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Gamma-ray angular distribution from the reaction D(p.[Delta])[3]He below 200 KeV Olivo, Miguel Angel 1968

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THE GAMMA-RAY ANGULAR DISTRIBUTION PROM THE REACTION D(p,o) 3He BELOW 200 KeV by. MIGUEL ANGEL OLIVO Licenciado en F i s i c a I n s t l t u t o de F i s l c a de S.C. de Bariloche, Unlversidad Nacional de Cuyo, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, I968 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h.i)s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Physics T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a Date August 8 , 1968 ABSTRACT The angular d i s t r i b u t i o n of the gamma-rays from the d i r e c t r a d i a t i v e capture reaction D(p,$)^He has been measured for 7 0 KeV and tkk KeV protons i n the laboratory system, using t h i n deuterated polyethylene targets. The study of thi s p a r t i c u l a r l y simple reaction i s of int e r e s t f o r determining some properties of the forces which bind nuclear p a r t i c l e s to each other. In addition i t plays a rol e i n a number of astrophyslcal processes. The ground state of -^ He i s predominantly a symmetric 2 k 2 S state with admixtures of a D state and a S, \ state of mixed symmetry. These admixtues are re l a t e d to s p e c i f i c com-ponents of the two body forces coupling the three p a r t i c l e s . The measurements were made with a high current 1 8 0 KeV accelerator, b u i l t by the author, using an ORTEC duoplasmatron ion source. Technical problems involved i n the development of the accelerator and the deuterated targets are discussed. The angular d i s t r i b u t i o n at Hi4 - 16'KeV i n terms of Legendre polynomials P^ i s given i n the centre of mass system by W(6) = A Q | P o + ( o 0 5 - . 0 2 ) P 1 - ( . 9 ^ - . 0 2 ) P 2 - ( . 0 5 i . 0 2 ) P 3 4 ( . 0 3 - o 0 2 ) P 4 j and at 70 - 2 0 KeV the angular d i s t r i b u t i o n i s given by w(9) = A orp o+(.o6i.o^)P 1-(.93 i.05)P 2-(.o6i . o 4)P 3+(.02i.05)pJ - i i i -The c o e f f i c i e n t s i n the Legendre polynomial expansion are r e l a t e d to the various t r a n s i t i o n s between the continuum and bound states. Their significance i n terms of the d i f f e r e n t com-3 ponents of the He ground state wave function i s discussed. The absolute cross section ( i . e . the c o e f f i c i e n t A ) o has not been measured. Plans for measuring i t i n the near future are discussed b r i e f l y . TABLE OP CONTENTS ABSTRACT . i l TABLE OP CONTENTS i v LIST OP TABLES v i i LIST OF FIGURES • • • • • v * 1* ACKNOWLEDGEMENTS x i PUBLICATIONS x i i CHAPTER I INTRODUCTION 1.1. General Introduction 1 1.2. Review of Previous Work 4-1.3. Present Work ... 6 CHAPTER II EXPERIMENTAL APPARATUS 2 . 1 . Angular D i s t r i b u t i o n Table 11 2 . 1 . 1 . Target Chamber 13 2 . 1 . 2 . The Collimator 16 2 . 1 . 3 . The Vacuum System 17 2 . 2 . The Targets 17 2 . 2 . 1 . Deuterium Gas Targets 21 2 . 2 . 2 . Heavy Ice Targets 21 2 . 2 . 3 . Deuterium Absorbed i n S o l i d — Elements ' 22 2,2.4-. Deuterated Compounds ...... 2 3 2 . 3 . The Detector, Collimator and Shielding 2 6 2.4 : The Ele c t r o n i c s ....... ............ 3 3 iv V CHAPTER III EXPERIMENTAL METHODS AND RESULTS 3. 1 . The Procedure 42 3.2. The Angular D i s t r i b u t i o n Function . 5 3 3.3. The F i t t i n g Procedure 5 3 3.4-. The Results ... 6 0 CHAPTER IV DISCUSSION 4-. 1. Discussion of the Results 6 5 4-.2. Comparison with the Theoretical Calculations 74-4-. 3. Future Work 86 33IB3LJ OGRAPHl^ o « o * * * o o o o o * o o » » o o o » * o « o » « « o e e « * o » * * * * o * a * * 9^ -i APPENDIX A THE-ANGULAR DISTRIBUTION OF THE 1 1 . 7 MeV GAMMA-RAYS FROM THE REACTION 1 1B(p , "8 ' ) 1 2 C .. 9 5 APPENDIX B THE ACCELERATOR AND MAGNETIC ANALYZER B . l . The Accelerator 107 B . l . l . The Ion Source and E l n z e l Lens 1 07 B.1.2. The Accelerating Tube 1 1 0 B . l . 3 . High Voltage . 114-B.1.4-. The Vacuum System 116" B.l . 5. The Shielding 1 16 B . l . 6 . C h a r a c t e r i s t i c s 1 1 7 B.2. The Magnetic Analyzer 117 B.2.1. The Magnet 120 B.2.2 The Power Supply 1 2 2 APPENDIX C THE ENERGY OF THE GAMMA-RAYS FROM THE RE-ACTION D(p,tf) 3He AND THE COORDINATE SYSTEM TRANSFORMATIONS 1 2 3 v i APPENDIX D DEUTERATED POLYETHYLENE TARGET PREPARATION 1 2 5 APPENDIX E MULTIPLE SCATTERING 127 APPENDIX F THE REACTIONS 1 2 C ( p , t f ) 1 3 N and 1 3 C ( p f 0 ) 1 \ 1 2 9 APPENDIX G CORRECTION DUE TO THE GAMMA-RAY ABSORPTION IN THE TARGET HOLDER 132 APPENDIX H BEAM DEPENDENT BACKGROUND H.l. Neutrons from the Accelerator .... 136 H.2. Neutrons from the Targets 137 APPENDIX I LIST OF COMPUTER PROGRAMS USED IN THIS THESIS 14-7 LIST OF TABLES I I - l C haracteristics of the deuterated polyethylene targets 2 5 I I - 2 Dimensions of the detector assembly #1 and #2 3^ 11 3 E1© C " f c l * O l " l l C Uni t S o o o o o o o o o a o ^ o o o o o v o o o o o o o o o o o 4^*0 I I I - l D(p,l$)^He angular d i s t r i b u t i o n data 90"KeV run 48 I I I - 2 D(p,T$)3He angular d i s t r i b u t i o n data 1 6 0 KeV run 4-9-50 I I I - 3 Smoothing factors f o r 5.58 MeV gamma-rays .... 53 I I I - 4- D(p,tf)-%e angular d i s t r i b u t i o n least squares f i t parameters and Chi-squared test f o r 90 KeV 9.ncL 1 6 0 K©V runs 9 * 0 0 0 0 0 0 * 0 0 ooo oooooooo©oo««o» 63™*^^' IV- l *D(p,tf)^He Legendre polynomial c o e f f i c i e n t s cor-rected f o r f i n i t e s o l i d angle of the detector 67 IV-2 D(p,"8)^He reaction. Comparison between experi-mental r e s u l t s and Donnelly's calculations ... 84 •4 A A Q A - l B(p,u") C angular d i s t r i b u t i o n data f o r E y — 11 e 7 M6V 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o e o o o o v o a o o o o o o o o 1 0 0 11 sS 1 P A-2 B(p,o) C angular d i s t r i b u t i o n least squares f i t parameters and Chi-squared test for E — 1 1 0 7 M@V 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 102 A-3 Smoothing factors for 1 1 , 7 MeV gamma-rays .... 1 0 5 1 1 1 2 A-4- B(p,tf) C Legendre polynomial c o e f f i c i e n t s corrected for f i n i t e s o l i d angle of the CL©t©CtOI* 0 0 O * O O O O O * O O 0 • • O O O O O 0 0 0 0 * 0 0 0 9 0 0 0 0 0 0 0 0 10^) B-l Accelerator's el e c t r o n i c units ............... 11.6 B-2 Accelerator conditions for a 1 6 0 KeV proton "bSQJIl O O O O O 0 0 O 0 0 O O 0 O O O O O O O O O O O O O O 0 O O 0 O O O O O 0 O 0 0 9 1 2 0 C-l D(p,tf)%e gamma-ray energies at Ep = 160 KeV and 90 KeV for d i f f e r e n t angles of observation 124 -a G-l Target holder correction parameters for D(p,u).^He 11 12 and B(p,tf) C reactions .................... 1 3 5 G-2 Target holder absorption measurements for E ^ — 11 o 7 M© V O O O O 0 0 O O O O O O 0 O O O O O O 0 O O O 0 O O O O 0 O O O 1 3 3 v l i LIST OP FIGURES ' I I - l Schematic diagram of the angular d i s t r i b u t i o n " f c3 . " b l@ e e 0 9 * 0 0 0 0 0 9 0 * 0 0 0 0 o o o o o « o * * o o o o * o o o * o o o * 12 II-2 Schematic diagram of the target chamber 14-I I - 3 Schematic diagram of the target holder rods . , 15 II-4- Schematic diagram of the target chamber-colli-JH3-toi* 9-SS6tnbly o e 0 0 * * 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o o * * e 13 I I - 5 View of the angular d i s t r i b u t i o n table 19 I I - 6 Schematic diagram of the detector assembly .. 28 I I - 7 ^°Co gamma-ray spectra 30 II-8 Block diagram of the electronic arrangement . 3 5 1 1 - 9 Photomultiplier c i r c u i t ... e „ 36 1 1 - 1 0 Preamplifier c i r c u i t 3 7 1 1 - 1 1 Preamplifier's regulated power supply c i r c u i t 3 9 I I - 12 Pulse generator c i r c u i t 4-1 I I I - l Detector-target configurations 4 3 III-2 Background spectrum (D(p,o")^He runs) 4 6 I I I - 3 D(p,O^He gamma-ray spectrum 8^  = 9 0 ° l60 K©V o o o o o o o o o o o o o * * o o * * * o * o o « o o o o e » o o *^7 I I I - 4- I n i t i a l estimate of the parameter K for the i t e r a t i v e least squares method .............. 5 6 IV- 1 D(p,tf)%e gamma-ray angular d i s t r i b u t i o n C 9 . S 6 o o o o o o o o o o o o o o o o o o o v o o o o e o o o o e o ' o o e o o o 63 IV-2 D(p,"Jf)-^He gamma-ray angular d i s t r i b u t i o n case ^7 9 0 6 O O o o o o o * * o * 0 * o « * * o Q O o o o o e o o o » < « o o e * ^ 9 IV-3 D(p,T{)%e gamma-ray angular d i s t r i b u t i o n case o o o o o o e o o o o o o o o o o * « o * o o o e * * * o o o o o o * * o 71 IV-4- D(p,7j)^He gamma-ray angular d i s t r i b u t i o n case $ 9 o o e o o * o o o o o * o o o o o e o o e * o o * o o * o o o « o o * * t ^ 72 v i i i i x IV-5 D(p,"tf)-%e gamma-ray angular d i s t r i b u t i o n case IV-6 D ( p , t f ) % e gamma-ray angular d i s t r i b u t i o n case #9 w i t h d e t e c t o r f i n i t e s o l i d angle cor-X * G C * b i O H iHClud- G C l 0 0 0 0 0 0 • » • # o o o o o ^ o o o o o o o o o o o o 7 3 IV-7 D(p,"tf)^He gamma-ray angular d i s t r i b u t i o n case #10 w i t h d e t e c t o r f i n i t e s o l i d angle cor-r e c t i o n i n cluded . ? 6 IV-8 D(p,~6)-%e gamma-ray angular d i s t r i b u t i o n case $^4* e e 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 * 0 77 IV-9 D(p,'o')%e gamma-ray angular d i s t r i b u t i o n case ^ 3 * * 0 0 * 0 0 0 0 0 * 0 0 0 O O O O O O 0 O B 0 0 O • O O * O O • * 0 O O © 7^ IV-10 Schematic diagram of the r o t a t i n g t a r g e t holder 8 9 12 A - l Some energy l e v e l s i n the G nucleus . .. 96 1 1 V 1 ? A-2 B(p,o) c gamma-ray spectrum 97 11 12 A-3 Background spectrum ( B(p , " 0 C run ) . . . o o o o o 98 I 1 V 12 A-4 B(p,o) c gamma-ray angular d i s t r i b u t i o n f o r Etf = 1 1 . 7 MeV (case 7^2 ) O O O O O O O O O * O O 0 O O O * * O O O O 1 0 3 I I 1 2 A-5 B(p,#) C gamma-ray angular d i s t r i b u t i o n f o r E* = 1 1 . 7 MeV (case # 2 ) , w i t h d e t e c t o r f i n i t e s o l i d angle c o r r e c t i o n i n c l u d e d .............. 104 B - l Schematic diagram of the duoplasmatron i o n source and ..Elmsel lens . system -,,. 108 B-2 Schematic diagram of the a c c e l e r a t o r ......... I l l B-3 View of the a c c e l e r a t o r 118 B-4 View of the a c c e l e r a t i n g tube 1 1 9 B-5 T r a j e c t o r y of the mean p a r t i c l e i n the h o r i z o n -t a l plane of d e f l e c t i o n of the a n a l y z i n g magnet pole t i p 121 G-l Target holder a b s o r p t i o n c o r r e c t i o n 132 H-l D(d,n)-%e spectrum obtained w i t h detector #1 .. 1 3 9 H-2 D(p,tf)^He gamma-ray spectrum 6 = 0 ° 160 KeV run 14-1 X H-3 D(P,V)^KE gamma-ray spectrum (background removed) 1^2 E-k D(p,ti)-%e gamma-ray spectrum (smoothed) ..... 1^5 H-5 D(p,ti)%e gamma-ray spectrum with 2% of D(d,"n)^He subtracted 1^6 ACKNOWLEDGEMENTS I wish to express my sincere gratitude to Dr. G.M. G r i f f i t h s f o r his u n t i r i n g supervision and conscientious assistance during the course of this work. His approachabillty together with his understanding of the problems involved, p a r t i c u l a r l y the language problem, made t h i s thesis possible. The h e l p f u l discussions of Drs. G.M. Bailey, J.H. Williamson and P.H.R. Orth on various aspects of this work i s appreciated. Furthermore, I wish to thank Mr. D. Hepburn and Dr. G.M. Bailey fo r t h e i r kind assistance i n obtaining experimental data during the p a i n f u l l y long hours of the night. The assistance of the members of the workshop and of the Van de Graaff group and i n p a r t i c u l a r that of the late G. Lang i s thankfully acknowledged. The author i s deeply g r a t e f u l to Dr. J.B. Warren fo r extending a scholarship to the University of B r i t i s h Columbia. To Dr. Ian McTaggart-Cowan, Dean of Graduate Studies, and other a u t h o r i t i e s of the University of B r i t i s h Columbia who made possible the transfer of my studies to the Ph.p. program of this University. A l Consejo Nacional de Investigaciones C i e n t i f i c a s y Tecnicas de l a Republica Argentina que p o s i b i l i t o ml v i a j e a esta Universidad. A mis padres por su constante apoyo durante e l transcurso de mis estudios. To my wife and Miguelito. x i PUBLICATIONS "Low Cost Deuterated Polyethylene Targets of Controlled Thickness for High Current Accelerators", M.A. Olivo and G.M. Bailey, Nucl. Instr. and Meth., 57 (1967) 353. "Use of the Maximum Likelihood Technique for F i t t i n g Counting D i s t r i b u t i o n s . Part I I . Application to Angular D i s t r i b u t i o n s " , P.H.R. Orth and M.A. Olivo, Nucl. Instr. and Meth., (to be published). x i i CHAPTER I INTRODUCTION 1 . 1 . General Introduction Direct r a d i a t i v e capture reactions i n nuclear physics involve a one-step t r a n s i t i o n between continuum and bound states of a p a r t i c l e where the energy difference i s transferred to the electromagnetic f i e l d and no intermediate compound state i s formed. These reactions provide a r e l a t i v e l y simple way of obtaining information about the bound state wave functions,since the properties of the continuum states can be Inferred from scat-tering data and the properties of the r e l a t i v e l y weak e l e c t r o ^ magnetic i n t e r a c t i o n are well known. Another d i r e c t capture-process known as a stripping reaction occurs when the neutron ; or proton from an incident deuteron i s transferred from the continuum to a bound state i n the f i n a l nucleus,while the energy difference i s taken up by the other p a r t i c l e (proton or neutron) from the deuteron. Similar information concerning the properties of bound states can be in f e r r e d from s t r i p p i n g and from d i r e c t r a d i a t i v e capture processes, however, the ra d i a t i v e capture i s i n practice more d i r e c t since i t i s mediated by the well understood electromagnetic i n t e r a c t i o n . On the other hand stripping depends on the much less well known strong nuclear i n t e r a c t i o n , not only i n forming the continuum and bound states but also i n the transfer process between them. I t might be noted however, that because - 2 -of the r e l a t i v e weakness of the electromagnetic coupling, the pr o b a b i l i t y f o r d i r e c t r a d i a t i v e capture i s i n general several orders of magnitude smaller than that for str i p p i n g . There i s a c o r r e l a t i o n between the structure of the bound state wave functions and s p e c i f i c properties of the nuclear forces. For few-nucleon systems many t h e o r e t i c a l studies have been ca r r i e d out to specify the nature of these correlations i n a quan-t i t a t i v e way. Therefore, knowledge about the bound state wave functions should i n p r i n c i p l e provide some understanding of the fundamental i n t e r a c t i o n between nucleons. The reaction D(p,tf)%e i s p a r t i c u l a r l y useful i n obtaining t h i s kind of information because: 1. The continuum states can be determined from proton-deuteron scattering data. . . 2. The continuum and bound states are coupled by the electromagnetic f i e l d which i s known exactly, and 3. Due to the weakness of the electromagnetic i n t e r -a c t i o n f i r s t - o r d e r perturbation theory can be used with some confidence i n computing t r a n s i t i o n proba-b i l i t i e s , or cross sections. Further, the f a c t that the bound state of -^ He has both s i n g l e t and t r i p l e t two-nucleon spin configurations and i s more t i g h t l y bound than the two body system (deuteron) indicates that the study of t h i s reaction could reveal properties of the nucleon-nucleon force to which the deuteron i s i n s e n s i t i v e , such as short - 3 -range components of the nuclear force or components sensitive to s i n g l e t spin configurations. The study of the reaction D ( p , t f ) % e i s also of i n t e r e s t i n a number of astrophysical processes. In the hydrogen-burning stage of small main sequence stars, the main energy supply comes from a series of reactions known as the p-p chain i n which the reaction D(p,»5)^He i s the second steps p + p — * D + | 9 + + v p + D — • 3He • 3He + % e — ^He + 2p The rate of energy release i n the p-p chain i s controlled by the f i r s t r e action since the y3 i n t e r a c t i o n i s much weaker: than the electromagnetic and nuclear interactions. However, the reac-t i o n D(p,"6')^He may have a s i g n i f i c a n t e f f e c t on the rate of con-densation of a star towards the main sequence, depending on the i n i t i a l amount of deuterium, since I t i s the f i r s t reaction to supply nuclear energy as the star condenses. Furthermore, the D ( p , ^ ) % e competes with the reaction D(d,n) JHe thus influencing the number of neutrons available from a given i n i t i a l amount of deuterium. Although the l a t t e r reaction has a cross section of a several order of magnitude greater than the D ( p , t f ) % e cross section the very much larger density of protons compared with deuterium would place the D ( p , u ) % e i n a compet-i t i v e p o s i t ion. The neutron y i e l d i s of interest,because i t i s believed that the neutron captures have influenced heavy elements isotope r a t i o s i n the early stages of the solar system. 1.2. Review of Previous Work The existence of the weak capture gamma r a d i a t i o n from •> the proton bombardment of deuterium was f i r s t reported by Curran and Strothers i n 1 9 3 9 (CU 3 9 ) . Further investigations of thi s r eaction were performed ten years l a t e r by Fowler, Lauritsen and Tollestrup (FO *J-9). I t was found that the angular d i s t r i b u t i o n p at a bombarding energy of l.k MeV was nearly pure s i n Q . This implies that the r a d i a t i o n involved emanates from an e l e c t r i c dipole aligned with the d i r e c t i o n of the incident proton. From the y i e l d , obtained at 9 0 ° , as a function of the bombarding energy from 0.5 to 1.5 MeV i t was also shown that the cross section was non-resonant In character i n d i c a t i n g a d i r e c t capture process. In 1952 Wilkinson (WI 5 2 ) measured the p o l a r i z a t i o n of the emitted gamma r a d i a t i o n showing that at 9 0 ° the gamma-rays were plane polarized with the e l e c t r i c dipole i n the reaction plane, therefore, confirming the suggestion of Fowler et. a l , that, the capture resulted from the emission of E l r a d i a t i o n as the proton made a t r a n s i t i o n from a continuum p-wave to the ground s-state 3 of ^He. He also suggested that the spin-orbit coupling must be 2 small since the s i n 9 d i s t r i b u t i o n was very pure, while spin-orbit coupling would induce t r a n s i t i o n s i n which Aj = - 1, -with a z 2 d i s t r i b u t i o n proportional to ( 1 + cos 0). The main tra n s i t i o n s correspond to AJ = 0, with a s i n 9 d i s t r i b u t i o n . A s i g n i f i c a n t amount of spin-orbit coupling would then give r i s e to gamma-ray y i e l d at 0 ° . - 5 -In 1955»with the advent of the s c i n t i l l a t i o n detectors, G r i f f i t h s and Warren (GR 5 5 ) measured the angular d i s t r i b u t i o n between 0 „ 5 and 2,0 MeV using heavy ice targets. They found that the d i s t r i b u t i o n was proportional to (a + b s i n Q) where a was small but not zero 9 and therefore put p a r t i c u l a r emphasis on the region around 0 ° i n order to determine the amount contributed by the spin- o r b i t i n t e r a c t i o n . They found however, that the energy dependence of the y i e l d at 0 ° was d i f f e r e n t from that at 9 0 ° . This suggested the p o s s i b i l i t y that the i s o t r o p i c component might ar i s e from magnetic dipole t r a n s i t i o n s following the capture,of s-wave protons. Such t r a n s i t i o n s may ari s e from non-central com-pone^jfcs i n the nuclear force (VE 5 0 ) . These authors also obtained an approximate value f o r the absolute cross section at E = 1,0 MeV, of k x 1 0 ~ 3 ° ( ± 50#) cm2. Measurements on the re a c t i o n D(p,u")%e were l a t e r r e -peated by G r i f f i t h s et. a l , (GR 6 2 ) , who measured the cross section and the angular d i s t r i b u t i o n f o r proton energies from 2 7 5 KeV to 1,75 MeV with more accuracy using both heavy ice and gas targets. Their r e s u l t s confirmed the assumption that the r a d i a t i o n observed at 0 ° i s due to s-wave capture. Because the s-wave capture should be more predominant with respect to the p-wave capture at low energies, G r i f f i t h s et. a l , (GR 6 3 ) measured the y i e l d and angular d i s t r i b u t i o n of this reaction i n the energy range from Zh to 48 KeV using heavy ice targets confirming once more the previous arguments. Assuming a - 6 -s i m p l i f i e d energy dependence for the cross section they analized the r e s u l t s to give separate cross section for p-wave and s-wave captures. At 2 5 KeV i n the laboratory frame the cross sections are: 0 ^ = ( 2 . 9 - 0.3) x 1 0 ~ 3 2 cm2 01 = ( 1 . 3 - 0.3) x 1 0 " 3 2 cm2 Recently W o l f l i et. a l . (WO 6 6 ) have measured the cap-ture cross section between 2 MeV and 12 MeV including angular d i s t r i b u t i o n s f o r several energies up to 5 . 2 5 MeV. 1.3. Present Work This work was o r i g i n a l l y undertaken i n order to obtain more accurate data on the absolute cross section at low energies both because t h i s reaction i s of i n t e r e s t i n astrophysics, and because more de t a i l e d t h e o r e t i c a l calculations were becoming a v a i l -able. Recent t h e o r e t i c a l studies on the three body system, i n p a r t i c u l a r t h i s reaction, indicate that an accurate determina-t i o n of the angular d i s t r i b u t i o n and of the absolute cross section including i t s energy dependence, would, i n p r i n c i p l e , provide i n -formation about the fundamental i n t e r a c t i o n between the p a r t i c l e s . An early group t h e o r e t i c a l c l a s s i f i c a t i o n of the permu-t a t i o n symmetries of the states of the three nucleon system was made by Verde (VE 5 0 ) for the purpose of c a l c u l a t i n g t r a n s i t i o n p r o b a b i l i t i e s between continuum and bound states. A more detailed - 7 -c l a s s i f I c a t i o n was considered by Derrick and Bl a t t (DE 5 8 ) f o r the ground states. In th i s work the r e l a t i o n between the wave function and the c e n t r a l , tensor and spin dependent parts of the nucleon-nucleon force was considered. Recently a more detailed discussion of the r a d i a t i v e t r a n s i t i o n s on the basis of better wave functions has been given by Eichmann (EI 6 3 ) , and a more complete c l a s s i f i c a t i o n of a l l possible r a d i a t i v e t r a n s i t i o n s has been presented by Davis (DA 6 7 ) . More complete l i s t s of r e f -erences are given i n these two papers. The data obtained from the present work i s compared with somewhat empirical t h e o r e t i c a l calculations of d i r e c t r a d i a -t i v e capture cross sections i n three nucleon systems given by Donnelly (DO 6 7 ) and Bailey, G r i f f i t h s and Donnelly (BA 6 7 ) i n which a two body approximation to the three nucleon system was used. Donnelly's theory has been used as a basis for comparison, because at the present time i t provides numerical r e s u l t s i n the energy range of i n t e r e s t which are based on accurate Coulomb p e n e t r a b i l i t i e s . More extensive comparisons with theory w i l l be made a f t e r the absolute cross section has been measured. 3 The vHe ground state i s known to have t o t a l angular momentum J = 1/2. The ground state wave function may then con-t a i n any one of, or a l i n e a r combination of the following compo-nents (SA 5 5 ) ; -8-Furthermore, the functions corresponding to each component can be c l a s s i f i e d according to t h e i r permutation symmetry properties. For three p a r t i c l e s the i n d i v i d u a l space, spin and i s o s p i n parts of the wave function can be decomposed into symmetric, antisym-metric and mixed-symmetry parts. I f the s p a t i a l part of the wave function i s symmetric then the spin-isospin part must be antisymmetric to s a t i s f y the Paul! Exclusion P r i n c i p l e . A b r i e f summary i s given here of how these various components of the ground state wave function a r i s e and how they 3 contribute to the structure of the ground state of the He* 2 The space-symmetric S state must be the main contribution to the ground state since i t has the lowest k i n e t i c energy of a l l three nucleon states. Further, i t would be the only component of the ground state i f the nuclear force were ce n t r a l and spin-indepen-dent. The other components are then present only because they 2 are coupled to the S state by a d d i t i o n a l parts of the two nucleon i n t e r a c t i o n . * •/ •. -2 Derrick (DE 6 0 ) has shown that the mixed-symmetry S^ m 2 state i s coupled to the symmetric S state due to the difference between the c e n t r a l t r i p l e t even and s i n g l e t even forces, and that the D state i s coupled i n by the tensor-even force compo-nent. Derrick (DE 6 0 ) has also shown that the amplitudes of the 2 V ~* -» P and P components, which would be coupled i n by the L.S i n t e r -action, are n e g l i g i b l e . Recently, however, Davis (DA 6 7 ) has p a r t i a l l y refuted Derrick-*s arguments. - 9 -In order to obtain an estimate of the e f f e c t that ad-2 im-mixtures of mixed symmetry s ( m ) state and D state have on the ra d i a t i v e capture process Donnelly (DO 67) has introduced a r b i -t r a r y amplitudes f o r states which approximate the character of 2 these admixtures into the ground state symmetric S wave function. The wave functions were generated for a square well p o t e n t i a l representing the Interaction of a proton and a deuteron i n both bound and free states. In t h i s model many of the s p e c i f i c three body aspects of the problem have been neglected so that the amplitude factors introduced cannot be d i r e c t l y r e l a t e d to the properties of the nucleon-nucleon forces coupling the three p a r t i c l e s . However, there i s reason to believe that the functions generated by Donnelly are approximately correct outside the range of the s p e c i f i c a l l y nuclear part of the force and should.there-fore lead to reasonable cross sections at low energies, for which most of the cross section arises from parts of the nuclear wave function outside the conventional nuclear radius. In thi s model square well parameters f o r the ground state were adjusted to f i t the binding energy of the proton i n % e ( 5 . ^ 9 MeV) assuming i t i s 2 predominantly a symmetric S state, and parameters f o r the contin-uum states were adjusted as a function of energy to f i t scattering data. Donnelly calculated angular d i s t r i b u t i o n s and cross sections to be expected on t h i s model as a function of energy f o r a range of values f o r the a r b i t r a r y amplitude parameters. In t h i s thesis the angular d i s t r i b u t i o n i s determined - 1 0 -at two bombarding energies 9 0 and 1 6 0 KeV i n the laboratory frame, and the r e s u l t s compared with Donnelly's predictions. A b r i e f d e s c r i p t i o n of the technique to be used, i n the future, to determine the absolute cross section i s outlined i n Chapter IV. CHAPTER II EXPERIMENTAL APPARATUS This chapter i s concerned with the design parameters and the t e c h n i c a l problems associated with the development of the apparatus used to measure the angular d i s t r i b u t i o n of the r a d i a t i o n from the reac t i o n D(p,"8) 3He. 2 . 1 . Angular D i s t r i b u t i o n Table A schematic drawing of the angular d i s t r i b u t i o n table, designed by the author, i s shown i n F i g . I I - l . Two aluminium " I " beams (A) are supported by b a l l bearings on an aluminium table so they can rotate about the centre post (B). The centre post has a concentric hole which locates the target chamber on the ro t a t i o n axis. The detectors with a hundred pounds of lead for shiel d i n g and co l l i m a t i o n were mounted on t r o l l e y s (C) so they r o l l i n the r a d i a l d i r e c t i o n on the " I " beams (A). A disc gradu-ated i n one degree steps was mounted on the centre post to define the angles between both detectors and the incident beam. The whole assembly i s s u f f i c i e n t l y r i g i d that r o t a t i n g the heavy detector assemblies does not e f f e c t target-detector centering or distance. The system was aligned using a theodolite. The c o l l i -mator, which defined the d i r e c t i o n of the beam, was adjusted u n t i l i t s axis met the t i p of a pointed spindle Inserted i n the centre post i n place of the target chamber. The axes of the detectors were, defined by f i n e wires placed on the detector's collimator. - 1 1 -F i g . 11-1 : S c h e m a t i c d i a g r a m of the a n g u l a r d i s t r i b u t i o n t a b l e . A l i g n m e n t o f the d e t e c t o r and c o l l i m a t o r w i t h r e s p e c t t o t h e c e n t e r o f r o t a t i o n i s shown . - 1 3 -These axes were aligned to int e r s e c t at the t i p of the spindle. The theodolite was also used to locate the degree disc so that the collimator axis passed through the zero degree mark. A l l adjust-ments are believed to have been made within one degree. 2 . 1 . 1 . Target Chamber The brass target chamber s i x inches high and three inches i n diameter i s shown i n Pig. I I - 2 . The 1/16 inch wall thickness was machined to a thickness of 0.021 inch over the centre region i n order to reduce gamma<-ray absorption. The bottom of the chamber was screwed through an insulator to a brass d i s c . The disc has a concentric c y l i n d r i c a l rod which f i t s i n the centre post of the table, l o c a t i n g the target chamber on the detector r o t a t i o n axis. Two d i f f e r e n t target assemblies shown i n Pig. I I - 3 were used i n t h i s experiment. The target holder "TA" (used throughout the 1 6 0 KeV runs) consists of a copper plate, with 0.082 inch diameter holes d r i l l e d lengthwise through the copper every 0.10 inches,, attached to a s t a i n l e s s s t e e l rod by means of brass tubes. Cooling water flows through these tubes, and through the holes i n the copper plate. The target holder "TB" (used throughout the 9 0 KeV runs) consists of a s o l i d 1/16 inch thick copper plate screwed to the water cooled copper t i p of a st a i n l e s s s t e e l rod. In th i s case the copper plate can be displaced sideways. Both rods "TA" and TARGET HOLDER ROD A WATER COOLING BEAM GRADUATED D I S C V I E W I N G PORT JVWAA/UL 1AA/UVI/" I N S U L A T I N G M A T E R I A L rt~T) rt~n i F i g . 11-2 S c h e m a t i c d i a g r a m o f t h e t a r g e t c h a m b e r . T h e t a r g e t c h a m b e r i s l o c a t e d i n t h e a n g u l a r d i s t r i b u t i o n t a b l e i n p l a c e o f t h e p o i n t e d s p i n d l e s h o w n h e r e f o r c o m p a r i s o n . n WATER COOLING S L O T S FOR V E R T I C A L 4T D I S P L A C E M E N T N S L S T A I N L E S S S T E E L r 4 4 -COPPER 1 C |o»o o ojoeoool C 1 i u-.Jl i " T D " COPPER T I P HOLES FOR HORIZONTAL D I S P L A C E M E N T ooooooooo — BEAM S c h e m a t i c d i a g r a m o f t h e t a r g e t h o l d e r r o d s . -16-"TB" have s l o t s which allow the rods to be located i n several d i f f e r e n t v e r t i c a l positions. The "TA" target holder was o r i g i -n a l l y made to be used with s o l i d deuterated targets as for example deuterium occluded i n zirconium since these targets need to be well cooled. The f i n a l 160 KeV runs were done using deuterated polyethylene targets and i t was found that these targets could be adequately cooled by conduction through the copper backing„ Therefore,, the "TB" rod was adopted f o r the 90 KeV runs since i t allows sideways displacement. In both holders the targets,, made on 0.012 Inch copper backings, were clamped to the target holders. Once everything was assembled the face of the target remained i n the plane con-t a i n i n g the axis of the rod which i s the same as the axis of ro-t a t i o n f o r the detectors. 2.1.2. The Collimator The collimator consists of two defining apertures and a skimmer. The f i r s t two have defining holes 0.100 i 0.005 inches i n diameter and the second has a 0.120 - 0.005 inch hole. The discs were mounted inside a machined st a i n l e s s s t e e l pipe and separated by two aluminium cylinders which are also used to conduct the heat to the supporting water cooled flange. The whole assembly was e l e c t r i c a l l y Isolated from the beam pipe. Although the angular d i s t r i b u t i o n measurements did not require knowledge of the charge c o l l e c t e d by the target, (Chapter I I I ) , provisions were made for future measurements of -17-the absolute cross section. F i g , II-4 shows the potentials which w i l l be applied to the target chamber and to the collimator for such measurements, 2 . 1 . 3 . The Vacuum System The angular d i s t r i b u t i o n table has i t s own vacuum sys-tem so that the target chamber can be pumped independently of the accelerator vacuum system. I t consists of a 1 0 0 1/sec (@ 1 0 ~ ^ mm of Hg) o i l d i f f u s i o n pump, a water cooled chevron r i n g b a f f l e and a l i q u i d nitrogen trap. DOW CORNING D C - 7 0 5 o i l was chosen because of i t s good backstreaming c h a r a c t e r i s t i c s . To provide the f o r e -pressure a 30 1/min (@ 1 0 ~ 3 mm of Hg) mechanical pump i s used. The collimator, because of i t s small defining holes, i s o l a t e s the vacuum i n the target region from that of the acceler-ator. This arrangement should prevent d i r t contamination i n the accelerator region from depositing on the target. I t also helps to maintain a good vacuum i n the target area, thus reducing i o n i z a t i o n due to the beam i n the r e s i d u a l gas and making measure-ments of the t o t a l beam-charge c o l l e c t e d i n the target more r e l i -able. With the beam "ON" the pressure i n the target chamber, under normal operating conditions, averages approximately -7 9 x 10 ' mm of Hg. F i g . I I - 5 shows photographs of the angular d i s t r i b u t i o n table and the detectors mounted on the t r o l l e y s . 2 . 2 . The Targets The choice of a suitable deuterium target was one of the main problems that had to be solved I n order to measure the l l Xv I N S U L A T I N G oo TO VACUUM PUMPS F i g . B i a s i n g v o l t a g e c o n f i g u r a t i o n and s c h e m a t i c o f the t a r g e t c h a m b e r - c o l 1 i m a t o r a s s e m b l y . d i ag ram FIG. 11-5 : (a) VIEW OF THE ANGULAR DISTRIBUTION TABLE AND AUXILIARY EQUIPMENT AND (b) CLOSE-UP VIEW OF THE ANGULAR DISTRIBUTION TABLE. -20-angular d i s t r i b u t i o n to a higher accuracy than had been achieved i n previous work. It was d i f f i c u l t to f i n d a target material that contained enough deuterium atoms to make i t possible to observe the low cross section r e a c t i o n i n a reasonable time, which at the same time was rugged enough to withstand the large beam current and did not involve a large f r a c t i o n a l energy loss for the low energy incident beam. On the basis of previous data (GR 62 ; GR 63) i t can be estimated that for a bombarding energy of 160 KeV i n the labora-tory frame the cross section f o r the reaction considered here i s about 0.08 yWb f o r the Isotropic component and 0.6 ywb for the non-i s o t r o p i c component. The experiment requires a target with enough deuterium to provide a y i e l d at l e a s t comparable to the background. Yet, the target must be t h i n enough so as to be able to discriminate between angular d i s t r i b u t i o n measurements at 90 KeV and 160 KeV. A target thickness was chosen so as to produce a maximum energy loes of 35 KeV f o r 160 KeV protons. I t i s also desirable to have a beam spot on the target as small as possible i n order to avoid s o l i d angle corrections, due to the f i n i t e size of the source. At the same time i t i s desirable to be able to work with as much beam current as possible, i n order to shorten the length of the runs and to keep the y i e l d higher than the background. Multiple s c a t t e r i n g of the incoming beam i n the target was also considered. The R.M.S. scat t e r i n g angle should be kept -21-as small as possible, otherwise the angular d i s t r i b u t i o n becomes d i f f i c u l t to analyze, p a r t i c u l a r l y because no r e l i a b l e t h e o r e t i c a l analysis or experimental data i s available on multiple scattering for massive charged p a r t i c l e s for the low energies considered here. Deuterium targets can be c l a s s i f i e d into four d i f f e r e n t kinds: deuterium gas, heavy i c e , deuterium absorbed i n s o l i d elements, and deuterated compounds. 2.2.1. Deuterium Gas Targets Gas targets were discarded because no physical window was avai l a b l e that would hold a reasonable pressure of gas and admit a small diameter beam of the required current (about 100 JAA). D i f f e r e n t i a l l y pumped gas targets were also impractical for t h i s experiment, for apart from the very large gas flow required, the gamma-ray source could not be accurately defined i n position. 2.2.2. Heavy Ice Targets The main d i f f i c u l t y with these targets i s that they would evaporate quickly under bombardment by the beam densities needed f o r t h i s work. Further, the determination of the thick-ness i s d i f f i c u l t . Previous low energy work with heavy ice tar -gets was done with thick targets that completely stopped the beam. I t should be pointed out here that f o r angular d i s t r i b u t i o n measurements one does not need to know exactly the amount of target material as long as i t s thickness i s kept below a c e r t a i n value. An estimate of the thickness could be made by l e t t i n g the vapor from a heavy water dispenser condense on a target attached to a l i q u i d nitrogen cooled copper plate. The s h i f t i n -22-11 12 the 163 KeV resonance, i n the reaction B(p,tf) C, would give d i r e c t evidence of the thickness of the heavy ice target. However, t h i s i s d i f f i c u l t to do, because the boron i n the beam spot tends to flake o f f , thus making a bad thermal contact between the ice and the copper plate. Some tests were done using "thin" targets. A 100 KeV proton beam of 30was collimated to give 2 a target spot of 4-0 mm on a t h i n heavy ice layer l a i d onto a l i q u i d a i r cpdled plate. The targets under these conditions did not l a s t longer than a few seconds and so t h i s method was d i s -carded. 2.2.3. Deuterium Absorbed i n S o l i d Elements Some elements have the property of absorbing and re-taining large quantities of hydrogen at r e l a t i v e l y high temper-ature. Among those which absorb the most are palladium, tantalum, zirconium, and titanium. I t was recently found that erbium and i n general most of the rare earth elements are also good absorbers. Deuterium targets of t h i s kind have been used for many years for neutron production. I t i s e s s e n t i a l that the gas once absorbed i s retained i n the target while under bombardment by a beam i n a vacuum. Targets of deuterium i n Zr and T i were obtained from the Oak Ridge National Laboratory. They were made as follows % A known amount of, say, zirconium was evaporated onto.a suitable, and previously outgassed backing such as copper, platinum or tungsten. The deposit was outgassed under vacuum at high temper--atures and placed i n a deuterium atmosphere at a suitable temper-ature. Absorption begins a f t e r the heat i s interrupted and the -23-system i s allowed to cool o f f . Angular d i s t r i b u t i o n measurements at a proton energy of 160 KeV were done using Zr-D targets ranging 2 2 2 from 80 yug/cm to 143 y«g/cm and Ti-D targets ranging from 47 yMg/cm 2 to 58 yKg/cm „ The r e s u l t s contained uncertainties a r i s i n g from the rather large angular spread of the incoming p a r t i c l e s i n the target, due to the multiple coulomb scattering. Thinner targets would have overcome th i s d i f f i c u l t y however they would have given too low a gamma-ra~y y i e l d . 2.2 .4. , The Deuterated Compounds There are several hundred commercially a v a i l a b l e deute-rated compounds. Most of these compounds are, however, i n gaseous or l i q u i d form or they have two or more d i f f e r e n t elements, besides deuterium i n t h e i r molecular structure. A simple compound i s deuterated polyethylene (CDg)^ Using t h i s compound as a target the R.M.S. multiple scattering angle i s reduced considerably, compared with the Zr-D and Ti-D due to the lower Z i n the target components. Although the 1 2 C ( p , t f ) 1 3 N and 1 3 C ( p , i ) l i f N reactions compete with D(p,tf) 3He, t h e - f i r s t produces gamma-rays of lower energy which can be e l i m i -nated by a high enough disc r i m i n a t i o n l e v e l and the second has a n e g l i g i b l e y i e l d . Both reactions are discussed i n Appendix F, Self-supporting deuterated polyethylene targets are being used s a t i s f a c t o r i l y i n t h i s laboratory (TR 67 ; MC 68). These targets, however, can withstand only small beam densities 2 at most of the order of 10 yMA/cm . Furthermore, i f an energy loss -24-i n the target of only 35 KeV f o r a 1 6 0 KeV incident proton beam i s required, the polyethylene layer w i l l be, ph y s i c a l l y , extremely t h i n and thus very d i f f i c u l t to handle. Consequently such targets were ruled out. I t was found that i f the polyethylene i s deposited on a. metal backing, the target so formed, can withstand large beam p currents of the order of 2 0 0 to 300 yKA/cm , without rapid loss of target material. Furthermore, t h i n targets (of the order of 3 0 KeV f o r incident protons of 1 6 0 KeV) could e a s i l y be made i n th i s way. Therefore, these targets were u t i l i z e d for the angular d i s t r i b u t i o n measurements of the D(p,tf) JHe reaction. The technique followed i n the preparation of the targets i s described i n Appen-dix D. A comparison between these targets and Zr-D targets, nor-malized to the same deuterium content i s also shown. The targets used throughout th i s experiment were pre-pared by depositing 364yWg t 10% and 3 6 4 / c o s 4 5 ° . . = 5 1 5 y u g - 10% of polyethylene on a 3.7 cm by 3 . 7 cm copper plate 0 . 0 3 cm thick. Both targets are equivalent because of the two d i f f e r e n t detector-target configurations used i n performing the angular d i s t r i b u t i o n measurements, (Chapter I I I ) , so that only one w i l l be considered 2 here. The 5 1 5 J^S when deposited on I 3 . 6 9 cm gives a target thickness ?t (CD 2) of 3 7 . 6 0 ywg/cm ., This corresponds to N ct = 1 . 4 l 6 x 1 0 1 8 carbon atoms/cm2 and N Dt = 2 . 8 3 2 x 1 0 1 8 2 deuterium atoms/cm . The c h a r a c t e r i s t i c s of th i s target are shown i n Table I I - l . - 2 5 -Table I I - l : C h a r a c t e r i s t i c s of the Deuterated Polyethylene Targets. (KeV} (IO'SV-C*?) 06,SeV-c«*) 160 1° 10' 14 4 . 5 1° 18' 144 °i0 r 6* 16 b 2 ° 4 3 ' 7 0 Ep i s the i n c i d e n t proton energy; 8^ and 6 . Q the stopping cross s e c t i o n f o r protons i n carbon and deuterium, r e s p e c t i v e l y ; AE the energy l o s t by the beam i n the t a r g e t and [ Q ] c = J <^92^>r and [9]=- are the R.M.S. m u l t i p l e s c a t t e r i n g angle f o r protons of P _ energies E and E = E„ -AE/2 r e s p e c t i v e l y . The energy l o s s was c a l c u l a t e d , (using the f o l l o w i n g e x p r e s s i o n ) , assuming the stopping cross s e c t i o n s remained the same as the beam t r a v e r s e d the t a r g e t : AE = e G N G t + 6 D N D t The values f o r the stopping cross s e c t i o n s were obtained from Whaling (WH 58). The stopping cross s e c t i o n f o r protons on carbon reaches i t s maximum a t about 90 KeV, whi l e the maximum f o r protons on deuterium occurs a t 50 KeV w i t h a value of 6.6 x 10" D eV-cm . Therefore, i f the v a r i a t i o n of the stopping cross s e c t i o n w i t h energy were, taken i n t o account the energy l o s s i n the t a r g e t w i l l be a t the most higher than the value 39.7 KeV g i v e n i n Table I I - l . At 90 KeV the energy l o s s i s somewhat higher than the -26-35 KeV referred to previously as the maximum. The targets were made thicker than 35 KeV to compensate for the loss of deuterium which occurs,.when the "beam i n i t i a l l y h i t s the target. (See Appen-dix D). From the observed i n i t i a l decrease i n the gamma-ray y i e l d , which i s attr i b u t e d to the loss of deuterium, i t was.. estimated that these targets were thinner than 35 KeV throughout most of the i r run. The same e f f e c t applies f o r the targets used at 160 KeV, Multiple scattering calculations are discussed i n Appendix E, so o&^s-tihe- bas'ie Idea Is Introduced here. Assume that a p a r a l l e l beam i s incident on a target. The angular d i s t r i -bution of the p a r t i c l e s emerging from the target w i l l c l e a r l y have c y l i n d r i c a l symmetry around the axis defined by the incident beam. Based on s t a t i s t i c a l considerations (SE 53) which are i n agreement with the experimental r e s u l t s obtained from the scatter-ing, of f a s t electrons (WI 39) one can expect the p a r t i c l e s to be Gaussian d i s t r i b u t e d around th i s axis. Thus s t a t i s t i c a l l y a f t e r traversing a c e r t a i n thickness of target 68% of,the incident par-t i c l e s l i e i n a region defined by a cone whose half-angle, with respect to that axis, i s c a l l e d the R.M.S. multiple scattering angle. The r e s u l t s of the c a l c u l a t i o n discussed i n Appendix E are shown i n Table I I - l . Because of the small multiple scatter-ing angle produced by t h i s target, i t s smearing,effect i n the angular d i s t r i b u t i o n of the gamma-rays was n e g l i g i b l e . 2,3. The Detector. Collimator and Shielding The gamma-ray detector (HARSHAW Type 20MBS16/B) consists of a 5 inch diameter by 4- inch deep c y l i n d r i c a l Nal(Tl) c r y s t a l - 2 7 -coupled to a 3 inch (RCA 8054) photomultiplier. Two i d e n t i c a l detectors mounted i n I d e n t i c a l lead shields and collimators were used i n t h i s experiment. A schematic drawing i s shown i n F i g . I I - 6 . The Detector Half-Angle ; The angular d i s t r i b u t i o n of the gamma-rays from the r e a c t i o n D(p,u")3He can be expressed p approximately by W(9) = a + b s i n 9 (Chapter I ) . Because a i s small compared to b , ^ 3 w a s chosen so that when the detector was placed at 0° most of the gamma r a d i a t i o n i n the s o l i d angle subtended by the counter arose from the I s o t r o p i c component. The t o t a l cross section i s expressed byO~ = C r _ + 0", 9 , D where <T& and CT^  are the t o t a l cross section f o r the i s o t r o p i c and non-isbtropic components respectively. Thus Thus the above condition i s given by •'o For ^3= 12° and O ^ A T ^ = 0.13 the i s o t r o p i c component contribution amounts to 80.4#-when the detector i s at 0° . The Source Distance R; The distance R was chosen such that the cone defined by >^ contains the back of the c r y s t a l . That i s F i g . 11-6 : A s c h e m a t i c d i a g r a m o f the d e t e c t o r a s s e m b l y . The d i m e n s i o n s a r e g i v e n i n T a b l e I I-2 -29-A tapered.collimator was placed i n front of the c r y s t a l . In t h i s way a haIf-angle of 12° was defined and the corners of the c r y s t a l remained shielded. This collimator has the following results? 1. The background counting rate i s reduced, since the c r y s t a l "looks" only at the source. 2t The edge ef f e c t s of the c r y s t a l are reduced with .two useful consequences: .. , . - a. I t improves the photopeak to t a i l r a t i o . Thus the r a t i o of information to background i s im-proved. Pig. II-7 shows.the e f f e c t of the collimator on the shape of the spectra obtained using a ^ C o source. The spectra were normalized to equal k i c k s o r t e r l i v e times of 40 minutes. The background was not substracted. Without the collimator the photopeak i s higher than with i t because the detector subtends a larger s o l i d angle. b. The angular d i s t r i b u t i o n measurements have to be corrected f o r the e f f e c t of the f i n i t e s o l i d angle of the detector (RO 53). As a r e s u l t of reducing the edge ef f e c t s the - estimation of the c o r r e c t i o n factors., u s u a l l y ; r e f e r r e d to as smoothing f a c t o r s , i s made more r e l i a b l e . This involves the evaluation of i n t e g r a l s of the form; -31-where 5 i s the l i n e a r attenuation c o e f f i c i e n t , x(^) i s the distance traversed by the r a d i a t i o n incident on the c r y s t a l at an angle ^with r e -spects to i t s axis, and P^ are the Legendre polynomials of order 1. ;The smoothing factors are defined by = J^/J ^ . Without the c o l l i -mators the above integration over the c r y s t a l volume becomes less r e l i a b l e for two reasons. F i r s t there w i l l be a larger number of gamma-rays scattered into the c r y s t a l from surrounding materials,and second a larger,number of gamma-rays w i l l i n t e r a c t near the edges of the c r y s t a l where the p r o b a b i l i t y of.secondary r a d i a t i o n and electrons escaping from the c r y s t a l i s much higher. Since the gamma-ray i n t e n s i t y i s ob-tained by Integrating the spectrum upwards from approximately h a l f the f u l l energy, many of these events w i l l not be counted. The; Collimator Thickness S: .The 1 gamma-ray i n t e n s i t y at the corners of the c r y s t a l depends on the thickness S of the collimator. For S = 6.5 cm the attenuation factor was found to be equal to 0.04-1 fo r 5.58 MeV gamma-rays i n lead. F i n a l l y we have to consider the contribution of those gamma-rays which are scattered towards the c r y s t a l by the front edge of the collimator. A rough estimate was made of the number -32-of gamma-rays that leave the source at an angle greater than the half-angle |2> of the collimator and scatter into the c r y s t a l from the edge of the collimator with the detector at 0°. Only Compton scattering i s relevant to t h i s estimate and since the f i n a l gamma-ray i n t e n s i t y i s "based on the number of counts i n the spec-trum between 2.95 MeV and 6.1 MeV, only those gamma-rays scattered with energies greater than 2.95 MeV need be considered. This corresponds to scattering through angles less than 23°. I t was assumed that a l l the electrons i n a layer of collimator one half r a d i a t i o n length,thick were located i n a r i n g at. the inner front part of the collimator and that the gamma-rays :that entered the fro n t of the collimator were scattered by these electrons. I f one h a l f of the gamma-rays scattered between 0°.and.23° entered the c r y s t a l then the collimator scattering could contribute a t most 0.8$ of the t o t a l number of gamma-rays that enter the c r y s t a l . The size of t h i s c r y s t a l i s considered to be optimum. A smaller c r y s t a l i s undesirable because f o r the same s o l i d angle and collimator shape the detector must be placed closer to the source with the r e s u l t that: a. the size of the source becomes c r i t i c a l b. the sca t t e r i n g at the edge of the fr o n t collimator increases c. v a r i a t i o n s i n the source to c r y s t a l distance are more c r i t i c a l . A bigger c r y s t a l i s also undesirable i n the spite of -33-the advantage of a decreased edge e f f e c t f o r the same s o l i d angle, because of the increase i n the background and increase i n the neutron induced a c t i v i t y which may be present f o r some bombarding energies. In general c r y s t a l s longer than one or two r a d i a t i o n lengths are undesirable.because the back part has a low gamma-ray f l u x but contributes background counts roughly proportional to i t s volume. For 5.5 MeV gamma-rays i n Nal the r a d i a t i o n length i s approximately 8 cm. Neutrons may a r i s e from the r e a c t i o n D(d,n)^He caused by deuterons i n the target which have picked up energy by c o l l i -sions with incident protons ( G E 55). The neutrons are not counted d i r e c t l y by the c r y s t a l but they are captured by 1 2 ? i which r e s u l t s i n the prompt emission of gamma-rays i n the energy range from 2 to 6 MeV. This i s followed by /S~ emission of 2.02 MeV or 1.59 MeV followed by gamma-rays of 0.4-28 MeV. The beta decay t r a n s i t i o n s do not ? however, i n t e r f e r e with the D(p,tf)^He spectrum since they are below the 2,95 MeV i n t e g r a t i o n bias l e v e l . Table II-2 shows the exact dimensions of the detector assembly. 2.4-. The E l e c t r o n i c s A block diagram of the e l e c t r o n i c s used i n the experi-ment i s shown i n ' F i g . II-8. A l i s t of the e l e c t r o n i c units used Is given i n Table l t - 3 . The output from the photomultipliers were sent to two i d e n t i c a l preamplifiers with 50 -fl output im-pedance. The photomultiplier and preamplifier c i r c u i t diagrams are shown i n F i g . II-9 and 11-10. The phototubes were operated -34-Table II-2 : Dimensions of the D,etector Assembly #1 and #2 Collimator Half-Angle 12.0 + 0.2 degrees Source to C r y s t a l Pace R 19.52 0.05 cm Source to Collimator Face P 12.46 + 0.05 cm Collimator Thickness S 6.54 + 0.05 cm C r y s t a l Diameter D 12.70 + 0.02 .•> ..cm C r y s t a l Thickness L 10.16 0.02 cm Collimator Face Inner Diameter I 5.30 + 0.05 cm Collimator Face Outer Diameter 0 11.6 + 0.1 .cm Thickness of Lead Shielding T 4.0 cm - 3 5 -H . V . POWER S U P P L Y (2) DETECTOR #2 (3) SOURCE DETECTOR #1 (3) P U L S E (1) GENERATOR P R E - (k) A M P L I F I E R K l C K S O R T E R (7) POWER S U P P L Y (5) P R E - {h) A M P L I F I E R A M P L I F (8 I E R - B ) S . C . A . - B (8) S C A L E R (9) K l C K S O R T E R (6) A M P L I F (8 r l E R - A ) S . C . A . - A (8) S C A L E R (9) F i g . I I — 8 : B l o c k d i a g r a m o f t h e e l e c t r o n i c a r r a n g e m e n t . T h e u n i t s a r e l i s t e d i n T a b l e M-3-- 3 6 -OUTPUT ft ©• H.V. T FOCUS R. G A I N R, 1 PIO D9 D8 D7 D6 D5 Dk D3 D2 ANODE DYNODE 1 FOCUS G R I D CATHODE RCA 8054 R1 100 K ±W 5% R2 7^0 K iW 5? R3 1.5 M P o t . R* 2 M P o t . c1 0.001 3 KV C2 0.01 JiF 600 V F i g . I 1-9 : P h o t o m u l t i p i i e r c i r c u i t 1N750 T E S T ( • ) I N P U T ( N E G ) ( • ) 1N462 2 . 68pF - A A A -5.6K 2N2925 lOytHy 47K T + 2 0 / F 1.2K —w— O . O O I ^ F 1 2 K f w H " C=0.001/F H ^ ® O U T P U T ( P O S ) * 3-3K - V V A — 1 20^F O . O O I j i F 2N2925 | | ^7 20pF R=5.6K : 3 9 V o l t s I I 20/*F O U T P U T ( N E G ) * ioyuHy - o + F i g . 11-10 P r e - a m p l i f i e r c i r c u i t . * F o r n e g a t i v e putse o u t p u t t h e p o s i t i v e o u t p u t must be g rounded (and v i c e - v e r s a ) - 38 -at 1100 Volts and the focus control was adjusted to obtain the best r e s o l u t i o n . The measured pulse height r e s o l u t i o n f o r 662 KeV gamma-rays was found to be 79k% f o r detector #1 and 7,8^ f o r detector #2. The shape of the pulses at the output of the preampli-f i e r s was adjusted by means of the r e s i s t o r R and capacitor C to s a t i s f y the low l e v e l input requirements of the N D - I 6 0 and ND-120 k i c k s o r t e r s . The 2.614- MeV pulses, from a RaTh source, across a 50X1 r e s i s t o r connected at the output of the preampli-f i e r (with R = 5.6 Ka and C = 0,001 yuF) have a rise-time of 0.6 jus and a f a l l - t i m e of 18 yUs. The pulse remains at nearly i t s maximum voltage l e v e l f o r approximately 0.5 yU-s with the maximum occuring at 1.2 ^*s, from the s t a r t . The preamplifiers have a voltage gain of approximately 0.08. They were b u i l t from a c i r c u i t designed by G. Jones (JO 65). A power supply was b u i l t to supply d.c. power to both preampli-f i e r s . The c i r c u i t diagram i s shown i n F i g . 11-11. The signals from the preamplifiers besides going to the k l c k s o r t e r s were also sent to two i d e n t i c a l scalers, through a dual l i n e a r a m p l i f i e r - s i n g l e channel analyzer system. An i n i t i a l estimate of the angular d i s t r i b u t i o n could then be obtained while the experiment was under way. An estimate of the rate of d e t e r i -o ration of the targets could also be obtained i n t h i s way. The e l e c t r o n i c system was checked f o r l i n e a r i t y using O - A +B O -27 • W -1N746 ^ 2N1480 > 680 < 1.1K > 1. 6K > 1. I \ CO, I C Q , r C 3-9K - A O — * -• O + I 9 V o l t s F i g . II — 11 : P r e - a m p l i f i e r 1 s r e g u l a t e d power s u p p l y c i r c u i t . -40-a pulse generator. I t was b u i l t using a mercury switch driven at 60 Hz, The c i r c u i t , shown i n F i g . 11-12, was designed to give a pulse whose shape a f t e r the 68 pF capacitor (test input of the preamplifier) was i d e n t i c a l to the one produced by the detector at the input of the preamplifier. The l i n e a r i t y of the HELIPOT potentiometer was checked using a FLUKE d i f f e r e n t i a l voltmeter 0 and i t was c a l i b r a t e d i n energy units using standard radioactive sources. The pulse generator was also used to make periodic checks of the windows of the single channel analyzers, Table II-3 : L i s t of the E l e c t r o n i c Units used i n t h i s Experiment. 1. U.B.C. Pulse generator. C i r c u i t diagram F i g . 11-12. 2. FLUKE Model 4-12-B High Voltage Power Supply. 3. HARSHAW Type 20MBS16/B. Detector Assembly Nal(Tl) 5" x 4-" c r y s t a l coupled to an RCA 8054- 3 inch photomultiplier. C i r c u i t diagram F i g . II-9. 4-. U.B.C. Preamplifier. C i r c u i t diagram F i g . 11-10. 5. U.B.C. Power Supply. C i r c u i t diagram F i g . 11-11. 6. NUCLEAR DATA ND-160 Dual Parameter Analyzer. 7. NUCLEAR DATA ND-120 Pulse Height Analyzer. 8. NUCLEAR DATA ND-500 Dual Amplifier and Single Channel Analyzer. 9. OR TEC Model 4-30 Scaler. 1:1 M E R C U R Y 5K 5K S W I T C H 110 V o— 1 J * i j • W — V S A ^ — I 5K If 5100pF 200K - A A A < r 1 10 T O A S T A B L E D . C . P O W E R S U P P L Y 100K ( H E L I P O T P o t e n t i o m e t e r ) O U T P U T 120 15K "p20pF I F i g . 11 -12 : P u l s e g e n e r a t o r c i r c u i t . N e g a t i v e p u l s e o u t p u t : r . t . = 80 ns , f . t . = 3 5 0 M s . CHAPTER III EXPERIMENTAL METHODS AND RESULTS. The t e c h n i c a l problems involved i n the measurements and the apparatus parameters chosen are discussed i n the previous chapter. In the present chapter the measurements and methods of data analysis are described. 3.1. Procedure Since a number of d i f f e r e n t targets were used and the targets tended to deteriorate during bombardment i t was not possible to r e l a t e one run to another i n terms of the integrated charge delivered to the target. Individual runs were therefore normalized i n terms.of the counts recorded by monitor counter #2 placed at a f i x e d angle. For a l l runs the beam spot on the target was 4 mm i n diameter which i s s u f f i c i e n t l y small compared to the 19.5 cm distance from the target to the detector so that the target can be considered as a point source of gamma-rays. The targets were l a i d down on a 3.7 cm x 3.7 cm copper backing and the average number of runs made on each target was 72. Due to the d e t e r i o r a t i o n of the target when subjected to a beam of 80 to 90 ykA -the beam was kept on the same target spot f o r approximately f i v e minutes, and then moved to a new spot. Two detector-target configurations shown : i n F i g . I I I - l were used f o r the angular d i s t r i b u t i o n measurements. For con-f i g u r a t i o n "A" the target plane was placed at 90° to the incident -42--43-#1 \ C O N F I G U R A T I O N " A " DETECTOR #2 ( F I X E D ) DETECTOR #1 I i C O N F I G U R A T I O N " B 1 F i g . I I 1-1 : D e t e c t o r t a r g e t c o n f i g u r a t i o n s -44-beam while the f i x e d monitor was placed at -120°., Although a higher count would have been obtained with the monitor at 90 the target absorption at that angle would have been large and uncertain. For t h i s geometry the moving detector angle 9^ was varied from -30° to +60° where the minus sign corresponds to being on the same-side of the beam axis as the monitor detector. For geometry "B" the target plane was at 45° t o t h e beam and the monitor was at -90° so i t observed gamma-rays coming through the target backing. The moving detector was rotated from 60° to 135° the maximum backward angle that could be reached with the appa-ratus used. As mentioned i n Chapter I I , two d i f f e r e n t target thick-nesses were used throughout t h i s experiment. The target of con-f i g u r a t i o n "A" was 1/cos 45° thicker than that of configuration "B" so that the beam passed through the same thickness of target material f o r both cases. The spectra obtained from both multichannel analyzers were integrated from 2.95 MeV to 6.1 MeV, the lower l i m i t being chosen to l i e above1'the HaTh f u l l energy photo peak, while the upper l i m i t was ichosen to l i e above the peak corresponding to the maximum gamma^ray energy of 5.65 MeV expected from the reaction D(p,tf) He. Because-the gain of the ele c t r o n i c system changed s l i g h t l y over a long period of time, each spectrum was s h i f t e d to a standard gain and integrated uising the IBM 7040/7044 computer. The f i n a l measurements at 90 KeV and 160 KeV took between seven and eight days to complete. - 4 5 -The energy c a l i b r a t i o n for each spectrum was obtained from the 2.614 and 1.4-62 MeV peaks from RaTh and which aris e as part of the room background. The walls of the room contain 4-0 s i g n i f i c a n t amounts of RaTh and K. F i g ; III-2 shows a t y p i c a l background run taken over a period of 69.5 hours. The background count above the 2.614- MeV peak arises p r i n c i p a l l y from the^A-meson component of the cosmic rays. In the region of i n t e r e s t from 3 MeV to 6 MeV th i s counting rate averages 370 counts per hour per MeV. A t y p i c a l gamma-ray spectrum from the reaction D(p,7$)-^He i s shown i n F i g . I I I - 3 . I t was taken for a bombarding energy of 160 KeV with the detector #1 placed at 6 = 90°. The t o t a l charge delivered to the target was approximately 300 mC. (A spectrum taken at 0° i s shown i n F i g . H-2 (Appendix H); here the t o t a l charge delivered was approximately 420 mC). The spectra obtained from detector #1 with the ND-160 kicksorter were put on paper tape and transferred . to the computing centre where they were converted to magnetic tape and punched on IBM cards. The monitor spectra c o l l e c t e d by the ND-120 kicksorter were printed out and manually punched on IBM cards. The gain s h i f t s and integrations were then c a r r i e d out on the computer. The angular d i s t r i b u t i o n r e s u l t s are shown i n Table I I I - l for the 90 KeV run and i n Table III-2 f o r the 160 KeV run. A and B are the integrated number of counts including the background from detectors #1 and #2 respectively. 0 ^ and 62 are the angular posi-tions of detectors #1 and #2 as shown i n F i g . I I I - l . The f i r s t row (i=0) shows the integrated number of counts due to the background taken when the machine was not In operation. I l/l CD TD QJ (D n O 7T rt tQ -1 1 HI O c in 3 3 " CL O 2 m — n 3 rt rt C in O —I z r z r QJ (D X) rt (D ft) 3 -I CD — ua in -< r o o o o 0) T ; — CD c r < -i \ QJ O rt 3 " — Q) O ro o in XI n c 3 01 3 CL ft) C 3 : : a a f o a a (V) rn I D CD rn a a a o a a cn i a a a o a a NUMBER OF COUNTS (X10 3 ) ,000 80.000 160.000 2140.000 320.000 400.OOC i i i i ; I * + + K (1.462 MeV) R a T h (2.614 MeV) TO a £75 CO > O 7^ CD O -917-X 10 o o o .CD CM O o u § o Ii . CO UJ rn CM O O o 4 4 4 4 4 % 4 imillHIHIIIIilimil -.000 ~! I-ODD > — i 1 II + ' 4 + 4 4 D(p,tf)3He 9 =90° E =160 KeV. P 4 4 \ 000 3.000 ENERGY LRB 4-ODO (MEV) 5.0O0 6-0O0 7.0O0 F i g . I I 1-3 : D ( p , t f ) 3 H e g a m m a - r a y s p e c t r u m . i si • . A ' • ©2 B T(sec) C D E F G G H cr2 H 0 101535 ,.99282 315000 • 1 -30 1793 -120 2734 3360 1083 1059 710 1675 1076 5272 1147 5996. 2 -22 1760 -120 3160 3840 . 1238 1210 522 1950 679 3389 721 3822 3 -15 1502 -120 2807 . 3840 1238 1210 264 1597 420 4025 445 4518 4 - 8 1461 -120 2880 3840 1238 1210 223 1669 339 3528 358 3948 5 0 2792 -120 5252 7680 2476 2421 317 2831 284 2344 300 2621 6 8 2995 -120 5996 7680 2476 2421 519 3575 368 1603 390 1794 7 15 1600 -120 2898 3840 1238 1210 362 1687 544 3952 576 4436 8 22 1627 -120 2724 3840 1238 1210 389 1514 652 5121 693 5775 9 30 1855 -120 2730 3360 1083 1059 772 1671 117.3.: 5655 1251 6432 10 45 2255 -120 2692 3840 1238 1210 1017 1482 1741 10391 1884 12166 11 60 4222 -120 4201 5280 1702 1664 2520 2537 2520 8423 2817 10527 12 60 718 -90 792 960 309 303 409 490 409 1272 13 . 67 1484 -90 1531 1920 619 605 865 926 456 792 14 75 1629 -90 1646 1920 619 605 1011 1041 476 706 15 82 1689 -90 1623 1920 619 605 1070 1017 515 809 16 90 4141/ -90 3860 5040 1625 1589 2517 2272 543 415 17 95 1598 -90 1595 2160 696 681 902 915 483 906 18 100 1513 -90 1503 1920 619 605 894 898 488 896 19 105 1491 -90 1573 1920 619 605 872 968 441 711 20 112 1641 -90 1792 1920 619 605 1022 1187 422 507 21 120 1467 -90 1713 1920 619 605 848 1108 375 484 22 127 •1035 -90 1305 1680 542 530 494 775 312 627 23 135 622 -90 948 960 309 303 313 646 237 487 • Table I I I - l : D(p,"^) He gamma-ray angular d i s t r i b u t i o n data (90 KeV Run) Table I I I - 2 : D(p,"o') He gamma-ray angular d i s t r i b u t i o n data (160 KeV Run) i 9 x A 6 2 B T(sec) C D E F G H c r2 H 0 101535 99282 315000 1 -30 2125 -120 3851 3227 1040 1017 1085 2834 1832 7701 1989 9278 2 -15 1444 -120 3962 2528 815 797 629 3165 950 3670 1023 4253 3 0 3094 -120 10602 6957 2242 2193 852 8409 485 1053 520 1214 4 8 1689 -120 4628 3695 1191 1165 498 3463 688 3432 739 3963 5 15 1797 -120 4690 3225 1040 1016 758 3674 987 3404 1062 3944 6 22 1780 -120 3901 2992 964 943 816 2958 1320 5460 1425 6366 7 30 2295 -120 4134 3151 1016 993 1279 3141 1948 6940 2115 8180 8 45 3058 -120 3824 2647 853 834 2205 2990 3527 13179 3901 16119 9 60 6078 -120 6293 4789 1544 1509 4534 4783 4534 11777 5229 15658 IP 60 5350 -90 5787 3191 1029 1006 4321 4781 4321 10096 11 67 1877 -90 1899 1049 338 331 1539 1568 4690 34443 12 75 3973 -90 3898 3382 1090 1066 2883 2832 4867 22904 13 79 4563 -90 4245 2553 823 805 3740 3441 5198 18527 14 82 4300 -90 3989 3266 1053 1029 3247 2960 5245 23806 15 86 1602 -90 1494 1029 332 324 1270 1169 5194 56284 16 90 7282 -90 6692 4962 1599 1564 5682 5128 5298 13520 (Continuation) 17 95 8752 -90 8310 5322 f.1715 1677 7037 6633 5072 9438:: 18 97 7277 -90 7038 4915 1584 1549 5692 5489 4958 11303 19 101 7882 -90 7439 4519 1457 1424 6425 6015 5107 10372 20 105 6736 -90 6809 4747 1530 1498 5206 5313 4685 10785 21 108 4849 -90 4985 2982 961 940 3888 4045 4595 13230 22 112 2568 -90 2776 1606 518 506 2050 2270 4319 21464 • 23 120 3652 -90 4341 3609 1163 1137 2489 3204 3714 14012 24 . 127 2178 -90 2818 1564 . 504 493 1674 2325 3442 15402 25 135 1561 -90 2677 1666 537 525 1024 2152 2274 10704 I O I -51-There was no appreciable beam dependent background that could a f f e c t the angular d i s t r i b u t i o n measurements. This i s discussed i n Appendix H. The separate runs are l i s t e d i n order of Increasing 0 ^ However, the actual order i n which runs were done was alternated Column T indicates the t o t a l running time at each angle. The dead time for both kicksorters was less than 0,5% and was determined primarily by the background counting rate. No correction has been applied f o r t h i s dead time and the time T was taken to be the actual running time f o r both detectors. For configuration "A" a correction was applied to account f o r the changing gamma-ray absorption i n the target holder as a function of counter angle. (See Appendix G), The corrected number of counts i s found i n column H, Absorptions i n the wall of the chamber and i n the c r y s t a l ' s container were not taken into account because these did not depend on the angu-l a r p o s i t i o n of the detector, A summarized explanation of the Tables I I I - l and III-2 i s given below. A^ = Integrated number of counts i n detector #1.: = Integrated number of counts i n detector #2, T^ = Total running time f o r each angle. C, = Number of background counts i n detector #1 normalized to 1 time T.. -52-D. = Number of background counts In detector #2 normalized to 1 time T±a = Number of counts less number of background counts C^. F i = Number of counts less number of background counts D^. G^ = Number of counts E^ ^ normalized to number of counts F^. H. = Number of normalized counts G. i n detector #1 corrected due to target holder absorption. A ( i = 0) = Integrated number of background counts i n detector #1. B ( i = 0) = Integrated number of background counts i n detector #2. T ( i = 0) = Total time i n which the background run was performed. The following expressions show the tabulated quantities with t h e i r standard deviations: A L t A A;. = Aj. +^A7 B i i A B , - B c t f B T To To 1 • • hi + AD; - (Bo TLA + IiJaT V To > ' To V  , . To ' • T0 Fc where V i s an a r b i t r a r y constant chosen to provide a convenient scale, and ^ Z i -53-where Z 1 i s the absorption correction factor discussed i n Appen-dix G. I t was assumed that Z, has no s t a t i s t i c a l error. This correction applies only to the target detector configuration "A". 3.2. The Angular D i s t r i b u t i o n Function I t is , r . convenient to express the r e s u l t s of an angular d i s t r i b u t i o n measurement as a Legendre polynomial s e r i e s : W(e) = ^  Be pe (cos 0) ( 3° 2 " 1 } This i s p a r t i c u l a r l y useful because i t s i m p l i f i e s the s o l i d angle corrections. Rose (RO 53) has shown that, i f t h e d a t a i s f i t t e d to a function of the form (3.2 - 1) then, the corrected angular d i s t r i b u t i o n function i s simply given by \ W(Q) = Y_ Ae Pe (cos 6 ) where A^ = B^/Q^o The smoothing factors can be obtained by an in t e g r a t i o n over the volume of the detector (See Chapter I I ) . The calculated smoothing factors f o r the detector assembly used i n t h i s experiment are shown i n Table III-3. Table III-3 : Smoothing Factors Calculated at E* = 5.58 MeV for the Detector Geometry Shown i n F i g . II-6. 1 0 1 2 3 4 «1 1,00000 0.98839 0.9654-6 0,93174- 0.88803 3. 3. The F i t t i n g Procedure For each angle 9. the p r o b a b i l i t y of observing N. counts -54-i s given by the Poisson d i s t r i b u t i o n R . I * 0 N - e " ^ / Nil where = WtBjS^) i s the curve to be f i t t e d where B stands f o r the set of angular d i s t r i b u t i o n coefficents B'^ . The j o i n t p r o b a b i l i t y of getting a p a r t i c u l a r arrange-ment of experimental r e s u l t s N, N. N at the angles i l p ^ Q^, . . . ,6^ t . . . ( Q i s the l i k e l i h o o d function L. = TT providing the events are independent. The problem here i s to f i n d the set of B 1 say B* which maximize the function L. The best f i t curve i s then given by W = W(B*;Q). I f we take the logarithm of L, then S , fen L m £ G» R a j[ kWi - MNil ) ] the solutions are then obtained from the r simultaneous equations « o e = o,i that i s : y ( A i ) = Q e=o,4 0 . 3 - 1 ) v ' s e e . These equations are non-linear i n B^, but the problem can be s i m p l i f i e d as indicated below; If i n the denominator of equation ( 3 . 3 - D i s re-placed by N^, that i s , i f the following approximation — i s made then the solutions can be found from I -55-where t h i s set of r equations i s now l i n e a r i n B^„ This r e s u l t can also be shown to be a d i r e c t consequence of the p r i n c i p l e of minimum variance which says that the best estimate f o r the set can be obtained by a least squares method; i.e. f 2, Y_ ™ l ( N i t - VX/i) = m i n i m u m 1=1 i f the weights m^  are inversely proportional to the variance N^. If we define M as N\ - V ( ML - wcf. then the solutions B^ = B* can be obtained from the r simultaneous equations d\A_ ^ O £ = O, 1 The standard deviations i n the parameters B* are given by the error matrix (OH 58) where (B 1-BJ)(B k-B*) = ( H " 1 ) 1 k l,k=0,r H, - 1 ^ 2 36<3&k The square root of the diagonal elements of the matrix H are the standard deviations i n the parameters B* and the off-diagonal elements AB^ AB^ define the degree of c o r r e l a t i o n between them„ - 5 6 -As was stated e a r l i e r i n this chapter the readings at the d i f f e r e n t angles were taken using two d i f f e r e n t configurations, In order to procede with the f i t t i n g analysis the experimental data obtained from these two configurations have to be r e l a t e d to each other. This could be done as follows„ At both 90 KeV and 160 KeV the discontinuity occurs at 6^  = 60° as shown i n F i g . III - 4 - . Therefore, i f we c a l l R the factor which when multi-p l i e d by the configuration "B" data would make i t f i t smoothly to the configuration "A" data, then from F i g . and Tables I I I - l and I I I - 2 R = HCG^O 0),,^, / GCe^O 0),,^, N, N 2 1 r >~-4 X 0 ° 66 CONFIGURATION _J^_ CONFIGURATION^ II A II »B" 1 e F i g . III -4- Experimental angular d i s t r i b u t i o n . N i s the r e l a t i v e number of counts taken i n both configurations as a function of the angle 9 In the laboratory frame. Q o denotes the s h i f t i n the experimental angular scale. The points shown here were a r b i t r a r i l y drawn. - 5 7 -The a p p l i c a t i o n of the least squares method w i l l then give the solut i o n sought. There i s , however, an important d i f f i c u l t y with t h i s approach. The set of data i n the configuration "B" may be affected by a systematic error, that i s , a l l the points may l i e above or below the actual value unless the data at 60° i n both configurations are taken to a high degree of accuracy. Assuming that t h i s i s done i t s t i l l w i l l not be the proper procedure because a l l the data points i n the configuration "B" w i l l be weighted according to what happened at one p a r t i c u l a r angle. The approach chosen to overcome th i s d i f f i c u l t y i s outlined below, The data i s to be f i t t e d to a function of the following type: W * [ Y_ B t Pe (cos 9)1 ( | +l\<) Uo where , <0 ( configuration "A") 1 ( configuration "B") K i s then treated as a new parameter to be determined by the l e a s t squares f i t . K corresponds to ("j^ ""^ ) ! however, i t must be pointed out that R i s a constant determined by the r a t i o between two experimental data points taken at one. p a r t i c u l a r angle while K i s a parameter determined by the least squares f i t which depends on a l l of the experimental data. F i n a l l y the uncertainty i n the zero of the angular scale -58-must be considered. Although the 1 graduations i n the angle scale of the angular d i s t r i b u t i o n table (Chapter II) were ma-chined to better than 0.2 degree, i t s orien t a t i o n with respect to the Incoming beam could not be determined better than 1°. This i s i n i t s e l f small. However, because a small asymmetry-around 90° i s to be expected (DO 6?) i t i s important to eliminate experimental factors which might contribute to such an asymmetry. Therefore, the experimental data, was f i n a l l y f i t t e d to a function of the following type: 1 l E-o 1 (3.3 - 2) where G Q was treated as another parameter to be determinated from the experimental data. Because t h i s function i s no longer l i n e a r i n a l l the parameters an i t e r a t i v e method devised by Falk (FA 65) and Orth (OR 67) was used to f i t t h i s function to the experimental data. B r i e f l y the method consists i n the expansion of ^ t l , and i n the f i r s t order Taylor series about i n i t i a l values of the parameters B^, K and Q q to be determined. For convenience we rename the parameters Q = B ^ o r+1 and K = B. r+2* B8e Then + L — Bc-Be. j-c a 6 e 3 6 i 6j .6)0 A6 1 = 0,r+2 We have here a set of r+2 equations which are l i n e a r i n the increments B^ i n the parameters. I f we apply the least squares method to f i n d the minimum value of M then 4*2 0 = 3n _ AB; ft 6 j o 1 = 0,r+2 -59-If one s t a r t s with a r b i t r a r y i n i t i a l values B . of the para-j» 0 meters B ^ one can calculate the f i r s t and second derivatives of M using i t s d e f i n i t i o n . The above r+2 equations can then be solved f o r the r+2 increments A B ^ i n the parameters to give a new set of parameters B . 1 = B . + A R which s a t i s f y the above con-d i t i o n s . These new values of the parameters B ^ w i l l d i f f e r from the best values B * i n the f i r s t i t e r a t i o n because we are consider-ing only the f i r s t term i n the Taylor series. Then the procedure i s to repeat the operation again, now using B . . i as the new i n i t i a l values of the parameters. This operation i s repeated u n t i l ^ E L - BjC - 6j(l-Q j _ 0 f r + 2 i s less than-some chosen value. A computer program written by Orth (OR 67A) to f i t a sum of two exponentials was modified to accept the function ( 3 . 3 - 2 ) . These i t e r a t i v e calculations must s t a r t with i n i t i a l values of the parameters which should be chosen reasonably close to the correct values i f the process i s to converge quickly or at a l l . The i n i t i a l value given to Q Q was obtained by p l o t t i n g the y i e l d around 0° f o r the 160 KeV and 90 KeV runs. A zero s h i f t of approximately 2° was noted and t h i s value was chosen f o r 8Q. The i n i t i a l estimate f o r K was obtained from the value of R, estimated for 60° data that i s K = 1/R - 1. The i n i t i a l estimates f o r the parameters B ^ were ob-tained by f i t t i n g the data to the function (3.2 - 1). A least squares f i t t i n g program for l i n e a r functions was used In t h i s - 6 0 -case. Here the data from both configurations were rel a t e d using the factor R and 0 was assumed to be zero. 3 . 4 . The Results Experimental r e s u l t s from previous work (Chapter I) indicate that the angular d i s t r i b u t i o n of the gamma-rays from the r e a c t i o n D(p,^)%e at low energies (24 KeV to 1.75 MeV) has, p at l e a s t i n f i r s t approximation, the form W(9) = a +. b s i n 9 (or i f expressed i n terms of Legendre polynomials W ( Q j r ^ P ^ A g P g ) However, recent t h e o r e t i c a l calculations (DO 67) indicate that terms higher than Pg may be present i n the angular d i s t r i b u t i o n of t h i s r eaction even at energies below 200 KeV. Table I I I - 4 shows the r e s u l t s of the f i t t i n g f o r the 90 KeV and 160 KeV runs. P i t s were obtained f o r several d i f f e r e n t sets of Legendre polynomial parameters B^. In rows 1 and 6 the experimental data was f i t t e d to the following Legendre polynomial series o Therefore, the function chosen i n the present analysis includes terms up to P^ In the Legendre polynomial ser i e s . with (configuration "A") (configuration "B") i n which the parameters B^, B_, and B^ were set i d e n t i c a l l y equal - 6 1 -to zero. S i m i l a r l y , rows 2 and 7 show the r e s u l t obtained when the parameters and B^ were set equal to zero. Rows 3 and 8 correspond to the case i n which a l l the parameters were l e f t free. In rows 5 and 10 the experimental points were f i t t e d to the same function i n which a l l the parameters but B^ were set free. .The pa r t i c u l a r r e s t r i c t i o n s imposed here are discussed i n Chapter IV. The condition imposed on th i s parameter was that the angular d i s -t r i b u t i o n obtained from the f i t must give the same value at 0° and 180° when the s o l i d angle correction was applied. , That i s , = -A^ which means that the condition imposed on the parameters B^ was B^ = -Q^/Q^ B^ where and are the smoothing factors. The function used for th i s case was F i n a l l y i n rows 4 and 9 the r e s u l t s are shown f o r the case when a l l the parameters but A^ were set free. Here however, the con-d i t i o n imposed on that parameter was that the corrected angular d i s t r i b u t i o n must be equal to zero at 9^  = 180°. This condition follows i f the value of A^ i s r e s t r i c t e d to A 4 - ~ Ao + A l " A 2 + A 3 In t h i s case the function used was W^ . [ 6 0 ( P o - < h ?*) -B.(R + 9iP.) <- 6 z ( - Q i PA) + 65 ( P » +Si P ^ (n-1K) The same program includes the Usual Chi-squared test. The test was made on each f i t and the r e s u l t s are shown i n Table I I I - 4 . The number of degrees of freedom corresponding to - 6 2 -each f i t are shown i n the column denoted by ^ . The normalized p r o b a b i l i t y of o b t a i n i n g a value of % g r e a t e r than or, equal to the value obtained i n each p a r t i c u l a r f i t was found from the % t a b l e s and i s shown i n column denoted by p. (1 - p) gives then the p r o b a b i l i t y of o b t a i n i n g a b e t t e r f i t to the f u n c t i o n a l r e a d y determined i f the experiment i s repeated under the same experimental c o n d i t i o n s . The best values obtained f o r Q Q and K i n each f i t and the square r o o t of the v a r i a n c e f o r a l l parameters (AB^,A&Q and^K) are shown i n Table For each f i t the i t e r a t i o n was c a r r i e d on u n t i l the r a t i o of the parameters f o r successive steps was l e s s than 0.001 (0.1$) f o r a l l parameters. On the average four i t e r a t i o n s were needed to achieve t h i s r a t i o . The angular d i s t r i b u t i o n parameters shown i n Table III-4 were c a l c u l a t e d f o r the centre of mass system. The i n p u t data were transformed to the centre of mass i n the same program u s i n g equations g i v e n i n Appendix G before the f i t t i n g procedure was c a r r i e d out. B o B l A B 1 B 2 * B 2 B 3 * B 3 B 4 & B 4 # 1 2438 103 0 0 -2142 117 0 0 0 0 # 2 2583 175 0 0 -2369 251 0 0 109 105 # 3 2288 298 185 173 -2138 300 -25 229 -15 207 # 4 2313 223 166 78 -2133 304 -53 79 7 104 # 5 2367 227 123 81 -2123 302 -116 76 57 111 # 6 4596 106 0 0 -4069 115 0 0 0 0 # 7 4805 134 0 0 -4396 177 0 0 157 76 # 8 4238 232 451 151 -4110 232 91 186 -158 163 # 9 4438 182 300-. 76 -4110 240 -100 74 14 80 #10- 4549 187 219 77 -4111 245 -206 73 106 89 Table I I I -4a : D(p5l5) He angular d i s t r i b u t i o n least squares f i t parameters fo r 90 KeV and 160 KeV runs. e 0 A6 0 M K AK r P E P (KeV) # 1 0.020 0.011 -0.856 0.007 12.79 • 18 0.79 # 2 0.016 0.011 -0.865 0.010 11.64 17 0.83 # 3 0.012 0.012 -0.847 0.019 9.53 15 0.84 70 #4 0.012 0.012 -0.848 0.016 9.54 16 0.89 # 5 0.011 0.012 -0.851 0.016 9.70 16 0.88 # 6 0.029 0.007 -0.216 0.020 35.14 20 0.02 # 7 0.026 0.007 -0.255 0.023 31.72 19 0.03 # 8 0.012 0.008 -0.166 0.043 22.22 17 0.18 144 # 9 0.012 0.008 -0.193 0.037 23.31 18 0.19 #10 0.012 0.008 -0.208 0.037 24.76 18 0.12 Table III-4b : D(p,tf) He angular distribution least squares f i t parameters and Chi-squared test for 90 KeV and 160 KeV runs. CHAPTER IV DISCUSSION In the previous chapter the measurement of the angular d i s t r i b u t i o n f o r the reaction D(p,"iJ)^He and i t s d e s c r i p t i o n i n terms of a Legendre polynomial series i s described. In this chapter the experimental r e s u l t s are discussed and compared with the t h e o r e t i c a l c a l c u l a t i o n s made by Donnelly (DO 6 7 ) . A b r i e f d e s c r i p t i o n of a technique to be used i n the future to determine the absolute cross section of t h i s reaction as a function of ener-gy i s also presented. 4.1. Discussion of the Results In table III-4 the Legendre polynomial c o e f f i c i e n t s B 1 were shown f o r the 90 KeV and 160 KeV runs without corrections f o r the f i n i t e s o l i d angle of the detector. In order to correct the angular d i s t r i b u t i o n s f o r the f i n i t e s o l i d angle of the de-tector (Chapter I I I ) , i t i s necessary to divide the Legendre poly-nomial c o e f f i c i e n t s by the smoothing factors given i n Table III This could have been done by including the smoothing factors d i -r e c t l y i n the Legendre polynomial f i t t i n g program before the f i t was c a r r i e d out. This would have led d i r e c t l y to the same cor-rected c o e f f i c i e n t s , as the present approach i n which the uncor-rected c o e f f i c i e n t s are determined f i r s t . Since the absolute cross section has not been measured i t i s convenient to remove the a r b i t r a r y i n t e n s i t y factor B q and - 6 5 -- 6 6 -express the other c o e f f i c i e n t s as a r a t i o B-^/B^ The f i n a l corrected r e s u l t s are shown i n Table IV-1. F, i s the expectation value of B,Q /B Qn = A../A and AF, i s the 1 l o o l l o l square root of i t s variance. The percentage error ^= AF^/F^ x 100 and the X* percentage p r o b a b i l i t y P (defined i n Chapter III) are also Included. The expectation value F^ and AF^ were obtained as f o l -lows : Fi - E (k\ rlBtQ*\- Q, [6e _ ( H " ' ) o e , Be (w*)**] u 0 and _1 where H i s the error matrix defined i n Chapter I I I . For the 144.KeV r e s u l t s i f we accept the usual c o n f i -dence l e v e l of 5%t the Chi-squared test eliminates case #6 with only A Q and A 2 c o e f f i c i e n t s as well as case #7 with c o e f f i c i e n t s A Q, A 2, and A^. These cases are shown i n F i g . IV-1 and F i g . IV-2, respectively. The functions plotted f o r comparison with the ex-perimental data are evaluated not with the c o e f f i c i e n t s i n Table IV-1 but with the c o e f f i c i e n t s i n Table III-4 which contain the e f f e c t of the f i n i t e s o l i d angle of the detector. In the remaining cases, #8, #9, and #10, a l l the c o e f f i c i e n t s were i n -cluded with the constraints described i n Chapter I I I . F l AV " l l F 2 ttF2 n2 F 3 3 % F 4 4 "U P P (KeV) # 1 0 0 0 -0 .910 0.014 1.5 0 0 0 0 0 . 0 79 # 2 . 0 0 0 -0 .948. 0.039 4 . 1 0 0 0 0.05 0.04 95 83 # 3 0.091 0.085 93 -0 .976 0.110 10.9 - 0 . 005 0.1 1980 0.02 0.1 536 84 70 # 4 0.075 0.038 51 - 0 . 9 5 1 0.049 5.1 - 0 . 027 0.04 141 0.003 0.05 1472 89 # 5 0.055 0.038 69 -0 .025 0.047 5 .1 - 0 . 055 0.038 69 0.023 0.05 216 88 # 6 0 0 0 -0 .917 0.007 0.8 0 0 0 0 0 0 2 # 7 0 0 0 -0 .947 0.015 1.5 0 0 0 0.037 0.017 47 3 # 8 0.109 0.040 37 -1 .010 0.048 4.8 0. 024 0.05 196 -0 .044 0.045 103 18 144 # 9 • 0.069 0.019 .27 -0 .959 0.020 2.0 - 0 . 025 0.018 75 0.004 0.02 570 19 #10 0.049 0.018 37 -0 .935 0.020 2 .1 - 0 . 049 0.018 37 0.026 0.021 83 12 Table IV -1 : Legendre polynomial c o e f f i c i e n t s corrected f o r f i n i t e s o l i d angle of the detector . F^ i s the expectation value of A./A |F i=E(A i/A o)] , fi| the percentage er ror A F . / F ^ and P the ^ t e s t as defined i n the ?ext* 1 0 1 1 RELATIVE INTENSITY -.000 .200 .1400 .600 .800 1.000 - 8 9 " RELATIVE INTENSITY -.000 .200 .HOO .600 .800 I.000 o a a -69-Consider case #8 for which no r e s t r i c t i o n s were imposed on any of the c o e f f i c i e n t s . The r e s u l t of t h i s f i t i s shown i n Pig. IV-3. I t i s obvious that t h i s case can not represent a phys-i c a l s i t u a t i o n because the angular d i s t r i b u t i o n becomes negative for angles greater than approximately 165°. Although t h i s f i t re-presents the general case, because a l l the c o e f f i c i e n t s were free i n the f i t t i n g process, i t i s not surprising to have obtained t h i s type of r e s u l t . This i s because f o r angles greater than 135° there was no experimental data. The least r e s t r i c t i o n that we can introduce =so the r e s u l t s have physical significance i s that the i n t e n s i t y function must be posi t i v e f o r a l l angles,. I t i s clear from the shape of the curve that t h i s condition can be met by making the function zero at 180°. This corresponds to case #9 shown i n F i g . IV-4-. Note that the function shown corresponds to the experimental curve including the e f f e c t of the f i n i t e s o l i d angle of the detector so that i t i s not zero at 180°. F i n a l l y f o r case #10 the angular d i s t r i b u t i o n was forced to have the same value at 0° and 180°. This i s j u s t i f i e d f o r physical reasons to be discussed l a t e r . The r e s u l t i s shown i n F i g . IV-5. Without biasing the i n t e r p r e t a t i o n of the data by a p r i o r i knowledge of t h e o r e t i c a l calculations one can say that the cases #9 and #10 (Fig. IV-4-, F i g . IV-5) represent good f i t s to the data and from the s t a t i s t i c a l point of view i t i s not possible to d i s t i n g u i s h between them. RELATIVE INTENSITY - U -„ 74-The angular d i s t r i b u t i o n s a f t e r correcting f o r the ef f e c t of the f i n i t e detector size are shown In Fig„ IV~6, corresponding to the case where the function i s zero at 180°, and F i g o IV-7 corresponding to the case where the value of the function at 0° equals the value at 180°, For the 70 KeV data the s i t u a t i o n Is not as clear as fo r the 14-4 KeV„ The Chi-squared test gives s i m i l a r answers f o r a l l f i v e f i t s to the data. Nevertheless i f i t i s assumed that the angular d i s t r i b u t i o n function at 70 KeV has the same form as that at 14-4- KeV then the f i r s t two cases can be rejected since they contain no odd Legendre polynomials while the t h i r d can be rejected as before since i t leads to a negative, value of the i n t e n s i t y function at backward angles. The f i n a l two cases are s t a t i s t i c a l l y indistinguishable; one corresponds to the require-ment that the d i s t r i b u t i o n go to zero at 180° while the other requires the same value at 0° and 180°. These d i s t r i b u t i o n s are of the same form as was required to f i t the 144- KeV data.and they do lead to a defined, although not very accurate, value f o r the c o e f f i c i e n t of the f i r s t odd Legendre polynomial. F i g , IV-8 and F i g , IV-9 show the f i t to the experimental data taken at 70 KeV for the parameters given In Table III-4, cases four and f i v e . 4,2, Comparison with the Theoretical Calculations As indicated i n Chapter I the t r a n s i t i o n scheme f o r this reaction can be represented i n the following ways -9L--LI-RELATIVE INTENSITY - 7 9 -In the upper part of the figure the v e r t i c a l l i n e s represent the components that have been considered In the con-tinuum state wave function of the D + p system. S i m i l a r l y , the lower v e r t i c a l l i n e s represent the components that have been considered i n the ground state wave function of the ^ He (D + p bound system). The d i r e c t capture tr a n s i t i o n s between the continuum and bound states are summarized below where the form of the angular dependence of the d i f f e r e n t i a l cross section i s indicated: -80-(1) (2) (3) w (5) (6) E 1 ( 2 P - 2 S ) E 2 ( 2 D - 2 S ) M 1 ( Z , ' S - 2 S ) E l ( V-\>) E K V - ^ D ) 4^ ^ So<n* Q dcr 1< i s o t r o p i c -1- co&2e) i s o t r o p i c and the interferences: (7) E1/E2 ( 2 P - 2 S / 2 D - 2 S ) (8) E l / E l ( W V ^ D ) ( 9 ) E1/E2 ( ^ P - V A s - ^ D ) (10) E1/E2 ( ^ F - ^ D / ^ S - ^ D ) (11) El/Ml ( ^ P - ^ D / ^ S ^ S ) din. u d £ A P t (cos G) d a * % Pa (cos e) d a zero (12) El/Ml (^-^D/^S-^S) zero (13) E2/M1 ( ^ S - ^ D / ^ S - 2 S ) zero The d i f f e r e n t i a l cross section can be expanded i n a Legendre polynomial series d £ = V Pi ( c o s e) where the t r a n s i t i o n s which contribute to the various Legendre -81-c o e f f i c l e n t s are shown below: A Q M1(^S-2S) ; E1( 2P- 2S) ; El(VA)) ; El(^F-^D) ; E2( 2D- 2S) ; E2{^S-^D) ; E K ^ D J / E K V ^ D ) A± E 1 ( 2 P - 2 S ) / E 2 ( 2 D - 2 S ) ; E l (V-^D)^ (^S-^D) A 2 E1( 2P- 2S) ; E 2 ( 2 D - 2 S ) ; E K V ^ D ) ; E l ( V ^ D ) ; E K V D J / E K V D ) A 3 E1( 2P- 2S)/E2( 2D- 2S) ; E1(^P-^D)/E2( V^D) A^ E2( 2D- 2S) After making a number of assumptions, which are discussed b r i e f l y belowi about the r e l a t i v e amplitudes of various components i n the wave functions.Donnelly calculated the cross sections f o r centre of mass energies between 1 6 KeV and 4- MeV, Approximate cross sections obtained by Donnelly f o r a centre of mass bombarding energy of 1 0 0 KeV for the d i f f e r e n t t r a n s i t i o n s are given below: T r a n s i t i o n 0"(^b) (1) E1( 2P- 2S) 0 , 6 (2) E2( 2D- 2S) 0 , 0 0 3 ( 3 ) H1(V 2S) 0,08 (40 El(V^D) 0.08 ( 5 ) El(^P-^D) 0.01 ( 6 ) < l O " 6 -82-Donnelly's model does not Incorporate the complete three body symmetry properties of the wave function, however, he introduced some of these properties i n an empirical way by 4 including components of a r b i t r a r y amplitude f o r the D state 2 and the s ( m ) state of mixed symmetry i n the ground state wave function, since these components are shown to be present for r e a l i s t i c nuclear forces (DE 60). L The D state was introduced with an a r b i t r a r y prob-a b i l i t y so that the ground state r a d i a l wave function was assumed to have the form U(r) = \ J 1-PD U s(r) + ^ P ~ U D(r) 2 where Ug(r) and Up(r) are the r a d i a l functions f o r the P and D^ components each normalized to unity. In previous work. (BA 67) i t was shown that the calculated t o t a l cross section f o r the y i e l d at 0° f i t t e d the rather l i m i t e d experimental data from low energies up to 1.5 MeV with 1% (P D = 0.01) D^ state. This value was used i n Donnelly's c a l c u l a t i o n s . 4 For the S continuum state the proton and deuteron have t h e i r spins aligned. Since the t o t a l wave function must be anti-symmetric and the spin function i s symmetric, while the i s o - s p i n function i s of mixed symmetry,the s p a t i a l wave function 4 of the S state must be of mixed symmetry. Because the magnetic dipole operator i s space-symmetric t h i s t r a n s i t i o n can only 2 proceed to the mixed symmetry s p a t i a l component i n the S ground - 8 3 -state of He, thus the o v e r a l l Ml t r a n s i t i o n i s i n h i b i t e d by L s e l e c t i o n r u l e s . In computing the Ml cross section for the S 2 state to S ( m ) state of mixed symmetry i t was assumed that the 2 r a d i a l form of the S, v state was the same as the r a d i a l form (m; 2 of the symmetric S state. Further i t was assumed to have an a r b i t r a r y amplitude which would need to be determined by experi-2 ment. Previous work (BA 6?) has shown that a s ( m ) State, ampli-2 tude of 0.33 times the S state amplitude gives good agreement between theory and experiment f o r the low energy 0° cross section. I t i s important to note here that the calculations of Donnelly and Bailey et. a l . have been devised to give a reasonably good energy dependence f o r the cross sections, p a r t i c -u l a r l y at low energies. However, due to the approximations made 2 4 the absolute values of the amplitudes of the s ( m ) a n < i D states contain a r b i t r a r y factors that make i t u n r e a l i s t i c to expect them to be accurate or to agree with amplitudes obtained by other h. workers. The D amplitude introduced here i s smaller than the, k% usually found necessary to f i t the magnetic moments of the three body nuclei (SP 50) (subject to considerable uncertainties p due to the neglect of exchange moments). The s ( m ) state ampli-tude i s much larger than the value required to f i t electron scattering data (GI 6 7 ) . Table IV-2 shows a comparison between the experimental r e s u l t s described here f o r cases 5 and 10, f o r which i t was assumed that A» = -A 1, and r e s u l t s obtained f o r Donnelly's E P (KeV) V A o A 3 / A o 4' o 70-20 Exp. (case # 5) Theory 0.06 - 0.04 0.18 -0.93 - 0.05 -0 84 -0.06 - 0.04 -0.18 0.02 - 0.05 -0.007 144-16 Exp. (case #10) Theory 0.05 i 0.02 0.15 -0.94 - 0.02 -0.88 -0.05 - 0.02 -0.15 0.03 - 0.02 r0.007 Table IV-2 : Comparison between present experimental r e s u l t s (case # 5 and case #10) and Donnelly 's c a l c u l a t i o n s . - 8 5 -calculations (DO 6 7 ) . As seen i n Table IV-2 the th e o r e t i c a l values of A„/A l o and k^/k^ are equal and of opposite sign. In the th e o r e t i c a l c a l c u l a t i o n there are small contributions from interference terms involving the D state which can produce a difference between A^ and -A^ however, the theory suggests that this d i f f e r -ence i s less than 0 . 1$ . The analysis, case #9 (Table I V - i ) , of the experimental data suggests that there may be a small d i f -ference between A^ and -A^ but, i t i s at the l i m i t of s t a t i s t i c a l s i g n i f i c a n c e . I f we assume then that A^ = -A^ as was done f o r case #10 then the value of A 1 / A q which r e s u l t s i s 0.05 t 0 . 0 2 , which i s one t h i r d of the value given by the Donnelly c a l c u l a t i o n f o r t h i s energy range. The A^ (and A^) terms a r i s e from i n t e r -2 2 2 2 ference between E2( D- S) and E l ( P- S) tra n s i t i o n s and the calculated angular d i s t r i b u t i o n c o e f f i c i e n t s depend on a model 2 dependent P phase s h i f t which i s not i n agreement with the C h r i s t i a n and Gammel (CH 53) phase s h i f t analysis of the low energy proton-deuteron scattering data. Furthermore, the d i s -agreement noted here suggests that either one or both of the 2 2 extrapolations of the phase s h i f t s of P and D continuum wave functions to low energies may be s i g n i f i c a n t l y i n error. Although, the term k^/kQ i s , as f a r as the sign and; order of magnitude concerned, i n agreement with the theory, the difference between the experimental value and t h e o r e t i c a l calou- ' l a t i o n i s beyond the s t a t i s t i c a l error. This suggests that 1% D state i n the ground state wave function i s too high since - 8 6 -the t r a n s i t i o n s involving the D state contribute more strongly to A q then to A^ as can be seen from the angular d i s t r i b u t i o n s . Bailey (BA 67) has shown that the 0° y i e l d i s very sensitive to the D state p r o b a b i l i t y and his tentative suggestion that t h i s p r o b a b i l i t y was 1%, was based on the analysis of data of low s t a t i s t i c a l accuracy. The data could be f i t t e d equally well by a smaller D state p r o b a b i l i t y as suggested by the present jresults. I t i s not surprising that the A^/AQ term remains 2 2 undefined since only the E2( D- S) t r a n s i t i o n can contribute to t h i s term and i t has a r e l a t i v e l y low cross section at these energies. The A q c o e f f i c i e n t i s not defined by the present work since i t requires the measurement of the absolute cross sec-t i o n which i s the object of future work. 4 . 3 . Future Work As shown above the main contributions to the i s o t r o p i c cross section are the M1(^S-2S) t r a n s i t i o n and the E1(^P-^D) term plus i t s interference with the smaller El( F- D) t r a n s i t i o n h. 2 4 involving the D state. Both the and D state p r o b a b i l i t i e s are of considerable i n t e r e s t since they are rel a t e d to spin dependent and non-central parts of the nucleon-nucleon force. I t i s not possible to separate the ef f e c t s of these contributions by angular d i s t r i b u t i o n measurements i n a narrow energy range. -8?-However, because these contributions have quite different.energy dependence (DO 6?) r e l a t i v e cross sections over a wide energy range, from 30 KeV to 3 Mev" say, would provide a basis f o r separating the Ml and E l cross sections. Furthermore, absolute cross sections would provide a more stringent test of any t h e o r e t i c a l models 2 4 f o r the amplitudes of the $ ( m) a n a ^ D states. In addition, the cross section In the energy range from 1 KeV to 25 KeV i s of i n t e r e s t i n a number of astrophysical processes. Absolute cross section measurements are to be done i n the energy range from 50 KeV to 180 KeV using the low energy accelerator and these r e s u l t s w i l l be combined with measurements at higher energies (4-00 KeV to 2 MeV) which are at the present time being c a r r i e d out i n t h i s laboratory by G.M. Bailey and R. Helmer using the U.B.C. Van de Graaff accelerator. In spite of improvements made i n the deuterium targets, the d e t e r i o r a t i o n continues to present a problem from the viewpoint of making accurate r e l a t i v e and absolute cross section measure-ments. One method that has been developed to partly a l l e v i a t e t h i s d i f f i c u l t y i s to produce a target over the surface of a plate which i s rotated r a p i d l y i n front of the beam so no part of the.target i s continuously exposed to the beam. A r o t a t i n g target holder was developed by G.M. Bailey and the author. I t consists of a f l a t copper disc 5" i n diameter and 1/16" thick mounted inside of a vacuum chamber i n such a way -88-that i t can be rotated externally by means of an e l e c t r i c motor. The speed at which the disc rotates can be varied i n a continuous way up to 600 rpm. 1 . . . . . . A s i m p l i f i e d schematic diagram i s shown i n F i g . IV-10. The water-cooled disc can be moved up and down with respect to the beam and can also be placed at d i f f e r e n t angles with respect to the incoming beam. This target holder has already been tested (BA 6 8 ) . Deuterated polyethylene was deposited over the area of the disc 2 with a thickness of 100yHg/cm ° An 800 KeV proton beam of approximately 5 yUA from the Van de Graaff accelerator was used. The spot on the target was approximately 6 mm i n diameter. The test was c a r r i e d out over a 10 hour period. Although during the f i r s t two and a half hours or so there was about b0% decrease i n the y i e l d the rate of de t e r i o r a t i o n i n the seven and a half subsequent hours was found to be less than 15%. For r e l a t i v e cross section measurements the i n i t i a l loss of target material presents no major problems because one can wait u n t i l the target i s s t a b i l i z e d to i n i t i a t e the measure-ments. For these measurements i t i s not necessary to know the 2 actual number of deuterium atoms per cm as long as the target thickness i s below a chosen value. For the absolute cross section measurements the s i t -- 8 9 -TOP T A R G E T CHAMBER T A R G E T D E P O S I T BEAM — WATER COOLING TO D R I V I N G MOTOR ROTATING VACUUM S E A L COPPER D I S C CENTER OF ROTATION OF THE ANGULAR D I S T R I B U T I O N T A B L E F i g . IV-10 R o t a t i n g t a r g e t h o l d e r . T h e c o p p e r d i s c i s c o o l e d by c o n d u c t i o n t h r o u g h t h e a x i s S . - 9 0 -uation i s d i f f e r e n t because one cannot use the i n i t i a l thickness as determined by weight to estimate the number of deuterium atoms 2 per cm . The target thickness after the equilibrium i s reached can be estimated by measuring the neutron f l u x produced when "a deuteron beam i s used instead of a proton beam. Prom the know-ledge of the D(d,n)-%e cross section, the t o t a l charge c o l l e c t e d by the target and the e f f i c i e n c y of the neutron detector one can determine the. amount of D present i n the target, . These measurements could be checked as follows. S t a r t -ing with a fresh target the neutron f l u x i s measured using a D beam of say 50 nA„ I t i s believed that the target w i l l not deteriorate using t h i s low beam current. Therefore one could compare the amount of deuterium as determined by the neutron f l u x with the amount of deuterium as determined by the weight of the polyethylene layer. Plans are underway to carry out the target t e s t i n g with the objective of making the absolute cross section measure-ments i n the near future. When the absolute cross sections have been measured over a range of energies i t should be possible to make better 2 4-estimates of the amplitudes of the a n d D components of the three body wave function. With continuing development on the t h e o r e t i c a l side i t should then be possible to r e l a t e these -91-amplitudes to spin-dependent and tensor parts of the two-nucleon force. BIBLIOGRAPHY AJ 59 F. Ajzehberg-Selove and T, Lauritsen, "Energy Levels i n Light Nuclei", North-Holland Publishing Co. Amsterdam, (1959) . AR 54 W.R. Arnold, J.A. P h i l l i p s , G.A. Sawyer, E.J. S t o v a l l Jr, and J o L „ Tuck, Phys. Rev., 21 U 9 5 4 ) ^ 3 . 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Segre, "Experimental Nuclear Physics - Volume IV,' John Wiley & Sons, New York, ( 1 9 5 3 ) . SI, 5 9 P.P. Singh, G.M. G r i f f i t h s , Y.I. Ssu and J.B. Warren, Can. J. Phys., 21 ( 1 9 5 9 ) 8 6 6 . SM 6 1 A.J. Stewart Smith, M.Sc. Thesis, University of B r i t i s h Columbia, ( 1 9 6 1 ) . SP 5 0 L. Spruch, Phys. Rev., 80 ( 1 9 5 0 ) 3 7 2 . TR 6 7 G.E. Tripard and B.L. White, Rev. S c i . Instrum., J 8 ( 1 9 6 7 ) 4 3 5 . VE 5 0 M. Verde, Helv. Phys., Acta 2 ^ ( 1 9 5 0 ) 4 5 3 . WH 58 W. Whaling, Handbuch der Physik, J 4 ( 1 9 5 8 ) 1 9 3 . WH 62 B.L. White, L.P. Robertson, K.K. Erdman and J.R. MacDonald, Rev. S c i . Instrum., ,33.(1962) 1111. WI 3 9 E.J. Williams, Proc. Roy. Soc., 16_2 ( 1 9 3 9 ) 5 3 1 . WI 52 D.H. Wilkinson, P h i l . Mag., 4 j ( 1 9 5 2 ) 6 5 9 . WO 52 E.J. Woodbury and W.A. Fowler, Phys. Rev., 8j> ( 1 9 5 2 ) 5 1 . WO 66 W. Wolf 1 1 , R. Bosch, J. Lang, R. Milller and P. Marmier, Phys. Lett., 2 2 (I966) 7 5 . YU 6 7 H.P. Yule, Nucl. Instr. and Meth., ^± ( I 9 6 7 ) 6 l . APPENDIX A THE ANGULAR DISTRIBUTION OP THE 11.7 MeV GAMMA RAYS FROM THE REACTION 1 : LB(p 9"S) 1 2C As a check on the procedure followed i n the deter-mination of the angular d i s t r i b u t i o n of the reaction D(p,tf)%e, the angular d i s t r i b u t i o n of the 11,7 MeV gamma-rays from the rea c t i o n BCp.tf) C was measured and the r e s u l t compared with measurements from previous work. This measurement checks the behavior of the angular d i s t r i b u t i o n table and the corrections due to the absorption i n the target holder as well as the i t e r a t i v e least squares method used i n the analysis of the data, 1 1 1 2 The re a c t i o n B(p,"tf) C has a sharp resonance (T= 7 KeV) at a proton bombarding energy of 163 KeV. The l e v e l i n C formed at t h i s resonance has an e x c i t a t i o n energy of l6„ll MeV and decays by either alpha-particle or gamma-ray emission. The decay scheme i s shown i n F i g . A - l which indicates only the le v e l s of i n t e r e s t . A 1 : LB target 25 yUg/cm2 thick, deposited on a 0.010 inch thick copper backing (obtained from the Atomic Energy Research Establishment, Harwell, England) was bombarded;-with 1 0 0 A of 170 KeV protons. The conditions of the beam on the target were sim i l a r to the D(p,"tf)%e runs. The target was mounted on target holder "TA" (Fig. II-3) and the detector target arrange--95--96-ment used Is shown i n Pig. I I I - l . The same target was used i n both configurations. At E = 170 KeV with the target placed at 45° with respect to the incoming beam, the energy loss by the beam i n the target was about 21 KeV and the R.M.S. multiple scattering angle was less than 1.1°. 16.11 2" • m m 9.63 4.43 12, (1") ^11.7i A- 0.16 U B + P 15.958 7.375 8 Be + OC 12 Pig. A - l : Some energy leve l s i n the C nucleus from Ajzenberg-Selove and Lauritsen, (AJ 59) . The. 6.5 MeV t r a n s i t i o n to the 9.63 MeV l e v e l leads to the break-up of the 12 C * into an alpha p a r t i c l e and Sfie as shown. (1) Assignment given by A.G. Gregory (GR 6 l ) . A t y p i c a l gamma-ray spectrum taken with the detector #1 at i Q ^ = 135° i s shown i n Pig. A-2 where the 6.5 MeV gamma-ray 11 8 peak from the competing reaction B(p,tf<*) Be i s indicated. F i g . A-3 shows a t y p i c a l background spectrum for detector #1. I CD TD ho CD 3 3 01 I -\ 01 TD o c 3 -.000 N U M B E R O F C O U N T S ( X 1 •1 ) 40.000 80.000 120.000 160.000 200.0001 • t a a • mg Z D rn m CD rn - CO a a a a i a a a (V) a a a a # c 1 o i 4 - 4 4 ^ 4 + 4 °K (1.462 MeV) 1 s . . . 4 H m — » II CO 1 1B(p,tfo<) 8Be E^= 6.5 MeV -C~ TD % 4 + 4 +4 + a> m — •< — II o ? — • - o 3 rvj n> o < u i — o — CO TD m -O CD -L6-I -n uo — 0) I Q n • 7T I D > - 1 I O r o c 3 — Q . l/l vn "O co a> n ^ r+ f D - 1 < C \ 3 o • 3~ QJ 3 -( 3 IT n> n> • <T> 3 (D -I n ai cr ai o 3 i n X ) fl> n c 3 QJ 3 Q. I a a a a N U M B E R O F C O U N T S ( X I O 3 1 ,000 UD.O0O 8 0 . 0 0 0 L 2 0 . 0 0 0 LB0.0OD 2O0.00D| I I I I : I m ZJ3 •0° m k a a a i a a a a a a • a AO K (1.462 MeV) R a T h (2.614 MeV) TO CD m o o TO > CD > o (7> 70 O -86--99-Th e spectra were analyzed following the procedure des-cribed i n Chapter I I I , Here, however, the spectra were i n t e -grated from 7.5 MeV to 13 MeV covering the 11.7 MeV gamma-ray peak. The lower l i m i t was chosen to be above the 6„5 MeV peak and below the 16.11 MeV peak which i s off the curve shown i n F i g . A-2. The r e s u l t s are summarized i n Table A - l using the same heading as described i n Chapter I I I . The absorption coef-f i c i e n t s used i n the correction due to the target holder ab-sorption are shown i n Table G-l. Although the i n t e n s i t y r a t i o of the 16.1 MeV to the 11.7 MeV gamma-rays i s about 3.3$ (CR 56) the o v e r a l l c o n t r i -bution of the 16.1 MeV gamma-rays to the energy range counted for angular d i s t r i b u t i o n measurement of the 11.7 MeV gamma-rays i s less than 0.3$ and was disregarded. The experimental data were f i t t e d to the following function; W(e) = [Y_ Be Pe] (\*-t*) U - 1) with /0 -45° < 6 < 50° M 60° i 9 4135° where P-^  = P-^  cos(0+6 Q) are the Legendre polynomials and K and 9 Q the parameters defined i n Chapter I I I . The least squares f i t t i n g procedure outlined i n Chapter III was followed and the i 9 i A B T(sec) C D E F G H 0 17811 16767 50400 1 -45 15638 -115 15844 180 64 60 15574 15784 15574 31064 16888 36526 2 -40 22048 -115 22313 300 106 100 21942 22213 15591 22124 16802 25694 3 -30 15486 -115 15071 300 106 100 15379 14971 16215 34894 17323 39828 4 -20 17728 -115 16759 180 64 60 17664 16700 16696 32589 17745 36813 5 -10 23705 -115 22433 300 106 100 23599 22333 16678 24352 17677 27355 6 0 18303 -115 16790 300 106 100 18197 16690 17210 34224 18224 38377 7 10 21335 -115 19936 300 106 100 21229 19836 16893 27969 17904 31418 8 20 14098 :-115 13533 180 64 60 14034 13473 16441 39797 17474 44956 9 30 12723 -115 12566 300 106 100 12616 12466 15974 41030 17066 46832 10 40 17582 -115 17674 300 106 100 17475 17574 15695 28279 16913 32840 11 50 14213 -115 14768 180 64 60 14149 14708 15185 32110 16600 38372 12 45 18955 -90 16434 240 85 80 18870 16354 18870 40836 13 60 13536 -90 12264 240 85 80 13451 12184 18055 50516 14 75 45933 -90 43016 480 170 160 45763 42857 17464 13832 15 90 15933 -90 15301 240 85 80 15848 15221 17028 37543 16 105 16050 -90 14959 240 85 80 15965 14878 17548 40198 17 120 16752 -90 15289 240 85 80 16667 15209 17922 40602 18 135 17050 -90 15011 240 85 80 16965 14931 18582 43707 Table A - l : B(p,tf) C gamma-ray angular d i s t r i b u t i o n data of the E5=11.7 MeV #-ray at E =170 KeV -101-r e s u l t s are summarized i n Table A-2. From the r e s u l t s of previous 2 workers the angular d i s t r i b u t i o n has the form (a + b cos 9). The data was f i t t e d to equation (A-l) i n which the parameters Bj, B^, and B^ were set equal to zero. The r e s u l t of t h i s i s , shown i n row 2,t of Table A-2. In addition, the experimental data were also f i t t e d to the same function (A-l) including the term. Although no P^ term was expected, a term of t h i s form was included i n the analysis as a check on the alignment and the f i t t i n g procedure. The r e s u l t s of t h i s f i t t i n g are shown i n row 1, of Table A-2; c l e a r l y the c o e f f i c i e n t B^ i s undefined with an error greater than 100$. The 'X test also indicates that a good f i t i s obtained without a P^ term. The values obtained for 6 are also undefined; This o i s to be expected since the angular d i s t r i b u t i o n i s rather f l a t and the accuracy of zeroing the angle scale was smaller, than the A8Q which r e s u l t s from the measurement. The f i t obtained f o r an angular d i s t r i b u t i o n of the form B P + B 0P 0 i s shown o o d c i n F i g . A-4. The angular d i s t r i b u t i o n c o e f f i c i e n t s expressed i n terms of F 1 = E(A.j/A ), following the procedure outlined i n Chapter IV, are shown i n Table A-4. The corrected angular d i s t r i b u t i o n i s shown i n F i g . A-5„ The calculated smoothing factors Q, f o r 11.7 MeV gamma-rays are shown i n Table A-3„ # 1 16252 • 19.6 12 194 1611 156 0.007 0.030 0.117 0.016 9.43 12 0.67 170 # 2 16261 112 0 0 1612 155 0.006 0.025 0.117 0.011 9.43 13 0.74 Table A-2 : B(p,tf) C angular d i s t r i b u t i o n least squares f i t parameters and Chi-squared t e s t . -30.000 -.ODD 30.000 60-000 90.000 120.OOO 150.000 RNGLE (CM.) F i g . A-4 : A n g u l a r d i s t r i b u t i o n o f t h e 11.7 MeV g a m m a - r a y s f r o m t h e r e a c t i o n 1 1 B ( p , t f ) 1 2 C a t E p = 170 KeV ( c a s e #2) 180.000 o o o C D - I O CD . LU I— LU :> i — a : — i Lxjg O C f M . a o o -30.0QD F i g . A-5 1 1 -.000 30.000 6D.DQQ RNGLE (CM.) 1 1 B ( p , * ) 1 2 C E = 170 KeV P 2 W(6)=1+(0.16±0.02)COS 6 o i 90-000 ~ l 120.000 ~ l 150.000 180.000 11 12 A n g u l a r d i s t r i b u t i o n o f t h e 11.7 MeV g a m m a - r a y s f r o m t h e r e a c t i o n B(p,"tf) C a t E = 170 KeV ( c a s e §2) w i t h d e t e c t o r f i n i t e s o l i d a n g l e c o r r e c t i o n i n c l u d e d , -105-Table A-3 : Smoothing factors calculated at Ey = 11,7 MeV for the detector geometry shown i n F i g . II- 6 . 1 0 1 2 Q l 1.00000 0.98860 O.96606 Table A-4 : Legendre polynomial c o e f f i c i e n t s corrected f o r f i n i t e s o l i d angle of the detector. F, i s the expectation value of A n/A |F, = E(A,/A ) and l o L l l o j P the Chi-squared t e s t r e s u l t as defined i n the text. P l A F 1 \ F r 2 AP 2 "I 2 P E P (KeV) #1 0.00,1 0.012 1390 0.103 0. 011 10.2 67 170 #2 0 0 0 0.103 0.010 10.2 74 In order to compare the r e s u l t obtained here with the r e s u l t s of other workers, the angular d i s t r i b u t i o n was expressed i n terms of a(l+b/a cos 9) with the r e s u l t shown below: Previous Work (KE 51) (HU 52) (GR 54) (GR 56) W(Q) = 1 + (0.15 - 0.03) cos 2 8 W(Q) = 1 + (0.23 t o.04) c o s 2 9 W(0) = 1 + (0.26 t 0.01) c o s 2 G I Q o / I 9 0 o = 1.18 i 0.02 Present Work w ( 8 ) = 1 + (0.16 i 0.02) cos 2 9 E E = 170 KeV 170 KeV 175 KeV 168 KeV E p = 170 KeV -106-The r e s u l t of th i s experiment i s i n reasonable agreement with previous measurements except f o r the re s u l t s of Grant et. a l . (GR 5 4 ) . APPENDIX B THE ACCELERATOR AND MAGNETIC ANALYZER Bo1. The Accelerator The DCp.o'^He measurements were made using a high cur-rent accelerator constructed by the author and based on an ORTEC duoplasmatron ion source A b r i e f d escription of the apparatus and i t s main c h a r a c t e r i s t i c s i s given below. B . l . l . The Ion Source and E i n z e l Lens The ion source,a modified Von Ardenne (AR 56) duoplas-matron, and E i n z e l lens are shown i n F i g . B - l . The source system (ORTEC Model 504) consists of the duoplasmatron (Model 350), the E i n z e l lens and the power supplies and controls to operate both. The system was mounted i n a aluminum box supported on i n s u l a t i n g posts so that i t s p o t e n t i a l could be changed with respect to ground by an external 150 KV power supply. In order to obtain a large ion current from the duo-plasmatron source the pressure i n the arc chamber has to be quite high, 0.2 mm of Hg. On the other hand the beam must be injected into a high vacuum region which means that the extraction canal between the two regions must be of small diameter. In order to get a large beam from t h i s small hole the duoplasmatron concen-trates a small dense plasma at the e x i t hole, which i s 0.008" i n diameter, by means of e l e c t r i c and magnetic f i e l d s . The c o i l C produces a magnetic f i e l d between the intermediate electrode IE -107-g . B-1 : D u o p l a s m a t r o n i o n s o u r c e a n d E i n z e l l e n s s y s t e m . T h i s i s n o t t h e a c t u a l s c h e m a t i c v i e w b u t a s i m p l i f i e d v e r s i o n . -109-and the anode A„ This combined with the e l e c t r i c f i e l d between IE and A tends to draw a column of plasma from the arc chamber to the tungsten a l l o y extractor canal EC i n the anode. Positive ions are drawn from the plasma (on the opposite side of the anode to the arc chamber) by the e l e c t r i c f i e l d between the extractor electrode EE and the anode A, Because of the low i n i t i a l k i n e t i c energy and high ion density of the beam leaving the extraction region there i s a tendency f o r the beam to diverge r a p i d l y due to space charge ef-f e c t s . To reduce th i s "blow-up" e f f e c t and minimize the loss of beam to the extractor electrode the extraction voltage needs to be r e l a t i v e l y high, that i s approximately 10 KV or more. The E i n z e l lens then focusses the diverging beam to a point P just beyond the lens. The beam i s then suitable for i n j e c t i o n into the accelerating tube. On s t a r t i n g the discharge i n the arc chamber, the' arc power supply provides approximately 350 Volts between the-anode and the filament. Before the arc strikes a small electron cur-rent from the hot filament flows to the intermediate electrode and returns to the arc supply through Rl„ Most of the arc supply voltage appears between the intermediate electrode and the filament and t h i s s tarts the arc which i n turn makes a large increase i n the current through R l . This causes the p o t e n t i a l of IE to f a l l towards the filament voltage and a dynamic equi-librium i s reached causing most of the current from the f i l a -ment to flow to the anode. -110-Th e arc current, which tends to vary with the gas flow or with the magnetic f i e l d , i s kept constant by means of a current regulated power supply. The i n i t i a l 350 V p o t e n t i a l drops to approximately 80 V under normal operating conditions. The platinum gauze fiiament i s i n i t i a l l y coated with a suspension of CaCO^. This carbonate i s converted to the oxide by approximately twenty four hours of filament heating under vacuum. A thermal leak (WH 62) i s used to control the flow of gas from a high pressure storage bottle to the i o n i z a t i o n chamber. Heat i s extracted from the magnet c o i l s and the f i l a -ment by a l i q u i d coolant c i r c u l a t i n g around the c o l l s . PREON 113 coolant flows i n a closed c i r c u i t c o n s i s t i n g of a pump, a water-cooled heat exchanger and a r e s e r v o i r . The coolant also removes heat from the whole high voltage terminal. A cut-off switch removes a l l power from the source i f the coolant pressure or flow rate f a l l below preset values. B .1 .2 . The Accelerating Tube The ion source E i n z e l lens system was coupled d i r e c t l y to an accelerating tube. The purpose of the tube i s to convert a generally divergent low energy beam into a well collimated higher energy beam. F i g . B-2 shows a beam diverging from P and t r a v e l l i n g through a z e r o - f i e l d region u n t i l i t reaches the R1 I 1 i g . B-2 : S c h e m a t i c d i a g r a m o f t h e a c c e l e r a t o r s h o w i n g t h e b e a m t r a j e c t o r y . T h e e l e c t r o n i c u n i t s s h o w n i n t h i s d i a g r a m by t h e n u m b e r e d s q u a r e d b o x e s a r e l i s t e d i n T a b l e B-1. - 1 1 2 -f i r s t electrode of the tube where i t i s converged. The beam then travels through an approximately constant-field region following a nearly parabolic path throughout the length of the tube. F i n a l l y i t i s diverged at the ex i t of the tube as i t enters a second z e r o - f i e l d region. This kind of accelerating strueture tknown as,a three element system (EL 53)» has a converging action as the beam passes from the f i e l d free region into the uniform f i e l d inside the tube and a diverging action as the beam leaves the tube.to enter a second f i e l d free region. The t o t a l e f f e c t i s to con-verge the beam since the beam enters the tube at low k i n e t i c energy and leaves at a higher k i n e t i c energy, so that the pos i t i v e a c t i o n of the input lens i s greater than the negative action of the output lens. A section of an old accelerating tube from the Chalk River Van de Graaff accelerator was used. I t consists of s i x -teen saucer shaped electrodes with uniformly increasing inside diameter separated by one inch thick glass i n s u l a t i n g rings. The electrode shape prevents the beam from "seeing" the glass, thus minimizing the build-up on the glass of any contamination scattered by the beam and protects the metal to glass vacuum seals from exposure to scattered beam. For p r a c t i c a l reasons i t was desirable to have the tube as short as possible. Because the column had some cracks i n the glass insulators,1 2 KV was considered to be the maximum safe -113-p o t e n t i a l difference between i n d i v i d u a l electrodes. A maxi-mum accelerating voltage of 180 KV then required a t o t a l of . sixteen electrodes. The diameter of the hole i n the f i r s t electrode was 8 cm. The distance between the f i r s t electrode of the a c c e l -erating tube and the l a s t electrode of the E l n z e l lens was thought to be not too c r i t i c a l , because the f o c a l distance (exit point) of the E i n z e l lens could be changed by varying the p o t e n t i a l i n the lens. However, there i s a maximum distance at which the f i r s t electrode can be placed, that i s , when the diameter of the beam equals the inside diameter of the electrode. With a beam diverging from the e x i t point of the E i n z e l lens at a half angle of 4-° the maximum distance f o r an electrode, 8 cm i n diameter, i s approximately 60 cm. To a r r i v e at the optimum distance a t r i a l and error method was used. Due to the f a c t that i t was desirable to have the whole assembly as short as possible, one-tenth of the maximum distance was chosen. Also there i s appre-ciable aberration i f the whole diameter i s used. The accelerating tube was tested with the ion source and E i n z e l lens operating under normal conditions. In the energy range 100 to 180 KeV a nearly p a r a l l e l beam, 3 to 6 mm i n diameter, was obtained. However, below t h i s energy i t was necessary to reduce the e f f e c t i v e number of electrodes to obtain s i m i l a r focusing c h a r a c t e r i s t i c s . This can be explained by the f a c t that by shortening the e f f e c t i v e length of the tube, the gradient between the remaining electrodes was increased to a -Up-value s i m i l a r to the one used i n the high energy range. The shortening can be done on either side of the tube, but i t was found that better r e s u l t s can be obtained i f i t i s done on the ion source side. The high voltage was d i s t r i b u t e d uniformly along the accelerating tube by means of 15 (20 Mn, 5 W each) high voltage resistors attached to the electrodes i n a zig-zag fashion and placed above the tube. To prevent corona from the somewhat i r r e -gular r e s i s t o r chain, f i v e f l a t aluminium rings were evenly: d i s t r i b u t e d along the tube. With the maximum high voltage applied to the tube, no corona was observed. Because of the short length of the accelerating tube and the r e l a t i v e l y large inside diameter of the electrodes, , the conductance of the tube was adequate f o r the gas load from the ion source. A short "extension tube" couples the accelerating tube to the analyzing magnet and provides a connection to the vacuum system.. This tube also holds a pair of water cooled tantalum beam choppers which are used to check the character-i s t i c s of the beam before i t i s analyzed. B.l.3 . High Voltage A d.c. UNIVERSAL VOLTRONICS Model BAL-130-14 power supply was used to provide the main accelerating voltage. I t contains a conventional s o l i d state Cockroft & Walton voltage doubler -115-i n one tank and a double LC f i l t e r unit i n a second tank. The power supply i s able to de l i v e r 5 mA at 150 KV, or lk mA maximum at 130 KV with a 3$ R.M.S. r i p p l e . The r i p p l e i s attenuated by a factor of 1/100 by the f i l t e r unit. The high voltage was l a t e r increased to 180 KV i n order to cover the f i r s t resonance i n the reaction B(p,tf) C which occurs at a proton energy of 163 KeV i n the laboratory frame. The extra 30 KV was provided by a UNIVERSAL VOLTRONICS Model BPE-32-5.5 power supply. I t was placed i n the accelerator terminal i n series with the main high voltage set. This power supply can de l i v e r 5.5 mA with a 1.5$ R.M.S. r i p p l e . A UNIVERSAL VOLTRONICS 5 KW, 115/115 V, 200 KV i s o -l a t i n g transformer supplies a.c. power to the electronic equip-ment i n the accelerator terminal. A chain of high voltage low temperature c o e f f i c i e n t r e s i s t o r s R2 (Fig. B-2) t o t a l i n g 2000 Mil i s used to determine the accelerating voltage (beam energy). The r e s i s t o r s , placed under o i l i n a PIREX tube, are connected between the anode electrode of the ion source and the ground through a 20 y*A, 0.5$ tracking microammeter. The whole assembly was ca l i b r a t e d to 1$. F i g . B-2 shows the power d i s t r i b u t i o n i n the a c c e l -erator terminal. The ele c t r o n i c units shown i n thi s diagram by the numbered square boxes are l i s t e d i n Table B - l . - 1 1 6 -Table B-l : Accelerator's electronic units 1. Filament a.c. supply ( 0 - 3 0 A) 2. Magnet d.c, supply ( 0 - 3 A) 3c Arc d „ C o supply ( 0 - 3 A) 4. Extraction d . c supply ( 0 - 3 0 KV) 5»- E i n z e l lens d.c. supply ( 0 - 6 KV) 6. Booster d.c. supply ( 0 - 3 0 KV) 7. High voltage d.c. supply ( 0 - 1 5 0 KV) 8. I s o l a t i o n transformer 1 : 1 ( I s o l . 40 KV) 9. Main i s o l a t i o n transformer 1 : 1 ( I s o l . 2 0 0 KV) B.1.4. The Vacuum System A 7 0 0 1/sec (@ 10"-> mm of Hg) o i l d i f f u s i o n pump provides vacuum to the machine. I t i s coupled, through a water-cooled chevron r i n g "baffle and a l i q u i d nitrogen trap, d i r e c t l y to the "extension tube". The fore-pressure i s provided through a b a l l a s t tank, by an 80 l/sec (@ 1 0 " ^ mm of Hg) mechanical pump. The pressure, under normal conditions, with the.ion , source "OFF", i s about 7 x 10 ' mm of Hg measured at the "extension tube". B.1.5. The Shielding The components i n the accelerator terminal were assembled on two s t e e l frames, one i s o l a t e d at the extractor p o t e n t i a l ( 3 0 KV) with respect to the other. Both frames are supported by four ceramic insulators attached to another s t e e l frame at ground po-t e n t i a l . -117-To avoid corona the whole high voltage assembly was enclosed i n an aluminium shielding box. The controls, situated inside the box, are manipulated extBrnally by means of LUCITE rods. A series of meters, mounted inside the box behind a LUCITE window, are used to Indicate the operating conditions. No corona was observed when the f u l l voltage was applied. An aluminium fence, supporting a 1/8 inch thick lead sheet, was b u i l t around the accelerator and accelerating tube, for protection against the high voltage and to s h i e l d the room from X-rays. B .1 .6 . C h a r a c t e r i s t i c s A t y p i c a l set of conditions f o r a 160 KeV proton beam under normal operating conditions i s shown i n Table B-2. An extractor channel 0.008 inch i n diameter was used throughout the experiment. The machine was operated for continuous periods up to 76 hours without observing any s i g n i f i c a n t change i n i t s , performance. The filament was found to have a l i f e of approx-imately 400 hours with hydrogen gas. A picture of the acceler-ator i s shown i n F i g . B-3 and the accelerating column i s shown i n F i g . B-4. B.2, The Magnetic Analyzer In order to analyze the nearly p a r a l l e l beam produced by the accelerator, a 45° d e f l e c t i o n magnetic analyzer was designed and b u i l t by the author. 38 I FIG. B -3 : VIEW OF THE ACCELERATOR. THE MAGNETIC ANALYZER IS SHOWN AT THE LEFT. -120-Table B-2 >: Typical accelerator conditions for a 160 KeV proton beam. Thermal leak 0.66 A (approx. 0.2 mm of Hg i n the arc chamber) Filament 26.0 A (approx. 30 W) Arc voltage 88.0 V Arc current 1.4 A Intermediate electrode 30.0 V Magnet current 0.6 A Extraction voltage 10.2 KV E i n z e l lens 0.0 V H* beam current 300 o0 y«AA -6 Vacuum 8.7 x 10~ mm of Hg B . 2 . 1 . The Magnet The magnet can transmit a ^He b e a m of 200 KeV. The yoke has a conventional C-shape with two i d e n t i c a l c o i l s placed at both sides of the magnet gap. The pole t i p s were designed to have a double focusing e f f e c t on the beam i n the manner discussed by W. Cross (CR 51). The conditions for double " l i n e focusing" (that i s , fo r concentrating to a point a p a r a l l e l beam of p a r t i c l e s which has a f i n i t e cross section) can be expressed by the following geometrical r e l a t i o n s h i p s : t<x* tz = I [ t o - v ^ - S i ] 4. i / ( $ - C o t 6 i ) ] (B . 2 . 1 . - 1) ![M$-£o - v(* -^ m (3 .2 .1 .-- 2) -121-where, following Cross' notation, 1£ i s the image distance ( i n units of the radius of curvature of the mean p a r t i c l e i n the uniform magnetic f i e l d ) measured from the edge of the pole t i p i i s the angle between the incident p a r t i c l e s and the normal to the edge of the pole t i p ; s i m i l a r l y £ 2 i s f o r t n e emerging mean p a r t i c l e ; and $ i s the d e f l e c t i o n angle of the mean p a r t i c l e i n the uniform f i e l d . The equations (B . 2 .1 . - 1) and (B . 2 .1 . - 2) are v a l i d provided the pole gap i s small compared to the length and radius of curvature of the p a r t i c l e ' s path i n the uniform magnetic f i e l d . F i g . B-5 shows the shape of the pole t i p chosen and the traje c t o r y of the mean p a r t i c l e , where f i s i t s radius of curvature. F i g . B-5 s View of the pole t i p In the horizontal plane of de f l e c t i o n , (B perpendicular to the page), and trajectory of the mean p a r t i c l e . -122-mlnimum i n to +12°. I t was desirable to have 1" as large as possible. The o the equation B-2 occurs for 6^ approximately equal Taking t h i s value for 61; the f i n a l design parameters were: 45° +12° +11° 9» 2.3 15.0 cm d 3.175 cm ( a i r gap) B .2 .2 . The Power Supply A regulated d.c. power supply was b u i l t . The c i r c u i t i s a modified version of the 100 A power supply used to drive the U.B.C. spectrometer (SM 6 l ) . Its main c h a r a c t e r i s t i c s are: I = 20 A (max.) ; E = 90V; r i p p l e = 0.05$ (R.M.S.), The s t a b i l -i t y was better than 0,3$ over an 8 hour period. APPENDIX C THE ENERGY OF THE GAMMA-RAYS FROM THE REACTION D(p,tf)%e AND THE COORDINATE SYSTEM TRANSFORMATIONS The energy of the gamma-rays i n the center of mass system i s given by; where E i s the energy of the incoming protons i n the laboratory system. Using the r e l a t i v i s t i c transformation equations, the gamma-ray energy i n the laboratory system i s found to be: 1 - |2> cos 6 U ie emitted g the Incoming p a r t i c l e i n the laboratory system and where 6^ i s the angle of th  gamma-ray with respect to ' M h + h o V r i p e 3 This reaction has a Q = 5.4-9 MeV. At E = 160 KeV the t h i r d term i n the equation ( C - l ) , which corresponds to the nuclear r e c o i l energy, i s n e g l i g i b l e . The energies of the gamma-rays as a function of the incident proton energy and as a function of the angle of observation, computed f o r t h i s experiment, are shown i n Table C - l . The v a r i a t i o n of the gamma-ray energy at E = 160 KeV over the observed angles Is less than 1.1$ (and less than 1% at -123--124-E = 90 KeV). In the computation of the gamma-ray i n t e n s i t y (Chapter III) this v a r i a t i o n was not taken into account, Table C-l : D(p 0TO^He gamma-ray energies at E = 160 KeV and E = 90 KeV f o r d i f f e r e n t ang?es of observation. E P (KeV) E* (MeV) e u =o° eL=90° eL=i35° 160 5.63 5.60 5.57 90 5.58 5.55 5.53 In order to obtain the angular d i s t r i b u t i o n i n the centre of mass system (Chapter III) the experimental data (Tables IIT-1 and III-2) were accordingly transformed using the following equations: Q' = tan"' ( SI* Qt- f^P * \ cose L -/2> and 1 (4-/2>co6 9,.)E \ A P P E N D I X D N U C L E A R I N S T R U M E N T S A N D M E T H O D S 57 (1967) 353^354; © N O R T H - H O L L A N D P U B L I S H I N G C O . LOW COST DEUTERATED POLYETHYLENE TARGETS OF CONTROLLED THICKNESS FOR HIGH CURRENT ACCELERATORS M. A. OLIVO and G. M. BAILEY Physics Department, University of British Columbia, Vancouver, Canada Received 13 September 1967 Thin copper backed deuterated polyethylene targets have been prepared and their performance and characteristics compared with commercial deuteride targets. Experimental studies on the reaction D(p,y)3He being carried out in this laboratory required thin deuterium targets of known composition capable of withstanding a large beam current of 160 keV protons. Solid copper backed targets of zirconium-deuteride and titanium-deuteride, soldered to a water cooled target rod have proved the most stable, but have the disadvantage of having an uncertain composition as well as producing considerable multiple scattering at these low energies. Thin self-supporting deuterium targets of poly-ethylene on carbon have been developed in this labora-. tory by Tripard and White1). We have applied their technique to prepare solid backed deuterated poly-ethylene targets and found them to have a number of advantages. These targets are relatively stable, have a well defined composition (C 2 D 4 ) n , and for the same energy loss give less multiple scattering and a higher y-ray yield than deuteride targets. Targets were prepared by dissolving a weighed quan-tity of deuterated polyethylene* in boiling xylene. The solution is gently boiled for at least 2 min and then carefully poured on to a horizontal 0.025 cm thick copper backing which had previously been cleaned and flattened. Surface tension keeps the solution within the confines of the target backing while the xylene slowly evaporates at room temperature, in a dust free atmos-phere. Tn the present case targets of about 40 /(g/cm were prepared on a 15 cm 2 copper backing by dissolving 600 fig of the polyethylene in 1 g of xylene. Target performance has been compared with commercial * Deuterated polyethylene (>98%D) obtained from Merck, Sharp and Dohme of Canada Ltd., Montreal, Canada. 100 100 B O M B A R D M E N T TIME IN MINUTES 160 Fig. 1. Target deterioration for solid water cooled targets of zirconium-deuteride and deuterated polyethylene. The curves have been normalized to correspond to an initial deuterium content of 2.8 x 1018 atoms/cm2. Targets A and B correspond to commercial deuteride targets of equal thickness (nominally 280,ug/cm2 for an assumed composition Z r D i . s ) , bombarded with 60/(A of 160 keV protons. Curves C, D and E correspond to polyethylene targets (C2D.i)n of thickness 40/tg/cm2 bombarded with 60/(A, 40 /iA and 25 /(A of 160 keV protons respectively. The beam spot in all cases was a circle of area 20 mm 2. 353 -125--126-M . A . O L I V O A N D G . M . B A I L E Y 354 T A B L E 1 Target Deuterium content (atoms/ cm2) Thickness (,ug/cm2) Energy loss (keV) <0>* (dea) ZrDi.s 2.8 x 101 8 280 71 10 (C2D4)n 2.8 x 10 1 8 40 32 l i . . . * The rms multiple scattering angle <8> has been calculated from the work of Williams2). deuteride targets by monitoring the 90° y-yield from the D(p,y) 3He reaction with a 12.5 c m x l O cm Nal(Tl) crystal. In all cases the targets were clamped to a 1.6 mm thick water cooled copper plate which was an integral part of the target rod assembly. Protons of 160 keV, collimated to give a target spot of 20 mm 2 were used to check target deterioration. The beam current variation was less than 5% for these tests and a number of target spots were run to allow for possible bad thermal contact with the cooled mount. The result of these tests are summarized in fig. 1. The difference between curves A and B illustrates the uncertainty in the composition of deuteride targets, which can contain anything from one to two atoms of deuterium per atom of zirconium. From these curves it can be inferred that the deuteride targets give superior yield and stability for a given deuterium content. How-ever, if the energy loss or the multiple scattering of the protons is of prime concern, the polyethylene targets are superior. This is indicated in table 1. The rapid initial deterioration of the polyethylene targets at high beam currents appears to be a surface effect and is probably due to poor thermal conduction through the polymer. It is quite possible that the polymer itself breaks down losing deuterium in the process, it is interesting to note that at a later stage the deterioration is comparable to the deuteride targets. The present tests at 60 correspond to a beam current density of 0.3 mA/cm 2 at the target. The polyethylene targets are extremely simple to make and with practice one can judge a good target from the uniformity of the surface. A reject target would have a noticeable shrinkage pattern on its sur-face. We have made as many as 30 targets in a day and had only two failures. Thickness variation across the surface (excluding the edges) of a target is typically 10% but this could be improved with careful attention to the surface flatness and horizontal mounting of the backing and a controlled drying environment. A characteristic of these targets is that they rapidly show a dark spot even when bombarded with quite small beams. This deposit, presumably carbon from breakdown of the polymer, does not seem to affect the performance of the target, and has in fact proved useful in determining the profile of the beam spot. Targets made by this technique are quite inexpensive compared with the commercial deuteride targets and can be made to any physical size. Further tests to reduce target deterioration are planned using a rapidly rotating target holder. References !)G. E. Tripard and B. L. White, Rev. Sci. Instr. 38(1967) 435. 2) E. J. Williams, Rev. Mod. Phys. 17 (1945) 217. APPENDIX E MULTIPLE SCATTERING The mean square multiple scattering angle of charged massive p a r t i c l e s i s given i n the centre of mass system by (MO 6 5 ) : <el> = * « «* U£-) ( E - i i where K = <?T Nt Z 2 Z 2 e^ (K± + Mg) 2 M~2 E ~ 2 ; Nt being the number of scattering nuclei/cm , Z 2 and M 2 the atomic number and mass of the scattering n u c l e i , and Z^ and M^  the corresponding quan-t i t i e s for the incident p a r t i c l e s , which possess an energy E i n the laboratory frame. Q m j _ n i s defined by: -2.1 z£/3 * (M1+M2) / (aQM2y2M 1E). ( Z! Z 2 e V ^ E M ^ O . ) (a). 0 ...«< min" (E -.2) 3.8 Z2 / 3e 2(M 1+M 2)/(2a oM 2E) (Z^e 2/•n^2EMj^>l) (b) a Q being the Bohr o r b i t radius, For the ( C D 2 ) n compound the t o t a l R.M.S. multiple scat-ter i n g angle was calculated using the following expression: [e] -V<e2>-*<ei> where and (©Q^ are the mean square multiple sacttering an-gles due to the deuterium and carbon atoms, respectively. To calculate [QJ s \ ^6*^ a program was written using a -127-.-.12 a* PDP-8 computer, a v a i l a b l e i n t h i s l a b o r a t o r y . A t e s t i s i n c l u d e d i n the program to determine which of the two c o n d i t i o n s r e f e r r e d to i n equation (E-2), (a) wave or (b) c l a s s i c a l , a p p l i e s . The values of the m u l t i p l e s c a t t e r i n g angle shown i n Table I I - l were c a l c u l a t e d assuming t h a t the energy of t h e ' i n -c i d e n t p a r t i c l e s remains constant as they t r a v e r s e the t a r g e t . The values i n column 2 were obtained a t an energy equal to the i n c i d e n t energy. The equation ( E - l ) i n d i c a t e s that the s c a t t e r -i n g angle i n c r e a s e s as the p a r t i c l e energy decreases. Thus a more r e l i a b l e estimate f o r the m u l t i p l e s c a t t e r i n g angle i s obtained (column 6) a t an energy which i s the average over the th i c k n e s s of the t a r g e t . That i s a t E = E - AE/2. APPENDIX F THE REACTIONS 1 2 C (p, &") 1 3 N AND 1 3 C ( p f t f J^N The maximum available energy for the gamma-ray tran-s i t i o n s i n the reaction 1 2 C ( p . t f ) 1 3 N i s which i s below the 2.95 MeV discrimination l e v e l used i n the computation of the gamma-ray i n t e n s i t y (Chapter I I I ) . The t o t a l 12 3 cross section, for 160 KeV protons, i s CT( C)=4.6 x 10" J yub. In the ^ C ( p , $ ) ^ N reaction the maximum available energy for the gamma-ray tr a n s i t i o n s i s E* - J ^ , , \ + Q = 77 0.160 + 7.546 = 7. 5 heV The t o t a l cross section, for 160 KeV protons, i s i n t h i s case G"( 1 3C)=2.5 x 10" 2 y^b (which i s comparable to the C(D)=8 x 10~ 2^b for the i s o t r o p i c component i n the D(p,tf)^He rea c t i o n at the same bombarding energy). The f i n i t e value of the cross section indicates the p o s s i b i l i t y of having gamma-rays of that energy 1 lk \ or lower (due to cascades to the various l e v e l s i n the N) which w i l l be present as an indiscriminated beam dependent background together with the 5.6 MeV from the D(p,l$)3He reaction. 13 Because only 1.11$ of J0 i s present i n the natural carbon the t o t a l gamma-ray contribution from the reac t i o n involving t h i s isotope w i l l be proportional to <T( 1 3C)x 1. llxK/100=2.8<K.10"" 2 compared with<T(D)«2,K=l6«K from the D(p,tf)^He, ( i n K were -129--130-included the appropriate units; the factor 2 arises from the composition of the target). This means that i n the gamma-ray y i e l d a r i s i n g from D(p,tf) 3He and 1 3 C ( p . t f ) o n l y 0.1?# w i l l be due to the second reaction. Its contribution can therefore be neglected. The t o t a l cross sections for the reactions C(p,tf) -% and " ^ C ( p . u " ) w e r e evaluated at 160 KeV from the r e s u l t s given by H a i l and Fowler (HA 50). In the f i r s t r e action the cross section was extrapolated using t h e i r semi-empirical expression (T( 1 2C) =0.0024 E""1 exp(-6 E~^) which was found to f i t the. 88: KeV and 128 KeV data. The extrapolation i s i n good agreement with the experimental value of 0"( 1 2 C ) = ( 5.0 - 0.3) x 10~ 3 y^b obtained at l 6 l KeV by Bailey and Stratton (BA 50). For the second 13 — 1 —~ reaction the same energy dependance CT( J C ) = a E~ exp(b, E~2.) was used. The parameters a and b were found by f i t t i n g t h i s expression to the experimental cross section obtained at 114 KeV and 126 KeV by Lamb and Hester (LA 57). The cross section so obtained may be somewhat out from the actual value. Woodbury and Fowler (W0 52) using the single l e v e l Breit-Wigner,dispersion formula determined the contribution of the 554 KeV and the broad 1.25 MeV resonances to the cross section at 129 KeV. I t was found that nearly 75% was due to these resonances. However. we are here only interested i n knowing the order of magnitude of the cross section. The extrapolated value i s then acceptable because: -131-the extrapolation was based on cross sections obtained experimentally, thus they include the contribution from the resonances and the extrapolation was done to an energy which i s only 30$ higher than the one i n which the experi-mental data was obtained.' APPENDIX G CORRECTION DUE TO THE GAMMA-RAY ABSORPTION IN THE TARGET HOLDER Assume a point source of gamma-rays whose i n t e n s i t y per unit of s o l i d angle i s I., F i g . G - l . i i BEAM t d ! v Pig. G-l : Target holder absorption correction t 1^ i s the transmitted gamma-ray i n t e n s i t y integrated over the s o l i d angle of the detector and d the thickness of the absorber. For s i m p l i c i t y i t i s assumed that the cone subtended by the detector cuts at the target holder i n SS». Then c = COS Q; and r = — cos p r = cos cos p -I32--133-where i s the t o t a l l i n e a r attenuation c o e f f i c i e n t . I f the target holder i s made of d i f f e r e n t materials, then where i s the t o t a l mass attenuation c o e f f i c i e n t for a given material, ^ i t s density and d^ i t s thickness. We have f i n a l l y h - J l / Z i where the correction factor i s The Target Holder "TA": A cross section of the target holder "TA" i s shown below: WATER COOLING 1 0.3^ cm v//;///////;////////T777\ TARGET BACKING (0.030 cm copper) O Q Q 0 O O Q O O O O O 0.25 cm 0.21 cm TARGET HOLDER (copper) -134-This was assumed to be equivalent to: ^ — WATER l IIIIIIIIIJ III ! COPPER The Target Holder "TB" : A cross section of the target holder "TB" i s shown below: TARGET BACKING (0.030 cm copper) TARGET HOLDER (copper) The data used f o r D(p,^) 3He and 11B(p,o') 1 2 C absorption corrections are shown i n Table G - l . An average gamma-ray energy of 5^58 MeV f o r the D(p,l$)%e reaction was chosen to determine the mass attenuation c o e f f i c i e n t s . These vary over the energy range of the gamma-rays shown i n Table G-l by less than 0.5$. V/////////////////?////A 0.16 cm - 1 3 5 -For the B(p,"tf) C the c o e f f i c i e n t s were determined for Efl = l l o 7 MeV. The mass attenuation c o e f f i c i e n t s were obtained from the work of G.W. Grodstein (GR 5 7 ) . Table G-l : Target holder correction parameters for the D(pVtf)3He and 11B(p,'S) 1 2 C reactions. "TA" "TB" WATER COPPER COPPER D(M)3He D(p,*)3He (r>(cm2/g) 0 . 0 2 8 6 0. 0206 0 .0312 0 . 0 3 0 8 0 .0312 ^(g/cm 3) 1 .0 1 .0 8 . 9 2 8 . 9 2 8 . 9 2 d (cm) 0.124 0.124 0.2^9 0 . 2 4 9 0.189 The target holder absorption correction for holder "TA" 1 1 v 1 2 was checked with 1 1 .68 MeV gamma-rays from the reaction B(p ? 0 ) C. The r e s u l t s obtained are summarized i n Table G - 2 . Table G-2 : Target holder absorption measurements for E^=11.7 MeV. MEASURED FRACTION TRANSMITTED 0 . 9 4 - 0 . 0 2 0 . 9 3 - 0 . 0 2 0 . 9 0 i 0 . 0 2 The experimental r e s u l t s are i n good agreement with the calculated absorptions. Q CALCULATED FRACTION TRANSMITTED 30° 0 . 9 3 5 8 4 5 ° 0 .9219 60° O .8914 • APPENDIX H BEAM DEPENDENT BACKGROUND The p o s s i b i l i t y of neutrons a r i s i n g from secondary processes i n the target or from the accelerator during the D(p,tf)%e experiment was considered since i t would a f f e c t the r e s u l t s of the angular d i s t r i b u t i o n measurements. Such neutrons would i n t e r a c t i n the Nal c r y s t a l and i n the surrounding materials giv i n g r i s e to an extra gamma-ray y i e l d . Because the gamma-ray y i e l d from the rea c t i o n D(p,"tf)3He i s very small, s p e c i a l l y at 0°, a c a r e f u l check for such neutron contributions was c a r r i e d out. At the bombarding energies considered here no d i r e c t neu-trons can a r i s e from the r e a c t i o n D(p,n)2p which has a threshold of 3.3 MeV. H. l , Neutrons A r i s i n g from the Accelerator The hydrogen used i n t h i s experiment was natural with I. 5 x 1 0 " 3 parts of D;,o therefore deuterium was present i n the mass two beam which struck inside of the analyzing magnet vacuum chamber. An accumulation of deuterium i n the s t a i n l e s s s t e e l magnet box would give r i s e to neutrons from the reaction D(d,n) 3He. A t h i r t y hours angular d i s t r i b u t i o n run was performed with a 160 KeV beam h i t t i n g a clean copper target. This run was made i n order to check whether a neutron background b u i l t up a f t e r a long period of running. The counting rate was found -136--137-to be independent of the po s i t i o n of the detector #1, and equal to the counting rate without the beam,, so within the accuracy of the D(pt'i)^Ee measurement no s i g n i f i c a n t contribution came from the deuterium h i t t i n g the magnet box. H.2. Neutrons A r i s i n g i n the Deuterated Polyethylene Targets As was mentioned i n Chapter I I , neutrons may arise : from the reaction D(d,n) 3He caused by the deuterohs i n the poly-ethylene target which have picked up energy by c o l l i s i o n s with incident protons. Neutron contributions of this kind have been observed for proton energies below 500 KeV when bombarding heavy ice targets (SE 59). A d i r e c t determination of the number of neutrons produced would not give a d i r e c t answer to the problem, because the e f f i c i e n c y of the Nal c r y s t a l for detecting neutrons was not known. Furthermore, because the neutrons w i l l be-scattered i n the surrounding materials i t would be d i f f i c u l t to evaluate how many w i l l enter the c r y s t a l . A further d i f f i c u l t y -is - to evaluate how many of those gamma-rays which aris e from the in t e r a c t i o n of the neutrons i n surrounding materials are scattered into the c r y s t a l . Because of these d i f f i c u l t i e s the shape of the-spectrum from the detector when bombarded with neutrons was measured and compared to the gamma-ray spectra from the reaction D(p,^) 3He. The neutrons were obtained from the reaction D(d,n)^He, -138-by bombarding a deuterium gas target with 876 KeV deuterons from the U.B.C. Van de Graaff accelerator. Using the same collimator and shielding geometry as for the D(p,tf) 3He runs the detector was placed at 0° with respect to the incoming beam, with the front face of the c r y s t a l 20 cm from the centre of the gas target. The target contained a O.83 cm beam path i n deuterium gas at 200 mm of Hg pressure with a 127 micron Ni window. The spectrum shown i n Pig. H-l was obtained a f t e r background subtraction for a t o t a l charge of 30 delivered to "the target i n a four minute run at an average current of about 135 nA. The maximum k i n e t i c energy available f o r the knock-on deuterium atoms i s E D(max.) = 8/9 E (head on c o l l i s i o n ) . Therefore, for 160 KeV protons we have E D = 142 KeV. The angular d i s t r i b u t i o n of the neutrons from the reaction D(d,n) 3He at a bombarding energy of E^ = 142 KeV Is approximately i s o t r o p i c . The cross section f o r the i s o t r o p i c component i n the reaction D(p,T£)3He ranges from approximately 0.08 M.b at E =£60 KeV to 0.07 yub at E p = 90 KeV (GR 62 ; GR 63) while the cross section f o r the reaction D(d,n) 3He varies from approximately 27 mb at E„ = 142 KeV to 12 mb at E~ = 80 KeV (AR 54). Because the cross section f o r the reaction D(d,n) 3He f a l l s more r a p i d l y than the D(p,*tf)3He the comparison was made with the D(p,lJ) 3He data obtained at 160 KeV with the detector at 0° where the gamma-ray y i e l d i s minimum. I f the neutron background does not show any e f f e c t at th i s energy i t c e r t a i n l y w i l l not show any e f f e c t -6CT -- 1 4 0 -at 90 KeV. I t should be mentioned here that the energy of the neutrons from the gas target at 0° f o r E D = 8?6 KeV, have an energy of 3 .99 MeV, while the energy of the neutrons leaving the polyethylene targets at 0° would have a maximum energy of 2 . 9 4 MeV (Ep = 142 KeV). However, the shape of the spectrum i n the gamma-ray detector does not change appreciably with neutron energy over th i s range. Pig. H -2 shows the gamma-ray spectrum from the reaction D(p,tf) 3He taken at 0° for E p = 160 KeV (Table I I I - 2 , i= 3 ) . . F i g . H -3 shows the 0° spectrum with the background removed. I t was obtained by subtracting the background spectrum shown i n F i g . I I I - 2 when i t was normalized to the same running time as for-the 0° run. The s t a t i s t i c a l errors i n the low energy chan-nels look very large. However, t h i s i s due to the f a c t that they correspond to small differences between large numbers. I t i s more convenient to remove this s t a t i s t i c a l scatter before comparing th i s spectrum with the D(d,n) 3He one. The method used to f i l t e r out the s t a t i s t i c a l fluctuations follows the technique described by H.P. Yule (YU 67). I t i s based on the le a s t squares f i t t i n g of the experimental,points (number of counts i n each channel) to a power function over a small region of the o r i g i n a l data. Let N. be the number of counts i n the channel i . X ID o o o d - l o. o o o CM o , 1 + — o + 1— ~ZL ZD + C_Jg 4 + + o 11 . + OZ + + LU + CO + . 2 1 0 + + iiiiimiimiiuiiiiiiiii - . 0 0 0 "1 1 .000 LA O I D ( p , t f ) 3 H e 9 = 0° E = 160 KeV 1 P LA II to T 2 . 0 0 0 3 . 0 0 0 U.OOO ENERGY LRB (MEV] 5 . 0 0 0 6 . 0 0 0 7 . 0 0 0 F i g . H-2 : D ( p , ^ ) ^ H e gamma-ray s p e c t r u m . o ( N _ | O o o a Q . CO O o o ZD o Li_o LU g o ZD<=> i o o Q o 03. I + + + + + +++ + + + + ++ + + + X 1 D(p,*) 3 He ° E = U P (BACKGROUND S U B T R A C T E D ) 8=0°   160 KeV 1  ( E j -0.511) MeV " 1 r E , = 5-6 MeV +++ + -.000 i.oao z.oao 3 . 0 0 0 u.ooo ENERGY LRB (MEV) 5.00Q 6.000 7.000 F i g . H-.3 : D ( p , t f ) ^ H e g a m m a - r a y s p e c t r u m s h o w n i n F i g . H-2 w i t h t h e b a c k g r o u n d r e m o v e d . - 1 4 3 -The smoothed value of i s defined as S^, where " ' • g ( V j 1^,1 ( H - l ) The constants a . and the normalization constant N depend m, j m upon the power of the function chosen to which the raw data i s to be f i t t e d . Tables of these constants for d i f f e r e n t degree of polynomials are given by A Savitzky and M. Golay (SA 6 4 ) , The equation (H-l) then gives a new value f o r which i s found by f i t t i n g m lower channels and m higher channels (including the channel to be smoothed) to a power function n k f. = > b, i . This process i s repeated for a l l the channels 1 k=0 * excluding the f i r s t and the l a s t m channels. This technique was applied to the spectrum shown i n F i g . H-3. The r e s u l t i s shown i n F i g . H-4. This spectrum was obtained under the following conditions; a. 19 point smooth was used (m=9) b. A quadratic function was used (n=2) c. The smoothing process was not c a r r i e d out for channels above approximately 4 MeV. d. The process was repeated twice; that i s , the o r i g i n a l points were smoothed and the new points were smoothed again. A computer program, written by Bailey (BA 6 8 ) , was used to carry out the smoothing operation. In order to assess the significance of a neutron contribution which may be present, the D(d,n) 3He neutron - 1 4 4 -spectrum, shown In Fi g . H-l was normalized so that the number of counts i n the energy range 2.95 to 6.1 MeV was equal to 2% of the number of counts i n the same energy range of the gamma-ray system shown i n Fi g . H-3. Then the normalized neutron spec-trum was subtracted from the smoothed gamma-ray spectrum shown i n F i g . H -4 to give the curve shown i n F i g . H-5. Since the re-su l t i n g curve i s negative i n the lower energy range i t i s clear that too much has been subtracted. Therefore the neutron con-t r i b u t i o n to the counting rate i n the energy range used for eval uating the gamma-ray f l u x i s s i g n i f i c a n t l y less than 2% and to the accuracy of these measurements i t can be said to be i n s i g -n i f i c a n t . O Q C D C M . O o o • o. CO o o o o o L L . O o r -CO LU 2 - 0 ZD a I o o o o C O . i A / % £ nun mini +^  1 J X 1 D ( p , « ) ; 5 H e (SMOOTHED) + -H--H-+ RAW S P E C T R U M I I 1 -.000 1.000 2-000 3.000 4.000 5.000 6-000 7.0O0 ENERGY LRB (MEV) F i g H-k : D ( p , t f ) He g a m m a - r a y s p e c t r u m o f F i g . H-3 w i t h t h e f i r s t 1^ 5 c h a n n e l s s m o o t h e d . o a CD f M . o a o CO O O O o o LL.C3 O CO L U 2 D a*. i a o o a C D . i X I D ( p , t f ) 3 H e - 2% D ( d , n ) 3 H e + •ft + -.000 I-000 2.000 3.0O0 4-000 5.000 6.000 7.000 ENERGY LRB (MEV) F i g . H-5 : G a m m a - r a y s p e c t r u m o b t a i n e d by s u b t r a c t i n g t h e n o r m a l i z e d n e u t r o n s p e c t r u m f r o m t h e s p e c t r u m s h o w n i n F i g . \\-k. APPENDIX I LIST OF COMPUTER PROGRAMS USED IN THIS THESIS Program Name ND-160 SPECTRA NORABS POLYLS MLKH1F COMPSC ' DE-WFC NDPTHE SMOOTH KONRAS Function IBM 7040/7044 TALLY paper tape decoder Energy c a l i b r a t i o n , energy s h i f t and integration of the spectra Background subtraction, normalization and absorption corrections I n i t i a l estimate of the parameters for the i t e r a t i v e least squares f i t I t e r a t i v e least squares f i t and p l o t t i n g Compton scattering c a l c u l a t i o n front collimator Detector e f f i c i e n c y and f i n i t e s o l i d angle corrections (smoothing factors) Spectra p l o t t i n g Gamma-ray smoothing spectra N o n - r e l a t i v i s t i c kinematics two body break-up used for the reaction D(djn) 3He PDP-8 RMSAMS R.M.S. Multiple scattering angle calculations - 1 4 7 -

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