations the distortion arises by scattering from the Coulomb field and the nuclear optical potential. For the (He ,n) reactions the fits are seen to be greatly improved over the plane wave calculations. III. THE LEVEIS IN B?, 015, AND C11 In the reactions studied for this thesis information was ob tained about spin and parity assignments for levels in the three nuclides listed above. In this section a brief summary w ill be given with regard to the information that is presently available about the levels of these three nuclides. In the summary the work w ill be mentioned and where appropriate a brief description included. B^. Stelson et al. (St 51) have measured the natural width of the ground state by total neutron cross section methods. Neutrons from Be9 (p,n)B? were used to make the measurements. These neutrons were then scattered from a sulfur disk and the sharp resonance in the total neutron cross section for sulfur and 585 kev (natural width 1 .5 kev) was* used to determine the width of the ground state group. An upper l i m i t o f 2 kev was set on the width of this group. Reynolds et al. (Re 5 6 ) measured deuteron groups from the ground and first excited state for B 1 0 (p,d)B?. The energy of the first excited state was assigned a value of 2.kQ + .1 5 Mev. Considerable complication was produced by deuterons from B"^(p,d)E^. Q values for the ground state groups in these two reactions are nearly equal. As a result the 10 deuteron groups are separated only by a small energy difference. Graphical subtraction was used to separate these groups. Calculations made from pickup theory on the angular distribution of ground state neutrons from B9 show good fits with angular momentum transfer i = 1. From these calculations a spin assignment of l/2 < J < 9 /2 c o u ld be made for this group. Bockelman et al. (Bo 5 6 ) measured ground state tritons from B^(d,t)B9 by magnetic analysis. The Q, value for this reaction was measured to be - 2.1&7 + .010 Mev. Because of the relatively low- resolution conditions for the experiment, no natural width was assigned to the group. Photographic emulsions with magnetic separation were used by Almqvist et al. (Al 55) to measure a particles from B'*'^(He^,a)E?. Alpha groups were observed for the ground state and at an excitation o f 2 .5 8 + .1 3 Mev i n B9 . Knowles et al. (Kn 5 8) at Livermore have measured a's from the ground and first excited (2.4 Mev) state by the reaction C^^(p,ct)E?. They also report evidence of a 7 Mev l e v e l i n B9 . H ow ever, c o n s id e r a b le 1 2 background from C (p,p)3c* was present. The data was fitted with Butler knock-on theory. Pulsed beam tim e-of-flight methods have been used by Marion et al. (Ma 59) to study the reaction Be9(p,n)E?. In the paper it is pointed out that part of the background attributed to (p,p'n) m ig h t be due to a level at ~ 1.4 Mev in B^. - - 11 Spencer et al. (Sp 5 9) at Rice used the annular magnet spec trometer to study a's from B^(He^,a)B?. The width of the first excited state was measured to be 83 + 9 k e v . Reynolds (Re 5 6 ) measured a's from the ground state and a level at 2.39 + -08 Mev for the reaction C^(p,a)B^. This data was super- 12 12* imposed on the continuum from C (p,p')C -> 3a* The angular distri butions were consistent with Butler pickup theory. Sher et al. (Sh 5 1 ) u s e d a 25 Mev betatron to measure photoneutron thresholds for B ^( 7 ,>n)B^. A ground state threshold of 8 .5 5 + .2 5 Mev was reported for this reaction. This threshold was measured by direct detection of the neutron yield as a function of maximum bremsstrahlung e n e rg y . 15 0 . There have been many experiments performed in which the 15 states in 0 have been studied. This summary w ill include only (He^,a), (d,n), (He^,d), (p,7) and (d,t) w ork. Pouh et al. (Po 59) have measured the Q values for the first (5.195 Mev) and second (5-247 Mev) excited states by studying a's from the reaction 0 1^(He^,a)0'1'^. No spin assignments were made for these groups. The same two states were measured to be 5.17^ Mev and 5 .2 3 3 Mev by Hinds et al. (Hi 59) using magnetic analysis of the a's. This same group of investigators (Hi 59a) studied the reaction between 5*7 Mev and 9-16 Mev to observe the change in the angular distribution. At low energies i.e . < 5 Mev this reaction takes place by a conpound nucleus process. At higher energies (~ 9 Mev), marked asymmetry appears 12 in the angular distribution which suggests competition from a direct process. This same asymmetry was reported by Holmgren (Ho 57) "the Naval Research Lab. Evans et al. (Ev 53) have measured the energy of the ground state and first five excited states by the reaction N 1 ^d,n)CT1'^. These measurements were made with 7*7 Mev deuterons on a gas target. Photographic plates were used to detect the outgoing neutrons. A spin assignment of ^ | was made for the ground state group from Butler stripping calculations. Nonaka (No 57) studied angular distributions from this same reaction for the ground state group. These measurements were made with photographic plates ax a deuteron energy of I .9 6 Mev. The angular distributions were fitted with a Butler calculation using angular momentum transfer J! = 1 . Forsyth (Fo 60) studied the reaction N 11*(He^,d)01''’ w ith a broad range magnetic spectrograph. He measured the angular distribution of 3 the ground state deuterons at a He energy of 5*2 Mev. The angular distribution was fitted with a Butler stripping curve. Tabata et al. (Ta 60) studied angular distributions of the 7 ’ s from at the 278 kev resonance for this reaction. The angular distribution of the 7*5^ Mev state was isotropic. This sup ported the Jrt = l/2+ assignment for this state. Levels at 6.82, 6 .1 8 and 5*23 Mev were established by Johnson et al. (Jo 5 2 ) by t h i s same r e a c t i o n . Keller (Ke 60) measured angular distributions for the ground ~| g state for the reaction 0 (_d,t )0 . With a deuteron energy of 15 Mev 13 he was able to produce copious yields of tritons. The ground state angular distributions were fitted with a & =1 Butler transfer and n a radius of 1 .7 5 **• C~^. Most of the energy levels assigned to the states in C ^1 come from the reaction B^(d,n)C^^ (El 53, Jo 52a, Va 51 )• H Is for this reason that the reaction w ill be used to summarize the states of excitation in C^. Photographic plates were used by Grave (Gr 5 6 ) t o m easure neutrons from the following states 2.02 + .01, 1.21 + . 03I , an d I .73 + .0 3 Mev. With a deuteron bombarding energy of 1.08 Mev it was necessary to use a compound nucleus isotropic distribution coupled with a Butler stripping curve to fit the angular distributions. This same technique was used by Johnson (Jo 52a). His level assignments w e re ; 1 . 8 5, 1 . 2 3 , I . 7 7 , 6 . 1 0 , 6 . 7 7 , 7 -3 9, 8 . 0 8, 8 . 3 9, 8 .6 2 a n d 8 .9 7 Mev. Bent et al. (Be 5 5 ) at Rice measured neutrons from the following C'*"*' s t a t e s 6 .I 5 , 8.10, 8.12 and 8 .6 5 Mev. Spin and parity assignments for these states are consistent with 7 ray measurements by Evans. Gamma-gamraa angular correlations were also made for these same states by Jones et al. (Jo 52). Cerineo (Ce 5 6 , Ce^56a) measured the angular distributions of the neutrons for the ground and first three excited states at a cyclotron energy of ~ 7-5 Mev. Butler theory was successful in analyzing the data with r = 5.8f and Z = 1 . A t E , = 9 Mev M a slin P u et al. (Ma 5 6 ) used the Liverpool cyclotron to get the same Butler type curves for nQ and n^. A three crystal pair spectrometer was used by l i f Sample et al. (Sa 55) "to measure 7 's for the following levels k.k-6, ^•75> 5-°3.> 5*35j 6 . 5 2 , 6."jQ, 7.29 a n d 8.2J Mev. For this work no angular distributions were measured. A summary of the above known spin and parity assignments for Q ■15 11 IT j 0 and C will be given in the last chapter along with new assignments that have been made on the basis of our calculations. In the next chapter a detailed outline of the tim e-of-flight spectrometer used for studying the three reactions in this thesis w ill be discussed. CHAPTER I I EXPERIMENTAL APPARATUS AND PROCEDURE In this chapter the techniques used to measure the flight times of (He ,n) neutrons are discussed. The first section treats the reso lution of the tim e-of-flight spectrometer and its individual sources of energy spread. In the second section sources of energy spread that are independent of the tim e-of-flight system are discussed. Following this section a simple picture of the method used to measure the neutron flight time is given. The modifications of the Van de Graaff and the O electronics for the (He ,n) reaction are discussed in the last sections. I . SPECTROMETER RESOLVING POWER The overall energy spread of a tim e-of-flight spectrometer is determined by the spreads that are produced by the tim e-of-flight system (Van de Graaff plus electronics) coupled with the energy spreads from other sources such as target thickness and the natural widths of the levels being studied. This section w ill treat the energy spreads introduced by the tim e-of-flight system. The resolving power of a spectrometer is given by the quantity =— , where AE is the uncertainty in measuring the energy E. Time-of- flight methods give the energy of the neutrons being measured by the expression; E (Mev) = 7 2 .3 L -r 00 16 where L is the flight path in meters and t is the flight time in mp sec. Equation (Ij-) can easily be differentiated to show that the re solving power Of the system is given by; AE 2A t ( _ \ E t ^ w here At is the uncertainty in measuring the flight time T. Therefore the energy resolving power is twice the time resolving power. The instrumental resolving time uncertainty (A t ) is given by; (ATb)2 + (ATd)2 + (ATj2 (6) where the AT, is the beam burst duration. AT, is the time spread in- b a troduced by the detector and AT is all of the other time uncertainties e introduced by the tim e-of-flight electronics. A discussion of each of the several components of A t w ill follow. It is rather difficult to estimate the magnitudes of the various A t* s even if you have a fair estimate of A t. Estimates of the beam burst duration can be made by varying the beam pulse length (for this example, pulsing the beam harder) and observing the overall change in system resolution. Measurements of this type have been made (Figs. 3 and and the results will be discussed later in this chapter. The beam associated time spread that can be estimated by the above measure ments is a combination of burst duration and the capacitive rise time of the target pick-off system. One of the timing signals is a voltage pulse taken from the target. This signal is used as a "time zero" 17 reference in measuring the neutron flight time. Its magnitude would Q be — , where Q is the charge in the beam pulse and C is the capacity o of the target system. Therefore it is necessary to minimize the capacity of the target system. Additional "time spreads" can be introduced by fluctuations in the beam pulse amplitude. For this experiment these fluctuations were reduced by clipping the target signal in a lim iter after it had been amplified by several Hewlett- Packard am plifiers. The rise time of the output pulse was almost entirely dependent on the number'of am plifiers used since the input pulse was of the order of 1 mp._sec. This point w ill be discussed in more detail later on in the chapter. The second component (AT^) in equation (4) w ill now be treated. The detector rise time can be thought of as being composed of two components, those associated with the crystal, and those dependent on the properties of the phototube. For a crystal of thickness | (meters) the time spread At^ which is produced by the neutron flight time in the crystal is given by; = ( l ) T ■ (7) To give an order of magnitude for this quantity, its range w ill be discussed for the 3" plastic scintillator used for this ejsperiment. If neutrons are being measured which have an energy range from 1-5 t o 10.5 Mev, Att would have a corresponding range from to I. 7 I mq s e c . In most cases At^ is larger than the phototube dependent component of 18 AT^. This latter component is the rms variation in the overall transit of the photoelectrons in the phototube. The major portion of this spread is probably produced by transit time differences from the various positions on the-photocathode to the first dynode (Ke 56 , Wi 6 l ) . These effects w ill be discussed further in the last part of this chapter. The final term in equation (4) is ATg which can be thought of as the sum of the other electronic components. Each of the components used to make a time spectrum measurement (Figs. 5* 7) has a 5t asso ciated with it. Experience indicates however, that the major factor contributing to ATg is the time spread introduced by the time con verter. Measurements (to be discussed later) of this time spread in dicate that 1 mp sec is probably the lower lim it of its value. I I . SOURCES OF ENERGY SPREAD In addition to the energy uncertainty introduced by the tim e-of- flight system there are other sources of spread in the reaction energy. Even If the resolution of the spectrometer is a few percent in energy, the observed groups may not be separable. The reason for this is that in the previous section nothing was said about the natural widths of the levels being measured or the finite thickness of the target. In the previous chapter a summary was given of the residual 9 15 11 s t a t e s a , 0 , and C . In the summary only the width of the ground state group from was given (< 2 kev). The natural widths of the other levels studied for this experiment have not been measured. These quantities would therefore enter into the final resolution as unknowns if the residual nucleus is unbound. The energy spread introduced by the finite thickness of the target is one that can be controlled. For a general reaction X(a,n)Y, the spread in the energy of the outgoing neutron is approximately pro portional to the target thickness. In order to determine this energy dE spread the (~ ) of particle a must be known in the target material X. CLX Once the minimum acceptable spread (AE) for the neutron has been deter mined, the target thickness can easily be calculated. For tim e-of-flight experiments it is convenient to use a plot of reciprocal velocity of the neutron vs the energy of the bombarding particle a. Figure 1 shows 9 ^ IX such a plot for Be (He ,n)C . From this curve dE a can be determined at the desired E . The tim e-of-flight spread A t S* X is then given by; where L is the flight path. As an example, a 30 Be^ target is ~ 50 k e v t h i c k f o r 2 Mev cm He particles. With a flight path of 6 meters, At^ = .36 mu sec for the ground state neutrons and 2 ,5 mu sec for neutrons from the 7 A 0 Mev 11 level in C (Fig. 10). Since these two levels span the region of RECIPROCAL VELOCITY (m/isec / meter) 40 0 8 60 20 i. . eircl eoiis o Nurn rus rm Be®{He^,r?)C^ from Groups Neutron for L Velocities Reciprocal 1. Fig. 5 Mev .50 6 .7 Mev 6.77 .6 Mev 4.26 Mev 4.75 .0 Mev 7.40 .9 Mev 1.99 GROUND (Mev) EES N C IN LEVELS 2 GROUND RLL-W 61537 ORNL-LR-DWG 6.77 4.26 4.75 6.50 7.40 UNCLASSIFIED 0 2 3 2 1 interest in with our detector, 30 is a reasonable target -- - cm thickness. However, it is always wise to make targets with a range of thicknesses, since the cross section of the reaction was not con sidered in the above argument. As w ill be described in Chapter III, the thick targets can always be used to take pulse spectra. In con clusion it can be said that the final target thickness is a compromise between Ar^ and the signal to noise ratio for the reaction being s tu d ie d . I I I . ELAPSED TIME MEASUREMENT In order to measure the neutron flight time from the target to the detector several methods can be used. For definition, "time zero" (tQ) w ill be the instant that the neutron leaves the target and t 1 i t s flight time from the target to the detector. The most elementary way to measure t^ would be to start the clock (in this case the time to pulse height converter) with the target pulse and stop it with the pulse that is produced when the neutron enters the detector. Therefore the voltage output of the time converter (which is proportional to the difference in time between the start and stop pulses) would be pro portional to the neutron flight time t^. In practice however, it is better to start the time converter with the detector pulse and stop it with the beam pulse which has been delayed a known amount (&d). With this arrangement the converter is only operating when there is an event in the detector and therefore the overload pulses (start pulses that occur without a stop pulse) which saturate the am plifier (Fig. 5) w ill 2 2 be essentially eliminated. With this arrangement the output from the time converter is proportional to t^ - t - 6d. This just means that the time scale has been reversed. Since the output of the time con verter is displayed on a multichannel (Fig. 5 ) the higher energy neutron groups w ill appear in the upper channels. Figure 10 illustrates this point. In the figure the neutrons in channel 125 are 1.95 Mev while those in 229 have an energy of 10 Mev. Gamma rays from the target would occur about 100 channels to the right of the 10 Mev group. In order to get a numerical value for t^ it is necessary to calibrate the time per channel of the analyzer. This can be done in a number of ways. One method is to observe the channel position shift of the time spectrum 7 rays as the delay in the beam pulse line is changed a known amount 6 d. If the system is completely linear a change in the delay of amount 5d w ill produce a channel shift 5c. From this the time per channel would be . This same calibration can be made by using a neutron group of known energy. For the purpose of this dis cussion this group w ill be called N^. From the calculated energy of its reciprocal velocity can be determined (Fig. l). First its position on the time spectrum is determined at a specific flight path Lq and angle 0. Next the flight path is increased an amount 5L. The group N is observed to move a definite number of channels 5c. The U> time per channel is then given by; 5 t 6L 5c v 5c (9 ) a where v is the velocity of the neutron group N . From equation (9 ) Qi Q 23 it is obvious that the energy of the group N should be as low as possible for optimum calibration. Therefore it is wise to choose 9 to be a back angle if possible, since v w ill be lower at the back La angles than in the foreward direction. For the work reported in this thesis both methods were used to calibrate the analyzer. In the next section the several modifications of the accelerator and the circuitry for the He reactions w ill be discussed. IV . REFINEMENTS FOR (He3,n ) REACTIONS Van de Graaff modifications. The instrumentation of the Oak Ridge National Laboratory 3 Mev accelerator for kev neutron tim e-of- flight studies has previously been described (Go $ 8 ). In order to study the (He ,n) reactions it was necessary to make several modifi cations to the Van de Graaff and the electronic system. These modi fications w ill be discussed in this section. The most important modifications to the accelerator were, 3 installation of a He ion source and the development of an "after 3 pulsing" system. The He source developed at ORNL w ill pioduce a dc beam o f 500 qamp. The average lifetim e of the source at this high 3 current is about 115 hours. In order to introduce He into the gas bottle a leak system was developed with improved characteristics (J o 6 l). Two sensitive leak valves were joined in series with a minimum ballast volume between them. One of the valves was set at a flow rate somewhat higher than the required operating rate and the other valve was varied to obtain the required rate (~ 2 cc/hr.). The 2b pressure in the ion bottle was controllable to within 2$ of the desired value. Therefore there was no fluctuations in the beam because of poor gas pressure control in the ion bottle. The beam was pulsed in the terminal at a repetition rate of 2 mcs 1. Pulses that emerged from the accelerator were variable in pulse length (given in terms of transit time from leading edge to trailing edge) from 10 t o 30 mp s e c . This pulsed beam was then bent- through a 90° analyzing magnet and directed towards the target. Before reaching the target these pulses were shortened further by the post-acceleration-pulsing system (Fig. 2). This system was triggered when the beam pulse passed through the signal-pickup-cylinder. This cylinder was grounded through a 10 K resistor. 'When the beam pulse passed through the cylinder, an induced charge was produced. The voltage pulse from this induced charge was amplified, clipped, and used to drive a tuned am plifier. From the tuned am plifier, the signal was fed into a frequency m ultiplier (2 t o 12 mcs which was properly phased to drive a tuned power amplifier. This 0-10 k.v.p.) output was applied across a set of deflecting plates which swept the beam. This voltage was in phase so that any desired portion of the beam pulse could be removed. In this series of experi ments the burst duration was varied from about 20 mp sec to 2 mp sec with the post-accelerator pulser. Figure 3 shows a plot of target current vs reciprocal deflector plate voltage. In theory the maximum pulser setting should give a time resolution which is lim ited only by the tim e-of-flight electronics and the other items mentioned in the section on time uncertainties. Figure 4 shows a plot of 7 resolution 25 UNCLASSIFIED ORNL-LR-DWG 54279 8 v PEAK 2 Me TUNED AMPLIFIER FREQUENCY MULTIPLIER 8v PEAK f\ 2 Me 8 vPEAK NEGATIVE / 12 Me ■ACCELERATOR CUPPER HIH TERMINAL 9999964 PULSER TUNED 4 HP ■ACCELERATOR AMPLIFIER AMPLIFIER 10 kv PEAK 30 mvPEAK 2 Me — BEAM PULSE SIGNAL PICKUP CYLINDER APERTURE Fig. 2. Block Diagram of Post Acceleration Pulsing System. TARGET CURRENT (^am p) 3.0 2.0 2.5 0.5 3.5 i. . vrg agtCret s eircl usr Yoltage. Pulser Reciprocal vs Current Target Average 3. Fig. EK CURRENT= PEAK CURRENT= AVG TARGET PLE VOLTAGE xIO4 1 /PULSER EK WE VOLTS SWEEP PEAK CONSTANT US DURATIONBURST -R- 2 4 0 7 5 G W -D L-LR N R O 00, 3) .3 ,4 0 (0 UNCLASSIFIED 26 MEASURED BURST TIME (nsec) 10 12 4 6 0 8 2 i. . esrdyRy uain s usr Voltage. Pulser vs Duration y*Ray Measured 4. Fig. USR VOLTAGEPULSER (PEAK) RLL-W 57043 4 0 7 5 ORNL-LR-DWG UNCLASSIFIED 27 2 8 (full width at half maximum) as a function of pulser voltage. The best obtainable 7 resolution for this experiment has been 2 .7 mp s e c . However, at that resolution the beam pulse was barely large enough to stop the time converter. With the addition of another Hewlett Packard Model 1j-60A am plifier in the beam pulse line, the stop pulse was large enough in amplitude to trigger the time converter; but its full width at half maximum lim ited the resolution. An ultimate solution to the problem might be to use the signal pick-up pulse as the stop pulse for the time converter. Cranburg (Cr 56 ) claims that the rise time of his pick-up pulse is only 2 mp sec after am plification with two wide-band Hewlett Packard am plifiers. This is about the rise time that one would expect with two such amplifiers and a very fast input pulse. Such a system might indicate whether 2 .7 mp sec is truly electronic resolution or whether it is still lim ited by the beam pulse. An alternate solution to the problem with the present system w ill be provided with the installation of the EUo-Plasmatron ion source on the 3-Mev accelerator. Results of the measurements made at ORNL (Ki 6 l) on a test bench Duo- Plasmatron indicate that the ion source w ill easily yield dc beam currents of 10 ma. This is a factor of ten greater than the output of a conventional rf ion source. Ion bunching systems (Mo 5 5 ) c o u p le d with ion sources like the IUo-Plasmatron would eliminate the need for am plification of the beam pulse. Mobley (Mo 6 l) has indicated that bunching factors of 30 have already been obtained with his system. With sub-mp sec pulses from the accelerator, time resolution w ill be 2 9 almost entirely determined by the electronics of the rest of the tim e-of-flight system. Detector time resolution studies. In order to separate neutron groups in (He ,n) reactions it is desirable to have very good time 7 O Q resolution. For example, in the reaction Li (He ,n)B there is some question about the validity of the 2. 83-Mev level in I?. If one wished to study this level at a He^ energy of 2 Mev and a lab angle of 0°, he would be looking at neutrons of 8.52 Mev fro m t h i s l e v e l and at neutrons of 8 .9 8 Mev from the 2.37 Mev level. The difference in the reciprocal velocities of these two neutron groups is . 64 mp sec/meter. At a. flight path of two meters and a time resolution capability of 1 mp. sec, he should see two distinct neutron groups in this region. An attempt to minimize the time-resolving properties of the ORNL detector system was undertaken so that levels with energy separations comparable to the one above could be studied. Figure 5 shows a block diagram of the electronics used to study the tim e-resolution properties of the time-pulse height converter and its associated equipment. A discussion of the important features of each of the components w ill follow. The first section w ill treat plastic scintillators. An excellent -survey of organic scintillators has been given by Brooks (Br 56 ). Our chief interest in organic scintillators is in their fast decay time. Probably the fastest are produced by the plastic scintillators (~ 3 mp sec). For this experiment Pilot B plastic scintillators were used. In order to seal the scintillator to the 3 0 UNCLASSIFIED ORNL-LR-DWG 54280 No22 SOURCE PLASTIC SCINTILLATOR SLOW FAST FAST SLOW HP AMPLIFIER PREAMPLIFIER PREAMPLIFIER DELAY T1ME-PULSE HEIGHT CONVERTER A8 AMPLIFIER A8 AMPLIFIER A8 AMPLIFIER MULTI-CHANNEL ANALYZER GATE SINGLE DZ4 SINGLE CHANNEL COINCIDENCE CHANNEL ANALYZER CIRCUIT ANALYZER Fig. 5. Electronics Used to Study Time Resolution Parameters. phototube, Corning Wo. 200 fluid was applied to the crystal. A spring-loaded can housed each crystal. With these cans, constant pressure could be applied against the crystal, so that it remained against the phototube face. For the two-detector assembly several sizes of crystals were used from 2" dia. to 3A" dia., with various thicknesses for each diameter. Results indicate that photoelectron transit-tim e spreads are noticeable with the larger crystals. In fact, for the C725 I photom ultiplier, the resolution changed from 1 .5 t o 2 .5 mp sec with a change from 1" to 2" in crystal diameter. These results seem to be consistent with those reported by Williams (Wi 6l) in which he used a mercury-capsule light-pulse generator to measure the transit-tim e differences for various positions on the photocathode surface. However, his measurements were performed at the anode with a Luraatron sampling oscilloscope, while ours were made by the indirect method of looking at the change in overall resolution of the system. The various photomultipliers used for the above crystals w ill be discussed in the next section. Probably one of the best listings of phototubes and their characteristics can be found in the Counting Handbook (La 59 )> The tubes that we tried were RCA's 6810A, C 725 I , an d 726 ^-. The v e ry excellent properties of the 726 ^ as a tim e-of-flight phototube were suggested by E. Eichler (Ei 60 ). Each of these phototubes is a l1*-- stage photomultiplier with a linear dynode m ultiplier structure. Our measurements indicate that using the 726 ^ as the start tube and a C725 I as the stop tube gave the best overall system resolution (less 3 2 than 1 mp sec). However, reported (Gr 5 8) transit-tim e spreads for a given type of phototube can vary by a factor of two or more. It might be that the start tube was an exceptionally good 7264. Certainly the 68lOA's had transit time spreads greater than the 7264, because our best resolution with a pair of them was 2 .5 mp sec. In the next section the other electronic components of Fig. 5 w ill be discussed. In order to provide a preliminary check on these fast detectors a "two detector" assembly was made (Fig. 5 ). In the assembly the two time correlated pulses come from the annihilation radiation of the 22 Na source. This source was placed the common axis of the two photo- - tubes and at an equal distance from each crystal. With this arrangement identical counting rates should be observed from the two y r a y s . Of course, this source also emits a 1.28-Mev y ray which produced random counts in both phototubes. Two pulses are taken from each phototube (called fast and slow pulses). The slow pulses which come from the next-to-last dynode on each phototube, are positive, and have rise times of the order of 5 mp sec. Fast pulses collected at the anode, are negative, and have rise times of the order of 1 mp sec. In both branches of the electronics the slow pulses have identical routing. They are first amplified with A 8 amplifiers and then fed into single channel analyzers. In order to achieve the best resolution it was necessary to set the single-channel windows at about yja o f t h e i r maximum possible value. The pulse-height base line was adjusted for each single channel by feeding its output into a scaler. With this alignment, the single-channel outputs were fed into a_ coincidence circuit which was used to gate the multichannel analyzer. One of the fast pulses was fed directly into the start side of the time converter ( F ig . 6 ), while the other was am plified, delayed a known amount T^, and fed into the stop side of the converter. The output of the time converter was amplified and displayed on a multichannel analyzer. A single narrow peak was observed on the scope of the analyzer. If the delay was changed a known amount (£T) the peak would move a given number of channels (Z£). By taking several delays the time per channel was determined. After this value was established the full width at half maximum of the y peak was determined by counting the number of channels that it spanned. Results of the measurements were very sensitive to the parameters of the time converter, particularly the bias levels of the 6AK5 ancL the 6 AU6 . V; . ELECTRONICS In this section the electronics for making the time measure ments and observing the pulse spectra w ill be discussed. In order to illustrate how the various components couple together several block diagrams w ill be shown. Time spectrum. A block diagram of the electronic apparatus used to take time spectra is shown in Fig. 7* The phototube used was an RCA 7014-6. It is a li stage, linear dynode, high gain, low -transit time tube. With a if" x 3" crystal rather high efficiencies were obtained. This subject w ill be discussed in some detail in the next UNCLASSIFIED 2-0I-077-NS3R3 10 K TELCO 150 K 3 3 0 3 3 0 Q. 1N252 2 0 0 /is e c IN252 4 7 K 100, 0.01 0.1 4 = • 404A 120 K LINEAR 100 0.01 6AK5 AMPLIFIER BEAM IN252 • 6AK5 DETECTOR PULSE (+) 0.14: 0.01 Meg PULSE (-) 50 K 1.5 Meg = 4 IN 67 100K 5 0 K MINIPOT =1=0.01 § 1 5 Meg 2 5 0 K MINIPOT 1 Meg MINIPOT -150v - 1 5 0 v ALL CAPACITANCES ARE IN MICROFARADS UNLESS OTHERWISE NOTED ALL RESISTANCES ARE IN OHMS UNLESS OTHERWISE NOTED Fig. 6. Time Converter. LO •P" 1 35 7046 UNCLASSIFIED ORNL-LR-DWG 53876 TARGET PLASTIC SCINTILLATOR DELAY FAST SLOW TIME-PULSE HEIGHT PREAMPLIFIER CONVERTER MULTI-CHANNEL ANALYZER MODEL DD2 PREAMPLIFIER AMPLIFIER MODEL A8 SINGLE CHANNEL GATE AMPLIFIER ANALYZER Fig. 7. Block Diagram {or Time-of-Flight Spectrum. chapter. As In the two-detector assembly, the start pulse came from the anode of the phototube. Slow pulses from the phototube were amplified and sent into a single-channel analyzer which gated the multichannel analyzer. The single-channel analyzer was operated on the integral range and its base line setting was determined by the lowest energy neutron group that could be seen with a good signal to noise ratio. Beam pulses at the target were amplified, delayed, and used to stop the time converter. After amplification the output of the converter was analyzed by an RCL 20ij-8-channel analyzer. Figures 8, 9, a n d 10, show typical time spectra for the three reactions that were studied. An example of the resolution with this system is the 9 ^ XX ground-state neutrons for Be (He ,n)C (far right group^ Fig. 10). The full width at half maximum for this group is 4 mp sec. Of course, t h e 7 ray for this time spectrum would have a fu ll width at half maximum o f a b o u t 3 mp s e c . Pulse spectrum. Figure 11 is a block diagram of one of the systems used to take pulse spectra. Pulses from the photomultiplier start the time converter and delayed beam pulses stop the converter. Output pulses from the time converter are amplified and fed into a single-channel analyzer. These pulses are used in coincidence with the slow pulses from the DD2 am plifier to gate the multichannel analyzer. Figure 12 shows a typical pulse spectrum for ground-state neutrons from Be (He ,n)C . The pulse spectrum in the figure has had the background subtracted. Background subtraction was accomplished in the following manner. Output pulses from the A 8 am plifier were fed directly into NUMBER OF COUNTS 0 0 0 1 0 0 4 0 0 6 0 0 8 0 0 5 0 0 7 0 0 9 n lgtPt 3m H* m. 3 Path Flight and 0 10 4 10 8 200 0 2 180 160 140 120 100 0 8 0 6 i. . ieo-lgtSetu o etos rm '(e,>05 t0|b= 0°, = |ob 0 at from C'^(He^,r>)0'5 Neutrons forSpectrum Time-of-Flight 8. Fig. N RY EES F 0 OFENERGY LEVELS 5.25 6.79 H NE NUMBERCHANNEL 6.86 20 .2 5 ORNL-LR- DWG 54281 ORNL-LR- UNCLASSIFIED E 3 ^ 2 Mev 2 ^ 3 UJ RELATIVE COUNTS 1000 1200 400 600 800 200 0 0 0 0 0 10 4 10 8 ' 0 20 4 260 240 220 200 ' 180 160 140 120 100 80 60 40 Fig. 9. Time Spectrum for Li7(He3,rj)B? ot H , * 2.35 Mev, 2.35 * , H ot Li7(He3,rj)B? for Spectrum Time 9. Fig. HNE NUMBERCHANNEL 0=0° and Flight Path 6 m.6 Path Flight and ORNL—LR—DWG 9 7 8 3 5 UNCLASSIFIED uo 00 RELATIVE COUNTS 2400 2800 2000 1600 1200 800 400 40 60 Fig. 10. Time Spectrum for Be9(He3,n)C’ 1 at at 1 Be9(He3,n)C’ forSpectrum Time 10. Fig. 80 100 120 CHANNEL NUMBER 140 E 3 = 2.5 Mev, 32.5 = He" 0=0° M 180 ad lgt ah6m ^ m.6 Path Flight and 200 ORNL-LR—DWG 53880 220 UNCLASSIFIED 240160 260 u> 4 o UNCLASSIFIED 7046 ORNL-LR-DWG 53877 TARGET PLASTIC SCINTILLATOR DELAY FAST SLOW TIME-PULSE PREAMPLIFIER HEIGHT CONVERTER MODEL DD2 AMPLIFIER' PREAMPLIFIER MULTI-CHANNEL ANALYZER SINGLE MODEL A8 CHANNEL AMPLIFIER ANALYZER GATE SINGLE COINCIDENCE CHANNEL CIRCUIT ANALYZER Fig. 11. Block Diagram for Pulse Spectrum. RELATIVE COUNTS 0 6 1 120 0 4 0 8 0 2 4 6 8 10 2 10 6 10 0 20 240 220 200 180 160 140 120 100 80 60 40 20 0 ------ • " • • • • < ► • i. 2 Ple egtSetu o .3Mv etos from Be^HeLnJC1'. Mev Neutrons 9.83 forSpectrum Height Pulse 12. Fig. • ------• • i = . _ — v ■ i l . ------*•. • * * * . . " • • ------» • O• • ° • • • • HNE NUMBER CHANNEL • < »• • ------► ••• » r - 4 ' Jf ------• • • 1 1 t ------• • • < RL RDG 53878 LR-DWG ORNL- * • • UNCLASSIFIED ------• ------<> • • • < ------*•••< H ■P" UNCLASSIFIED ORNL-LR-DWG 59130 PLASTIC SCINTILLATOR 7046 TARGET DELAY SLOW FAST T1ME-PULSE PREAMPLIFIER HEIGHT CONVERTER MODEL DD 2 AMPLIFIER PREAMPLIFIER SINGLE MODEL A8 CHANNEL SIGNAL AMPLIFIER ANALYZER RCL 2 0 4 8 CHANNEL ANALYZER BACKGROUND PULSE SINGLE SINGLE CHANNEL CHANNEL PROMPT COINCIDENCE GATE MEMORY SPLITTER Fig. 13. Block Diagrom for Pulse Spectrum with Memory Splitter. the multichannel analyzer, which was gated by the timer single channel. In this manner the single-channel window could be set directly on the neutron group whose pulse spectrum was being studied. In order to look at the background pulse spectrum a sim ilar procedure was followed, except that the single-channel window was set in the background region near the peak being studied. If the background was time dependent, some errors would be introduced by taking the pulse spectra and back ground spectra at two different times. This difficulty was overcome with the addition of a "memory splitter" on the IK)L 2048 channel analyzer (Fig. 13)* The windows of the single channels were set in the manner described above, except the pulse spectrum was stored in channels O- 5II and its background was simultaneously stored in channels 512-1024. A Mosely Precision plotter was used to plot the results directly from the memory of the RCL 2048. If the plotter was set so that the background spectrum was plotted directly below the pulse spectrum, graphical subtraction could be performed to get the true pulse spectrum in a very short time. In the course of the experiment pulse spectra were taken once a day. These spectra were usually taken with 9 a thick Be target and a flight path of 3 meters. This target would enable us to measure pulse spectra from four groups of neutrons in about 2 hours. With this precaution any gain shift that occurred in the photom ultiplier tube or am plifier system could be observed. The error introduced into the efficiency calculation of the detector by gain shift in the am plifier system w ill be discussed in the next chapter. CHAPTER I I I PRESENTATION OF nATA In this chapter several topics w ill be discussed concerning the experimental data and the necessary calculations for its final form. The first section is concerned with the efficiency of the plastic scintillator for single and multiple scattering. In the second section pulse spectra measurements and calculations are discussed. Sections 3> k, 5, and 6 treat the three reactions studied and the presentation of the data. In the final section, errors are discussed for these measure m ents . I . PLASTIC SCINTILLATOR EFFICIENCY Single scattering calculations. Plastic scintillators are among the most efficient detectors for neutrons of energies from .5 Mev to 15 Mev (Mu 58)• Hie recoil proton spectrum in the scintillator can be evaluated to determine the original neutron spectrum (Se 5^, Cr 51)* However, in most experiments several groups of neutrons are present with their associated 7 rays. In order to look at the pulse spectrum of a specific neutron group additional instrumentation is re quired. In tim e-of-flight experiments the pulse spectrum can easily be gated with the time spectrum so that observations can be made on a single neutron group. The circuitry used in our experiment to accom plish this gating is described in Chapter II. The single scattering efficiency ( ) for a very thin plastic scintillator containing only hydrogen and. carbon is given by: -aZr x - g \ ~ w here a = V i + n l 2 ° l 2 n^ and n ^ - number of hydrogen and carbon atoms/cm and cr^ = neutron scattering cross sections for hydrogen a n d c a rb o n Zq = thickness of the crystal. — - Of course equation (10)ignores the non linear response of the crystal light output (Bi 51, Bi ^2, Ta 5 1 ) nnd edge effects (Sw 5 6 ), that is, the loss of recoil protons from the ends and sides of the crystal. The pulse spectrum for equation ( 1 0 ) would be a rectangular distribution with a maximum pulse height proportional to E^ (energy of neutron group being studied). For thick crystals (where Zq is of the order of a mean free path for neutrons of energy E ) multiple scattering correc tions must be made to determine the efficiency of the crystal (Cr 5 1 )* 12 These corrections should include the variation of the n,p and n,C scattering cross sections as a function of energy and angle (Hu 55)* The best way to correctly solve this complex problem is to make a Monte Carlo calculation. Several "special geometry" calculations of this type have been made (Cl 52, Da 6 0 ). However, with the increasing use of plastic scintillators as neutron detectors, more of these cal cinations should be made available for the experimenter. k6 Multiple scattering calculations. For this report average multiple scattering corrections w ill "be made for equation (10). In order to make these calculations the following assumptions are made: (i) The recoil carbon nucleus produces a negligible pulse (Bi 51) 12 (ii) The n,C and n,p scattering cross sections are isotropic in the center of mass system (Ma V 7 , Ba 5 1 ) 1 p (iii) An average value through a resonance in the n,C scattering cross section can be used 12 (iv) The neutrons once scattered from C have an average Tt energy E’ = ^ J' E'(©) sin © d 9 where E*(©) is de- 0 12 termined by the kinematics of the (n,C ) scattering process (see Appendix) (v) The neutrons E' travel an average path length Z^ before a second scattering occurs. With these assumptions the average efficiency is given by: f V n121’l2(l * C > + 1 1 e2 = 1 I ----- :------5 ^ ------} M where the prime indicates that the scattered neutron energy in (iv) is to be used in calculating o ^ ', p 1, and a1. For a (V x 3") crystal, assumption No. (iii) is not too critical. A factor of 2 increase in Z^ gave only a few per cent change in e^. A plot of as a function of incident neutron energy is shown in Fig. l l . Double scattering from hydrogen w ill not change since the two events occur in such a UNCLASSIFIED ORNL-LR-DWG 58630 \\ \ V / i X L w / r ■— - i j / — • i 0 2 4 6 8 10 12 NEUTRON ENERGY (Mev) Fig. 14. Calculated Efficiency of 4 x 3 in. Plastic Scintillator. i+8 f \ \ short time ( J that the phototube records them as a single event. This summing w ill of course be smeared out because of the non-linear response of the crystal. The effect of double scattering from hydrogen on pulse spectra w ill be discussed in the section to follow. I I . PUU3E SPECTRA For crystals with high efficiencies (e^ > 10^>) multiple scat tering w ill cause a noticeable change in pulse spectra. The average effect is to produce a peaking on the high energy end of the spectrum. Fig. 12 shows this effect for 9*83 Mev neutrons from Be^{He^,n)C^' be tween channels 120 and 170. For an infinitely thick plastic scintil lator the pulse spectrum for neutrons of energy E^ would be a single line at pulse height E^. Of course the line would be broadened because of crystal response. In most experimental arrangements it is necessary to set a lower bias voltage (£„) so that only pulses above the bias level are counted. Sj The reason for setting the bias is chiefly to eliminate photomultiplier tube noise or low energy neutrons. For tim e-of-flight experiments the bias level is usually determined by the best signal to noise ratio for the lowest energy neutron group that-is being studied. Since some recoil proton pulses from neutrons of all energies fall below the bias it is necessary to correct for these lost counts. This correction is made by determining the area of the pulse spectrum curve under the bias level. The ratio of this area to the total area is then the num ber of recoil proton pulses lost. The spectrum fraction (f) is the ratio of the number of counts recorded to the total number present. For a flat pulse spectrum f is given by; f = 1 - r r • ( 1 2 ) N If the multiple scattering of the neutrons in the crystal is considered the pulse spectrum is usually more difficult to evaluate. The difficulty comes in trying to determine the shape of the spectrum curve under the bias level. Once its shape is known f is given by; E o J N(E)dE EB f = e------(1 3 ) Jf ° N(E)dE o where IKE) is the pulse spectrum curve for neutrons of energy E. Swartz (Sw 5 6 ) has shown that for double scattering by hydrogen N(E) takes the form; N(E) = 1 + A IA = --1) v ! ) -;E„”m o I (14) where A and m are determined from the efficiency (e^) curve by the expression; = Ae“m (15) and E^ is the energy of the incident neutrons. Fig. 15 shows a theoretical pulse spectrum of 10 Mev neutrons for a 4" x 3" plastic scintillator. In this work the spectrum fraction curve was determined i N(E) O 0 4 2 5 0 i. 5 Tertcl le pcr o 1-e Nurn fr4 i. asi Scintillator. stic la P in. 3 x 4 for Neutrons 10-Mev of Spectra ulse P Theoretical 15. Fig. US HIH (Mev) HEIGHT PULSE 6 4 RLL-W 58629 ORNL-LR-DWG UNCLASSIFIED 8 10 VJ1 O 51 above the bias by measuring and calculating its value. The two curves were normalized with a 5$ normalization factor to a single curve. Below the bias the calculated value of f was used. Fig. 1 6 shows the product (e^f) for a given bias setting. In order to determine the number of neutrons in a time spectrum group, the recorded number was divided by (e^f). The probable error associated with the overall efficiency of the scintillator w ill be discussed in the last section of this chapter. III. THE Be9 (He3 ,n )C 1;L REACTION Figure 10 shows a time spectrum for this reaction. In the spectrum are shown neutrons from the ground state (channel 2 2 9) those from the first seven excited states. The peak in channel 125 is composed of neutrons from the unresolved fourth and fifth excited states. This time spectrum shows the maximum number of resolvable groups obtained for the reaction. In order to see these groups it was necessary to set the bias voltage at a relatively low value (l.l Mev). To illustrate this point; the peak in channel 125 is for neutrons of 1.95 Mev while the one in channel 229 is for 10 Mev neutrons. For the differential cross sections two bias settings were used (l.l Mev and 2.5 Mev). The higher setting provided a better signal to noise ratio for the high energy groups. The yield for this reaction was copious enough that 6 m e te r flight paths could be used when available. However, the dimensions ABSOLUTE EFFICIENCY (% ) 30 40 0 6 50 20 i. 6 Aslt Efcec f3 -n Plsi Sitlao wt Ba Lvl t . Mev. 1.1 at Level Bias with Scintillator lastic P 4-in. x 3 of Efficiency Absolute 16. Fig. RLL-W 60372R ORNL-LR-DWG UNCLASSIFIED vn to 53 of the scattering area allowed only 3 meter flight paths at the back a n g l e s . Angular distributions were measured for neutrons from the 1 'I following states of excitation in C , ground (Pig. 17)> first (Fig. 18), second (Fig. 19)> third (Fig. 20), and fourth (Fig. 21). These measurements were made at a He 3 energy of 2.075 Mev. Excitation functions were measured at 0° and 81.5° for the same states, ground (Fig. 22), first (Fig. 23), second (Fig. 24), third (Fig. 25), and fourth (Fig. 26). Figure 27 shows the sum of these excitation curves. For com parison the Chalk River data at 0° for the same reaction are also on the curve. This data was normalized at E ^e 3 ~ 2 Mev t o th e ORNL d a t a . It was necessary to normalize the data since it was reported only as a relative yield. IV . THE C1 3 (He3 ,n ) 0 15 REACTION F ig u re 8 shows a time spectrum for this reaction. In the figure the ground state neutrons (channel 172) have an energy of 9*^-3 Mev and those from the third excited state (channel 139) are 2 .9 8 Mev. These two peaks represent the only resolved groups for this measurement. A flight path of 3 meters gave a time separation of 16 mu se c between n^ and the unresolved group n^ + n^. There was no evidence of neutrons from C^(He 3 ,n)0'L^ even at the highest bombarding energy. In F ig . 8 they would appear in about channel 90. UNCLASSIFIED ORNL-LR-DWG 60368 .7.40 6.77 6.50 4.75 4.26 1.99 ENERGY LEVELS OF C 0 40 80 120 160 CENTER-OF-MASS ANGLE (deg) Fig. 17. Angular Distribution lor Ground State Neutrons from Be 5(He3,n)C1' at £ , = 2.1 Mev. , DIFFERENTIAL CROSS SECTION (mb/steradian) Q5 1.0 Mev. 0 i. 8 Aglr itiuin f s Ectd tt Nurn fo Be^He^nJC n ^ e H ^ e B from Neutrons State Excited 1st of Distribution Angular 18. Fig. ENERGY LEVELS OF C OF ENERGY LEVELS 40 .7.40 4.26 4.75 6.50 6.77« 1.99 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS 80 N-RD 60371 G RNL-LR-DW O 120 UNCLASSIFIED 15 at at E , = 2.1 2.1 = , 160 I V I V f . Mv Ho Mev. 2.1 DIFFERENTIAL CROSS SECTION (mb/steradian) 0.75 0.25 0.50 i. 9 Aglr srbto fr n Exie Stt Netos rm ^He^nJC e^fH B from eutrons N tate S xcited E 2nd for istribution D Angular 19. Fig. ENERGY LEVELS OFC11 40 ‘4.26 .7.40. 4.75- 6.77. 6.50 ETRO-AS ANGLECENTER-OF-MASS (deg) 1.99 80 ORNL-LR-DWG60369 120 UNCLASSIFIED 31 a t t a E 3 160 56 , DIFFERENTIAL CROSS SECTION (mb/s+eradian) e. H* Mev. 0.5 1.0 g 2. nua Ditiuin f r Exis Sae urn fo Be He JC n e^ fH e’ B from eutrons N State xcitsd E 3rd of istribution D Angular 20. ig. F 0 0 4 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS NRY EES OFC LEVELSENERGY '6.50 .7.40 4.26 4.75. 6.77 1.99 ORNL-LR-DWG60370 120 UNCLASSIFIED 11 t £ at 3 2.1 = 57 16080 DIFFERENTIAL CROSS SECTION (mb/steradian) 2.0 .0 3 . Mev. 2.1 1.0 g 2. nua Ditiuin f4h ctd tt Netos rm ^He^nJC e^fH B from eutrons N State xcited E 4th of istribution D Angular 21. ig. F 0 40 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS NRY EES OFC ENERGY LEVELS 80 .7.40 4.26 4.75 6.50 6.77 1.99 RLL-W 60367 6 3 0 6 ORNL-LR-DWG 120 UNCLASSIFIED 1 1 at at E 58 160 ^7T, DIFFERENTIAL CROSS SECTION (mb/sterodian) 0.4 0.8 0.2 0.6 1.4 1.0 i. 2 Ectto Fnto fr e(e,) 1 Gon Sae Neutrons. State Ground '1, Be9(He3,n)C for Function Excitation 22. Fig. 'LAB = 0° LAB 81-5 = £“He3 (Mev) 2 ENERGY — LEVELS OFCH ORNL-LR-DWG 55356 4.26 4.75 6.77 7.40 6.50 1.99 UNCLASSIFIED 3 59 .DIFFERENTIAL CROSS SECTION (mb/sterodian) 0.4 0.6 0.3 0.2 0.5 i. 3 Exiain ucin o Bo for Function xcitation E 23. Fig. NRY EES OFC ENERGY LEVELS 4.75 6.50 4.26 6.77 7.40 F He3 9 (H* (Mev) 2 3 MOH UV FOR CURVE SMOOTH LAB 81.5° 0 = ,n)C 1 s Ectd State. Excited 1st RLL—W 55362 ORNL-LR—DWG LAB81-5 = A “ ° LAB° “ UNCLASSIFIED 60 3 blcs DIFFERENTIAL CROSS SECTION ( mb/steradian) 0.6 0.4 0.5 0.3 0.2 0 NRY EES F C OF LEVELS ENERGY i. 4 Ectto Fnto (r e(e,n)C'2d xiao State. Excitatod 2nd ' C ) n Be?(He3, (or Function Excitation 24. Fig. 4.26 4.75 6.50 6.77 7.40 E He0 3 (Mev) MOH UV FOR CURVE SMOOTH DATA ° 0 RLL-W 55363 ORNL-LR-DWG UNCLASSIFIED A 81.5 1 LAB-8 A _0 LAB _ l 6 -^-.DIFFERENTIALD CROSS SECTION (mb/steradian) .4 0 0.2 0.6 0.8 Fig. 25. Excitation Function of the 3rd Excited State for Be^(He^,«)C^ '• Be^(He^,«)C^ for State Excited 3rd the of Function Excitation 25. Fig. NRY EES F C OF LEVELS ENERGY MOH UV FR 0 FOR CURVESMOOTH • •/'' ' / • • ▲ 77 .7 6 26 .2 4 75 .7 4 0 .4 7 50 .5 6 .99 E He3 (Mev) 3 2 A = 81-5 = LAB u " LAB RLL-W 55420 ORNL-LR-DWG UNCLASSIFIED 3 62 DIFFERENTIAL CROSS SECTION (mb/steradian) 0 3 2 Fig. 26. Excitation Function for 4th Excited State of Be, (He3,n)C* *. (He3,n)C* Be, of State Excited for4th Function Excitation 26. Fig. NRY EES F C OF LEVELS ENERGY 4.75 4.26 6.50 6.77 7.40 1.99 f He3 (Mev) 3 2 MOH CURVESMOOTH A - 81'5 - LAB LAB “ RLL-W 55418 ORNL-LR-DWG UNCLASSIFIED 63 .DIFFERENTIAL CROSS SECTION (mb / steradian) 3.0 6.0 4,0 5.0 2.0 0 0 g. 7 Toa Exiain ucin fr B He (H BB, for Functions xcitation E otal T 27. . ig F 1.5 0° CHALK0° RIVER E He3 (Mev) 0° ORNL0° 2.0 3 ,n)C ORNL-LR-DWG 61538 11 UNCLASSIFIED • 2,5 6b Absolute cross sections could not be measured since the thickness of the target was not known. Excitation functions were measured at 0° for the ground state (Fig. 28) and third excited state (Fig. 2 9). The yield curves were also measured for these states at 90°, ground (Fig. 3 0 ), and third ( F ig . 3D- Angular distributions were measured at a He energy of 2.66 Mev. They were made for the ground (Fig. 32) and third excited state (Fig. 33). For this reaction the signal to noise ratio was low at the back angles. Because of this high background, considerable error was pro duced in the angular distribution measurements at these angles. V. THE L i7 (He3 ,n )B 9 REACTION Figure 9 shows a time spectrum for this reaction. The neutrons for the ground state appear in channel 239* and have an energy of about 11.70 Mev. Those in channel 222 are from the first and second excited 9 states in B . In this picture they are unresolved Bince their flight time difference is only k mp sec. Between the ground state and the first excited state there is a flight time difference of 1 0 . 2k mp s e c . Calculations show that the first excited state neutrons in Fig. 9 h av e an energy of 9*35 Mev. The broad continuum present is a consequence of four body breakup given by; RELATIVE DIFFERENTIAL CROSS SECTION 10 0 4 6 8 2 . 15 . 19 2.1 1.9 1.7 1.5 1.3 g 2. ctto Cre o C for Curve xcitation E 28. ig. F 0 deg = 0 6 He3 ENERGY ENERGY He3 1 3 {He 3 n)0 ,n 1 5, Ground S tate N eutrons at at eutrons N tate S Ground 5, (Mev) RLL-W 55914 ORNL-LR-DWG UNCLASSIFIED Q «= 0°. 66 RELATIVE DIFFERENTIAL CROSS SECTION 10 0 4 6 2 8 . 15 . 19 2.1 1.9 1.7 1.5 1.3 F ig . 29. E xcitation Curve for C *^{H e^,n)0*^( 3rd Excited State N eutrons at at eutrons N State Excited 3rd e^,n)0*^( *^{H C for Curve xcitation E 29. . ig F He3 ENERGY ENERGY He3 (Mev) RLL-W 55913 ORNL-LR-DWG UNCLASSIFIED 6 * 0°- * 67 RELATIVE DIFFERENTIAL CROSS SECTION 0.8 .4 0 0.6 0.2 i. 0 Ectto Cre o C for Curve Excitation 30. Fig. 1.7 13 (He e H 3 ,n )0 1s, Ground State Neutrons at $ |ab -= 90°. |ab $ at Neutrons State Ground 1s, )0 ,n 3 Mev) v e (M Y G R E N E 2.1 .3 2 N-RD 8 2 6 8 5 G RNL-LR-DW O UNCLASSIFIED .5 2 .7 2 CD ON RELATIVE DIFFERENTIAL CROSS SECTION 0.4 0.5 0.6 0.7 0.3 0.2 0.1 0 i. 1 Ectto CrefrC^He^nJO1, r Ectd tt Nurn at ot — t 90°. |o 0 t a Neutrons State Excited 3rd 15, O J n ^ e H ^ C for Curve Excitation 31. Fig. e H 3 Mev) v e (M Y G R E N E 2.3 RLL-W 58627 ORNL-LR-DWG UNCLASSIFIED 2.5 2.7 VO ON RELATIVE DIFFERENTIAL CROSS SECTION .4 0 0.6 0.2 0.8 .6 e, i Pt 3 m. 3 Path t h lig F Mev, 2.66 i. 2 Aglr srbto fr rud ae urn fo C' C from eutrons N tate S Ground for istribution D Angular 32. Fig. 20 140 0 4 CENTER MASS OF ANGLE (deg) 80 0 6 100 3 (H» 3 ,n)O ls a t t a ls ,n)O 1200 RLL-W 59131 ORNL-LR-DWG UNCLASSIFIED E 0 7 160 UNCLASSIFIED ORNL-LR-DWG 59132 2 LI 0 o I - 0 .8 LlJ Q 0.6 S 0 .4 0.2 0 0 20 4 060 80 100 120 140 160 CENTER OF MASS ANGLE (deg) Fig* 33. Angular Distribution for 3rd Excited State Neutrons from C 13{He3,n )0 ,s at E 3 = 2.66 Mev, Flight Path 3 m. He 7 2 He3 + Li7 -» B10 + 17.75 "» B10 -> He^ + He^ + n + p + 9.61 Mev. ( l 6 ) This continuum is present at a ll energies below that of the ground state group. Figure 3^ shows an energy spectrum for this reaction that has been corrected for counter efficiency. Note that in this figure i 6 plotted against E^. The peak a t k , 5 Mev curiously appears 9 where neutrons from the 7 Mev level in B should be located. This group might be the broad 7 Mev level. The analyzed data is for the ground state only, since the first and second excited states could not be resolved. It includes an exci tation function at 0° (Fig. 35) and an angular distribution at 2.075 Mev (Fig. 36). Because of the presence of the four body continuum, special background subtraction techniques were used for this reaction. These techniques w ill be discussed in the last section of this chapter. V I. MEASURED Q VALUES In order to determine the Q of a nuclear reaction it is neces sary to measure th e ' energy of one of the reaction products at a known angle and machine energy. With this information and the masses of the reaction, the kinematic equations can be solved for the Q, v a lu e. In (He ,n) reactions several groups of neutrons are usually seen, corre sponding to energy levels, in the residual nucleus. For this reason it is necessary for maximum precision to make the energy measurements at (/ib/steradian • Mev) 30 42 48 36 54 24 0 6 0 0. 8 8 .1 -0 i H -/7 +He Li 346 4 .3 9 2 2.37 7.0 3 i. 4 Eeg Setu o Li L for Spectrum Energy 34. Fig. 4 5 Li7(He3, 2. 0=0, p=3m 3 = fp 0°, 0 = , 5 7 .0 2 3= f En (Mev) 6 7 (He 3 ,n)B , at at , ,n)B 7 0 ■= 0°. n) 8 B -— B9 RLL-W 55454 ORNL-LR-DWG UNCLASSIFIED Fig. 35. L i7(He3,n)B9 Excitation Function at at Function Excitation i7(He3,n)B9 L 35. Fig. m e H ^ A 3 ▲ 6 & A « o Gon Sae Neutrons. State Ground for ° 0 « A AA i A RLL-W 55445 ORNL-LR-DWG A A UNCLASSIFIED A t A -3 -F-- —, DIFFERENTIAL CROSS SECTION (mb/steradian) 0 4 5 2 3 Fig. 36. Angular D istribution of Ground State N eutrons from LI^(H e^,n)B^ at at e^,n)B^ LI^(H from eutrons N State Ground of istribution D Angular 36. Fig. 1 O 0 4 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS - 188 8 8 .1 ■ -0 NRY EES OFB ENERGY LEVELS Be8+ 346 4 .3 9 p B9 0 8 ______7.0 . 7 2.3 2.83 RLL-W 60366 ORNL-LR-DWG 120 UNCLASSIFIED E 3 =. Mev. *=2.1 75 160 back angles where the neutron groups have maximum energy separation. After the neutron flight time has been measured the energy of the group is given by; (1 7 ) where L is the flight path in meters and t is the flight time in mp. sec. Solving the kinematic equation y i e l d s ; ( 1 8) Table I shows the measured neutron energies and Q values for the reactions studied. With our time resolution capabilities (4 mu sec) neutron energies below 15 Mev were measured within yjo. This gave a somewhat less accurate measurement of Q since the middle term in equation (l 8 )is large compared to the cosine tenn and the coefficient of En in the first term is nearly unity for these three reactions. VI. DISCUSSION OF ERRORS There are many factors which can cause considerable error with measurements of this type. Only the more important sources w ill be discussed in this section. In the final paragraph estimates w ill be made with regard to the coupling together of all of these errors for this experiment. 77 TABLE I MEASURED Q VALUES State Measured Energy of Neutrons Measured Q Reported Q Be9(He3,n)C11, ©L = 70°, E ^ = 2.075 Mev Kq 8 .7 8 7 -6 1 7 .5 7 Nx 6.79 5*50 5-58 N2 ^-59 3.17 3.31 N3 J^.13 2 .6 8 2 .8 2 2 .5 6 1.037 1.07 C1 3 (He3 , n ) 0 1 5 , ©L = 88° , ^ 3 = 2 . 6 2 Nq 8 .4 7 7 .1 4 7 .1 3 n 3 2 .7 5 . 91^ .9 8 L i7 (He3 ,n )B 9 , 9h = 80°, E ^ = 2.075 Nq 9.90 9.^7 9.35 n l 7 .6 7 . 7 .0 1 6 .9 8 78 Current integrator checks were made every 2^ hours. Measurements of the calibrated value were reproducible to within 1% for this period of time. All measurements were reproducible to within 2$ for a three month period of time. It Is therefore assumed that the error associ ated with the current integrator was controllable to within 1$ . Amplifier d rift was checked by using an ORNL model P.G .I. mercury pulser. Pulses were fed into the pream plifier of the system being checked. The position of the output pulse from the am plifier was then displayed on the multichannel analyzer. In this same manner linearity checks were also made on the am plifier-analyzer system. Over all gain checks on the photom ultiplier-am plifier system were made every 2k hours. These were made by observing the pulse spectra of neutron 9 groups with known energies. For this purpose a thick Be target was used at a flight path of 3 meters. With this arrangement the energy resolution was good enough that gating from the time spectrum could easily be used. From these pulse spectra, neutron pulse heights were plotted as a function of neutron energy. These plots were reproducible to w ith in 5%. For the absolute differential cross section measurements target 9 thickness uncertainty produced considerable error. Be target thick nesses were analyzed by chemical and spectroscopic methods. These measurements were always in agreement to within 10%. Variations in the 9 thickness of the Be layer as a function of the radius of the target were also studied by spectroscopic analysis. These variations were never greater than 10%. For the lithium targets, thicknesses were 79 determined “by weighing before and after evaporation. This method was fairly accurate since LiF is very easy to evaporate. Relative yield measurements for LiF targets of various thicknesses indicate that this method is easily good to 10$ . y o 9 For the reaction Li (He ,n)B it was necessary to subtract the 9 continuum neutrons from those of the ground state group of B . This was done by extrapolating the edge of the continuum (Fig. 9) through the ground state region. Since the calculated shape of the continuum is not known a straight line extrapolation was used. The area under the curve was then subtracted from the ground state group. This method seemed to yield consistent results. Efficiency calculations for the plastic scintillator are probably good to within 10$. The error is produced mainly by the fact that the pulse spectra curve could not easily be determined below the bias level. For the low energy neutron groups 50$ or more of the recoil proton pulses fell below the bias value and therefore were not counted. The 10$ error mentioned above is the uncertainty in determining the number of pulses that were not counted. Of course the overall efficiency is much better than 10$ for the higher energy neutron groups. Upper lim its on ail of the errors for these reactions seem to indicate that the relative differential cross sections are good to w ith in 1 5$ while the absolute measurements should be good to about 30$. CHAPTER IV CALCULATIONS AND RESULTS In the first section of this chapter a plane wave analysis of (He ,n) reactions is treated. This section is followed by a distorted wave calculation of the reactions. In these calculations the distortion is produced by interaction with both the Coulomb field and the nuclear "optical" potential. In the final section the theoretical fits to the experimental data w ill be discussed and the spin and parity assign ments made from these fits w ill be given. I . PLANE WAVE CALCULATIONS Butler theory has been quite successful in explaining differential cross sections and their angular dependence in terms of "stripping" calculations for deuteron induced reactions (Ge 53j Hu 5 2 , F r 53> Da 53)- The theory has been applied in most cases to (d,n) and (d,p) reactions in the intermediate and high energy range. More recently the inverse stripping process or "pickup" theory has been successful with (p,d), (n,d) and (d,t) reactions (Ne 5 2 , Fu 5 2 ). In the last example a mass three particle is involved in this inverse "stripping" process. This introduces the possibility that triton and He foreward "stripping" reactions might take place. Some (He^,d) reactions have been fitted with Butler type curves (Fo 5 9) however, more recently the two-nucleon transfer reactions have become of interest. This is due in part at least to the recent "double stripping" theory proposed by Newns (Ne 60). Several workers have been successful in calculating angular distributions with this theory for (t,p) reactions (Ja 60, Ja 60a, Hi 59)* Also for He in duced reactions the theory has shared equal success. Proton groups -j /T ^ "I O from 0 (He ,p)F have been fitted from 5 to 9 Mev by Hinds (Hi 59a). In addition the theory has produced good fits for C^XHe^n^O1^ neutrons above 4 Mev (Ga 60, To 60). However it should be mentioned here that at these higher energies the angular distributions for this reaction show definite stripping peaks (Fig. t9). A Butler plane wave analysis can easily be used to fit the experimental data (we have made both plane and distorted wave calculations for this reaction, they w ill be discussed in the last section of this chapter) with an Z - 0 t r a n s f e r . At lower energies all of the (He ,n) and (He ,p) reactions reported thus far seem to be more complicated in structure. It would indeed be surprising if the simple form of the "double stripping" theory could be used to fit this low energy data. That is, in the calculations reported for the C'*"^(He^,n)0^ reactions (Ga 60, To 60) no attempt was made to use the form factor proposed by Newns (Ne 60). The justification being that the neglect of Coulomb and nuclear distortion would outweigh the importance of this factor. In order to look at the predictions of this model, its formulation for (He ,n) reactions w ill be given. The "double stripping" differential cross section has the form (for the reaction A(He^,n)B); 8 2 da di 2 (1 9 ) In equation ( 1 9) -8 has its usual meaning of to tal angular momentum transfer for the reaction, r is the radius of the interaction, Q, 3 o is the momentum transfer vector (see figure), and the A^'s depend on the in itial and final configuration of the states Involved in the r e a c t i o n . The spin selection rules are given by; ( 20) J B “ J A + £ + S w here & and s are the orbital angular momentum and spin of the captured O —> particle. For (He ,n) and (T,p) reactions s is only allowed the value zero. It should be pointed out here that in the case of the (He ,n) reaction the particle being captured is a di-proton. The Pauli prin ciple demands its capture with its spins anti-parallel. The same is true for the (T,p) reaction where a di-neutron is being captured. Since there is no spin-orbit interaction in the calculations the spin of the observed particle is not allowed to flip. Thus the selection rules allow unique spin assignments if either A or B has spin zero. Even if this is not the case the range of spin assignments is greatly reduced —) by s being zero. It would seem that this model is quite a valuable 8 3 spectroscopic tool at these higher energies. However it was pointed out by Gale (Ga 60) that for the & = 0 transfer the shape of the angular distribution for "double stripping" is indistinguishable from that of a "knock on" process, This is true since in both cases a z e ro ^*1 order Bessel function is being squared to prodace the angular distribution. Theoretical predictions of the absolute magnitude of the cross sections should solve the problem when more is known about the configurations being studied. The theoretical approach made in this thesis is, in general, to look in detail at the result of distortion effects for the three (He ,n) reactions studied. These effects are perhaps best illustrated when they are compared to plane wave calculations for the same reaction. These plane wave calculations were made in two fashions. A discussion of the first method of making these calculations w ill follow. In the second formulation the IBM code was used to calculate the transition amplitudes without the Coulomb and nuclear distortion. This reduces to solving for the appropriate Bessel functions, or making a plane wave calculation. For these plane wave calculations several simplifying assump tions will be made. First of all it is assumed that there is no distortion present, that is the wave function of the relative motion —> —» ik • y can be represented as e . Secondly both the structure and finite 3 size of the incident He particles will be ignored. Furthermore it is assumed that the capture of the di-proton is a one-stage process with 81+ 3 the born approximation being valid. The interaction between the He and the neutron is assumed to have the form; V = V 6 (r - r ) . (21) He ,n 3 Initial and final wave functions can be w ritten in the product form; i k 3 ' r 3 *i = e I ^i 9„ f T Be ik *r n n f = e _ 0 ( 2 2 ) y v c w here hl V 1/2 I 3/2 O O W I *X/2 \ V, rn^rn *1 an d 1 /2 £ 3 J f 11 V O Ri . ( r ^ ^ 1 /2 (2 3 ) Be Be m3m£. m3mI. In equations ( 2 3 ) the relative orbital angular momenta are designated by th e £*s and their corresponding projection on the Z axis by the mfs. The A’s are the appropriate fractional parentage amplitudes. Initially the Y. and Y. ^ are spherical harmonics of the two separate co- 1 . 3 ordinates hut after the integration over V .. the co-ordinate He ,n systems of the two vectors are the same. The matrix elements for the final transition amplitudes are then given by; M „ e«-r Ri(r) E* (r) <21*> v i y 3 iQ *r where Q has been made the axis of quantization and e can be expanded in terms of JT(Qr). Q is the momentum transfer for the inter- action. It is given by; Q = K - . ( 2 5 ) In equation (2t) R (r) and R,, (r) are radial wave functions (spherical 3 3 Hankel functions are used) describing the neutron and the He as 2 ft 2 particles moving freely with energy E = (ik) . dm Now after the angular integrals are made for (2U) and the above substitutions made for the respective R (r)'s, the radial integral < I > becomes; oo < I > = J JL(Q r)h^ (i^r)!^0) (ip 3r ) r 2 d r ( 2 6 ) R- 1 3 o 8 6 ■where ./*A a n d p 3 = K ■ ft Now the differential cross section for the reaction w ill be given by; r U?L " “ c J X < I > 1 ) 0 0 0 (2 7 ) The appropriate Clebsch-Gordan coefficients w ill be discussed, later. It is obvious at this point that the shape of the angular distribution is determined by < I >. A solution to equation (27) w ill be given for only an & = 2 transfer. The procedures followed for its solution with other angular momenta transfers contains the same formu l a t i o n . W ith a n & = 2 transfer equation (26) becomes; 0 0 3. Q Q q . j r _ < I > = / 3_ — ) s i n p ^r cos p Py 2 2 V 9 ■Plp P i P ' L^3 P p2p2 - e " a p P2 ' dp ( 28) ■ Q3 • where p = Qr. p = QR and a = o o Now it can be seen that < I > is of the form 8 7 oo —f V 1 -ap s i n p -a p c o s p < I > = a e dp (2 9 ) / , V N +I M M M p N o Therefore it is convenient to define the following integrals; ao e ap sin p dp I w H------ an d ao -ap cos p dp (3 0 ) N N With these definitions < I > takes the following form; < I > = - I, + I_ - 3 " V . r 2 r LW Pi P3 PxP3 P i P3 2 2 / 2 - 2 2 "3 J"2 3 3 ato 3Q to B 2 + □ o 2 y 3 " 0 2 2 ^ ( 3 1 ) P i P 3 P1 P 3 P>2_ P 3 8 8 o ° Now the 1^ and 1^ integrals can be expressed in terms of 1^ and 1^ w h ere; co f e ”ap s i n p dp I 1 po a n d oo j o Jr e “a P cos p dp ^ 2 ) po This is done by expanding I jj and 1^ by the following recursion formulas; e”ap° sin pQ 1 p ° e ap cos p dp a p ° e ^ sin p dp N (N - 1 ) poN-1 N - 1 J pN_1 N - 1 J p” "1 (3 3 ) an d -a p 0 oo -ap , ao -ap ^ , Q e ° cos pQ ^ p e sin p dp a p e cos p dp ^ (N - 1 ) p N"1 N - 1 ^ PW_1 N - 1 ^ p1^"1 ° Po Po ( 3*0 With these expansions introduced into (31) it takes the following sim plified form; oo oo —ap . p . —ap / e p _ p _ + a_oJ e 22LJ1 + C (35) po po Of course the expansion of (31) in terms I and I ° would contain k6 terns but the combination of the coefficients w ill give a much reduced form. A check on the expansion is provided by the a^° term. The coefficients that sum to give a^° must be zero since I^° is not well behaved at co . After sim plification the a^ term becomes; 3(3 Q 1 (36) ^(3-, 8^3P32 L 1 ^ 3 & tKl \ 2 "3 ~K1 ^3 The constant term C w ill contain 71 terms which are a ll of the form m* m" n* b ^ l ^3 Q It is rather obvious at this point why computer techniques were used to solve for the < I >'s. Now there is no way to analytically calculate 1^ and therefore in order to approximate its value numerical integration was performed by using Simpson's method. The expression for < I > was then substi tuted into the simplified form of the differential cross section equation giving: f. k do r jM ,L 1 c 1 3 X < I > (37) <3X1 “ ST ( 2 i 3 + 1} ooo In (37) the appropriate Clebsch-Gordan coefficients are calculated from the following formula (Co 53); (L + 1 - O (L - 1 + O (1 + i_ - L) (L ) (2L + 1) ;V 3 L 'ooo (L + 2 + i ^ ) ( ^ ) ) 9 0 (38) (L - 1 + i - k) I (L - k) I k (k + 1 - je,)l 3 * * J * Summing ( 3 8) for the allowed values of and k we obtain for (37) j (39) The relative fits of these plane-wave calculations for the data w ill be discussed at the end of this chapter along with the distorted wave calculations. In general it might be said that at best the plane wave calculations only reproduce the data where it peaks sharply at small angles. The introduction of Coulomb distortion displaces the angular distributions towards the larger angles (To 55) while the nuclear effects introduced by the optical potential tend to move the peaks back to the smaller angles. The net effect is to give a much better fit for the (He ,n) reactions studied for this report. I I . DISTORTED WAVE CALCULATIONS In order to make the distorted wave calculations the IBM 709 O code of Satchler et ad. (Sa 6 l , Dr 6 l , Dr 6 l a , Ha 6 l) was used. In these calculations it is assumed that the elastic scattering of the *3 *3 He waves is the most important process and that the (He ,n) reaction can be treated as a perturbation of this process. For the solution to the Schrodinger equation it is assumed that the functional dependence of these waves is related only to the vector r which is the separation 91 of the colliding pair. If these distorted waves are denoted by 0(k,r) they satisfy the Schrodinger equation; A2 + t 2 . % u(r) - ia 0 ( k , r ) = 0 (4 0 ) ft r 2 Zl Z2 e where q is the reduced mass, and t] is the Coulomb parameter ------. fiv In equation (40) U(r) is the optical-model potential. For calculations with this code the real part of the optical potential Is a Woods-Saxon tw ellt given by; “Mreea = ‘ e + 1 ™ where x = ----- — , R = r (a )"^3 and a is the diffuseness of the 'v eil.' a o It should also be mentioned here that the Coulomb potential is that which would be generated by a uniform charge of radius rcA A1 ' / .3 . Note also that there are in general two different sets of parameters for U(r). One set for the incident channel or the He 3 and a set for the exit channel or the neutrons. For the imaginary part of the U(r) there is a choice of a Woods- Saxon or surface Gaussian. The Saxon has the same form as (4l) except that V is replaced by W. Surface-Gaussian imaginary potentials are generated by; U ( r ) i = - Ve~KX ) (4 2 ) Y _ X/S where x' = ----- ;— and Rf = r 'A ' . It might be mentioned here that a ' o both Saxon and surface Gaussians were tried for combinations of both chaimels. Results indicated that no appreciable difference was seen for the fits with a lim ited number of choices for the parameters in (42). It was therefore decided to use Saxon imaginary potentials since this choice reduces the number of parameters. For large values of r the solution of (40) is; (43) The transition amplitudes which are used to calculate the differential cross sections are generated from the solutions of (40) (for the reaction A(a,b)B) by; For (44) the < b,B|v|a,A >'s are the matrix elements of the interaction between the initial and final nuclear internal states. In these calcu lations it is used as a form factor. They axe calculated from the bound state wave functions by; (*5) The effective "zero range" approximation considerably sim plifies both (44 and 45). That is the vectors r^ and r are rendered parallel by p u t t i n g Now the co-ordinate systems for both the incoming and outgoing particles are the same. 93 The effective interaction < V > is expanded in terms of the transfer of to tal angular momentum J which is composed of an orbital —) —> — —> —> —> p a r t 8, and a spin part s. Where i + s = J„ - J. and the corresponding .D A Z components are defined as usual in the Clebsch-Gordan coefficients. Matrix elements for a definite transfer of angular momentum are then g iv e n by; / W T T ^ = M 8(rbB - fL raA) ^(i)aA ^a^aA 5 ^aA ^bB ' (ll6) Note that in (^ 6 ) the effective interaction has been replaced by Fgs ^. 6 (r). This is the so called "form factor" for these calculations. For "stripping" calculations = u_g^r ) where the u^(r)*s are the harmonic oscillator radial wave functions of principal quantum number N and orbital angular momentum 8, These are matched to the Hankel function at the boundary ( R ^ ) s o t h a t : p r 2 UN i( r ) * r& e " F ( Z N ; * + 3/ 2 ; 2 ) for r < ^ an d u K Whittaker function. _ Once the T's in (4*0 have been calculated the differential cross section is given by; 2 ao = v s \ v iT| ______“ ( 2 iii2 )2 ka ^ ( 2 s a + 1 ) ( 2J a + 1 ) where the sura n is over all of the Z projections of spin. It is interesting at this point to review the number of parameters that are involved in the calculation of (48). They are; V & v He He ( r Q) y V y a^, and (rQ)n for the real part of the "optical potential" in (42), for the He3 and neutron channels. For the imaginary potential with a Woods-Saxon choice we have only. W and W . In addition to He3 n _ these there is still (r ) ^ the Coulomb radius and Z the angular C He-3 momentum of the captured di-proton. In all about 200 independent runs were made to try to fit the data for the three reactions studied. This is not really too surprising when it is considered that there were seven levels to be fitted. There was some sim ilarity between the parameter sensitivity of (48) for the two reactions Be^He^nJC^1 and IdJ(He^,n)B^. This is also not surprising since the Q values and masses are very sim ilar. In addition the ground state spins and parities of Be^ and are both 3 /2 . In the next section the relative fits for the experimental data w ill be discussed and the spin and parity assignments w ill be given. 95 I I I . DISCUSSION OF THEORETICAL CALCULATIONS AND RESULTS The spin assignments made in this section (Table II) are based 3 on the assumption that the di-proton is stripped from the He with zero spin angular momentum. The justification for this assumption comes from the fact that the Pauli principle calls for the capture of the di-proton with its spins anti-parallel. In addition a spin flip of the neutron would be unfavored since there is no spin orbit dependence in the distorted wave calculations and, these calculations seem to fit the experimental results fairly well. That is, they fit in the forward direction and that is usually sufficient for "stripping" calculations. 13 However these (He ,n) reactions do show extremely large back angle effects that are generally not present in such proportions in (d,n) and (d,p) measurements. The "best fit" optical model parameters appear in Table III. Where excitation functions were calculated, the optical model parameters used were the ones that best described the angular distributions for the reaction. The fact that the Woods-Saxon "well" for the imaginary part of the optical potential fitted the experimental curves as well as the surface Gaussian probably means that the reaction takes place essentially on the surface since the Gaussian is quite different in the interior region of the nucleus, while they are quite similar in the surface region (Ag 60). Since the reaction (as previously described) is treated as a perturbation of the elastic scattering of the He^'s the approximate 96 TABLE I I SPIN AND PARITY ASSIGNMENTS ENERGY LEVEIS OF B9 Ex i n B^ J 71 (previous) Jn (distorted-wave) 0 > l /2 1 / 2 “ -> 7 / 2 " ENERGY LEVEIS OF C11 Ex i n C^" Jn (previous) Jn (distorted-wave) 0 ( 3 / 2 ') 1 / 2 “ -> 7 / 2 “ 1 .9 9 (3/2“ -*9/2") l / 2 _ -> 7 / 2 " h.2 6 ( 3/ 2 " - > 9/ 2 ") 1/2" -> 7/2“ 4 .7 5 (3/2" ->9/2“) None 6 .5 0 (3/2" -> 9/2") 3 /2 " ENERGY LEVELS OF 015 Ex i n 0 15 jn (previous) Jn (di st ort e d-wave) 0 ( 1 / 2 )" 1 / 2 " 6 . l 6 - 3 / 2 " 5/2+ -> 7/2+ 97 TABLE I I I OPTICAL MODEL PARAMETERS R e a c tio n W r a V 3 W 3 - n Vn n HeJ He r °He3 r c He3 a HeJ 3 °n B e ^ H e ^ n J C 11 62 50 1 .6 0 1 .3 0 .7 0 6 .0 40 1 .4 5 .4 0 Id 7 (H e 3 ,n )B ? 40 50 i . 6 o 1 .3 0 .7 0 6 .0 40 1 .4 5 .4 0 CI 3 (He3 ,n ) 0 15 80 30 l . 8o 1 .3 .7 0 6 .0 40 1 .4 5 .4 0 C1 2 (He3 ,n ) 0 lJ+ 8o 30 1 .8 1 -3 .7 0 6 .0 40 1 .4 5 .4 0 9 8 values of the optical model parameters were taken from several sources (Ag 60, Gr 6l, Ho 60). The approach used to fit the data was to first establish the relative sensitivity of the calculated curve to each of the parameters. Next the variation of two or more parameters was tried, etc. It is easy to see that there are many possibilities and combinations in this ten dimensional parameter space. Perhaps (at this point) the justification of the 200 runs seems more profound. In order to normalize the calculated angular distributions to the measured curve they were m ultiplied by a factor S^. In ordinary deuteron stripping calculations this quantity is the reduced width. For di-proton stripping calculations it loses its meaning since it is really the product of three reduced widths and therefore nothing explicit can be said about its meaning. Figure 37 shows the calculated angular distribution of the ground state neutrons from Be^(He^,n)C'*"\ The £ - 2 distorted wave calculation seems to fit the experimental points back to about 105° . From this description a spin and parity assignment of (l/2~ -> j / 2 ) was made for this state. On the same curve is shown the £ = 2 p la n e wave calculations. It is evident, as mentioned previously that the plane wave calculations could never be made to fit this angular d istri bution. The £ = 0 distorted wave curve is shown on the curve for com- 11 parison. Figures 38 and 39 (the first and second excited states of C ) are also fitted with an £ - 2 transfer. The optical model parameters used for these excited states are the same as those for the ground state. For comparison other £ transfers are shown on the curves. DIFFERENTIAL CROSS SECTION (mb/steradian) 0.5 0 E H« i. 7 Cacltd nua Ditiuin o Gon Sae etos rm Be from Neutrons State Ground for istribution D Angular alculated C 37. Fig. 3 . Mev. 2.1 - 20 40 ETRO-AS NL (deg) CENTER-OF-MASS ANGLE 080 60 £= 2 LN WAVE PLANE 2 100 120 9 (He LR- 61534 G W -D R -L L N R O 3 ,n )C ^ at at ^ )C ,n UNCLASSIFIED 160 180 VO , DIFFERENTIAL CROSS SECTION (mb/steradian) 0.5 1.0 at at - E i. 8 Cacltd nua Ditiuin o 1t xie Sae etos rm ’t e^nJC tH e’ B from Neutrons State Excited 1st for istribution D Angular alculated C 38. Fig. 0 H. »■ Mev. 2.1 40 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS 80 RLL-W 61604 ORNL-LR-DWG UNCLASSIFIED 1 * tl J 160 DIFFERENTIAL CROSS SECTION (mb /steradion) 0.2 0.4 T 0.4 0.5 0.3 0.1 0 t£ , »21 Mev. 2.1 » , £ at 20 i. 9 Cacltd nua Ditiuin fr n Ectd tt Nurn fo Be from Neutrons State Excited 2nd for istributions D Angular alculated C 39. Fig. H* 60 0 4 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS 80 100 0 2 1 9 (He 4 180 140 3 ,n)C LR- 3 0 6 1 6 G W -D R -L L N R O 1 ’ UNCLASSIFIED 160 101 1 0 2 Figure 40 shows the calculations for the third excited state group. It is obvious that no spin assignment should be ventured on the basis of the fits that are shown. However, it should be pointed out that changes made in the neutron channel for the optical potential would be ju sti fiable for the excited states and these changes (when they are made) might give better agreement for this group. Figure 4l shows the improvement of the distorted wave £ = 0 transfer over that from plane waves for the fourth excited state in C ^. Other £ values are shown on the curve for comparison. With the £ = 0 fit an assignment of 3 /2 was made for this state. Figures 42, 43, 44, 45, and 46 show the calculations made for C'L^(He^,n)0’*'''* reaction. Figure 42 shows an attempt to calculate the shape of the excitation function for the ground state neutrons at 0°, The parameters used were those which best described the ground state angular distribution (Fig. 44). It is interesting to note, that while this curve does not reproduce the shape of the measured excitation function (independent of the resonance) the $0° data (Fig. 43) can be fitted quite well with the same parameters. It would seem, from the arguments presented in Chapter I, that the 0° data should be more easily fitted with direct interaction than the lower energy neutrons at 90°• Figure 44 shows the calculated angular distribution for the ground state neutrons. The £ = 0 distorted wave curve reproduces the minimum at 45° and the general shape of the curve is correct. From this fit an assignment of l/2~ was made for the group. It is interesting to note here that the distorted wave calculations are ^T, DIFFERENTIAL CROSS SECTION (mb/sterodian) 0.2 .9 0 .3 0 .4 0 0.8 0.6 .5 0 .7 0 0.1 t “ . Mev. 2.1 “ ! £ at 0 g 4. luae Aglr srbto o 3d ctd tt Netos rm e B from eutrons N State xcited E 3rd of istribution D Angular alculated C 40. ig. F H. 20 CENTER-OF-MASS ANGLE 4 080 8 046 0 100 (deg) 120 0 4 1 RLL-W 61602 ORNL-LR-DWG 9 UNCLASSIFIED He (H 3 160 ,n)C 13 3 0 1 0 8 1 DIFFERENTIAL CROSS SECTION (mb/sterodion ) 0 tH ” . Mv -pr Mev. 2.1 ” - H at 2 3 H.3 H I 0 i. 1 Cacltd nua Ditiuin fr t Ectd tt Nurn fo Be from Neutrons State Excited 4th for istributions D Angular alculated C 41. Fig. 20 LN WAVEPLANE 0 = J 06 80 60 40 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS 100 120 140 -R- 5 3 5 1 6 G W -D L-LR N R O 9 (He UNCLASSIFIED 3 ,n)C 1 ' 6 180 160 g \ (RELATIVE) 6.0 .0 3 .0 4 .0 5 2.0 .0 7 - * 5 J 0-0* i- 2 Cacltd xiain ucin o Gon Sae etos rm C from Neutrons State Ground for Function Excitation alculated C 42* Fig- e ENERGY(Mev) He3 THEORY- V LR- 3 4 3 1 6 G W -D R -L L N R O 13 (He .5 2 EXPERIMENT 3 UNCLASSIFIED ,jj)0 ^5 for for \ RELATIVE DIFFERENTIAL o if) § if) W 0.6 LU o 0.8 F o 0.2 0.4 1.0 1.2 1.4 0 1.5 i.4. luae Ectto Cre a C^ (at Curve Excitation alculated C 43. Fig. 1 \ 1.7 9 * 1.9 ) v e M ( Y G R E N E 3 e H i 3 > (He 3 ,n )0 ' Ground-State Neutron* a t 0 ^ = 90°. = ^ 0 t a Neutron* Ground-State ' )0 ,n 2.1 t ► 3 i 2.3 RLL-W 61342 ORNL-LR-DWG y EXPERIMENTAL RLL-W 61345 ORNL-LR-DWG 13 UNCLASSIFIED He (H 3 n)0 ,n 1 s a t t a s 107 ^-(RELATIVE) ,-4 -3 -2 g. 5 Cacltd ctto Fnto (r rud tt Nurn fo C1{e,n)0'5. 5 ' 0 ) n 13{He3, C from Neutrons State Ground (or Function xcitation E alculated C 45. . ig F 2 3 ENERGY (Mev) e3 H 3 90 45 RLL-W 61344 ORNL-LR-DWG UNCLASSIFIED 8 0 1 4 DIFFERENTIAL CROSS SECTION (RELATIVE) 0.4 0.2 0.8 0.6 1.4 0 at at E i. 6 Cacltd nua Dsrbto fr r Ectd tt Nurn fr C for Neutrons State Excited 3rd for Distribution Angular alculated C 46. Fig. H. 20 .6Mv ^ Mev. 2.66 , 40 ETRO-AS NL (deg) ANGLE CENTER-OF-MASS 60 80 EXPERIMENTAL 100 13 140 (He 3 ,n)Q ORNL-LR-DWG 61601 ORNL-LR-DWG i - 15 UNCLASSIFIED 0 = 160 180 (3 1 1 0 trying to peak in the back angles (as the experiment does) while the plane wave back angle amplitudes are much lower. In order to investigate the change in the shape of the excitation function as 0 was varied, the calculations in Fig. 45 were made. The parameters used were those which gave the best fit to the ground state angular distribution. The excitation function is seen to change smoothly from 0° down to its value at 45° and then back up at 90°. Figure 46 shows the calculated angular distributions for the third excited state. The Z = 3 transfer is seen to fit the experimental curve fairly well. From the Z = 3 transfer an assignment of ( 5/ 2+ 7 / 2+) was made for this state. Figures 47 and 48 show the calculations for the Li^(He~^,n)B? reaction. In Fig. 4-7 an attempt has been made to calculate the shape of the excitation function for the ground state group. The experi mental. curve seems to show a broad reversal of slope from 2 .2 t o 2 .7 Mev while the stripping calculations rise monatonically. However, it should be re-stated here, that the calculated shape of the four body continuum (B 9 -» He^ + He^ + n + p) is not known and the background sub traction (recall, a straight line extrapolation of the continuum was used) could produce a considerable error. Figure 48 shows the calculated angular distribution for the ground state neutrons. In this figure it can be seen that the distorted wave calculation fits the data quite well back to 100° while the plane wave curve is not at all descriptive of the experimental results. From the Z = 2 transfer an assignment of ( l / 2 ~ -» 7 / 2 ”) was made for the ground state of $ . DIFFERENTIAL CROSS SECTION (mb/sterodian) 0.4 2.0 0.8 0 1.0 - i. 7 Cacltd ctto Fnto fr rud tt Nurn fo Li L from Neutrons State Ground for Function xcitation E alculated C 0 47. Fig. °. EXPERIMENTAL AT 9 = 0 He3f (Mev) 2.2 0' 0 = 9 45' ' 0 9 RLL-W 61533 ORNL-LR-DWG 7 He (H unclassified 3 ,n)B 2.6 9 at 1 1 1 (RELATIVE) 7 0 4 6 5 2 3 E 0 0 0 10 4 10 180 160 140 120 100 0 8 60 0 4 20 0 ■= Mev. , 2.1 H. g 4. luae Aglr srbto fr i L for istribution D Angular alculated C 48. ig. F LN WAVEPLANE i-Z 2 = i \ 0 - 1 9 c m (deg) 7 (He 3 nB9 Gon Stt Netos at eutrons N tate S Ground 9, ,n)B ORNL-LR-DWG 61305R ORNL-LR-DWG UNCLASSIFIED 12 1 113 F ig u re k-9 shows an attempt to calculate the angular distribution 12 ^ 1^+ for the ground state neutrons from the C (He ,n)0 reaction (the experimental points were taken by Gale (Ga 60) at Manchester). The optical model parameters used were the ones that best described our C^(He^,n)0^ ground state angular distribution (Table III). The distortion effects seem to produce a second maximum which is not in the experimental data. Plane wave calculations with an Z = 0 transfer were also made for the reaction. The curve is not shown since it almost exactly reproduces the double stripping curve. In summarizing the data and calculations It might be said that in general the distorted wave calculations can be made which describe the experimental curves in the forward direction. On the basis of these fits the tentative assignments were made. These assignments are in agreement with previous measurements in all cases except for the 15 third excited state in 0 . Certainly more measurements must be made before definite conclusions can be reached about the distorted-wave description of these reactions. In addition attempts should be made to perform other types of calculations for these (He ,n) reactions. Certainly the resonance in the C^^He^jnJO1^ reaction Indicates that some "compound nucleus" is present. Also as mentioned previously, there might be appreciable "heavy particle" stripping amplitudes present. In almost every case there are large back angle cross sections which would tend to favor this model. Gale (Ga 60) has pointed out that "knock on" calculations can be used to describe the C"*"^(He^,n) 0^ reaction. It is obvious at this point that there are many other DIFFERENTIAL CROSS SECTION (mb/steradign) 3.0 2.0 5.0 Mev. 4 0 Fig. 49. C alculated Angular D istribution for Ground State N eutrons from C 1 z(H e3,n )0 14 a t t a 14 )0 e3,n 1 C z(H from eutrons N State Ground for istribution D Angular alculated C 49. Fig. 20 i = (DOUBLE 0 i STRIPPING) 40 60 CENTER-OF-MASS ANGLE (deg) 80 i = (DISTORTED 0 WAVE) 100 140 RLL-W 61536 ORNL-LR-DWG UNCLASSIFIED 160 4 l I 180 channels of approach which deserve investigation before definite con clusions can be reached. However, it should be pointed out again, that if the (He ,n) reactions can be described in terms of the model presented in this thesis, then a strong spectropic tool has been de veloped which can be used to make spin and parity assignments to many of the proton rich nuclides which are virtually inaccessible from other r e a c t i o n s . BIBLIOGRAPHY (Ag 60) Aguilar, J., Proc. Roy. Soc. 2 5 7 , 13 ( i 9 6 0 ). (A1 5 5 ) Almqvist, E.. K. W. Allen, and C. Bigham, Phys. Rev. 99, 631A (1955). (A1 59) Almqvist, E., and D. A. Bromley, Phys. Rev. Ilk , lOkO (1959). (B a 5 1 ) Baldwin, E. M., Phys. Rev. 8 3, 1+95 (1951) • (Be 5 5 ) Bent, R. D., T. W. Bonner, J. H. McCrary. W. A. Ranken, and R. F. Sipple, Phys. Rev. 99 , 710 (19555* (Bi 51) Birks, J. B., Phys. Rev. 8k , 36 k (1951)* (B i 5 2 ) Birks, J. B., Phys. Rev. 8 6 , 569 (1952)* (Bo 3 6 ) Bohr, N., Nature 137, 3kk ( 1 9 3 6 ). (Bo 5 6 ) Bockelman, C. K., A. Levegue, and W. W. Buechner, Phys. Rev. 10k , k^6 ( 1 9 5 6 ). (Br 5^) Brooks, F. D., Progr. in Nuclear Phys. 252 ( 1 9 5 6 ). (B r 5 8) Bromley, D. A., and E. Almqvist, Nuclear Reactions with He Ions, Chalk River Report, 88l , (1 9 5 9 )• (Bu 5 0 ) Butler, S. T., Phys. Rev. 80, IO 95 (1 9 5 0 ). (Bu 5l) Butler, S. T., Proc. Roy. Soc. (London) A208, 559 (1951)* (Bu 57) Butler, S. T., and 0. H. Iiittmair, Nuclear Stripping Reactions, New York: John Wiley and Sons, Inc., 1957* (Ce 5 8) Cerineo, M., Nuclear Phys. 2, 113 ( 1 9 5 6 ). (Ce 58a) Cerineo, M., Physica 22, 115k ( 1 9 5 8). (C l 5 2 ) Cleland, M. R., N.B.S. Report 2063 (1 9 5 2 ). (Co 53) Condon, E. U., and G. H. Shortley, Theory of Atomic Spectra, New York: Cambridge Press, 1951* (Cr 51) Cross, W. G., Phys. Rev. 8^ , 873 (1 9 5 1 ). (C r 5 6 ) Cranberg, L., and J. S. Levin, Phys. Rev. 103, 3^3 (1956). (Da 53) Dalitz, R. H., Proc. Phys. Soc. A6 6 , 28 (1953). 117 (Da 60) Day, R. B., Los Alamos Scientific Laboratory, private communications, i 9 6 0 . (Dr 61) Drisko, R. M., R. H. Bassel, and G. R. Satchler, Bull. Am. Phys. Soc. 6 , 56 ( 1 9 6 1 ). (D r 6 l a ) Drisko, R. M. and G. R. Satchler, Bull. Am. Phys. Soc. 6 , 67 ( 1 9 6 1 ). (Ei 60) Eichler, E., Oak Ridge National Laboratory, private communications, i 9 6 0 . ( E l 5 3 ) Elkind, M. M., Phys. Rev. 92, 127 (1953)* (E v 53) Evans, W. H., T. S. Green, and R. Middleton, Proc. of Phys. S o c. a 6 6 , 108 ( 1 9 5 3). (Ev 54) Evans, N. T. S. and W. C. Parkinson, Proc. Phys. Soc. (London) A7 8 , 684 (1954). (Fo 60) Forsyth, P. D., F. De S. Barros, A. A. Jaffee, I. J. Taylor, and S. Ramavataram, Proc. Phys. Soc. rQJ 291 ( i 9 6 0 ). (E r 53) Friedman, F. L. and W. Tobocman, Phys. Rev. 92. 93 (1953)* (Fu 52) Fulbright, F., Phys. Rev. 8 8, 700 (1952). (Ga 60) Gale, N. H. J. B. Garg, J. M. Calvert, and K. Ramavataram, Nucl. Phys. 20, 313 ( i 9 6 0 ). (Ge 53) Gerguloy, E., Phys. Rev. 91. 645 (1953)* (Ge 5 8 ) Good, W. M., J. H. Neiler, and J. H. Gibbons, Phys. Rev. 109. 926 (1958). (G r 5 6 ) Grave, A., Phil. Mag. 1, 1027 (1956). (G r 5 8) Greenblatt, M. H., IRE Trans. Nuc. Sci., NS-5, 13 ( 1 9 5 8). (G r 6 l ) Greenless, G. W., Nucl. Phys. 24, 334 ( 1 9 6 1 ). (Ha 6 l ) Halbert, E. C., R. M. Drisko, and G. R. Satchler, Rutherford Conference, Manchester, England ( 1 9 6 1 ). (H i 59) Hinds, S. and R, Middleton, Proc. Phys. Soc. (London) A73. 727 (1959)* (H i 5 9 a) Hinds, S. and R. Middleton, Proc. Phys. Soc. J4, 196 (1959)* 1 1 8 (Hi 59b) Hinds, S. and R. Middleton, Proc. Phys. Soc. r]h_, 762 (1 9 5 9 )- (Hi 59c) Hinds, S. and R. Middleton, Proc. Phys. Soc. Jk_, 775 (1959)• (Ho 5 3 ) Horowitz, A. M. and M. L. Massiah, Phys. Rev. 92, 1326 (1953)* (Ho 5 6 ) Holmgren, H. D., M. L. Bullock, and W. E. Kunz, Phys. Rev. lQtf, 1^46 (1956). (Ho 57) Holmgren, H. D., Phys. Rev. 10 6 , 100 ( 1 9 5 7 ). (Ho 59) Holmgren, H. D., E. A. Wolicki, and R. L. Johnson, Phys. Rev. 11b, 1281 (1959). (Ho 60) Hodgson, P. E., Nuc. Phys. 21, 28 (i 9 6 0 ). (Hu 5 2 ) Huby, R., Proc. Roy. Soc. (London) A215, 3^5 (1952). (Hu 55) Hughes, D. J. and J. A. Harvey, Neutron Cross Sections, BNL Report 325 (1 9 5 5 ). (ja 60) Jaffe, F., De S. Barros, P. D. Forsyth, J. Mito, I. J. Taylor, and S. Ramavataram, Proc. Phys. Soc. (London) 9k0 (i 9 6 0 ). Ja 60a) Jaffe, F., De S. Barros, P. D. Forsyth, J. Muto, I. J. Taylor, and S. Ramavataram, Proc. Phys. Soc. (London) 7 6 , ^92 ( i 96 0 ). (J o 5 2 ) Johnson, C. H., G. P. Robinson, and C. D. Moak, Phys. Rev. §1, 931 (1952). (Jo 52a) Johnson, V. R., Phys. Rev. 8 6 , 302 (1952). (Jo 52b) Jones, A. and D. H. WiLkinson, Phys. Rev. 8 8, k23 (1952). (J o 6 l) Johnson, J. W. and W. M. Good, Rev. Sci. Instr. ^2 (2), 219 (1 9 6 1 ). (Ke 5 6 ) Kerns, Q., IRE Trans. N.S. 3, No. k, H k ( 1 9 5 6 ). (Ke 60) Keller, E. L., Bull. Am. Phys. Soc. II 2 k6 ( i 9 6 0 ). (K i 6 l) King, R. F., C. D. Moak, and H. E. Banta, private communications, Physics Division, ORNL ( 1 9 6 1 ). (Kn 5 8) Knowls, H. B., Bull. Am. Phys. Soc. 33O ( 1 9 5 8). (La 57) Lane, A. M., Rev. Mod. Phys. 2 9, 191 (1957). (La 59) Lawrence Radiation Laboratory, Counting Handbook, UCRL, 3307 (1959). 119 (Ma 1+7) Marshak, R. E., Rev. Mod. Phys. 1^, 185 (1 9 5 7 ). (Ma 5 6 ) Maslin, E. E., J. M. Calvert, and A. A. Jaffee, Proc. Phys. S o c. A6 9 , 754 ( 1 9 5 6 ). (Ma 59) Marion, J. B. and J. S. Levin, Phys. Rev. 119, 144 (1959) ■ (Mo 55) Mobley, R. C. and B. R. Albritton, Phys. Rev. , 232 ( 1 9 5 5). (Mo 6 l) Mobley, R. C., Dept, of Physics, Louisiana State University, private communications ( 1 9 6 1 ). (Mu 5 8) Murray, R. B., Scintillation Counters, ORNL Progress Report (1 9 5 8 ). (Ke 5 2 ) Newns, H. C., Proc. Phys. Soc. (London) A 6 9 , 916 (1952). (Ke 60) Keiler, J. H. and W. M. Good, Fast Neutron Physics, Vol. 4 New York: Interscience Publishing Co., 1960. (Ne 6 l) Newns, H. C., Proc. Phys. Soc. (London), to be published (1 9 6 1 ). (No 57) Nonaka, I., J. Phys. Soc. Japan 12, 84l (1957). (Ow 57) Owens, G. E., and L. Madansky, Phys, Rev. 105, 1766 (1 9 5 7 )- (Po 59) Povh, B., Phys. Rev. 1 1 6 , 1114 ( 195 9 ). (Re 5 5 ) Reynolds, J. B., Phys. Rev. § 8 , 1289 (1955). (Re 5 6 ) Reynolds, J. B. and K. G. Standing, Phys. Rev. 101, 158 ( 1 9 5 6 ). (Ry 60) Rybakov, B. V. and V. A. Sidorof, Fast Neutron Spectroscopy, New York: Consultants Bureau Inc., i 9 6 0 . (Sa 55) Sample, J. T., G. C. Neilson, G. B. Chadwick, and J. B. Warren, Canad. Jour. Phys. 32.> 828 (1 9 5 5 )- (S a 6 l) Satchler, G. R., R. M. Drisko, and R. H. Bassel, Bull. Am. Phys. Soc. 6 , 66 ( 1 9 6 1 ). (Se 47) Serber, R., Phys. Rev. J2f 1008 ( 1 9 4 7 ). (Se 54) Segel, R. E., C. D. Swartz, and G. E. Owen, Rev. Sci. Instr. 2 5 , No. 2, 140 (1954). (S h 5 1 ) Sher, R., J. Halpern, and A. K. Mann, Phys. Rev. 84, 387 (1 9 5 1 ). 1 2 0 (Sh 5 6 ) Shiffer, J. P. and T. W. Bonner, Phys. Rev. 104, 1064 (195&)* (Sp 59) Spencer, R. P. and G. C. Phillips, Bull. Am. Phys. Soc. II, 4, 95 (1959). ( S t 5 1 ) Stelson, P. H. and W. M. Preston, Phys. Rev. 8 3, 469 (1951)* (Sv 5 6 ) Swartz, C. D. and G. E. Owen, NYO Report 2053* U.S.A.E.C., p. 3* 1956. (T a 5 1 ) Taylory, C. J., W. K. Jetschke, and M. E. Remley, Phys. Rev. 84, 1034 (1951)- (T a 6 0 ) Tabata, T. and K. Kotoyuki, J. Phys. Soc. Japan 15, 27 O (I 9 6 0 ). (Th 55) Thomas, R. G., Phys. Rev. 100, 25 (1955)* (To 54) Tobocman, W., Phys. Rev. gib 1&55 (1954). (To 55) Tobocman, W., and M. H. Kalos, Phys. Rev. 9 J.j 132 (1955)* (To 60) Towle, J. H. and B. E. F. Macefleld, Proc. Phys. Soc. (L ondon) XL, 399 (l96l). (Va 5 1 ) Van Patter, D. M. and D. M. Buechner, Phys. Rev. 82, 248 (1 9 5 1 )- (Wi 5 5 ) Wilkinson, D. H., Phys. Rev. 100, 3 2 (1955)* (Wi 6 l) Williams, C. W. R. P. Cumby, and J. H. Neiler, ORNL Physics Division Annual Progress Report, 1961 (Wo 59) Wolicki, E. A., H. D. Holmgren, R. L. Johnson, and E. G. Illsley, Phys. Rev. Il 6 , 1558 (1959)* APPENDIX AVERAGE ANGLE OF SCATTERING AND ENERGY FOR THE (n ,C 1 2 ) AND ( n ,p ) CROSS SECTIONS I- (n,C12) CASE The kinematics for th is reaction can be solved to give the average energy (E* ) of the scattered neutrons. This value is given a v b y ; Ea v = h i I E ' ^ 2n s in S d® ' ■where E'(e) is energy of the scattered neutrons as a function of angle. 12 From (n,C ) kinematic equations E^ becomes; E p r 1 +'mJ + 2 VM c o s ® *5 E f slnO d© (50) a v ■ ? S 12 where m is the mass of the proton, M is the mass of C , and Eq i s th e energy of the incident neutron. This integration gives; E* = .857 E . (5 1 ) a v o Now substituting E* back into the appropriate kinematic equation oiy g iv e s ; e = 90° . ( 5 2 ) a v v 1 22 II. (n,p) CASE F o r (n,p) scattering the center of mass angle is twice the laboratory angle. therefore takes the following form; E K v ■= 5! / I t1 + C0S 29L> Eln9L deL • (53) The integration gives; E Eiv ' 2s • (5*0 If an isotropic distribution in the center of mass system is assumed th e n ; E ~ i (l + cos© ) . (55) E 2 ' cm' o Solution of the above equation gives a center of mass angle of 90° or a lab angle of ^5°* VITA Jerome Lewis Duggan was bora August 4, 1933* in Columbus, Ohio. He attended public schools in Ohio and Texas, graduating in 1952 fro m Denison High School in Denison, Texas. He entered North Texas State College and received his Batchelor of Arts degree with a double major in physics and mathematics. He entered graduate school at North Texas State and received his Master of Arts degree in physics in August 1956. From September 1956 until August 1957* tie was an instructor in the Department of Physics at North Texas State College. In September 1957* tie entered graduate school in the Department of Physics at Louisiana State University. In September 1959* he received a Graduate Fellowship from the Oak Ridge Institute of Nuclear Studies. This Fellowship enabled him to do his research at the Oak Ridge National Laboratory. He is presently a candidate for the degree of Doctor of Philosophy. EXAMINATION AND THESIS REPORT Candidate: Jerome L. Duggan Major Field: Physics Title of Thesis: "A Study of the Reactions, Be9 (He3, n) C11, Li7(He3 ,n)B9 and 13 3 15 c (He ,n)0 , by Time-of-Fiight Techniques" Approved: Major Professor and Chairman Dean of the Graduate School EXAMINING COMMITTEE: \ V a A Y W ^ A S r> [ f \ ccjjy (Is. Date of Examination: September 19, 1961