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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) He BELOW 200 KeV 3  by. MIGUEL ANGEL OLIVO L i c e n c i a d o en F i s i c a Instltuto  de F i s l c a de S.C. de B a r i l o c h e ,  U n l v e r s i d a d N a c i o n a l 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 a c c e p t t h i s t h e s i s as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA August, I968  In  presenting  for  an  that  advanced  the  I  thesis  for  Department  partial  the  freely  purposes  or  representatives.  h.i)s  of  this  of  thesis  may b e  for  permission.  Physics  August 8  Columbia  , 1968  of  for  granted  It  is  financial  of  British  available  permission  scholarly  by  fulfilment  University  it  that  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Date  in  make  agree  my w r i t t e n  Department  at  shall  further  publication  without  thesis  degree  Library  Study.  or  this  for  the  Columbia,  I  reference  and  extensive  by  the  requirements  copying  Head  understood  gain  shall  of  this  my  that  not  of  agree  be  copying  allowed  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 r e a c t i o n D(p,$)^He has been measured f o r 7 0 KeV and tkk KeV protons i n the l a b o r a t o r y system, u s i n g t h i n deuterated polyethylene targets. The interest  study o f t h i s p a r t i c u l a r l y  f o r d e t e r m i n i n g some p r o p e r t i e s of the f o r c e s which  bind nuclear p a r t i c l e s role  simple r e a c t i o n i s o f  t o each o t h e r .  In a d d i t i o n i t p l a y s a  i n a number o f a s t r o p h y s l c a l p r o c e s s e s . The ground s t a t e of -^He i s predominantly  2  S s t a t e w i t h admixtures  mixed symmetry.  of a  k  D s t a t e and a  2  a symmetric  S, \ s t a t e o f  These admixtues are r e l a t e d t o s p e c i f i c com-  ponents o f the two body f o r c e s c o u p l i n g the three p a r t i c l e s . The measurements were made w i t h a h i g h c u r r e n t 1 8 0 KeV a c c e l e r a t o r , b u i l t by the author, u s i n g a n ORTEC duoplasmatron i o n source.  T e c h n i c a l problems i n v o l v e d i n the development o f  the a c c e l e r a t o r and  the d e u t e r a t e d t a r g e t s are d i s c u s s e d .  The angular d i s t r i b u t i o n a t Hi4 Legendre  W(6)  =  16'KeV i n terms of  polynomials P^ i s g i v e n i n the c e n t r e o f mass system by  A  Q  |P  o  +(  o  05-.02)P  1  -(.9^-.02)P  2  -(.05i.02)P  4(.03-o02)P  3  4  j  and a t 7 0 - 2 0 KeV the angular d i s t r i b u t i o n i s g i v e n by w(9) =  A rp +(.o6i.o^)P -(.93 .05)P -(.o6i.o4)P +(.02i.05)pJ i  o  o  1  2  3  -iii-  The c o e f f i c i e n t s i n the Legendre p o l y n o m i a l expansion are  related  t o the v a r i o u s t r a n s i t i o n s between the continuum and  bound s t a t e s . ponents of the  Their 3  significance  i n terms of the d i f f e r e n t  He ground s t a t e wave f u n c t i o n  The a b s o l u t e c r o s s s e c t i o n has not been measured. are  discussed  briefly.  com-  i s discussed.  ( i . e . the c o e f f i c i e n t A ) o  Plans f o r measuring i t i n the near  future  TABLE OP CONTENTS ABSTRACT  .  i  TABLE OP CONTENTS  i v  LIST OP TABLES  v i i  LIST OF FIGURES  • •• • • v*  ACKNOWLEDGEMENTS  x i  PUBLICATIONS CHAPTER I  CHAPTER I I  l  x i i INTRODUCTION 1.1.  General Introduction  1.2.  Review  1.3.  Present Work  1  o f P r e v i o u s Work  4...  6  EXPERIMENTAL APPARATUS 2.1.  2.2.  Angular D i s t r i b u t i o n Table 2 . 1 . 1 .  Target Chamber  13  2 . 1 . 2 .  The C o l l i m a t o r  16  2 . 1 . 3 .  The Vacuum System  17  The Targets Deuterium Gas Targets  21  2 . 2 . 2 .  Heavy I c e T a r g e t s  21  — 2,2.4-.  2.4:  17  2 . 2 . 1 .  2 . 2 . 3 .  2.3.  11  Deuterium Absorbed i n S o l i d Elements ' Deuterated Compounds ......  22 2 3  The D e t e c t o r , C o l l i m a t o r and Shielding  2 6  The E l e c t r o n i c s  33  iv  ....... ............  1  *  V  CHAPTER I I I EXPERIMENTAL METHODS AND RESULTS  CHAPTER IV  3.1.  The Procedure  3.2.  The Angular D i s t r i b u t i o n F u n c t i o n .  5 3  3.3.  The F i t t i n g Procedure  5 3  3.4-.  The R e s u l t s  ...  6 0  DISCUSSION 4-. 1.  Discussion  4-.2.  Comparison w i t h the T h e o r e t i c a l Calculations F u t u r e Work  4-. 3 . 33IB3LJ OGRAPHl^  42  o  «  o  *  *  *  o  o  o  o  o  *  o  o  »  »  o  o  of the R e s u l t s  o  »  *  o  «  o  »  «  «  o  e  e  «  *  o  »  6 5  *  *  *  *  o  *  7486  a  *  *  9^-  i  APPENDIX A  THE-ANGULAR DISTRIBUTION OF THE 1 1 . 7 MeV GAMMA-RAYS FROM THE REACTION B ( p , " 8 ' ) C .. 11  APPENDIX B  THE ACCELERATOR AND MAGNETIC B.l.  APPENDIX C  9 5  ANALYZER  The A c c e l e r a t o r B.l.l.  B.2.  1 2  107  The I o n Source and E l n z e l Lens 1 0 7  B.1.2.  The A c c e l e r a t i n g Tube  B.l.3.  High V o l t a g e .  114-  B.1.4-.  The Vacuum System  116"  B . l . 5.  The S h i e l d i n g  B.l.6.  Characteristics  The Magnetic A n a l y z e r B.2.1.  The Magnet  B.2.2  The Power Supply  1 1 0  1 1 6 1 1 7  117 1 2 0  1 2 2  THE ENERGY OF THE GAMMA-RAYS FROM THE REACTION D(p,tf) He AND THE COORDINATE SYSTEM TRANSFORMATIONS 1 2 3 3  vi  APPENDIX D  DEUTERATED POLYETHYLENE TARGET PREPARATION  125  APPENDIX E  MULTIPLE SCATTERING  127  APPENDIX F  THE REACTIONS  APPENDIX G  CORRECTION DUE TO THE GAMMA-RAY ABSORPTION  1 2  C ( p , t f ) N and 1 3  1 3  C(p  ) \ 1  f 0  IN THE TARGET HOLDER APPENDIX H  APPENDIX I  129  132  BEAM DEPENDENT BACKGROUND H.l.  Neutrons from the A c c e l e r a t o r  H.2.  Neutrons from the Targets  LIST OF COMPUTER PROGRAMS USED IN THIS THESIS  ....  136 137 14-7  LIST OF TABLES II-l  C h a r a c t e r i s t i c s o f the d e u t e r a t e d p o l y e t h y l e n e targets  25  II- 2  Dimensions of the d e t e c t o r assembly # 1 and # 2  3^  11  E1©  3  C  "fcl* O l " l l C  t  Uni  S  o  o  o  o  o  o  o  o  o  a  o  ^  o  o  o  o  o  v  o  III- l  D(p,l$)^He  III-2  D(p,T$) He angular d i s t r i b u t i o n data  III-3  Smoothing f a c t o r s f o r  I I I - 4-  angular d i s t r i b u t i o n data  IV-2  E  A  0  9  B(p,u")  y  —  A  o  o  o  o  o  ^4*0  run  90"KeV  KeV r u n  160  MeV gamma-rays ....  5.58  0  0  0  0  0  *  0  0  —  1  1  0  7  0  M6V  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  63™*^^'  67 84  P  0  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  9  0  0  0  102  105  12  B(p,tf) C Legendre p o l y n o m i a l c o e f f i c i e n t s c o r r e c t e d f o r f i n i t e s o l i d angle of the 00 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  B-l  Accelerator's electronic units  B-2  A c c e l e r a t o r c o n d i t i o n s f o r 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  120  D ( p , t f ) % e gamma-ray e n e r g i e s a t Ep = 1 6 0 KeV and 9 0 KeV f o r d i f f e r e n t angles of o b s e r v a t i o n Target h o l d e r c o r r e c t i o n parameters 11  and  10^)  11.6  -a  G-2  53  100  Smoothing f a c t o r s f o r 1 1 , 7 MeV gamma-rays ....  C L © t © C t O I *  G-l  4-9-50  C angular d i s t r i b u t i o n data f o r  1  sS  48  B(p,o) C angular d i s t r i b u t i o n l e a s t squares f i t parameters and Chi-squared t e s t f o r  11  C-l  o  Q  e 7  11  11  E  A-4-  o  D(p,"8)^He r e a c t i o n . Comparison between e x p e r i mental r e s u l t s and Donnelly's c a l c u l a t i o n s ...  A-l  A-3  o  D(p,tf)-%e angular d i s t r i b u t i o n l e a s t squares f i t parameters and Chi-squared t e s t f o r 9 0 KeV 9.ncL K©V runs * ooo oooooooo©oo««o» *D(p,tf)^He Legendre p o l y n o m i a l c o e f f i c i e n t s c o r r e c t e d f o r f i n i t e s o l i d angle o f the d e t e c t o r  •4  A-2  o  3  160  IV- l  o  124  f o r D(p,u).^He  12  C r e a c t i o n s ....................  B(p,tf)  135  Target h o l d e r a b s o r p t i o n measurements f o r E ^  —  11  o7  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  vli  133  LIST OP FIGURES ' II-l  Schematic diagram of the angular d i s t r i b u t i o n "fc3."bl@  e e  09*00  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 o f the t a r g e t chamber  II-3  Schematic diagram of the t a r g e t holder rods .  II-4-  Schematic diagram of the t a r g e t JH3-toi* 9 - S S 6 t n b l y  o  e  0  0  *  *  0  *  0  0  0  0  0  0  0  0  14,  15  chamber-colli0  0  0  0  0  0  13  o o o o o * *e  II-5  View o f 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  II-6  Schematic diagram of the d e t e c t o r assembly  II-7  ^°Co gamma-ray s p e c t r a  II-8  Block diagram of the e l e c t r o n i c arrangement  11-9  Photomultiplier c i r c u i t  11-10  Preamplifier c i r c u i t  3 7  11-11  P r e a m p l i f i e r ' s r e g u l a t e d 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  III- l  Detector-target configurations  4 3  III-2  Background  III-3  D(p,O^He gamma-ray spectrum l60  I I I - 4IV- 1  K©V  spectrum  19 ..  28 30  .  ... „  3 5 36  e  (D(p,o")^He runs)  8^  =  4 6  90°  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 n i t i a l estimate of the parameter K f o r the i t e r a t i v e l e a s t squares method .............. D ( p , t f ) % e gamma-ray a n g u l a r d i s t r i b u t i o n  5 6  o o o o o o o o o v o o o o e o oooeo'ooeooo  63  C 9 . S 6  o o o o  o o o o o o  IV-2  D(p,"Jf)-^He gamma-ray a n g u l a r d i s t r i b u t i o n case  IV-3  D(p,T{)%e gamma-ray a n g u l a r d i s t r i b u t i o n case 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  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  ^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 *  o  IV-4-  viii  ^ 9  ix  IV-5  D(p,"tf)-%e gamma-ray a n g u l a r case  IV-6  D ( p , t f ) % e gamma-ray a n g u l a r 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 a n g l e c o r iHClud-GCl  X * G C * b i O H  IV-7  IV-8  0  0  0  0  • »  0  •  #  o o  o  o  o  ^  o  o  o  o  o  o  o  o  o  o  o  o  73  D(p,"tf)^He gamma-ray a n g u l a r d i s t r i b u t i o n case # 1 0 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 rection included . e  e  0  0  0  0  0  0  0  0  0  0  0  0  0  *  0  0  0  0  0 0  D(p,'o')%e gamma-ray a n g u l a r case ^3  *  ?6  gamma-ray a n g u l a r d i s t r i b u t i o n  D(p,~6)-%e  case $^4* IV-9  0  distribution  *  0 0  *  0  0  0  0  0  *  0  0  0  O  O  O  O  O  0  0  0  0  0  0  0  9  0  0  0  0  0  0  *  0  77  •  *  0  O  O  ©  7^  distribution O  0  O  B  0  0  IV-10  Schematic diagram o f t h e r o t a t i n g  A-l  Some energy l e v e l s i n t h e  O  •  O  O  *  O O  target holder  89  12  11  A-2  G n u c l e u s . ..  c gamma-ray spectrum  B(p,o)  11  A-3  Background I 1  A-4  V  B-l  97 12  ( B(p,"0  C run  )  .  .  .  o  o  o  o  o  98  c gamma-ray a n g u l a r d i s t r i b u t i o n f o r MeV (case ) O O O O O O O O O * O O 0 O O O * * O O O O 7^2  11.7  A-5  spectrum  12  B(p,o) Etf = II  96  1 ?  V  103  12  B(p,#) C gamma-ray a n g u l a r 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 a n g l e c o r r e c t i o n i n c l u d e d .............. Schematic diagram o f t h e duoplasmatron i o n  104  source and ..Elmsel l e n s . system -,,.  108  B-2  Schematic diagram o f t h e a c c e l e r a t o r .........  I l l  B-3  View o f the a c c e l e r a t o r  B-4 B-5  View o f t h e a c c e l e r a t i n g tube T r a j e c t o r y o f t h e mean p a r t i c l e i n t h e h o r i z o n t a l p l a n e o f d e f l e c t i o n o f t h e a n a l y z i n g magnet pole t i p  119  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 o b t a i n e d w i t h d e t e c t o r # 1 ..  139  H-2  D(p,tf)^He gamma-ray spectrum 6  118  = 0 ° 1 6 0 KeV r u n  121  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 , t i ) % e gamma-ray spectrum w i t h 2% of D(d,"n)^He subtracted  1^6  ACKNOWLEDGEMENTS I wish to express my s i n c e r e g r a t i t u d e to Dr. G.M.  Griffiths  f o r h i s u n t i r i n g s u p e r v i s i o n and c o n s c i e n t i o u s a s s i s t a n c e the course of t h i s work.  H i s a p p r o a c h a b i l l t y together  during  with h i s  understanding of the problems i n v o l v e d , p a r t i c u l a r l y the language problem, made t h i s t h e s i s p o s s i b l e . The and  h e l p f u l d i s c u s s i o n s of Drs. G.M. B a i l e y , J.H. W i l l i a m s o n  P.H.R. Orth on v a r i o u s aspects  of t h i s work i s a p p r e c i a t e d .  Furthermore, I wish to thank Mr. D. Hepburn and Dr. G.M. B a i l e y f o r t h e i r k i n d a s s i s t a n c e i n o b t a i n i n g experimental  data  during  the p a i n f u l l y long hours of the n i g h t . The Van  a s s i s t a n c e of the members of the workshop and of the  de G r a a f f group and i n p a r t i c u l a r t h a t of the l a t e G. Lang  i s t h a n k f u l l y acknowledged. The  author i s deeply g r a t e f u l to Dr. J.B. Warren f o r  extending  a s c h o l a r s h i p to the U n i v e r s i t y of B r i t i s h Columbia. To Dr. I a n McTaggart-Cowan, Dean of Graduate S t u d i e s , and other a u t h o r i t i e s of the U n i v e r s i t y of B r i t i s h Columbia who made p o s s i b l e the t r a n s f e r of my s t u d i e s t o the Ph.p. program of t h i s University. A l Consejo N a c i o n a l de  l a Republica  Argentina  de I n v e s t i g a c i o n e s  que p o s i b i l i t o ml v i a j e a e s t a  A mis padres por su constante mis  C i e n t i f i c a s y Tecnicas  estudios. To my wife and M i g u e l i t o .  xi  Universidad.  apoyo durante e l t r a n s c u r s o de  PUBLICATIONS "Low Cost Deuterated P o l y e t h y l e n e Targets of C o n t r o l l e d f o r High Current A c c e l e r a t o r s " ,  Thickness  M.A. O l i v o and G.M. B a i l e y , N u c l . I n s t r . and Meth., 57 (1967) 353. "Use of the Maximum L i k e l i h o o d Technique f o r F i t t i n g Counting Distributions. P a r t I I . A p p l i c a t i o n to Angular D i s t r i b u t i o n s " , P.H.R. Orth and M.A. O l i v o , N u c l . I n s t r . and Meth., (to be  published).  xii  CHAPTER I INTRODUCTION 1.1.  General  Introduction  D i r e c t r a d i a t i v e capture r e a c t i o n s i n n u c l e a r  physics  i n v o l v e a one-step t r a n s i t i o n between continuum and bound s t a t e s of a p a r t i c l e where the energy d i f f e r e n c e i s t r a n s f e r r e d to the electromagnetic  f i e l d and no intermediate  compound s t a t e i s  formed. These r e a c t i o n s provide obtaining information  a r e l a t i v e l y simple way of  about the bound s t a t e wave f u n c t i o n s , s i n c e  the p r o p e r t i e s o f the continuum s t a t e s can be I n f e r r e d from s c a t t e r i n g data and the p r o p e r t i e s 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 a r e w e l l known.  Another d i r e c t  capture-  process known as a s t r i p p i n g r e a c t i o n occurs when the neutron  ;  or proton from an i n c i d e n t deuteron i s t r a n s f e r r e d from the continuum t o a bound s t a t e i n the f i n a l nucleus,while the energy d i f f e r e n c e i s taken up by the other from the deuteron.  particle  Similar information  (proton or neutron)  concerning  the p r o p e r t i e s  of bound s t a t e s can be i n 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 r a d i a t i v e capture i s i n  p r a c t i c e more d i r e c t s i n c e i t i s mediated by the w e l l understood electromagnetic  interaction.  On the other hand s t r i p p i n g depends  on the much l e s s w e l l known s t r o n g n u c l e a r  i n t e r a c t i o n , not only  i n forming the continuum and bound s t a t e s but a l s o i n the t r a n s f e r 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  c o u p l i n g , the  p r 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 g e n e r a l orders  of magnitude s m a l l e r  several  than t h a t f o r s t r i p p i n g .  There i s a c o r r e l a t i o n between the s t r u c t u r e of the bound s t a t e wave f u n c t i o n s and s p e c i f i c p r o p e r t i e s of the n u c l e a r forces.  F o r few-nucleon systems many t h e o r e t i c a l s t u d i e s have been  c a r r i e d out t o s p e c i f y the nature of these c o r r e l a t i o n s i n a quant i t a t i v e way. functions  Therefore,  should  knowledge about the bound s t a t e wave  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  t h i s k i n d of i n f o r m a t i o n 1.  i s p a r t i c u l a r l y u s e f u l i n obtaining  because:  The continuum s t a t e s can be determined from deuteron s c a t t e r i n g data.  2.  ..  The continuum and bound s t a t e s a r e coupled by the electromagnetic  3.  proton-  f i e l d which i s known e x a c t l y , and  Due to the weakness of the e l e c t r o m a g n e t i c a c t i o n f i r s t - o r d e r p e r t u r b a t i o n theory w i t h some confidence bilities,  Further, s i n g l e t and t r i p l e t  or c r o s s  inter-  can be used  i n computing t r a n s i t i o n probasections.  the f a c t t h a t the bound s t a t e of -^He has both two-nucleon s p i n c o n f i g u r a t i o n s and i s more  t i g h t l y bound than the two body system (deuteron) i n d i c a t e s that the  study of t h i s r e a c t i o n c o u l d r e v e a l p r o p e r t i e s of the nucleon-  n u c l e o n f o r c e t o which the deuteron i s i n s e n s i t i v e , such as short  -3-  range components of the n u c l e a r singlet spin  f o r c e or components s e n s i t i v e to  configurations.  The  study of the r e a c t i o n D ( p , t f ) % e i s a l s o of i n t e r e s t  i n a number of a s t r o p h y s i c a l p r o c e s s e s .  In the  hydrogen-burning  stage of s m a l l main sequence s t a r s , the main energy supply comes from a s e r i e s of r e a c t i o n s reaction  p +  p — * D + | 9 D  —•  3  He  +  p-p  chain  i n which  the  + v  •  —  ^He  + 2p  He  + %e  The  r a t e of energy r e l e a s e  3  the  the  D(p,»5)^He i s the second steps p +  by  known as  the f i r s t r e a c t i o n s i n c e e l e c t r o m a g n e t i c and  t i o n D(p,"6')^He may  i n the  p-p  chain  i s controlled  the y3 i n t e r a c t i o n i s much weaker than :  nuclear  interactions.  However, the  reac-  have a s i g n i f i c a n t e f f e c t on the r a t e of con-  d e n s a t i o n of a s t a r towards the main sequence, depending on  the  i n i t i a l amount of deuterium, s i n c e  to  supply n u c l e a r  energy as the  I t i s the f i r s t  s t a r condenses.  Furthermore, the D ( p , ^ ) % e D ( d , n ) H e thus i n f l u e n c i n g the J  a cross  reaction  Although the  latter  reaction  s e c t i o n of a s e v e r a l order of magnitude g r e a t e r  the D ( p , t f ) % e c r o s s  s e c t i o n the v e r y much l a r g e r d e n s i t y  compared w i t h deuterium would p l a c e i t i v e position. believed  competes w i t h the  number of neutrons a v a i l a b l e from  a g i v e n i n i t i a l amount of deuterium. has  reaction  The  the D ( p , u ) % e  of  than protons  i n a compet-  neutron y i e l d i s of i n t e r e s t , b e c a u s e  i t is  t h a t the n e u t r o n captures have i n f l u e n c e d heavy elements  i s o t o p e r a t i o s i n the e a r l y stages of the s o l a r system. 1.2.  Review o f Previous Work The  e x i s t e n c e of the weak capture gamma r a d i a t i o n from • >  the p r o t o n bombardment of deuterium and S t r o t h e r s i n 1 9 3 9 (CU 3 9 ) . r e a c t i o n were performed Tollestrup  (FO  was f i r s t r e p o r t e d by Curran  Further i n v e s t i g a t i o n s of t h i s  t e n years l a t e r by Fowler,  I t was found t h a t the angular  *J-9).  a t a bombarding energy  L a u r i t s e n and distribution p  o f l.k MeV was n e a r l y pure s i n Q .  This  i m p l i e s t h a t the r a d i a t i o n i n v o l v e d emanates from an e l e c t r i c d i p o l e a l i g n e d w i t h the d i r e c t i o n o f the i n c i d e n t proton. the y i e l d , o b t a i n e d a t 9 0 ° , as a f u n c t i o n o f the bombarding from  From energy  0 . 5 t o 1 . 5 MeV i t was a l s o shown t h a t the c r o s s s e c t i o n was  non-resonant  I n c h a r a c t e r i n d i c a t i n g a d i r e c t capture process.  In 1 9 5 2 W i l k i n s o n (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 t h a t a t 9 0 ° the gamma-rays were plane p o l a r i z e d w i t h the e l e c t r i c d i p o l e i n the r e a c t i o n plane, t h e r e f o r e , c o n f i r m i n g the s u g g e s t i o n o f Fowler  e t . a l , that, the  capture r e s u l t e d from the e m i s s i o n of E l r a d i a t i o n as the p r o t o n made a t r a n s i t i o n from a continuum p-wave t o the ground s - s t a t e 3  of ^He.  He a l s o suggested  t h a t the s p i n - o r b i t c o u p l i n g must be  2  s m a l l s i n c e the s i n 9 d i s t r i b u t i o n was v e r y pure, while s p i n - o r b i t c o u p l i n g would induce t r a n s i t i o n s i n which A j = - 1 , -with a z 2  d i s t r i b u t i o n p r o p o r t i o n a l t o ( 1 + cos 0). The main t r a n s i t i o n s correspond  t o AJ  = 0 , with a s i n 9 d i s t r i b u t i o n .  A significant  amount o f s p i n - o r b i t c o u p l i n g would then g i v e r i s e t o gamma-ray y i e l d at 0 ° .  -5-  In  1955»with  the advent  G r i f f i t h s and Warren (GR between 0 „ 5 and 2 , 0 MeV the d i s t r i b u t i o n was s m a l l but not z e r o  9  of the s c i n t i l l a t i o n d e t e c t o r s ,  5 5 ) measured the angular u s i n g heavy i c e t a r g e t s .  p r o p o r t i o n a l to (a + b s i n Q)  They found t h a t where a  was  and t h e r e f o r e put p a r t i c u l a r emphasis on the  r e g i o n around 0 ° i n order to determine the s p i n - o r b i t i n t e r a c t i o n .  the amount c o n t r i b u t e d by  They found however, t h a t the  dependence of the y i e l d a t 0 ° was T h i s suggested  distribution  energy  d i f f e r e n t from t h a t a t 9 0 ° .  the p o s s i b i l i t y t h a t the i s o t r o p i c component might  a r i s e from magnetic d i p o l e t r a n s i t i o n s f o l l o w i n g the c a p t u r e , o f s-wave protons.  Such t r a n s i t i o n s may  pone^jfcs i n the n u c l e a r f o r c e (VE 5 0 ) .  a r i s e from n o n - c e n t r a l  These authors a l s o obtained  an approximate v a l u e f o r the a b s o l u t e c r o s s s e c t i o n a t E MeV,  of  k  x  1 0 ~  3  ° ( ±  50#)  com-  = 1,0  cm . 2  Measurements on the r e 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 e t . a l , (GR  6 2 ) , who  measured the c r o s s s e c t i o n  and the angular d i s t r i b u t i o n f o r p r o t o n e n e r g i e s from 2 7 5 KeV 1 , 7 5 MeV  w i t h more accuracy u s i n g both heavy i c e and gas  T h e i r r e s u l t s confirmed the assumption a t 0 ° i s due  t h a t the r a d i a t i o n  to  targets. observed  to s-wave c a p t u r e .  Because the s-wave capture should be more predominant w i t h r e s p e c t to the p-wave capture a t low e n e r g i e s , G r i f f i t h s e t . al,  (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 t h i s  r e a c t i o n i n the energy range from Zh to 48 KeV  u s i n g heavy i c e  t a r g e t s c o n f i r m i n g once more the p r e v i o u s arguments.  Assuming a  -6-  s i m p l i f i e d energy dependence f o r the  cross section  they  analized  the r e s u l t s to g i v e separate c r o s s s e c t i o n f o r p-wave and captures.  At 2 5 KeV  i n the  laboratory  frame the  cross  s-wave  sections  are:  0 ^ = ( 2 . 9  01  =(1.3  -  0.3)  x  10~  -  0.3)  x  10"  cm  3 2  cm  3 2  R e c e n t l y W o l f l i e t . a l . (WO ture c r o s s s e c t i o n between 2 MeV distributions for several 1.3.  and  2  2  6 6 ) have measured the  12 MeV  e n e r g i e s up  including  to 5 . 2 5  cap-  angular  MeV.  Present Work T h i s work was  more a c c u r a t e data on  o r i g i n a l l y undertaken i n order to  the a b s o l u t e c r o s s s e c t i o n a t low  both because t h i s r e a c t i o n  obtain  energies  i s of i n t e r e s t i n a s t r o p h y s i c s ,  and  because more d e t a i l e d t h e o r e t i c a l c a l c u l a t i o n s were becoming a v a i l able. Recent t h e o r e t i c a l s t u d i e s in particular this reaction,  indicate  t i o n of the angular d i s t r i b u t i o n and including  on the  three body system,  that an a c c u r a t e determinaof the a b s o l u t e c r o s s  section  i t s energy dependence, would, i n p r i n c i p l e , p r o v i d e i n -  f o r m a t i o n about the An  fundamental i n t e r a c t i o n between the  particles.  e a r l y 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  t a t i o n symmetries of the made by Verde (VE  states  5 0 ) f o r the  of the  three nucleon system  purpose of c a l c u l a t i n g  p r o b a b i l i t i e s between continuum and  bound s t a t e s .  permuwas  transition  A more d e t a i l e d  -7-  c l a s s i f I c a t i o n was c o n s i d e r e d by D e r r i c k and B l a t t the ground s t a t e s .  (DE 5 8 ) f o r  I n t h i s work the r e l a t i o n between the wave  f u n c t i o n and the c e n t r a l , tensor and s p i n dependent p a r t s of the nucleon-nucleon  f o r c e was c o n s i d e r e d .  R e c e n t l y a more d e t a i l e d  d i s c u s s i o n of the r a d i a t i v e t r a n s i t i o n s on the b a s i s of b e t t e r wave f u n c t i o n s has been g i v e n by Eichmann (EI 6 3 ) , and a more complete c l a s s i f i c a t i o n o f a l l p o s s i b l e r a d i a t i v e has been presented by Davis  (DA 6 7 ) .  transitions  More complete l i s t s of r e f -  erences a r e g i v e n i n these two papers. The d a t a o b t a i n e d from the present work i s compared w i t h somewhat e m p i r i c a l t h e o r e t i c a l c a l c u l a t i o n s o f d i r e c t  radia-  t i v e capture c r o s s s e c t i o n s i n three nucleon systems g i v e n by Donnelly  (DO 6 7 ) and B a i l e y , G r i f f i t h s and Donnelly  which a two body approximation  (BA 6 7 ) i n  to the three nucleon system  was  used. D o n n e l l y ' s t h e o r y has been used as a b a s i s f o r comparison, because a t the present time i t p r o v i d e s n u m e r i c a l r e s u l t s i n the energy range of i n t e r e s t which are based penetrabilities.  on a c c u r a t e Coulomb  More e x t e n s i v e comparisons w i t h theory w i l l be  made a f t e r the a b s o l u t e c r o s s s e c t i o n has been measured. 3  The He ground s t a t e i s known to have t o t a l angular v  momentum J = 1 / 2 .  The ground s t a t e wave f u n c t i o n may then  t a i n any one o f , or a l i n e a r combination nents  (SA 5 5 ) ;  con-  of the f o l l o w i n g compo-  -8-  Furthermore, the f u n c t i o n s be c l a s s i f i e d a c c o r d i n g For  three  c o r r e s p o n d i n g to each component  to t h e i r permutation symmetry  p a r t i c l e s the i n d i v i d u a l space, s p i n and  can  properties.  i s o s p i n parts  of the wave f u n c t i o n can be decomposed i n t o symmetric, antisymmetric  and mixed-symmetry p a r t s .  I f the s p a t i a l p a r t of  the  wave f u n c t i o n i s symmetric then the s p i n - i s o s p i n p a r t must be antisymmetric to s a t i s f y the P a u l ! E x c l u s i o n P r i n c i p l e . A b r i e f summary i s g i v e n here of how  these  components of the ground s t a t e wave f u n c t i o n a r i s e and contribute  to the  s t r u c t u r e of the ground s t a t e of the  various how  3  they  He*  2  The  space-symmetric  S s t a t e must be  the main c o n t r i b u t i o n to  ground s t a t e s i n c e i t has  the  nucleon s t a t e s .  i t would be the only component of  Further,  ground s t a t e i f the n u c l e a r dent.  The  the  lowest k i n e t i c energy of a l l three  f o r c e were c e n t r a l and  the  spin-indepen-  other components are then present o n l y because they 2  are coupled to the  S s t a t e by a d d i t i o n a l p a r t s of the two  nucleon  interaction. * •/  Derrick  (DE  6 0 ) has  •. -  shown t h a t the mixed-symmetry  2  S^  m  2  s t a t e i s coupled to the symmetric  S s t a t e due  between the c e n t r a l t r i p l e t even and t h a t the  difference  s i n g l e t even f o r c e s ,  and  D s t a t e i s coupled i n by the tensor-even f o r c e compo-  nent.  Derrick  2  V  P and  to the  (DE  6 0 ) has  a l s o shown t h a t the amplitudes of ~*  -»  P components, which would be coupled i n by the L.S  a c t i o n , are n e g l i g i b l e . R e c e n t l y , however, Davis p a r t i a l l y r e f u t e d Derrick-*s arguments.  (DA  67)  the  interhas  -9-  In order  to o b t a i n an estimate of the e f f e c t t h a t ad2s  m i x t u r e s of mixed symmetry  im-D  ( ) s t a t e and m  s t a t e have on the  r a d i a t i v e capture process D o n n e l l y (DO 67) has i n t r o d u c e d  arbi-  t r a r y amplitudes f o r s t a t e s which approximate the c h a r a c t e r of 2  these admixtures i n t o the ground s t a t e symmetric The  wave f u n c t i o n s were generated f o r a square w e l l  potential representing  the I n t e r a c t i o n o f a p r o t o n and a deuteron  i n both bound and f r e e s t a t e s . three  S wave f u n c t i o n .  I n t h i s model many of the s p e c i f i c  body a s p e c t s o f the problem have been n e g l e c t e d  the amplitude f a c t o r s i n t r o d u c e d  cannot be d i r e c t l y r e l a t e d t o  the p r o p e r t i e s o f the nucleon-nucleon f o r c e s c o u p l i n g particles.  However, there  so that  the three  i s r e a s o n to b e l i e v e t h a t the f u n c t i o n s  generated by D o n n e l l y a r e approximately c o r r e c t o u t s i d e of the s p e c i f i c a l l y n u c l e a r  p a r t of the f o r c e and  the range  should.there-  f o r e l e a d to r e a s o n a b l e c r o s s s e c t i o n s a t low e n e r g i e s ,  f o r which  most o f the c r o s s s e c t i o n a r i s e s from p a r t s o f the n u c l e a r wave f u n c t i o n outside  the c o n v e n t i o n a l  nuclear  radius.  I n t h i s model  square w e l l parameters f o r the ground s t a t e were a d j u s t e d the b i n d i n g  energy o f the p r o t o n i n % e  to f i t  ( 5 . ^ 9 MeV) assuming i t i s  2  predominantly a symmetric uum s t a t e s were a d j u s t e d data.  S s t a t e , and parameters f o r the c o n t i n as a f u n c t i o n of energy to f i t s c a t t e r i n g  D o n n e l l y c a l c u l a t e d a n g u l a r d i s t r i b u t i o n s and c r o s s  sections  to be expected on t h i s model as a f u n c t i o n of energy f o r a range of v a l u e s  f o r the a r b i t r a r y amplitude  parameters.  In t h i s t h e s i s the angular d i s t r i b u t i o n i s determined  -10-  a t two and  bombarding e n e r g i e s 9 0 and  1 6 0 KeV  the r e s u l t s compared w i t h D o n n e l l y ' s  i n the  laboratory  frame,  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 f u t u r e , to determine the a b s o l u t e c r o s s i n Chapter  IV.  section i s outlined  CHAPTER I I EXPERIMENTAL APPARATUS T h i s chapter i s concerned w i t h the d e s i g n parameters and the t e c h n i c a l problems a s s o c i a t e d w i t h the development o f 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 r e a c t i o n D(p,"8) He. 3  2.1.  Angular  Distribution  A schematic designed "I"  Table  drawing of the angular d i s t r i b u t i o n t a b l e ,  by the author, i s shown i n F i g . I I - l .  beams (A) a r e supported  by b a l l bearings  t a b l e so they can r o t a t e about the c e n t r e post  Two aluminium on an aluminium (B).  The c e n t r e  post has a c o n c e n t r i c h o l e which l o c a t e s the t a r g e t chamber on the rotation axis.  The d e t e c t o r s w i t h a hundred pounds of l e a d f o r  s h i e l d i n g and c o 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 d i s c gradua t e d i n one degree steps was mounted on the centre post t o d e f i n e the angles between both d e t e c t o r s and the i n c i d e n t beam.  The whole  assembly i s s u f f i c i e n t l y r i g i d t h a t r o t a t i n g the heavy d e t e c t o r assemblies  does n o t e f f e c t t a r g e t - d e t e c t o r c e n t e r i n g o r d i s t a n c e . The  system was a l i g n e d u s i n g a t h e o d o l i t e .  The c o l l i -  mator, which d e f i n e d the d i r e c t i o n o f the beam, was a d j u s t e d its  until  a x i s met the t i p o f a p o i n t e d s p i n d l e I n s e r t e d i n the c e n t r e  post i n p l a c e of the t a r g e t chamber.  The axes of the d e t e c t o r s  were, d e f i n e d by f i n e wires p l a c e d on the d e t e c t o r ' s c o l l i m a t o r . -11-  Fig.  11-1  :  Schematic diagram 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 . Alignment o f t h e 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 is shown.  -13-  These axes were a l i g n e d to i n t e r s e c t a t the t i p of the s p i n d l e . The t h e o d o l i t e was a l s o used t o l o c a t e the degree d i s c so t h a t the c o l l i m a t o r a x i s passed through the zero degree mark.  A l l adjust-  ments a r e b e l i e v e d to have been made w i t h i n one degree.  2 . 1 . 1 .  Target Chamber The b r a s s t a r g e t chamber s i x i n c h e s h i g h and three inches  i n diameter i s shown i n P i g . I I - 2 . The 1 / 1 6 i n c h w a l l t h i c k n e s s was machined t o a t h i c k n e s s of 0 . 0 2 1 i n c h over the c e n t r e r e g i o n i n order t o reduce gamma<-ray a b s o r p t i o n .  The bottom of the chamber  was screwed through an i n s u l a t o r to a b r a s s d i s c . a c o n c e n t r i c c y l i n d r i c a l r o d which f i t s  The d i s c has  i n the c e n t r e post of the  t a b l e , l o c a t i n g the t a r g e t chamber on the d e t e c t o r r o t a t i o n a x i s . Two d i f f e r e n t t a r g e t assemblies shown i n P i g . I I - 3 were used i n t h i s  experiment.  The t a r g e t h o l d e r "TA" (used throughout the 1 6 0 KeV r u n s ) c o n s i s t s of a copper p l a t e , w i t h drilled  0.082  i n c h diameter h o l e s  l e n g t h w i s e through the copper every 0 . 1 0 inches,, a t t a c h e d  to a s t a i n l e s s s t e e l r o d by means of b r a s s tubes.  C o o l i n g water  flows through these tubes, and through the h o l e s i n the copper plate. The t a r g e t h o l d e r "TB" (used throughout the 9 0 KeV runs) c o n s i s t s of a s o l i d 1 / 1 6 i n c h t h i c k copper p l a t e screwed to the water c o o l e d copper t i p of a s t a i n l e s s s t e e l r o d . the copper p l a t e can be d i s p l a c e d sideways.  In t h i s case  Both rods "TA" and  WATER TARGET  HOLDER  COOLING  ROD  GRADUATED  DISC  VIEWING  PORT  i  JVWAA/UL BEAM  A  1AA/UVI/" INSULATING  MATERIAL  rt~n  rt~T)  Fig.  11-2  Schematic diagram of the target chamber. l o c a t e d in the a n g u l a r d i s t r i b u t i o n table s p i n d l e shown h e r e f o r comparison.  The t a r g e t chamber is in p l a c e of the pointed  WATER COOLING  n 4T  SLOTS FOR VERTICAL DISPLACEMENT  N  SL  STAINLESS STEEL  COPPER  TIP H O L E S FOR H O R I Z O N T A L DISPLACEMENT  u-.Jl ooooooooo COPPER  r C  4 4-  —  1  |o»o o ojoeoool  C  BEAM  1  i  i  "TD" Schematic  diagram of  the  target  holder  rods.  -16-  "TB"  have s l o t s which a l l o w  the rods to be l o c a t e d i n s e v e r a l  different v e r t i c a l positions.  The "TA" t a r g e t holder was o r i g i -  n a l l y made to be used w i t h s o l i d d e u t e r a t e d deuterium occluded w e l l cooled.  i n zirconium  could  by c o n d u c t i o n through the copper backing„  the "TB" r o d was adopted f o r the 90 KeV runs s i n c e i t  sideways d i s p l a c e m e n t . I n both h o l d e r s  t h e targets,, made on 0.012 Inch copper  b a c k i n g s , were clamped t o the t a r g e t h o l d e r s . was  deuterated  t a r g e t s and i t was found t h a t these t a r g e t s  be a d e q u a t e l y c o o l e d  allows  s i n c e these t a r g e t s need t o be  The f i n a l 160 KeV runs were done u s i n g  polyethylene  Therefore,,  t a r g e t s as f o r example  Once  everything  assembled the f a c e of the t a r g e t remained i n the plane con-  t a i n i n g the a x i s o f the r o d which i s the same as the a x i s of r o t a t i o n f o r the d e t e c t o r s . 2.1.2.  The C o l l i m a t o r The  a skimmer.  c o l l i m a t o r c o n s i s t s o f two d e f i n i n g a p e r t u r e s and  The f i r s t  two have d e f i n i n g holes  0.100 i 0.005 inches  i n diameter and t h e second has a 0.120 - 0.005 i n c h h o l e .  The  d i s c s were mounted i n s i d e a machined s t a i n l e s s s t e e l pipe and separated  by two aluminium c y l i n d e r s which a r e a l s o used t o conduct  the heat t o the s u p p o r t i n g  water c o o l e d  flange.  The whole assembly was e l e c t r i c a l l y I s o l a t e d from the beam p i p e .  A l t h o u g h the a n g u l a r d i s t r i b u t i o n measurements d i d  not r e q u i r e knowledge o f t h e charge c o l l e c t e d by the t a r g e t , (Chapter I I I ) , p r o v i s i o n s were made f o r f u t u r e measurements of  -17-  the a b s o l u t e  cross  section.  F i g , II-4  shows the p o t e n t i a l s which  w i l l be a p p l i e d to the t a r g e t chamber and  to the c o l l i m a t o r f o r  such measurements, The  2 . 1 . 3 .  Vacuum System  The tem  a n g u l a r d i s t r i b u t i o n t a b l e has  i t s own  vacuum  sys-  so t h a t the t a r g e t chamber can be pumped independently of  a c c e l e r a t o r vacuum system. of Hg)  I t c o n s i s t s of a 1 0 0 1/sec  (@ 1 0 ~ ^ mm  o i l d i f f u s i o n pump, a water c o o l e d chevron r i n g b a f f l e  a l i q u i d nitrogen  trap.  DOW  CORNING  DC-705  of i t s good backstreaming c h a r a c t e r i s t i c s . p r e s s u r e a 3 0 1/min The  (@ 1 0 ~  3  mm  of Hg)  o i l was  To p r o v i d e the  fore-  mechanical pump i s used.  c o l l i m a t o r , because of i t s s m a l l d e f i n i n g  holes, acceler-  T h i s arrangement should prevent d i r t c o n t a m i n a t i o n i n the  a c c e l e r a t o r r e g i o n from d e p o s i t i n g to m a i n t a i n a good vacuum i n the i o n i z a t i o n due  on the t a r g e t .  target area,  thus  to the beam i n the r e s i d u a l gas  With the  beam "ON"  under normal o p e r a t i n g  the p r e s s u r e i n the  I t a l s o helps reducing  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 able.  and  chosen because  i s o l a t e s the vacuum i n the t a r g e t r e g i o n from t h a t of the ator.  the  t a r g e t more r e l i -  target  chamber,  c o n d i t i o n s , averages approximately  -7  9 x 1 0 ' mm  of Hg.  F i g . I I - 5 shows photographs of the  d i s t r i b u t i o n t a b l e and 2.2.  The  the d e t e c t o r s  mounted on the  angular  trolleys.  Targets The  choice  o f a s u i t a b l e deuterium t a r g e t was  the main problems t h a t had  to be  one  s o l v e d I n order to measure  of the  ll  Xv INSULATING  oo  TO VACUUM PUMPS  Fig.  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 d i ag ram 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 .  FIG. 11-5 : (a) VIEW OF THE ANGULAR DISTRIBUTION TABLE AND AUXILIARY EQUIPMENT AND (b) CLOSE-UP VIEW OF THE ANGULAR DISTRIBUTION TABLE.  -20-  a n g u l a r d i s t r i b u t i o n to a h i g h e r accuracy than had been achieved i n p r e v i o u s work. I t was d i f f i c u l t enough deuterium  to f i n d a target m a t e r i a l that contained  atoms to make i t p o s s i b l e to observe  the low c r o s s  s e c t i o n r e a c t i o n i n a r e a s o n a b l e time, which a t the same time was rugged enough to w i t h s t a n d the l a r g e beam c u r r e n t and d i d not i n v o l v e a l a r g e f r a c t i o n a l energy beam.  l o s s f o r the low energy  On the b a s i s o f p r e v i o u s data  incident  (GR 62 ; GR 63) i t can be  e s t i m a t e d t h a t f o r a bombarding energy  of 160 KeV i n the l a b o r a -  t o r y frame the c r o s s s e c t i o n f o r the r e a c t i o n c o n s i d e r e d here i s about 0.08 yWb f o r the I s o t r o p i c component and 0.6 ywb f o r the nonisotropic  component. The  experiment  r e q u i r e s a t a r g e t w i t h enough  deuterium  t o p r o v i d e a y i e l d a t l e a s t comparable t o the background.  Yet,  the t a r g e t must be t h i n enough so as t o be a b l e to d i s c r i m i n a t e between a n g u l a r d i s t r i b u t i o n measurements a t 90 KeV and 160 KeV. A t a r g e t t h i c k n e s s was chosen so as t o produce a maximum l o e s o f 35 KeV f o r 160 KeV p r o t o n s .  energy  I t i s a l s o d e s i r a b l e t o have  a beam spot on the t a r g e t as s m a l l as p o s s i b l e i n order t o a v o i d s o l i d angle c o r r e c t i o n s , due to the f i n i t e  s i z e o f the source.  At the same time i t i s d e s i r a b l e t o be a b l e t o work w i t h as much beam c u r r e n t as p o s s i b l e , i n order t o s h o r t e n the l e n g t h o f the runs and t o keep the y i e l d h i g h e r than the background. M u l t i p l e s c a t t e r i n g of the incoming was a l s o c o n s i d e r e d .  beam i n the t a r g e t  The R.M.S. s c a t t e r i n g angle should be kept  -21-  as s m a l l as p o s s i b l e , otherwise the angular d i s t r i b u t i o n becomes difficult  to a n a l y z e , p a r t i c u l a r l y because no r e l i a b l e  theoretical  a n a l y s i s or experimental data i s a v a i l a b l e on m u l t i p l e s c a t t e r i n g f o r massive charged p a r t i c l e s f o r the low e n e r g i e s c o n s i d e r e d here.  Deuterium t a r g e t s can be c l a s s i f i e d  kinds:  deuterium gas, heavy i c e , deuterium  elements, 2.2.1.  absorbed  i n solid  and d e u t e r a t e d compounds.  Deuterium Gas Gas  was  into four d i f f e r e n t  Targets  t a r g e t s were d i s c a r d e d because no p h y s i c a l window  a v a i l a b l e t h a t would h o l d a reasonable pressure of gas  admit a s m a l l diameter  and  beam of the r e q u i r e d c u r r e n t (about 100 JAA).  D i f f e r e n t i a l l y pumped gas t a r g e t s were a l s o i m p r a c t i c a l f o r t h i s experiment,  f o r a p a r t from the v e r y l a r g e gas flow r e q u i r e d , the  gamma-ray source c o u l d not be a c c u r a t e l y d e f i n e d i n p o s i t i o n . 2.2.2.  Heavy Ice Targets The main d i f f i c u l t y w i t h these t a r g e t s i s t h a t they  would evaporate q u i c k l y under bombardment by the beam d e n s i t i e s needed f o r t h i s work. ness i s d i f f i c u l t . gets was  F u r t h e r , the d e t e r m i n a t i o n of the  thick-  P r e v i o u s low energy work w i t h heavy i c e t a r -  done w i t h t h i c k t a r g e t s t h a t completely stopped  I t should be p o i n t e d out here t h a t f o r angular  the beam.  distribution  measurements one does not need to know e x a c t l y the amount of t a r g e t m a t e r i a l as long as i t s t h i c k n e s s i s kept below a c e r t a i n value.  An estimate of the t h i c k n e s s c o u l d be made by l e t t i n g  vapor from a heavy water d i s p e n s e r condense on a a t t a c h e d to a l i q u i d n i t r o g e n c o o l e d copper  plate.  the  target The  shift in  -22-  11 the 163 KeV resonance, i n the r e a c t i o n  12 B(p,tf)  C, would g i v e  d i r e c t evidence of the t h i c k n e s s of the heavy i c e t a r g e t . However, t h i s i s d i f f i c u l t t o do, because  the boron i n the beam  spot tends to f l a k e o f f , thus making a bad thermal c o n t a c t between the i c e and the copper p l a t e .  Some t e s t s were done u s i n g " t h i n "  A 100 KeV p r o t o n beam of 30was 2  targets.  a t a r g e t spot of 4-0 mm  c o l l i m a t e d to g i v e  on a t h i n heavy i c e l a y e r l a i d onto a  l i q u i d a i r cpdled plate.  The t a r g e t s under these c o n d i t i o n s d i d  not l a s t longer than a few seconds and so t h i s method was  dis-  carded. 2.2.3.  Deuterium Absorbed  i n Solid  Elements  Some elements have the p r o p e r t y of a b s o r b i n g and r e t a i n i n g l a r g e q u a n t i t i e s of hydrogen a t r e l a t i v e l y high temperature.  Among those which absorb the most are p a l l a d i u m , tantalum,  z i r c o n i u m , and t i t a n i u m .  I t was  r e c e n t l y found t h a t erbium  and  i n g e n e r a l most of the r a r e e a r t h elements are a l s o good a b s o r b e r s . Deuterium  t a r g e t s of t h i s k i n d have been used f o r many years f o r  neutron p r o d u c t i o n .  I t i s e s s e n t i a l t h a t the gas once absorbed  i s r e t a i n e d i n the t a r g e t w h i l e under bombardment by a beam i n a vacuum.  Targets of deuterium i n Zr and T i were obtained from the  Oak Ridge N a t i o n a l L a b o r a t o r y .  They were made as f o l l o w s %  A known amount o f , say, z i r c o n i u m was  evaporated onto.a  suitable,  and p r e v i o u s l y outgassed backing such as copper, platinum or tungsten.  The d e p o s i t was  outgassed under vacuum a t h i g h temper--  a t u r e s and p l a c e d i n a deuterium atmosphere a t a s u i t a b l e ature.  temper-  A b s o r p t i o n begins a f t e r the heat i s i n t e r r u p t e d and the  -23-  system  i s a l l o w e d to c o o l o f f .  a t a p r o t o n energy from 80 yug/cm 2  2  to 58 yKg/cm „  Angular d i s t r i b u t i o n measurements  of 160 KeV were done u s i n g Zr-D  2 2 t o 143 y«g/cm and Ti-D t a r g e t s r a n g i n g from 47 yMg/cm The r e s u l t s c o n t a i n e d u n c e r t a i n t i e s a r i s i n g  the r a t h e r l a r g e angular spread of the incoming t a r g e t , due  targets ranging  to the m u l t i p l e coulomb s c a t t e r i n g .  from  p a r t i c l e s i n the Thinner t a r g e t s  would have overcome t h i s d i f f i c u l t y however they would have g i v e n too low a gamma-ra~y y i e l d . 2.2.4.,  The Deuterated Compounds There are s e v e r a l hundred commercially a v a i l a b l e  r a t e d compounds.  Most of these compounds a r e , however, i n gaseous  or l i q u i d form or they have two deuterium  deute-  i n t h e i r molecular  or more d i f f e r e n t elements,  besides  structure.  A simple compound i s d e u t e r a t e d p o l y e t h y l e n e  (CDg)^  U s i n g t h i s compound as a t a r g e t the R.M.S. m u l t i p l e s c a t t e r i n g angle i s reduced c o n s i d e r a b l y , compared w i t h the Zr-D and due 1 2  to the lower Z i n the t a r g e t components.  C ( p , t f ) N and 1 3  1 3  C(p,i)  t h e - f i r s t produces  l i f  Although  Ti-D  the  N r e a c t i o n s compete w i t h D(p,tf) He, 3  gamma-rays of lower energy which can be  elimi-  nated by a h i g h enough d i s c r i m i n a t i o n l e v e l and the second has a negligible yield.  Both r e a c t i o n s are d i s c u s s e d i n Appendix F,  S e l f - s u p p o r t i n g d e u t e r a t e d p o l y e t h y l e n e t a r g e t s are being used s a t i s f a c t o r i l y i n t h i s l a b o r a t o r y (TR 67  ; MC  68).  These t a r g e t s , however, can w i t h s t a n d o n l y s m a l l beam d e n s i t i e s 2 a t most of the order of 10 yMA/cm .  Furthermore,  i f an energy  loss  -24-  i n the t a r g e t of o n l y 35 KeV f o r a 1 6 0 KeV i n c i d e n t proton beam i s r e q u i r e d , the p o l y e t h y l e n e  l a y e r w i l l be, p h y s i c a l l y , extremely  t h i n and thus v e r y d i f f i c u l t t o handle.  Consequently such t a r g e t s  were r u l e d out. I t was found t h a t i f the p o l y e t h y l e n e  i s deposited  on  a. metal b a c k i n g , the t a r g e t so formed, can w i t h s t a n d l a r g e beam p  currents  of 2 0 0 to 300 yKA/cm , without r a p i d l o s s  of the order  of t a r g e t m a t e r i a l .  Furthermore, t h i n t a r g e t s  (of the order of  3 0 KeV f o r i n c i d e n t protons of 1 6 0 KeV) c o u l d e a s i l y be made i n t h i s way.  Therefore,  these t a r g e t s were u t i l i z e d f o r the angular  d i s t r i b u t i o n measurements of the D(p,tf) He r e a c t i o n .  The technique  J  followed  i n the p r e p a r a t i o n  of the t a r g e t s i s d e s c r i b e d  i n Appen-  d i x D.  A comparison between these t a r g e t s and Zr-D t a r g e t s , nor-  malized  t o the same deuterium content i s a l s o shown. The  t a r g e t s used throughout t h i s experiment were 364yWg  pared by d e p o s i t i n g  on a 3.7  of p o l y e t h y l e n e  t 10% and  364/cos  4 5 ° . . =  515yug  pre- 10%  cm by 3 . 7 cm copper p l a t e 0 . 0 3 cm t h i c k .  Both t a r g e t s a r e e q u i v a l e n t  because of the two d i f f e r e n t 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 used i n performing the a n g u l a r d i s t r i b u t i o n measurements, (Chapter I I I ) , so t h a t only one w i l l be  considered  2  here.  The  thickness N t c  =  1 . 4 l 6  5 1 5  J^S when d e p o s i t e d  ?t (CD ) of 2  x  1 0  1  3 7 . 6 0  on  gives a target  ywg/cm ., T h i s corresponds to  carbon atoms/cm  8  cm  I 3 . 6 9  2  and N t = D  2 . 8 3 2  x  1 0  1  8  2  deuterium atoms/cm . shown i n Table I I - l .  The c h a r a c t e r i s t i c s of t h i s t a r g e t a r e  -25-  Table I I - l  :  C h a r a c t e r i s t i c s of the Deuterated Targets.  (IO'SV-C*?) 06 eV-c«*)  (KeV}  ,S  160  °i0  Ep  Polyethylene  1° 10'  14  4.5  1° 18'  r  16  b  2 ° 43'  6*  144  70  i s t h e i n c i d e n t p r o t o n energy; 8 ^ and 6 . t h e s t o p p i n g c r o s s Q  s e c t i o n f o r p r o t o n s i n c a r b o n and d e u t e r i u m , r e s p e c t i v e l y ; AE the energy l o s t by t h e beam i n t h e t a r g e t and [ Q ] = J <^9 ^>r 2  c  and [9]=- a r e the R.M.S. m u l t i p l e s c a t t e r i n g a n g l e f o r p r o t o n s o f P _ e n e r g i e s 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 , ( u s i n g t h e f o l l o w i n g  e x p r e s s i o n ) , assuming t h e s t o p p i n g c r o s s s e c t i o n s r e m a i n e d t h e same as t h e beam t r a v e r s e d t h e t a r g e t : AE = e G  N  G  t + 6  D  N  D  t  The v a l u e s f o r t h e s t o p p i n g c r o s s s e c t i o n s were o b t a i n e d from W h a l i n g (WH 58). reaches  The s t o p p i n g c r o s s s e c t i o n f o r p r o t o n s on c a r b o n  i t s maximum a t about 90 KeV, w h i l e t h e maximum f o r p r o t o n s  on d e u t e r i u m  o c c u r s a t 50 KeV w i t h a v a l u e o f 6.6 x 10"  D  eV-cm .  T h e r e f o r e , i f t h e v a r i a t i o n o f the s t o p p i n g c r o s s s e c t i o n w i t h energy were, t a k e n i n t o a c c o u n t be a t t h e most Table I I - l .  t h e energy l o s s i n t h e t a r g e t w i l l  h i g h e r t h a n t h e v a l u e 39.7 KeV g i v e n i n  A t 90 KeV t h e energy l o s s i s somewhat h i g h e r t h a n t h e  -26-  35 KeV r e f e r r e d to p r e v i o u s l y as the maximum.  The t a r g e t s were  made t h i c k e r than 35 KeV to compensate f o r the l o s s of deuterium which occurs,.when the "beam i n i t i a l l y h i t s the t a r g e t . d i x D).  (See Appen-  From the observed i n i t i a l decrease i n the gamma-ray y i e l d ,  which i s a t t r i b u t e d to the l o s s of deuterium, i t was.. estimated  that  these t a r g e t s were t h i n n e r than 35 KeV throughout most of t h e i r run.  The same e f f e c t a p p l i e s f o r the t a r g e t s used a t 160 KeV, Multiple s c a t t e r i n g c a l c u l a t i o n s are discussed i n  Appendix E, so o&^s-tihe- bas'ie Idea I s Introduced here. t h a t a p a r a l l e l beam i s i n c i d e n t on a t a r g e t .  Assume  The angular  b u t i o n of the p a r t i c l e s emerging from the t a r g e t w i l l  distri-  clearly  have c y l i n d r i c a l symmetry around the a x i s d e f i n e d by the i n c i d e n t beam.  Based on s t a t i s t i c a l c o n s i d e r a t i o n s  (SE 53) which a r e i n  agreement w i t h the e x p e r i m e n t a l r e s u l t s obtained ing, o f f a s t e l e c t r o n s  (WI 39) one can expect the p a r t i c l e s to be  G a u s s i a n d i s t r i b u t e d around t h i s a x i s . t r a v e r s i n g a c e r t a i n thickness ticles  from the s c a t t e r -  Thus s t a t i s t i c a l l y a f t e r  o f t a r g e t 68% of,the i n c i d e n t par-  l i e i n a r e g i o n d e f i n e d by a cone whose h a l f - a n g l e , with  respect  t o t h a t a x i s , i s c a l l e d the R.M.S. m u l t i p l e s c a t t e r i n g  angle.  The r e s u l t s o f the c a l c u l a t i o n d i s c u s s e d  are shown i n Table I I - l . ing  i n Appendix E  Because of the s m a l l m u l t i p l e s c a t t e r -  angle produced by t h i s t a r g e t , i t s s m e a r i n g , e f f e c t  i n the  angular d i s t r i b u t i o n o f the gamma-rays was n e g l i g i b l e . 2,3.  The D e t e c t o r . The  C o l l i m a t o r and S h i e l d i n g  gamma-ray d e t e c t o r  (HARSHAW Type 20MBS16/B) c o n s i s t s  of a 5 i n c h diameter by 4- i n c h deep c y l i n d r i c a l N a l ( T l )  crystal  -27-  coupled to a 3 inch  (RCA  8054) p h o t o m u l t i p l i e r .  Two  d e t e c t o r s mounted i n I d e n t i c a l l e a d s h i e l d s and used i n t h i s experiment. Fig.  identical  c o l l i m a t o r s were  A schematic drawing i s shown i n  II-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") He can be 3  expressed  p  a p p r o x i m a t e l y by W(9)  = a + b s i n 9 (Chapter I ) .  Because a i s  s m a l l compared to b , ^ 3 w a s chosen so t h a t when the d e t e c t o r  was  p l a c e d a t 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  s e c t i o n i s expressed  byO~=Cr_  +  9,  where <T  &  and  and  0", D  CT^ are the t o t a l c r o s s s e c t i o n f o r the i s o t r o p i c  non-isbtropic  components r e s p e c t i v e l y .  Thus the above c o n d i t i o n i s g i v e n  Thus  by  •'o  For ^3= 12°  and O ^ A T ^ = 0.13  the  i s o t r o p i c component c o n t r i b u t i o n  amounts to 80.4#-when the d e t e c t o r The  Source D i s t a n c e  R;  i s at The  d i s t a n c e R was  such t h a t the cone d e f i n e d by ^> c o n t a i n s That i s  0°. chosen  the back of the  crystal.  Fig.  11-6  :  A s c h e m a t i c d i a g r a m of the d e t e c t o r are given in Table II-2  assembly.  The  dimensions  -29-  A t a p e r e d . c o l l i m a t o r was way  a haIf-angle  of 12° was  remained s h i e l d e d . 1.  The  p l a c e d i n f r o n t of the c r y s t a l . d e f i n e d and  T h i s c o l l i m a t o r has  the corners  The .two  -  a.  of the  crystal  the f o l l o w i n g r e s u l t s ?  background c o u n t i n g r a t e i s reduced, s i n c e the  c r y s t a l " l o o k s " o n l y a t the 2t  In t h i s  source.  edge e f f e c t s of the c r y s t a l are reduced w i t h u s e f u l consequences:  ...  ,  .  I t improves the photopeak to t a i l r a t i o . Thus the r a t i o of i n f o r m a t i o n to background i s improved.  P i g . I I - 7 shows.the e f f e c t of the  c o l l i m a t o r on the shape of the s p e c t r a  obtained  using a ^ C o  normalized  source.  The  s p e c t r a were  to equal k i c k s o r t e r l i v e times of 40 minutes. The  background was  not s u b s t r a c t e d .  Without  the c o l l i m a t o r the photopeak i s h i g h e r it  than with  because the d e t e c t o r subtends a l a r g e r 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 c o r r e c t e d f o r the e f f e c t of the f i n i t e angle  of the d e t e c t o r  reducing  (RO  53).  solid  As a r e s u l t  the edge e f f e c t s the - e s t i m a t i o n of  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 . i n v o l v e s the e v a l u a t i o n of i n t e g r a l s of form;  This the  -31-  where 5 i s the l i n e a r a t t e n u a t i o n c o e f f i c i e n t , x(^) i s the d i s t a n c e t r a v e r s e d by the r a d i a t i o n i n c i d e n t on the c r y s t a l a t an angle ^ w i t h r e spects t o i t s a x i s , and P^ a r e the Legendre polynomials of order 1. T h e smoothing f a c t o r s ;  are d e f i n e d by  = J^/J^.  Without  the c o l l i -  mators the above i n t e g r a t i o n over the c r y s t a l volume becomes l e s s r e l i a b l e f o r two reasons. First  there w i l l be a l a r g e r number of gamma-  r a y s s c a t t e r e d i n t o the c r y s t a l from  surrounding  m a t e r i a l s , a n d second a larger,number  of gamma-  r a y s w i l l i n t e r a c t near the edges o f 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 e l e c t r o n s e s c a p i n g 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-  t a i n e d by I n t e g r a t i n g the spectrum a p p r o x i m a t e l y h a l f the f u l l  upwards from  energy, many of these  events w i l l not be counted. The; C o l l i m a t o r Thickness S:  .The 1 gamma-ray i n t e n s i t y a t  the c o r n e r s o f the c r y s t a l depends on the t h i c k n e s s S o f the collimator.  F o r S = 6.5 cm the a t t e n u a t i o n f a c t o r was found t o  be e q u a l t o 0.04-1 f o r 5.58 MeV gamma-rays i n l e a d . F i n a l l y we have t o c o n s i d e r the c o n t r i b u t i o n of those gamma-rays which a r e s c a t t e r e d towards the c r y s t a l by the f r o n t edge o f the c o l l i m a t o r .  A rough estimate was made of the number  -32-  of gamma-rays t h a t leave  the source a t an angle g r e a t e r  than the  h a l f - a n g l e |2> of the c o l l i m a t o r and s c a t t e r i n t o the c r y s t a l from the edge o f the c o l l i m a t o r w i t h the d e t e c t o r a t 0°.  Only Compton  s c a t t e r i n g i s r e l e v a n t to t h i s estimate and s i n c e 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 spectrum between 2.95 MeV and 6.1 MeV, o n l y those gamma-rays s c a t t e r e d w i t h energies  greater  than 2.95 MeV need be c o n s i d e r e d .  corresponds t o s c a t t e r i n g through angles l e s s than 23°.  This I t was  assumed t h a t a l l the e l e c t r o n s i n a l a y e r o f c o l l i m a t o r one h a l f r a d i a t i o n l e n g t h , t h i c k were l o c a t e d i n a r i n g at. the i n n e r f r o n t p a r t o f the c o l l i m a t o r and t h a t the gamma-rays that entered the :  f r o n t of the c o l l i m a t o r were s c a t t e r e d by these e l e c t r o n s . one  h a l f of the gamma-rays s c a t t e r e d between 0°.and.23°  If  entered  the c r y s t a l then the c o l l i m a t o r s c a t t e r i n g c o u l d c o n t r i b u t e a t most 0.8$ of the t o t a l number of gamma-rays t h a t e n t e r The A smaller and  s i z e of t h i s c r y s t a l i s considered  c r y s t a l i s undesirable  the c r y s t a l .  t o be optimum.  because f o r the same s o l i d  c o l l i m a t o r shape the d e t e c t o r must be p l a c e d  angle  c l o s e r t o the  source w i t h the r e s u l t t h a t : a.  the s i z e of the source becomes c r i t i c a l  b.  the s c a t t e r i n g a t the edge o f the f r o n t c o l l i m a t o r increases  c.  v a r i a t i o n s i n the source t o c r y s t a l d i s t a n c e are more  A bigger  critical. c r y s t a l i s also undesirable  i n the s p i t e 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 i n c r e a s e i n the background and i n c r e a s e i n the neutron induced a c t i v i t y which may energies.  be p r e s e n t f o r some bombarding  I n g e n e r a l c r y s t a l s longer than one  or two  radiation  l e n g t h s are u n d e s i r a b l e . b e c a u s e the back p a r t has a low gammaray to  f l u x but c o n t r i b u t e s background counts r o u g h l y p r o p o r t i o n a l i t s volume.  F o r 5.5 MeV  length i s approximately 8 Neutrons may by deuterons  gamma-rays i n Nal the r a d i a t i o n cm.  a r i s e from the r e a c t i o n D(d,n)^He  i n the t a r g e t which have p i c k e d up energy by  s i o n s w i t h i n c i d e n t protons  (GE  55).  1  2  the prompt e m i s s i o n of gamma-rays i n the energy range  to  6 MeV.  e m i s s i o n of 2.02  f o l l o w e d by gamma-rays of 0.4-28 MeV. ?  MeV  MeV  the exact dimensions The  from 2  or 1.59  integration bias l e v e l .  s i n c e they  Table II-2 shows  of the d e t e c t o r assembly.  Electronics A b l o c k 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 . I I - 8 .  A list  Is  output from the p h o t o m u l t i p l i e r s  g i v e n i n Table l t - 3 .  were sent to two pedance.  MeV  beta decay t r a n s i t i o n s  however, i n t e r f e r e w i t h the D(p,tf)^He spectrum  are below the 2,95  2.4-.  The  counted  ? i which r e s u l t s  in  T h i s i s f o l l o w e d by /S~  colli-  The neutrons are not  d i r e c t l y by the c r y s t a l but they are c a p t u r e d by  do n o t  caused  The  of the e l e c t r o n i c u n i t s  i d e n t i c a l p r e a m p l i f i e r s w i t h 50 -fl output  The p h o t o m u l t i p l i e r and p r e a m p l i f i e r c i r c u i t  are shown i n F i g . I I - 9 and 11-10.  The  phototubes  used  im-  diagrams  were operated  -34-  Table II-2 :  Dimensions o f the D,etector Assembly #1 and 12.0  Collimator Half-Angle  + 0.2  #2  degrees  0.05  cm  0.05  cm  0.05  cm  12.70  + 0.02  . • > ..cm  L  10.16  0.02  cm  C o l l i m a t o r Face Inner Diameter  I  5.30  0.05  cm  C o l l i m a t o r Face Outer Diameter  0  11.6  T h i c k n e s s of Lead S h i e l d i n g  T  4.0  Source to C r y s t a l Pace  R  19.52  Source to C o l l i m a t o r Face  P  12.46  Collimator Thickness  S  6.54  Crystal  D  C r y s t a l Thickness  Diameter  + +  +  + 0.1  .cm cm  -35-  H.V. POWER SUPPLY (2)  SOURCE DETECTOR  DETECTOR  #2  #1  (3)  (3)  PULSE  (1)  GENERATOR  PRE(k) AMPLIFIER  POWER SUPPLY  (5)  PRE{h) AMPLIFIER  KlCKSORTER  KlCKSORTER  (6)  (7)  AMPLIF IER-B  AMPLIF l E R - A r  (8)  (8)  S.C.A.  -  S.C.A.  B  SCALER  Fig.  I I —8  :  SCALER  (9)  Block The  -  A  (8)  (8)  diagram  units  are  of  the e l e c t r o n i c  listed  in Table  (9)  arrangement. M-3-  -36-  OUTPUT  1  ft  ©•  T  H.V.  ANODE  PIO  RCA 8054 R  D9  R  D8  D7 D6 D5  Dk  D3 D2 DYNODE 1 FOCUS  FOCUS  R.  GRID  CATHODE  GAIN  R,  Fig.  I 1-9  :  Photomultipiier  circuit  5%  100  K  ±W  2 ^70  K  iW  1.5  M  Pot.  2  M  Pot.  1  R  3  R  *  c  1  C  2  0.001  5?  3  KV  0.01 JiF 600  V  lOytHy O.OOI^F  1N750  47K  T +  2  0  /  F  1.2K  — f w w— H  H  12K  68pF TEST  (•)  1N462 2 .  C=0.001/F 2N2925  (NEG) ( • )  Fig.  -VVA—  R=5.6K  11-10  OUTPUT  (POS)*  20^F  "  9 Volts I  2N: 2N2925  |  I  | OUTPUT  3-3K INPUT  ®  O.OOIjiF  - A A A -  5.6K  ^  1  20/*F  3  ^7  (NEG)*  20pF  Pre-amplifier circuit. * F o r n e g a t i v e putse o u t p u t must be g r o u n d e d (and v i c e - v e r s a )  -o  +  ioyuHy  the p o s i t i v e  output  -38-  a t 1100  V o l t s and the focus c o n t r o l was  resolution.  a d j u s t e d to o b t a i n the best  The measured pulse h e i g h t r e s o l u t i o n f o r 662  gamma-rays was  f o r d e t e c t o r #1  found to be 7 k% 9  for  #2.  detector  The f i e r s was  shape of the p u l s e s a t the output of the  preampli-  a d j u s t e d by means of the r e s i s t o r R and c a p a c i t o r C  to s a t i s f y the low l e v e l i n p u t requirements ND-120 k i c k s o r t e r s . a c r o s s a 50X1 fier  and 7,8^  KeV  The  2.614- MeV  r e s i s t o r connected  of the N D - I 6 0  and  p u l s e s , from a RaTh source,  a t the output of the  preampli-  (with R = 5.6 K a and C = 0,001 yuF) have a r i s e - t i m e of  0.6 jus and a f a l l - t i m e of 18 yUs. The p u l s e remains a t n e a r l y i t s maximum v o l t a g e f o r approximately the s t a r t . 0.08.  The  fiers.  0.5 yU-s w i t h the maximum o c c u r i n g a t 1.2 ^*s, from  p r e a m p l i f i e r s have a v o l t a g e g a i n of  They were b u i l t from a c i r c u i t designed  A power supply was The  level  by G.  approximately Jones (JO 65).  b u i l t to supply d.c. power to both  preampli-  c i r c u i t diagram i s shown i n F i g . 1 1 - 1 1 .  The  s i g n a l s from the p r e a m p l i f i e r s b e s i d e s g o i n g to the  k l c k s o r t e r s were a l s o s e n t to two linear amplifier - s i n g l e  i d e n t i c a l s c a l e r s , through a d u a l  channel a n a l y z e r system.  An  initial  estimate of the a n g u l a r d i s t r i b u t i o n c o u l d then be o b t a i n e d the experiment was  under way.  An estimate  of the r a t e of d e t e r i -  o r a t i o n of the t a r g e t s c o u l d a l s o be o b t a i n e d i n t h i s The  e l e c t r o n i c system was  while  way.  checked f o r l i n e a r i t y u s i n g  O  2N1480  27 +B O  -A  -•  • W -  -  O + I  1N746  > 680  ^  I  < 1.1K > 1. 6K > 1. \  CO,  I C Q ,  r  C  9 Volts  3-9K  -A  O — *  Fig.  II — 11  :  P r e - a m p l i f i e r s regulated 1  power  supply  circuit.  -40-  a pulse generator. a t 60 Hz,  I t was b u i l t u s i n g a mercury s w i t c h d r i v e n  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 c a p a c i t o r ( t e s t i n p u t o f the p r e a m p l i f i e r ) was i d e n t i c a l to the one produced by the d e t e c t o r a t the i n p u t o f the p r e a m p l i f i e r . potentiometer  The l i n e a r i t y o f the HELIPOT  was checked u s i n g 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 u n i t s u s i n g standard r a d i o a c t i v e sources.  The p u l s e g e n e r a t o r was a l s o used t o make p e r i o d i c  checks o f the windows o f the s i n g l e channel a n a l y z e r s ,  Table I I - 3 :  L i s t o f the E l e c t r o n i c U n i t s used i n t h i s Experiment. C i r c u i t diagram F i g . 11-12.  1.  U.B.C. Pulse g e n e r a t o r .  2.  FLUKE Model 4-12-B High V o l t a g e Power  3.  HARSHAW Type 20MBS16/B. D e t e c t o r Assembly N a l ( T l ) 5" x 4-" c r y s t a l coupled to an RCA 8054- 3 i n c h p h o t o m u l t i p l i e r . C i r c u i t diagram F i g . I I - 9 .  4-.  U.B.C. P r e a m p l i f i e r .  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 A n a l y z e r .  7.  NUCLEAR DATA ND-120 Pulse Height  8.  NUCLEAR DATA ND-500 D u a l A m p l i f i e r and S i n g l e Channel A n a l y z e r .  9.  OR TEC Model 4-30 S c a l e r .  Supply.  Analyzer.  M  1:1  V1  *  110  o—  i  5K  j  •  5K  E  S  R  W  C  I  U  T  R  C  Y  H  5100pF  J  - A A A  r  100K 10  1  O  If  5K  <  200K  W — V S A ^ — I  U  T  P  T O  U  T  120 15K  Fig.  11-12 :  Pulse generator c i r c u i t . Negative pulse output: r.t.=  "p20pF  80 ns  ,  f.t.=350Ms.  A  (  H  E  S  T  A  L  I  P  B  O  L  T  E  D . C .  P  O  W  E  R  S  U  P  P  L  Y  Potentiometer) I  CHAPTER I I I EXPERIMENTAL METHODS AND RESULTS. The  t e c h n i c a l problems i n v o l v e d i n the measurements and  the apparatus parameters chosen are d i s c u s s e d chapter.  I n the present  i n the previous  chapter the measurements and methods  of d a t a a n a l y s i s a r e d e s c r i b e d . 3.1.  Procedure Since a number of d i f f e r e n t t a r g e t s were used and the  t a r g e t s tended t o d e t e r i o r a t e d u r i n g  bombardment i t was not  p o s s i b l e t o r e l a t e one r u n t o another i n terms of the i n t e g r a t e d charge d e l i v e r e d t o the t a r g e t .  I n d i v i d u a l runs were t h e r e f o r e  n o r m a l i z e d i n terms.of the counts recorded p l a c e d a t a f i x e d angle. was 4 mm  by monitor counter #2  For a l l runs the beam spot on the t a r g e t  i n diameter which i s s u f f i c i e n t l y s m a l l compared t o the  19.5 cm d i s t a n c e  from the t a r g e t t o the d e t e c t o r  t a r g e t can be c o n s i d e r e d The  so that the  as a p o i n t source of gamma-rays.  t a r g e t s 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 t a r g e t was 72. Due to the d e t e r i o r a t i o n of the t a r g e t when s u b j e c t e d  to a beam  of 80 t o 90 ykA -the beam was kept on the same t a r g e t spot f o r approximately f i v e minutes, and then moved t o a new Two 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  spot.  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.  F o r con-  f i g u r a t i o n "A" the t a r g e t plane was p l a c e d a t 90° t o the i n c i d e n t -42-  -43-  #1  \ CONFIGURATION  "A"  DETECTOR  DETECTOR  #2  (FIXED)  I i  CONFIGURATION  Fig.  I I 1-1  : Detector  "B  1  target configurations  #1  -44-  beam w h i l e the f i x e d monitor was  p l a c e d a t -120°.,  Although a  h i g h e r count would have been o b t a i n e d w i t h the monitor a t 90 the  t a r g e t a b s o r p t i o n a t t h a t angle would have been l a r g e and  uncertain. was  F o r t h i s geometry  the moving d e t e c t o r angle  9^  v a r i e d from -30° to +60° where the minus s i g n corresponds  to being on the same-side of the beam a x i s as the monitor d e t e c t o r . For  geometry  monitor was  "B" the t a r g e t plane was  a t -90° so i t observed gamma-rays coming  target backing. the  a t 45° t o t h e beam and the through the  The moving d e t e c t o r was r o t a t e d from 60° to 135°  maximum backward angle t h a t c o u l d be reached w i t h the appa-  r a t u s used. As mentioned  i n Chapter I I , two d i f f e r e n t t a r g e t  nesses were used throughout t h i s experiment. f i g u r a t i o n "A" was  thick-  The t a r g e t of con-  1/cos 45° t h i c k e r than t h a t of c o n f i g u r a t i o n  "B" so t h a t the beam passed through the same t h i c k n e s s of t a r g e t m a t e r i a l f o r both c a s e s . The s p e c t r a o b t a i n e d from both m u l t i c h a n n e l a n a l y z e r s were i n t e g r a t e d from 2.95 MeV  to 6.1 MeV,  the lower l i m i t being  chosen to l i e above 'the HaTh f u l l energy photo peak, w h i l e the 1  upper l i m i t was ichosen to l i e above the peak c o r r e s p o n d i n g to the  maximum gamma^ray energy of 5.65 MeV  D(p,tf) He.  expected from the r e a c t i o n  Because-the g a i n of the e l e c t r o n i c system  s l i g h t l y over a long p e r i o d o f time, each spectrum was  changed shifted  to a standard g a i n and i n t e g r a t e d uising the IBM 7040/7044 The f i n a l measurements a t 90 KeV and 160 KeV and e i g h t days to complete.  computer.  took between seven  -45-  The energy c a l i b r a t i o n f o r each spectrum was o b t a i n e d from the 2.614  and 1.4-62 MeV  peaks from RaTh and  as p a r t of the room background.  which a r i s e  The w a l l s of the room c o n t a i n  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 r u n taken over a p e r i o d of 6 9 . 5 count above the 2.614- MeV  6 MeV  The  background  peak a r i s e s p r i n c i p a l l y from the^A-meson  component of the cosmic r a y s . to  hours.  I n the r e g i o n of i n t e r e s t from 3  t h i s c o u n t i n g r a t e averages 370 counts per hour per  MeV  MeV.  A t y p i c a l gamma-ray spectrum from the r e a c t i o n D(p,7$)-^He i s shown in Fig. III-3.  I t was  taken f o r a bombarding  w i t h the d e t e c t o r #1 p l a c e d a t 6 = 90°. to  the t a r g e t was approximately 300 mC.  i s shown i n F i g . H-2  energy of 160  KeV  The t o t a l charge d e l i v e r e d (A spectrum taken a t 0°  (Appendix H); here the t o t a l charge d e l i v e r e d  was approximately 420 mC).  The s p e c t r a o b t a i n e d from d e t e c t o r #1  w i t h the ND-160 k i c k s o r t e r were put on paper tape and t r a n s f e r r e d . to  the computing  c e n t r e where they were converted to magnetic  and punched on IBM c a r d s .  tape  The monitor s p e c t r a c o l l e c t e d by the  ND-120 k i c k s o r t e r were p r i n t e d out and manually punched on IBM cards. the  The g a i n s h i f t s and i n t e g r a t i o n s were then c a r r i e d out on  computer. The a n g u l a r 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 r u n and i n Table I I I - 2 f o r the 160 KeV run.  are  the i n t e g r a t e d number of counts i n c l u d i n g the background  d e t e c t o r s #1 and #2 r e s p e c t i v e l y .  0^  shows the i n t e g r a t e d number of counts due to the  taken when the machine was  from  and 62 are the angular p o s i -  t i o n s of d e t e c t o r s #1 and #2 as shown i n F i g . I I I - l . (i=0)  A and B  not In o p e r a t i o n .  The f i r s t  row  background  NUMBER OF COUNTS ( X 1 0 ) 3  ,000  80.000 i  C3  160.000 i  2140.000 i  320.000 i  ;  400.OOC I  : :  a f  a I  o a a  l/l CD TD QJ  (D n  O 7T rt tQ -1 1 HI O in 3"  O  *  +  +  K (1.462 MeV)  c  3 CL  (V)  2 m — n 3  rt  rt in  C  O zr QJ X) rt  ft) -I  O 3"  RaTh  (2.614  MeV)  (D 3 CD  ro o o o 0) \  CD  —I  — ua  CD <  ID  zr (D  in -<  T ;  rn  —  cr -i  a  TO  rn a a a  QJ  rt —  Q) O  £75  ro o o a a in  XI  n  cn  c 3  01 3 CL  ft)  i  a a a  CO > O  7^ CD O  o a a  -917-  X 10 D(p,tf) He 3  o o o  9 =90°  E =160 KeV. P  6-0O0  7.0O0  .CD  CM O  >  o  § o Ii . u  II 4  CO UJ  4 4  rn  4 4  %4  CM  +' + 4  4 4  O O  o  4 4  \  imillHIHIIIIilimil  -.000  —i  ~!  I-ODD  1  000  3.000  4-ODO  ENERGY LRB (MEV) Fig.  I I 1-3  :  D(p,tf) He 3  gamma-ray  spectrum.  5.0O0  i 0  s  i  • .  B  A ' • ©2  101535  T(sec)  C  D  E  F  G  ,.99282 315000  cr 2  H  G •  1  -30  1793  -120  2734  3360  1083  1059  710  1675  1076  5272  1147  H 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  i  A  9x  0  :  D(p,"o') He gamma-ray a n g u l a r d i s t r i b u t i o n d a t a  62  101535  B  T(sec)  C  D  E  F  (160 KeV Run)  H  G  cr2 H  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  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  1053  (Continuation) 17  95  8752  -90  8310  5322  f.1715  1677  7037  6633  5072  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  9438::  •  I O I  -51-  There was  no a p p r e c i a b l e beam dependent background  a f f e c t the angular d i s t r i b u t i o n measurements. i n Appendix  that c o u l d  This i s discussed  H.  The separate runs are l i s t e d i n order of I n c r e a s i n g 0 ^ However, the a c t u a l order i n which runs were done was  alternated  Column T i n d i c a t e s the t o t a l running time a t each a n g l e . The dead time f o r both k i c k s o r t e r s was and was  determined p r i m a r i l y by the background  l e s s than 0,5%  counting r a t e .  No c o r r e c t i o n has been a p p l i e d f o r t h i s dead time and the time T was  taken t o be the a c t u a l running time f o r both d e t e c t o r s . For  c o n f i g u r a t i o n "A" a c o r r e c t i o n was  a p p l i e d to  account f o r the changing gamma-ray a b s o r p t i o n i n the t a r g e t h o l d e r as a f u n c t i o n of counter a n g l e .  (See Appendix G),  c o r r e c t e d number of counts i s found i n column H,  The  Absorptions  i n the w a l l of the chamber and i n the c r y s t a l ' s c o n t a i n e r were not taken i n t o account because  these d i d not depend on the angu-  l a r p o s i t i o n of the d e t e c t o r , A summarized e x p l a n a t i o n of the Tables I I I - l and  III-2  i s g i v e n below. A^ = I n t e g r a t e d number of counts i n d e t e c t o r #1.: = I n t e g r a t e d number of counts i n d e t e c t o r #2, T^ = T o t a l running time f o r each a n g l e . C, = Number of background time T.. 1  counts i n d e t e c t o r #1 normalized to  -52-  D. = Number o f background time T  counts I n d e t e c t o r #2 n o r m a l i z e d t o  = Number o f counts  l e s s number o f background counts C^.  = Number of counts  l e s s number of background  1  ±a  F  i  counts D^.  G^ = Number o f counts E^^ n o r m a l i z e d to number of counts F^. H. = Number of n o r m a l i z e d counts G. i n d e t e c t o r #1 c o r r e c t e d due to t a r g e t h o l d e r a b s o r p t i o n . A ( i = 0) = I n t e g r a t e d number of background  counts i n d e t e c t o r #1.  B ( i = 0) = I n t e g r a t e d number of background  counts i n d e t e c t o r #2.  T ( i = 0) = T o t a l time i n which the background r u n was performed. The f o l l o w i n g e x p r e s s i o n s show the t a b u l a t e d q u a n t i t i e s with t h e i r standard deviations:  A  L  t  A A;.  hi + AD;  =  Aj. +^A7  Bi i A B ,  To - (Bo TLA + IiJaT To  To > '  V  To  1  BctfBT  •  •  V  , . To ' •  T  0  Fc  where V i s an a r b i t r a r y c o n s t a n t chosen to p r o v i d e a convenient s c a l e , and  ^  Zi  -53-  where Z  1  d i x G.  i s the a b s o r p t i o n c o r r e c t i o n f a c t o r d i s c u s s e d  I t was assumed t h a t Z, has no s t a t i s t i c a l e r r o r .  correction applies 3.2.  i n Appen-  o n l y to the t a r g e t d e t e c t o r  This  configuration  "A".  The Angular D i s t r i b u t i o n F u n c t i o n 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 p o l y n o m i a l s e r i e s :  W(e) = ^ e e ( ) B  This  cos 0  p  (3  ° " 2  1}  i s p a r t i c u l a r l y u s e f u l because i t s i m p l i f i e s the s o l i d  corrections.  Rose (RO 53) has shown t h a t ,  angle  i f thedata i s fitted  to a f u n c t i o n o f the form (3.2 - 1) then, the c o r r e c t e d  angular  d i s t r i b u t i o n f u n c t i o n i s simply g i v e n by \ W(Q) where A^ = B^/Q^o  = Y_  e  A  Pe  (cos6)  The smoothing f a c t o r s  can be obtained by  an i n t e g r a t i o n over the volume of the d e t e c t o r The  c a l c u l a t e d smoothing f a c t o r s f o r the d e t e c t o r  i n t h i s experiment are shown i n Table Table I I I - 3  :  1  «1 3. 3.  (See Chapter I I ) . assembly used  III-3.  Smoothing F a c t o r s C a l c u l a t e d a t E * = 5.58 MeV f o r the D e t e c t o r Geometry Shown i n F i g . I I - 6 . 0  1  2  3  4  1,00000  0.98839  0.9654-6  0,93174-  0.88803  The F i t t i n g For  Procedure  each angle 9. the p r o b a b i l i t y of o b s e r v i n g N. counts  -54i s g i v e n by the P o i s s o n d i s t r i b u t i o n  R . I*0 -  " ^ / Nil  N  where  e  = WtBjS^) i s the curve to be f i t t e d where B stands  f o r the s e t of a n g u l a r d i s t r i b u t i o n c o e f f i c e n t s B'^. The  j o i n t p r o b a b i l i t y of g e t t i n g a p a r t i c u l a r  ment of e x p e r i m e n t a l r e s u l t s N, i  Q^,...,6^ ... Q t  (  N  a t the angles p ^  i s the l i k e l i h o o d f u n c t i o n  p r o v i d i n g t h e events The problem  L. = TT  are independent. here i s to f i n d  maximize the f u n c t i o n L. W = W(B*;Q).  N. l  arrange-  the s e t o f B  1  say B* which  The b e s t f i t curve i s then g i v e n by  I f we take the l o g a r i t h m of L, then  S , fen L  m  £  G» R  a  j[  kWi  - MNil)]  the s o l u t i o n s a r e then o b t a i n e d from the r simultaneous  equations  e = o,i  « o that i s :  y  ( v  A  i  )  =  ' see  e=o,4  Q  0 . 3 - 1 )  .  These equations a r e n o n - l i n e a r i n B^, but the problem  can be  s i m p l i f i e d as i n d i c a t e d below; If  i n the denominator of e q u a t i o n ( 3 . 3 - D  p l a c e d by N^, t h a t i s , i f the f o l l o w i n g approximation i s made then the s o l u t i o n s can be found  from  is re—  I  -55-  where t h i s s e t of r equations i s now  l i n e a r i n B^„  T h i s r e s u l t can a l s o 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 v a r i a n c e which says t h a t the best estimate f o r the s e t i.e.  can be obtained by a l e a s t squares method;  f  2,  Y_  ™l  ( N i t - VX/i)  minimum  =  1=1  if  the weights m^  I f we  are i n v e r s e l y p r o p o r t i o n a l to the v a r i a n c e  N^.  d e f i n e M as  V  N\ -  (  ML  -  wcf.  then the s o l u t i o n s B^ = B* can be obtained from the r  simultaneous  equations ^ O  d\A_  The  £ = O,  1  standard d e v i a t i o n s i n the parameters B* are g i v e n by  error matrix  the  58)  (OH  (B -BJ)(B -B*) = ( H " ) 1  1  k  1  k  l,k=0,r  where  H, The  -  1  2  ^  36<3&  k  square r o o t of the d i a g o n a l elements of the m a t r i x H  are  the standard d e v i a t i o n s i n the parameters B* and the o f f - d i a g o n a l elements AB^ AB^  d e f i n e the degree of c o r r e l a t i o n  between them„  -56-  As was s t a t e d e a r l i e r i n t h i s chapter the r e a d i n g s a t the d i f f e r e n t angles were taken u s i n g two d i f f e r e n t c o n f i g u r a t i o n s , I n order t o procede w i t h the f i t t i n g a n a l y s i s the experimental d a t a o b t a i n e d from these two c o n f i g u r a t i o n s have t o be r e l a t e d to each o t h e r .  At both 90 KeV  T h i s c o u l d be done as follows„  and 160 KeV the d i s c o n t i n u i t y occurs a t 6^ = 60° as shown i n Fig.  III-4-.  T h e r e f o r e , i f we c a l l R the f a c t o r which when m u l t i -  p l i e d by the c o n f i g u r a t i o n "B" data would make i t f i t smoothly t o the c o n f i g u r a t i o n "A" d a t a , then from F i g . and  and Tables  III-l  III-2 R = HCG^O ),,^, / G C e ^ O ) , , ^ , 0  0  X  N, 1  r  >~-4  N2  e  0°  6  6  CONFIGURATION _J^_ CONFIGURATION^ II A II »B" 1  Fig.  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 c o n f i g u r a t i o n s as a f u n c t i o n of the angle 9 I n the l a b o r a t o r y frame. Q o denotes the s h i f t i n the experimental angular scale. The p o i n t s shown here were a r b i t r a r i l y drawn.  -57-  The a p p l i c a t i o n of the l e a s t squares method w i l l then g i v e the solution  sought. There i s , however, an important d i f f i c u l t y w i t h  approach.  The  s e t of d a t a i n the c o n f i g u r a t i o n "B" may  by a s y s t e m a t i c e r r o r , t h a t i s , a l l the p o i n t s may below the a c t u a l v a l u e u n l e s s the d a t a a t 60° are taken to a h i g h degree of accuracy.  be  affected  l i e above or  i n both c o n f i g u r a t i o n s  Assuming t h a t 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  d a t a p o i n t s i n the c o n f i g u r a t i o n "B" w i l l be weighted to what happened a t one p a r t i c u l a r  this  according  angle.  The approach chosen to overcome t h i s d i f f i c u l t y i s o u t l i n e d below, following  The d a t a i s to be f i t t e d  to a f u n c t i o n of the  type:  W  * [ Y_ B P (cos 9)1 ( | +l\<) t  e  Uo where  <  0  (configuration  "A")  1  (configuration  "B")  K i s then t r e a t e d as a new l e a s t squares f i t .  ,  parameter t o be determined  K corresponds  to ("j^""^) ! however, i t must  be p o i n t e d out t h a t R i s a c o n s t a n t determined two  by the  by the r a t i o between  e x p e r i m e n t a l d a t a p o i n t s taken a t one. p a r t i c u l a r angle while  K i s a parameter determined  by the l e a s t squares f i t which depends  on a l l of the e x p e r i m e n t a l d a t a . F i n a l l y the u n c e r t a i n t y i n the zero of the angular  scale  -58must be c o n s i d e r e d .  Although the 1  g r a d u a t i o n s i n the angle  s c a l e of the angular d i s t r i b u t i o n t a b l e c h i n e d to b e t t e r than 0.2 to  degree,  (Chapter I I ) were  i t s o r i e n t a t i o n with respect  the Incoming beam c o u l d not be determined  This i s i n i t s e l f small. around  ma-  b e t t e r than 1°.  However, because a s m a l l asymmetry-  90° i s to be expected  (DO 6?) i t i s important to e l i m i n a t e  e x p e r i m e n t a l f a c t o r s which might c o n t r i b u t e to such an asymmetry. T h e r e f o r e , the e x p e r i m e n t a l d a t a , was of  the f o l l o w i n g  finally  fitted  to a f u n c t i o n  type:  1 (3.3 - 2) where G Q  was  l  1  E-o  t r e a t e d as another parameter to be  determinated  from the e x p e r i m e n t a l d a t a .  Because t h i s f u n c t i o n 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 d e v i s e d by  F a l k (FA 65)  and Orth (OR  the e x p e r i m e n t a l d a t a . expansion of  ^tl  67)  was  used to f i t t h i s f u n c t i o n to  B r i e f l y the method c o n s i s t s i n the ,  and  i n the f i r s t  s e r i e s about i n i t i a l v a l u e s of the parameters be determined.  F o r convenience  and K = B. r+2*  B^, K and Q  we rename the parameters ^  to  q  Q  = B o  Then  B8e  We  order T a y l o r  +L —  A6  1 = 0,r+2  Bc-Be. j-c e i 6j .6)0 have here a s e t of r+2 equations which are l i n e a r i n the a  increments B^ i n the parameters.  6  3  6  I f we  apply the l e a s t  squares  method to f i n d the minimum v a l u e of M then 4*2  0 = 3n  _  AB; ft 6 j o  1 = 0,r+2  r+1  -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 . j»  meters B ^ one can c a l c u l a t e the f i r s t M using i t s d e f i n i t i o n .  of parameters B .  ditions.  The above r+2  These new  1  = B.  + AR  o n l y the f i r s t  using B . .  i  i t e r a t i o n because we  as the new  (OR  67A)  from  are c o n s i d e r -  i n i t i a l v a l u e s of the parameters. ^EL -  l e s s than-some chosen v a l u e .  Orth  which s a t i s f y the above con-  i s t o r e p e a t the o p e r a t i o n a g a i n ,  o p e r a t i o n i s repeated u n t i l is  new  term i n the T a y l o r s e r i e s .  Then the procedure now  equations can then be  v a l u e s of the parameters B ^ w i l l d i f f e r  the b e s t v a l u e s B * i n the f i r s t ing  and second d e r i v a t i v e s of  increments A B ^ i n the parameters to g i v e a  s o l v e d f o r the r+2 set  of the p a r a 0  to f i t a sum  BjC - 6j(l-Q  j _  0  f  r  This +  2  A computer program w r i t t e n by  of two  e x p o n e n t i a l s was  m o d i f i e d to  accept the f u n c t i o n ( 3 . 3 - 2 ) . These i t e r a t i v e c a l c u l a t i o n s must s t a r t w i t h  initial  v a l u e s of the parameters which should be chosen r e a s o n a b l y c l o s e to  the c o r r e c t v a l u e s i f the process i s to converge q u i c k l y or  at  all.  The  i n i t i a l value g i v e n to Q  the y i e l d around 0° f o r the 160 KeV of The  approximately initial  2° was  Q  and 90 KeV  t a i n e d by f i t t i n g  runs.  plotting A zero  chosen f o r  shift 8. Q  o b t a i n e d from the v a l u e of R,  estimated f o r 60° d a t a t h a t i s K = 1/R initial  o b t a i n e d by  noted and t h i s v a l u e was  estimate f o r K was  The  was  - 1.  estimates f o r the parameters B ^ were  the d a t a to the f u n c t i o n (3.2 - 1).  squares f i t t i n g program f o r l i n e a r f u n c t i o n s was  ob-  A least  used In t h i s  -60-  case.  Here the data from both c o n f i g u r a t i o n s were r e l a t e d u s i n g  the f a c t o r R and 0 3.4.  o  was assumed t o be z e r o .  The R e s u l t s E x p e r i m e n t a l r e s u l t s from previous work (Chapter I )  i n d i c a t e t h a t the angular d i s t r i b u t i o n of the gamma-rays the r e a c t i o n D ( p , ^ ) % e a t low energies (24 KeV t o 1.75 at  l e a s t i n f i r s t approximation,  (or  i f expressed  the form  W(9)  W(Qjr^P^AgPg)  (DO 67) i n d i c a t e t h a t  terms h i g h e r than Pg may be present i n the angular of  MeV) has, p  = a +. b s i n 9  i n terms of Legendre polynomials  However, r e c e n t t h e o r e t i c a l c a l c u l a t i o n s  from  distribution  t h i s r e a c t i o n even a t e n e r g i e s below 200 KeV. T h e r e f o r e , the f u n c t i o n chosen i n the present a n a l y s i s  i n c l u d e s terms up to P^ I n the Legendre p o l y n o m i a l  series.  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 r u n s .  P i t s were o b t a i n e d f o r s e v e r a l d i f f e r e n t s e t s of  Legendre p o l y n o m i a l parameters B^. In rows 1 and 6 the experimental data was f i t t e d t o the f o l l o w i n g Legendre p o l y n o m i a l  series  with (configuration  "A")  (configuration  "B")  i n which the parameters B^, B_, and B^ were s e t i d e n t i c a l l y  equal  -61-  to zero.  S i m i l a r l y , rows 2 and 7 show the r e s u l t o b t a i n e d when  the parameters  and B^ were s e t equal t o zero.  Rows 3 and 8  correspond t o the case i n which a l l the parameters were l e f t  free.  In rows 5 and 10 the e x p e r i m e n t a l p o i n t s were f i t t e d t o the same f u n c t i o n i n which a l l  the parameters but B^ were s e t f r e e . .The  p a r t i c u l a r r e s t r i c t i o n s imposed here a r e d i s c u s s e d i n Chapter IV. The c o n d i t i o n imposed on t h i s parameter was t h a t the a n g u l a r d i s t r i b u t i o n o b t a i n e d from the f i t must g i v e the same v a l u e a t 0° and 180° when the s o l i d angle c o r r e c t i o n was a p p l i e d . , That i s , = -A^ which means t h a t the c o n d i t i o n imposed on the parameters B^ was B^ = -Q^/Q^ B^  where  and  a r e the smoothing  factors.  The f u n c t i o n used f o r t h 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 a r e shown f o r the case when a l l the parameters but A^ were s e t f r e e .  Here however, the con-  d i t i o n imposed on t h a t parameter was t h a t the c o r r e c t e d angular d i s t r i b u t i o n must be e q u a l t o zero a t 9^ = 1 8 0 ° .  This c o n d i t i o n  f o l l o w s i f the v a l u e o f A^ i s r e s t r i c t e d t o  A  4 - ~ o A  +  A  l  " 2 A  +  A  3  In t h i s case the f u n c t i o n used was W^  .[60(Po-<h  ?*) -B.(R 9iP.) <- 6 z ( - Q i PA) 65 +  +  ( P »  +Si P ^ (n-1K)  The same program i n c l u d e s the U s u a l Chi-squared t e s t . The t e s t was made on each f i t and the r e s u l t s a r e shown i n Table I I I - 4 .  The number o f degrees o f freedom c o r r e s p o n d i n g t o  -62-  each f i t a r e shown i n the column denoted by ^ . The n o r m a l i z e d p r o b a b i l i t y o f o b t a i n i n g a v a l u e of  %  g r e a t e r t h a n or, e q u a l t o the v a l u e o b t a i n e d i n each p a r t i c u l a r f i t was by p.  found from the %  (1 - p)  t a b l e s and i s shown i n column denoted  g i v e s t h e n t h e 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 t h e experiment  under the same e x p e r i m e n t a l c o n d i t i o n s . for Q  Q  i s repeated  The b e s t v a l u e s o b t a i n e d  and K i n each f i t and t h e square r o o t of the v a r i a n c e f o r  a l l p a r a m e t e r s (AB^,A& and^K) a r e shown i n Table  For  Q  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 o f the  parameters f o r s u c c e s s i v e s t e p s a l l parameters.  was  l e s s t h a n 0.001  (0.1$) f o r  On t h e average f o u r i t e r a t i o n s were needed t o  achieve t h i s r a t i o . The a n g u l a r d i s t r i b u t i o n parameters shown i n T a b l e were c a l c u l a t e d f o r t h e c e n t r e o f mass system.  The  III-4  input data  were t r a n s f o r m e d t o the c e n t r e of mass i n the same program u s i n g e q u a t i o n s g i v e n i n A p p e n d i x G b e f o r e the f i t t i n g procedure carried  out.  was  B o  B  l  A B  1  B  2  * 2 B  B  3  * 3 B  B  &B  4  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 - 4 a :  D(p l5) He angular d i s t r i b u t i o n l e a s t squares f i t parameters f o r 90 KeV and 160 KeV runs. 5  K  AK  r  E  # 1  0.020  A6 M 0.011 -0.856  # 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  #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  # 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  e  0  0  P  0.007  12.79 •  18  0.79  P (KeV)  70  144  Table III-4b : D(p,tf) He 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 and 160 KeV runs.  CHAPTER IV DISCUSSION In the p r e v i o u s chapter the measurement of the angular d i s t r i b u t i o n f o r the r e a c t i o n 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 p o l y n o m i a l s e r i e s i s d e s c r i b e d .  In t h i s  chapter the e x p e r i m e n t a l r e s u l t s are d i s c u s s e d and compared w i t h (DO 6 7 ) .  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 D o n n e l l y  d e s c r i p t i o n of a technique to be used i n the f u t u r e to  A brief determine  the a b s o l u t e c r o s s s e c t i o n of t h i s r e a c t i o n as a f u n c t i o n of energy i s a l s o 4.1.  presented.  D i s c u s s i o n of the R e s u l t s In t a b l e I I I - 4 the Legendre p o l y n o m i a l c o e f f i c i e n t s  were shown f o r the 90 KeV f o r the f i n i t e  and  160 KeV  runs without  s o l i d angle of the d e t e c t o r .  the a n g u l a r d i s t r i b u t i o n s f o r the f i n i t e tector  B  1  corrections  I n order to c o r r e c t  s o l i d angle of the  de-  (Chapter I I I ) , i t i s n e c e s s a r y to d i v i d e the Legendre p o l y -  nomial c o e f f i c i e n t s by the smoothing f a c t o r s  g i v e n i n Table I I I  T h i s c o u l d have been done by i n c l u d i n g the smoothing f a c t o r s d i r e c t l y i n the Legendre p o l y n o m i a l f i t t i n g was  c a r r i e d out.  program before the f i t  T h i s would have l e d d i r e c t l y  r e c t e d c o e f f i c i e n t s , as the p r e s e n t approach r e c t e d c o e f f i c i e n t s a r e determined  to the same c o r -  i n which the  uncor-  first.  Since the a b s o l u t e c r o s s s e c t i o n has not been measured it  i s convenient to remove the a r b i t r a r y i n t e n s i t y f a c t o r B  -65-  q  and  -66-  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 c o r r e c t e d r e s u l t s a r e shown i n Table IV-1. F, i s the e x p e c t a t i o n value of B,Q /B Q = A../A 1 l o o l l o n  square r o o t of i t s v a r i a n c e . and the X* also  percentage  The percentage  probability  and AF, i s the l  error  ^=  P ( d e f i n e d i n Chapter  AF^/F^ x 100 I I I ) are  Included. The e x p e c t a t i o n value F^ and AF^ were obtained as f o l -  lows :  Fi - E (k\  rlBtQ*\- Q, [6e  _  (H"')oe  ,  Be (w*)**]  u  0  and  _1 where H  i s the e r r o r matrix d e f i n e d i n Chapter I I I . For the 144.KeV r e s u l t s  dence l e v e l of 5%t the Chi-squared only A  Q  and A  2  A , A , and A^. Q  2  respectively.  coefficients  i f we accept the u s u a l c o n f i t e s t e l i m i n a t e s case #6 w i t h  as w e l l as case #7 w i t h  coefficients  These cases are shown i n F i g . IV-1 and F i g . IV-2, The f u n c t i o n s p l o t t e d  f o r comparison w i t h the ex-  p e r i m e n t a l data are e v a l u a t e d not w i t h the c o e f f i c i e n t s i n Table IV-1 but w i t h the c o e f f i c i e n t s the e f f e c t of the f i n i t e  i n Table I I I - 4 which c o n t a i n  s o l i d angle of the d e t e c t o r .  I n 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 c l u d e d w i t h the c o n s t r a i n t s d e s c r i b e d i n Chapter I I I .  F  A  l  V  "ll  F  2  ttF  2  n  2  F  3  %  3  F  4  4  P (KeV)  P  "U  #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  #4  0.075  0.038  51  -0.951  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  #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 I V - 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 o f A./A |F =E(A /A )] , fi| the percentage e r r o r A F . / F ^ and P the ^ t e s t as defined i n the ?ext* i  i  1  o  0  1  1  70  144  -.000  RELATIVE  .200  INTENSITY  .1400  -89"  .600  .800  1.000  -.000  RELATIVE  .200  INTENSITY  .HOO  o a a  -69-  .600  .800  I.000  Consider case #8 f o r 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 . P i g . IV-3.  I t i s obvious  The r e s u l t of t h i s f i t i s shown i n  t h a t t h i s case can not r e p r e s e n t 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 f o r angles g r e a t e r than approximately 165°.  Although  this f i tre-  p r e s e n t s the g e n e r a l case, because a l l the c o e f f i c i e n t s were f r e e i n the f i t t i n g p r o c e s s , i t i s not s u r p r i s i n g to have obtained type of r e s u l t . there was  T h i s i s because f o r angles g r e a t e r than  this  135°  no experimental data. The  l e a s t r e s t r i c t i o n that we  can i n t r o d u c e  =so  the  r e s u l t s have p h y s i c a l s i g n i f i c a n c e i s t h a t the i n t e n s i t y f u n c t i o n must be p o s i t i v e f o r a l l angles,. I t i s c l e a r from the shape of the curve t h a t t h i s c o n d i t i o n can be met zero a t 180°.  T h i s corresponds  t o case #9  Note t h a t the f u n c t i o n shown corresponds i n c l u d i n g the e f f e c t of the f i n i t e t h a t i t i s not zero a t 180°. d i s t r i b u t i o n was  by making the f u n c t i o n shown i n F i g . IV-4-.  to the experimental  curve  s o l i d angle of the d e t e c t o r so  F i n a l l y f o r case #10  the angular  f o r c e d to have the same value a t 0° and  T h i s i s j u s t i f i e d f o r p h y s i c a l reasons  180°.  to be d i s c u s s e d l a t e r .  The  r e s u l t i s shown i n F i g . IV-5. Without b i a s i n g 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 c a l c u l a t i o n s one cases #9 and #10  ( F i g . IV-4-, F i g . IV-5)  can say t h a t the  r e p r e s e n t good f i t s  to the  d a t a and from the s t a t i s t i c a l p o i n t of view i t i s not p o s s i b l e to d i s t i n g u i s h between them.  RELATIVE  INTENSITY  -U-  „ 47  The angular d i s t r i b u t i o n s a f t e r c o r r e c t i n g f o r the e f f e c t o f the f i n i t e d e t e c t o r s i z e are shown I n Fig„ IV~6, c o r r e s p o n d i n g t o the case where the f u n c t i o n i s zero a t 180°, and  F  i  g  o  IV-7 c o r r e s p o n d i n g t o the case where the value of the  f u n c t i o n a t 0° equals the v a l u e a t 180°, For the 70 KeV data the s i t u a t i o n Is not as c l e a r as for  the 14-4 KeV„  a l l five f i t s  The Chi-squared t e s t g i v e s s i m i l a r answers f o r  t o the d a t a .  N e v e r t h e l e s s i f i t i s assumed t h a t  the angular d i s t r i b u t i o n f u n c t i o n a t 70 KeV has the same form as t h a t a t 14-4- KeV then the f i r s t  two cases can be r e j e c t e d s i n c e  they c o n t a i n no odd Legendre polynomials w h i l e the t h i r d can be r e j e c t e d as b e f o r e s i n c e i t leads to a negative, v a l u e of the i n t e n s i t y f u n c t i o n a t backward a n g l e s . statistically  The f i n a l two cases are  i n d i s t i n g u i s h a b l e ; one corresponds  to the r e q u i r e -  ment t h a t the d i s t r i b u t i o n go to zero a t 180° while the other r e q u i r e s the same v a l u e a t 0° and 180°. of  These d i s t r i b u t i o n s a r e  the same form as was r e q u i r e d t o f i t the 144- KeV data.and  they do l e a d t o a d e f i n e d , although not v e r y a c c u r a t e , v a l u e f o r the c o e f f i c i e n t of the f i r s t  odd Legendre p o l y n o m i a l .  F i g , IV-8  and F i g , IV-9 show the f i t t o the experimental data taken a t 70 KeV f o r the parameters g i v e n I n Table I I I - 4 , cases f o u r and five. 4,2,  Comparison w i t h the T h e o r e t i c a l C a l c u l a t i o n s As i n d i c a t e d i n Chapter  I the t r a n s i t i o n scheme f o r  t h i s r e a c t i o n can be r e p r e s e n t e d i n the f o l l o w i n g ways  -9L-  -LI-  RELATIVE  INTENSITY  -79-  In the upper p a r t of the f i g u r e the v e r t i c a l l i n e s represent  the components t h a t have been c o n s i d e r e d  tinuum s t a t e wave f u n c t i o n of the D + p system. lower v e r t i c a l l i n e s r e p r e s e n t considered  I n the con-  S i m i l a r l y , the  the components t h a t have been  i n the ground s t a t e wave f u n c t i o n of the ^He (D + p  bound system). The d i r e c t capture t r a n s i t i o n s between the continuum and  bound s t a t e s a r e summarized below where the form o f the  angular dependence of the d i f f e r e n t i a l cross  section i s indicated:  -80-  (1)  E1( P- S)  4^ ^  (2)  E2( D- S)  dcr  (3)  M1( 'S- S)  w  El(  (5)  EKV-^D)  2  2  2  2  Z ,  So<n* Q  1<  2  isotropic  V-\>) -1- co& e) 2  (6)  isotropic  and the i n t e r f e r e n c e s :  (7)  E1/E2  (  (8)  El/El  (9)  E1/E2 ( ^ P - V A s - ^ D )  (10)  E1/E2  2  P -  2  S /  2  D din. - S ) 2  u  ( W V ^ D ) d£  A  da  P (cos G) t  ( ^ F - ^ D / ^ S* - ^ %D ) Pa (cos e) da  (11)  El/Ml  ( ^ P - ^ D / ^ zero S ^ S )  (12)  El/Ml  (^-^D/^S-^S)  (13)  E2/M1  zero  ( ^ S - ^ D / ^ S - zero S ) 2  The d i f f e r e n t i a l c r o s s s e c t i o n can be expanded i n a Legendre p o l y n o m i a l s e r i e s d£  =  V  Pi  ( c o s e)  where the t r a n s i t i o n s which c o n t r i b u t e t o the v a r i o u s Legendre  -81-  c o e f f i c l e n t s a r e shown below: A  M1(^S- S) ; E 1 ( P - S ) 2  Q  2  E2{^S-^D) 2  ±  El(VA))  ; El(^F-^D) ; E2( D- S) ; 2  2  ; E l ( V - ^ D ) ^ (^S-^D)  2  ; E2( D-2S)  E1( P- S) 2  2  ;  ; E K ^ D J / E K V ^ D )  E1( P-2S)/E2( D-2S)  A  A  2  2  2  ;  E K V ^ D )  ;  E l ( V ^ D )  ;  EKVDJ/EKVD) A  E1( P- S)/E2( D- S) 2  3  A^  2  2  2  ; E1(^P-^D)/E2(  V^D)  E2( D- S) 2  2  A f t e r making  a number o f assumptions, which a r e  d i s c u s s e d b r i e f l y belowi  about the r e l a t i v e amplitudes of v a r i o u s  components i n the wave f u n c t i o n s . D o n n e l l y  calculated  the c r o s s  s e c t i o n s f o r c e n t r e o f mass e n e r g i e s between 1 6 KeV and 4- MeV, Approximate c r o s s s e c t i o n s o b t a i n e d by Donnelly  energy of 1 0 0 KeV f o r the d i f f e r e n t  mass bombarding are g i v e n  below: Transition  0"(^b)  (1)  E1( P- S)  0,6  (2)  E2( D- S)  0,003  (3)  H1(V S)  0,08  (40  El(V^D)  0.08  (5)  El(^P-^D)  0.01  (6)  f o r a c e n t r e of  2  2  2  2  2  <lO"  6  transitions  -82-  D o n n e l l y ' s model does not three he  body symmetry p r o p e r t i e s  introduced  I n c o r p o r a t e the  complete  of the wave f u n c t i o n , however,  some of these p r o p e r t i e s  i n an e m p i r i c a l way  by  4 i n c l u d i n g components of a r b i t r a r y amplitude f o r the  D  state  2 and  the  s  ( )  s t a t e of mixed symmetry i n the ground s t a t e wave  m  f u n c t i o n , s i n c e these components are shown to be present f o r r e a l i s t i c nuclear  forces  60).  (DE  L  The ability  D s t a t e was  introduced  with an a r b i t r a r y prob-  so t h a t the ground s t a t e r a d i a l wave f u n c t i o n  assumed to have the form U(r) = 1-P U (r) \ J  D  s  +  ^  P  was  U (r)  ~  D  2 where Ug(r) ^D  Up(r)  are the r a d i a l f u n c t i o n s  components each n o r m a l i z e d to u n i t y .  i t was  f o r the  f i t t e d the r a t h e r  e n e r g i e s up  v a l u e was  to 1.5  MeV  P  and  In p r e v i o u s work. (BA  shown t h a t the c a l c u l a t e d t o t a l c r o s s s e c t i o n f o r  y i e l d a t 0° low  and  67)  the  l i m i t e d e x p e r i m e n t a l data from  w i t h 1% ( P  D  = 0.01)  ^D  state.  This  used i n D o n n e l l y ' s c a l c u l a t i o n s .  4 For  the  S continuum s t a t e the p r o t o n and  have t h e i r spins a l i g n e d . be anti-symmetric and  the  deuteron  S i n c e the t o t a l wave f u n c t i o n must s p i n f u n c t i o n i s symmetric, while  the  i s o - s p i n f u n c t i o n i s o f mixed symmetry,the s p a t i a l wave f u n c t i o n  4 of the S s t a t e must be of mixed symmetry. Because the magnetic d i p o l e o p e r a t o r 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  -83-  s t a t e 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  selection rules.  by  In computing the Ml c r o s s s e c t i o n f o r the  L  S  2 s t a t e to  S( )  s t a t e of mixed symmetry i t was  m  2  r a d i a l form of the  S,  v s t a t e was (m;  assumed t h a t the  the same as the r a d i a l  form  2  of the symmetric S state. F u r t h e r i t was assumed to have an a r b i t r a r y amplitude which would need to be determined by e x p e r i -  2 ment.  P r e v i o u s work (BA 6?)  has shown t h a t a  s  ( ) State, a m p l i m  2 tude of 0.33  times the  S s t a t e amplitude  between t h e o r y and experiment I t i s important  g i v e s good agreement 0° c r o s s s e c t i o n .  f o r the low energy  to note here t h a t the c a l c u l a t i o n s  of D o n n e l l y and B a i l e y e t . a l . have been d e v i s e d to g i v e a r e a s o n a b l y good energy  dependence f o r the c r o s s s e c t i o n s , p a r t i c -  u l a r l y a t low e n e r g i e s .  However, due  to the approximations made  2  4  the a b s o l u t e v a l u e s of the amplitudes of the ( ) D states c o n t a i n a r b i t r a r y f a c t o r s t h a t make i t u n r e a l i s t i c to expect them s  a n < i  m  to be a c c u r a t e or to agree w i t h amplitudes  o b t a i n e d by other  h.  workers.  The  D amplitude  i n t r o d u c e d here i s s m a l l e r than the,  k% u s u a l l y found necessary to f i t the magnetic moments of the t h r e e body n u c l e i  (SP 50)  (subject to considerable u n c e r t a i n t i e s p  due  to the n e g l e c t of exchange moments).  The  s  ( ) state amplim  tude i s much l a r g e r than the v a l u e r e q u i r e d to f i t e l e c t r o n 67).  s c a t t e r i n g data (GI Table IV-2  shows a comparison between the  r e s u l t s d e s c r i b e d here f o r cases 5 and assumed t h a t A» = -A , 1  10,  experimental  f o r which i t was  and r e s u l t s o b t a i n e d f o r Donnelly's  E P  V o A  (KeV) Exp. (case # 5) 70-20  Theory  0.18  Exp. (case #10) 144-16  Theory  Table IV-2 :  0.06 - 0.04  -0.93 - 0.05 -0 84  A  3  / o  4' o  A  -0.06 - 0.04 -0.18  0.05 i 0.02  -0.94 - 0.02  -0.05 - 0.02  0.15  -0.88  -0.15  0.02 - 0.05 -0.007 0.03 - 0.02 r  0.007  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 .  -85-  calculations  (DO 6 7 ) .  As seen i n Table I V - 2 the t h e o r e t i c a l v a l u e s of A„/A l o and k^/k^  are e q u a l and o f opposite s i g n .  I n the t h e o r e t i c a l  c a l c u l a t i o n t h e r e are s m a l l c o n t r i b u t i o n s from i n t e r f e r e n c e terms i n v o l v i n g the  D s t a t e which can produce a d i f f e r e n c e  between A^ and -A^ however, the theory suggests ence i s l e s s than 0 . 1 $ .  that this  differ-  The a n a l y s i s , case #9 (Table I V - i ) ,  of the e x p e r i m e n t a l data suggests t h a t there may be a s m a l l d i f f e r e n c e between A^ and - A ^ but, i t i s a t the l i m i t o f s t a t i s t i c a l significance.  I f we assume then t h a t A^ = - A ^ as was done f o r  case #10 then the v a l u e of A / A which r e s u l t s i s 0 . 0 5 t 0 . 0 2 , 1  q  which i s one t h i r d of the v a l u e g i v e n by the Donnelly f o r t h i s energy range.  2  2  calculation  The A^ (and A^) terms a r i s e from  2  2  inter-  f e r e n c e between E2( D- S) and E l ( P- S) t r a n s i t i o n s and the c a l c u l a t e d 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 w i t h the  C h r i s t i a n and Gammel (CH 53) phase s h i f t a n a l y s i s of the low energy  proton-deuteron  s c a t t e r i n g data.  agreement noted here suggests  Furthermore,  the d i s -  t h a t e i t h e r one or both of the  2 e x t r a p o l a t i o n s o f the phase s h i f t s o f  2 P and  D continuum wave  f u n c t i o n s t o low e n e r g i e s may be s i g n i f i c a n t l y i n e r r o r . Although, the term k^/k  Q  order o f magnitude concerned,  i s , as f a r as the s i g n and  ;  i n agreement w i t h the theory, the  d i f f e r e n c e between the experimental v a l u e and t h e o r e t i c a l c a l o u - ' l a t i o n i s beyond the s t a t i s t i c a l e r r o r .  T h i s suggests t h a t 1%  D s t a t e i n the ground s t a t e wave f u n c t i o n i s too h i g h s i n c e  -86-  the t r a n s i t i o n s i n v o l v i n g the to A  then t o A^ as can be seen from the angular d i s t r i b u t i o n s .  q  Bailey the  D s t a t e c o n t r i b u t e more s t r o n g l y  (BA 67) has shown t h a t the 0° y i e l d i s very  s e n s i t i v e to  D s t a t e p r o b a b i l i t y and h i s t e n t a t i v e suggestion  that  this  p r o b a b i l i t y was 1%, was based on the a n a l y s i s o f data of low statistical a smaller  accuracy.  The d a t a c o u l d be f i t t e d  e q u a l l y w e l l by  D s t a t e p r o b a b i l i t y as suggested by the present  jresults. I t i s not s u r p r i s i n g t h a t the A^/A  Q  2  term remains  2  u n d e f i n e d s i n c e o n l y the E2( D- S) t r a n s i t i o n can c o n t r i b u t e t o t h i s term and i t has a r e l a t i v e l y low c r o s s s e c t i o n a t these energies. The A  q  c o e f f i c i e n t i s not d e f i n e d by the present  work s i n c e i t r e q u i r e s the measurement of the absolute  cross  sec-  t i o n which i s the o b j e c t of f u t u r e work. 4.3.  Future Work As shown above the main c o n t r i b u t i o n s t o the i s o t r o p i c  c r o s s s e c t i o n are the M1(^S- S) 2  t r a n s i t i o n and the E1(^P-^D)  term plus i t s i n t e r f e r e n c e w i t h the s m a l l e r E l ( F- D) t r a n s i t i o n h. 2 4 i n v o l v i n g the D s t a t e . Both the and D s t a t e p r o b a b i l i t i e s are of c o n s i d e r a b l e  i n t e r e s t s i n c e they are r e l a t e d to s p i n  dependent and n o n - c e n t r a l  p a r t s o f the nucleon-nucleon f o r c e .  I t i s not p o s s i b l e t o separate the e f f e c t s of these c o n t r i b u t i o n s 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 c o n t r i b u t i o n s have q u i t e 6?)  dependence (DO from 30 KeV Ml and  r e l a t i v e c r o s s s e c t i o n s over a wide energy range,  to 3 Mev"  say, would provide a b a s i s f o r s e p a r a t i n g  E l cross sections.  Furthermore, absolute  would p r o v i d e a more s t r i n g e n t t e s t of any  2 for  the amplitudes of the  cross  different.energy  cross  the  sections  t h e o r e t i c a l models  4 $( ) m  a n a  ^  D  states.  s e c t i o n In the energy range from 1 KeV  In a d d i t i o n , the to 25 KeV  i s of  i n t e r e s t i n a number of a s t r o p h y s i c a l p r o c e s s e s . Absolute cross  s e c t i o n measurements are  i n the energy range from 50 KeV a c c e l e r a t o r and  time being c a r r i e d out Helmer u s i n g  using  the low  energy  these r e s u l t s w i l l be combined w i t h measurements  a t h i g h e r e n e r g i e s (4-00 KeV  R.  to 180 KeV  to be done  to 2 MeV)  which are a t the  i n t h i s laboratory  the U.B.C. Van  de G r a a f f  by G.M.  present  Bailey  and  accelerator.  In s p i t e of improvements made i n the deuterium the d e t e r i o r a t i o n continues to present a problem from the of making a c c u r a t e r e l a t i v e and ments.  One  method t h a t has  this d i f f i c u l t y  absolute  cross  been developed to p a r t l y a l l e v i a t e  i s to produce a t a r g e t over the  i s continuously  surface  of a  the author.  and  1/16"  part  exposed to the beam.  A r o t a t i n g t a r g e t h o l d e r was and  viewpoint  s e c t i o n measure-  p l a t e which i s r o t a t e d r a p i d l y i n f r o n t of the beam so no of t h e . t a r g e t  targets,  developed by G.M.  I t c o n s i s t s of a f l a t copper d i s c 5"  Bailey  i n diameter  t h i c k mounted i n s i d e of a vacuum chamber i n such a  way  -88-  t h a t i t can be r o t a t e d e x t e r n a l l y by means of an e l e c t r i c motor. The speed a t which the d i s c r o t a t e s can be v a r i e d i n a continuous up to 600  way  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 d i s c can be moved up and down w i t h r e s p e c t to the beam and can a l s o be p l a c e d a t d i f f e r e n t angles w i t h r e s p e c t to  the incoming beam. T h i s t a r g e t h o l d e r has a l r e a d y been t e s t e d  Deuterated p o l y e t h y l e n e was  (BA  d e p o s i t e d over the area of the d i s c 2  w i t h a t h i c k n e s s of 100yHg/cm °  An 800 KeV  p r o t o n beam of  approximately 5 yUA from the Van de G r a a f f a c c e l e r a t o r was The  spot on the t a r g e t was The  t e s t was  68).  approximately 6 mm  used.  i n diameter.  c a r r i e d out over a 10 hour p e r i o d .  Although d u r i n g the f i r s t  two and a h a l f hours or so there  was  about b0% decrease i n the y i e l d the r a t e of d e t e r i o r a t i o n i n the seven and a h a l f subsequent  hours was  found to be l e s s  than  15%. For r e l a t i v e c r o s s s e c t i o n measurements the  initial  l o s s of t a r g e t m a t e r i a l presents no major problems because  one  can wait u n t i l the t a r g e t i s s t a b i l i z e d to i n i t i a t e the measurements.  For these measurements i t i s not necessary to know the 2  a c t u a l number of deuterium atoms per cm  as long as the t a r g e t  t h i c k n e s s i s below a chosen v a l u e . For the a b s o l u t e c r o s s s e c t i o n measurements the s i t -  -89-  —  WATER  T O P T A R G E T CHAMBER  TO  COOLING DRIVING  ROTATING SEAL TARGET  MOTOR  VACUUM  DEPOSIT  BEAM  COPPER  DISC  C E N T E R OF R O T A T I O N OF THE ANGULAR D I S T R I B U T I O N T A B L E  Fig.  IV-10  Rotating target holder. The c o o l e d by c o n d u c t i o n t h r o u g h  copper disc the a x i s S.  is  -90-  u a t i o n 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  a f t e r the e q u i l i b r i u m i s reached  can be estimated by measuring the neutron f l u x produced when "a deuteron beam i s used i n s t e a d of a p r o t o n beam.  Prom the know-  ledge of the D(d,n)-%e c r o s s s e c t i o n , the t o t a l charge c o l l e c t e d by the t a r g e t and  the e f f i c i e n c y of the neutron d e t e c t o r  can determine the. amount of D present  one  i n the t a r g e t , .  These measurements c o u l d be checked as f o l l o w s .  Start-  i n g w i t h a f r e s h t a r g e t the neutron f l u x i s measured u s i n g a D beam of say  50 nA„  I t i s b e l i e v e d that the t a r g e t w i l l  d e t e r i o r a t e u s i n g t h i s low beam c u r r e n t .  Therefore  compare the amount of deuterium as determined by the  one  not could  neutron  f l u x w i t h the amount of deuterium as determined by the weight of the p o l y e t h y l e n e  layer.  Plans are underway to c a r r y out the t a r g e t t e s t i n g w i t h the o b j e c t i v e of making the absolute  c r o s s s e c t i o n measure-  ments i n the near f u t u r e . When the a b s o l u t e over a range of e n e r g i e s  c r o s s s e c t i o n s have been measured  i t should  be p o s s i b l e t o make b e t t e r 2  e s t i m a t e s of the amplitudes of the three body wave f u n c t i o n .  4a  n  d  D  components of  With c o n t i n u i n g development on  the  the  t h e o r e t i c a l s i d e i t should t h e n be p o s s i b l e t o r e l a t e these  -91-  amplitudes to spin-dependent and tensor p a r t s of the two-nucleon force.  BIBLIOGRAPHY A J 59  F. A j z e h b e r g - S e l o v e and T, L a u r i t s e n , "Energy L e v e l s i n L i g h t N u c l e i " , North-Holland P u b l i s h i n g Co. Amsterdam, ( 1 9 5 9 ) .  AR 54  W.R. A r n o l d , J.A. P h i l l i p s , G.A. Sawyer, E . J . S t o v a l l J r , and J o L „ Tuck, Phys. Rev., 21 U 9 5 4 ) ^ 3 .  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Erdman and J.R. Rev. S c i . Instrum., ,33.(1962) 1111.  WI  39  E . J . W i l l i a m s , Proc. Roy.  WI  52  D.H.  WO  52  E . J . Woodbury and W.A.  Soc., 16_2 ( 1 9 3 9 )  W i l k i n s o n , P h i l . Mag.,  4j (1952)  193. MacDonald,  531.  659.  Fowler, Phys. Rev.,  8j> ( 1 9 5 2 )  51.  WO  66  YU 6 7  W.  Wolf 1 1 , R. Bosch, J . Lang, R. M i l l l e r and P. Phys. L e t t . , 2 2 (I966) 7 5 .  H.P.  Y u l e , N u c l . I n s t r . and Meth., ^±  (I967)  Marmier,  6l.  APPENDIX A THE ANGULAR DISTRIBUTION OP THE 11.7 MeV REACTION B(p "S) C 1:L  GAMMA RAYS FROM THE  12  9  As a check on the procedure f o l l o w e d i n the d e t e r m i n a t i o n of the angular d i s t r i b u t i o n of the r e a c t i o n D ( p , t f ) % e , the angular d i s t r i b u t i o n of the 11,7 MeV reaction  BCp.tf)  gamma-rays from  the  C was measured and the r e s u l t compared w i t h  measurements from p r e v i o u s work. T h i s measurement checks  the behavior of the angular  d i s t r i b u t i o n t a b l e and the c o r r e c t i o n s due to the a b s o r p t i o n i n the t a r g e t h o l d e r as w e l l as the i t e r a t i v e l e a s t  squares  method used i n the a n a l y s i s of the data, 11  The r e a c t i o n  12  B(p,"tf)  a t a p r o t o n bombarding energy of 163 KeV. formed a t t h i s resonance and decays  The  7  (T=  C has a sharp resonance level in  KeV)  C  has an e x c i t a t i o n energy of l6„ll  MeV  by e i t h e r a l p h a - p a r t i c l e or gamma-ray emission.  The decay scheme i s shown i n F i g . A - l which i n d i c a t e s o n l y the l e v e l s of i n t e r e s t . A  1:L  B  t a r g e t 25 yUg/cm  i n c h t h i c k copper backing  2  t h i c k , d e p o s i t e d on a  ( o b t a i n e d from the Atomic  Research E s t a b l i s h m e n t , H a r w e l l , England) was 100A  of 170 KeV  protons.  Energy  bombarded;-with  The c o n d i t i o n s of the beam on the  t a r g e t were s i m i l a r to the D(p,"tf)%e runs. on t a r g e t h o l d e r "TA"  0.010  ( F i g . II-3)  -95-  The t a r g e t was  and the d e t e c t o r t a r g e t  mounted arrange-  -96-  ment used Is shown i n P i g . I I I - l . i n both c o n f i g u r a t i o n s .  At E  The same t a r g e t was used  = 170 KeV w i t h the t a r g e t  placed  a t 45° w i t h r e s p e c t t o the incoming beam, the energy l o s s by the beam i n the t a r g e t was about 21 KeV and the R.M.S. m u l t i p l e s c a t t e r i n g angle was l e s s than  1.1°.  ^11.7i 16.11  • mm  A-  2" U  9.63  B  +  0.16  P  15.958  (1") 7.375 8Be + OC  4.43  12, 12 Pig. A - l :  Some energy l e v e l s i n the C nucleus from AjzenbergSelove and L a u r i t s e n , (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 o f the 1 2 * i n t o an a l p h a p a r t i c l e and Sfie as shown. (1) Assignment g i v e n by A.G. Gregory (GR 6 l ) . C  A t y p i c a l gamma-ray spectrum taken w i t h the d e t e c t o r at  i Q ^ = 135° i s shown i n P i g . A-2 where the 6.5 MeV  11 peak from the competing r e a c t i o n F i g . A-3 shows a t y p i c a l background  gamma-ray  8  B(p,tf<*) Be i s i n d i c a t e d . spectrum f o r d e t e c t o r #1.  #1  NUMBER  -.000  40.000  OF  COUNTS  80.000  (X1•  120.000  1  )  160.000  200.0001  •  4 -  I  t  s. . .  ho CD  3 3  01  I  -\ 01  mg Z  ^  1  a a •  TD  4  °K (1.462 MeV)  4 + 4  CD  4  H  4  D  rn m CD  m  II  TD  —»  CO  -C~ TD  o 11  c  3  B(p,tfo<) Be 8  E^= 6.5 MeV  %  rn - CO  a a a  a a a a i  4  + 4  +  4  a>  +  (V)  a a a  u i  m •< II  —•  a # c 1 o i  3  n> <  —  CO  o ?  TD  m  - o  rvj  o  -L6-  —  o —  —  O  CD  -  ,000 I  N U M B E R OF COUNTS (XIO UD.O0O 80.000 L20.000 I I I  3  1  LB0.0OD I :  2O0.00D| I  a I  AO -n uo — 0) • >  a a a  n  IQ  7T  ID  I  RaTh  K (1.462 MeV)  (2.614 M e V )  -1  O  ro c —  3  Q .  l/l  vn "O co a> n ^  r+  fD <  -1 C  \ 3 o • 3~  QJ 3 3  m  ZJ3  -( IT  n> n> •  <T> 3  (D -I  n ai cr ai  •0° m k  a a TO  o 3  i n  o o  CD m  a i a a a  X)  fl> n  TO  >  c  3 QJ 3  Q.  CD >  a a a  o  (7> 70 O  • a  -86-  -99-  Th e s p e c t r a were a n a l y z e d f o l l o w i n g the procedure desc r i b e d i n Chapter I I I , g r a t e d from 7.5 peak.  MeV  Here, however, the s p e c t r a were i n t e -  to 13 MeV  The lower l i m i t was  and below the 16.11 MeV F i g . A-2.  c o v e r i n g the 11.7 MeV  gamma-ray  chosen to be above the 6„5 MeV  peak  peak which i s o f f the curve shown i n  The r e s u l t s are summarized i n Table A - l u s i n g the  same heading as d e s c r i b e d i n Chapter I I I .  The a b s o r p t i o n c o e f -  f i c i e n t s used i n the c o r r e c t i o n due to the t a r g e t h o l d e r abs o r p t i o n 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 11.7 MeV  gamma-rays i s about 3.3$  b u t i o n of the 16.1 MeV  (CR 56)  to the  the o v e r a l l  contri-  gamma-rays to the energy range  counted  f o r angular d i s t r i b u t i o n measurement o f the 11.7 MeV  gamma-rays  i s l e s s than 0.3$ and was d i s r e g a r d e d . The e x p e r i m e n t a l data were f i t t e d to the f o l l o w i n g function;  U - 1)  W(e) = [Y_ B Pe] (\*-t*) e  with  /0  -45° <  M Q  Q  < 50°  60° i 9 4135°  where P-^ = P-^ cos(0+6 ) and 9  6  are the Legendre  polynomials and K  the parameters d e f i n e d i n Chapter I I I .  f i t t i n g procedure o u t l i n e d i n Chapter I I I was  The l e a s t  squares  f o l l o w e d and the  i  9i  0  A  B  17811  16767  50400  T(sec)  C  D  E  F  G  H  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 E =11.7 MeV #-ray at E =170 KeV 5  -101-  results  a r e 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 The d a t a was f i t t e d  (a + b cos 9).  to e q u a t i o n ( A - l ) i n which the parameters  Bj, B^, and B^ were s e t equal to zero.  The r e s u l t o f t h i s i s ,  shown i n row 2, o f Table A-2. t  In a d d i t i o n ,  the experimental data were a l s o  to the same f u n c t i o n ( A - l ) i n c l u d i n g  the  term.  fitted  Although no  P^ term was expected, a term of t h i s form was i n c l u d e d i n the analysis  as a check on the alignment and the f i t t i n g  The r e s u l t s  procedure.  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 w i t h an e r r o r g r e a t e r than 100$.  The 'X t e s t a l s o  indicates  t h a t a good f i t i s obtained  without a P^ term. The v a l u e s obtained f o r 6  are a l s o undefined;  This  o i s to be expected and  s i n c e the angular d i s t r i b u t i o n i s r a t h e r  the accuracy o f z e r o i n g the angle s c a l e  the A8  Q  which r e s u l t s  from the measurement.  flat  was smaller, than The f i t o b t a i n e d  f o r an angular d i s t r i b u t i o n of the form B P + B P i s shown o o d c i n F i g . A-4. 0  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 terms o f F Chapter  1  = E(A.j/A ), f o l l o w i n g the procedure  IV, a r e shown i n Table A-4.  d i s t r i b u t i o n i s shown i n F i g . A-5„ factors  0  expressed i n outlined i n  The c o r r e c t e d The c a l c u l a t e d  angular smoothing  Q, f o r 11.7 MeV gamma-rays a r e 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  Table A-2 :  0  0  1612  155  0.006  0.025  0.117  0.011  9.43  B(p,tf) C angular d i s t r i b u t i o n l e a s t squares f i t parameters and Chi-squared t e s t .  13  0.74  -30.000  -.ODD  30.000  60-000  RNGLE Fig.  A-4  :  Angular 1 1  B(p,tf)  distribution 1 2  C  at  E  p  =  90.000  120.OOO  150.000  (CM.)  of  the  11.7  170  KeV  (case  MeV #2)  gamma-rays  from  the  reaction  180.000  o  o o  B(p,*)  1 1  CD-I  E =  170  1 2  C  KeV  2 W(6)=1+(0.16±0.02)COS 6 P  O  CD .  LU I—  o i  LU :>  i— a: —i  Lxjg O C f M .  a o o -30.0QD Fig.  A-5  1 30.000  -.000  1 6D.DQQ  ~ l  90-000  ~ l  RNGLE ( C M . ) Angular  distribution  at  170  E  =  KeV  (case  of  the  §2)  11.7  with  11  MeV g a m m a - r a y s  detector  180.000  150.000  120.000  finite  from solid  the  reaction  angle  12 B(p,"tf)  correction  C  included,  -105-  Table A-3 :  Q  Smoothing f a c t o r s c a l c u l a t e d a t Ey = 11,7 MeV f o r the d e t e c t o r geometry shown i n F i g . I I - 6 .  1  0  1  2  l  1.00000  0.98860  O.96606  Table A-4 :  Legendre p o l y n o m i a l c o e f f i c i e n t s c o r r e c t e d f o r f i n i t e s o l i d angle of the d e t e c t o r . F, i s the e x p e c t a t i o n v a l u e of A / A |F, = E(A,/A ) and n  l o L l  P the Chi-squared text. AF  l  P  \  1  l  o  j  t e s t r e s u l t as d e f i n e d i n the F r  2  AP  2  "I  P  2  #1  0.00,1  0.012  1390  0.103  0. 011  10.2  67  #2  0  0  0  0.103  0.010  10.2  74  E  P (KeV)  170  In order t o compare the r e s u l t o b t a i n e d here w i t h the results  of other workers, the angular d i s t r i b u t i o n was  i n terms o f  a(l+b/a cos 9)  expressed  w i t h the r e s u l t shown below:  P r e v i o u s Work (KE 51)  W(Q) = 1 + (0.15 - 0.03)  (HU 52)  W(Q) = 1 + (0.23 t  o.04) c o s 9  (GR 54)  W(0) = 1 + (0.26 t  0.01)  (GR 56)  I o/I Q  9 0  o  cos 8  170 KeV  2  2  170 KeV  E  175 KeV  cos G 2  = 1.18 i 0.02  = 168 KeV  E  Present Work  w(8)  = 1 + (0.16 i 0.02) c o s 9 2  E  p  = 170 KeV  -106-  The r e s u l t of t h i s experiment  i s i n reasonable agreement w i t h  p r e v i o u s measurements except f o r the r e s u l t s (GR 5 4 ) .  of Grant e t . a l .  APPENDIX B THE ACCELERATOR AND Bo1.  The  MAGNETIC ANALYZER  Accelerator The  DCp.o'^He measurements were made u s i n g a h i g h  r e n t a c c e l e r a t o r c o n s t r u c t e d by the author and duoplasmatron i o n s o u r c e and  based on an ORTEC  A b r i e f d e s c r i p t i o n of the apparatus  i t s main c h a r a c t e r i s t i c s i s g i v e n below.  B.l.l.  The  Ion Source and E i n z e l Lens  The  i o n source,a m o d i f i e d Von Ardenne (AR  matron, and E i n z e l l e n s are shown i n F i g . B - l . (ORTEC Model 504) E i n z e l l e n s and The  cur-  system was  The  56)  duoplas-  source  system  c o n s i s t s of the duoplasmatron (Model 350),  the power s u p p l i e s and  c o n t r o l s to operate  mounted i n a aluminum box  supported  on  power  both.  insulating  posts so t h a t i t s p o t e n t i a l c o u l d be changed w i t h r e s p e c t ground by an e x t e r n a l 150 KV  the  to  supply.  In order to o b t a i n a l a r g e i o n c u r r e n t from the duoplasmatron source h i g h , 0.2  mm  the pressure  of Hg.  i n the a r c chamber has to be q u i t e  On the other hand the beam must be i n j e c t e d  i n t o a high vacuum r e g i o n which means t h a t the e x t r a c t i o n c a n a l between the two  r e g i o n s must be of s m a l l diameter.  In order to  get a l a r g e beam from t h i s s m a l l hole the duoplasmatron concent r a t e s a s m a l l dense plasma a t the e x i t h o l e , 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 . produces a magnetic f i e l d between the i n t e r m e d i a t e  -107-  The  coil C  e l e c t r o d e IE  g.  B-1  :  Duoplasmatron ion s o u r c e and E i n z e l lens s c h e m a t i c view but a s i m p l i f i e d v e r s i o n .  system.  This  is  not  the  actual  -109-  and  the anode A„  T h i s 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 a r c chamber to the tungsten a l l o y e x t r a c t o r c a n a l EC  i n the anode.  ions are drawn from the plasma (on the opposite to the a r c chamber) by the e l e c t r i c f i e l d e l e c t r o d e EE and  Positive  s i d e of the anode  between the  extractor  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  d e n s i t y of the beam l e a v i n g the e x t r a c t i o n r e g i o n there i s a tendency f o r the beam to d i v e r g e r a p i d l y due fects.  To reduce t h i s  to space charge e f -  "blow-up" e f f e c t and minimize the l o s s of  beam to the e x t r a c t o r e l e c t r o d e the e x t r a c t i o n v o l t a g e needs to be r e l a t i v e l y high, t h a t i s approximately 10 KV E i n z e l l e n s then f o c u s s e s beyond the l e n s .  The  or more.  The  the d i v e r g i n g beam to a p o i n t P  just  beam i s then s u i t a b l e f o r i n j e c t i o n i n t o  the a c c e l e r a t i n g tube. On s t a r t i n g the discharge power supply and  provides  the f i l a m e n t .  i n the a r c chamber, the' arc  approximately 350 V o l t s between the-anode  Before  the a r c s t r i k e s a s m a l l e l e c t r o n c u r -  r e n t from the hot f i l a m e n t flows and r e t u r n s to the a r c supply  to the i n t e r m e d i a t e  through Rl„  Most of the a r c  supply v o l t a g e appears between the i n t e r m e d i a t e the f i l a m e n t and  electrode  and  t h i s s t a r t s the a r c which i n t u r n makes a l a r g e  i n c r e a s e i n the c u r r e n t through R l . of IE to f a l l  electrode  T h i s causes the p o t e n t i a l  towards the f i l a m e n t v o l t a g e and a dynamic e q u i -  l i b r i u m i s reached c a u s i n g most of the c u r r e n t from the ment to flow to the anode.  fila-  -110-  Th e a r c c u r r e n t , which tends to v a r y w i t h the gas or  w i t h the magnetic f i e l d ,  r e g u l a t e d power supply. approximately The  flow  i s kept constant by means of a c u r r e n t  The  i n i t i a l 350 V p o t e n t i a l drops  to  80 V under normal o p e r a t i n g c o n d i t i o n s . p l a t i n u m gauze f i i a m e n t i s i n i t i a l l y  a suspension of CaCO^. by a p p r o x i m a t e l y  T h i s carbonate  coated w i t h  i s converted to the  oxide  twenty f o u r hours of f i l a m e n t h e a t i n g under  vacuum. A thermal l e a k (WH of  62)  i s used to c o n t r o l the f l o w  gas from a h i g h p r e s s u r e storage b o t t l e to the  ionization  chamber. Heat i s e x t r a c t e d from the magnet c o i l s and the f i l a ment by a l i q u i d c o o l a n t c i r c u l a t i n g around the c o l l s .  PREON  113  c o o l a n t flows i n a c l o s e d c i r c u i t c o n s i s t i n g of a pump, a waterc o o l e d heat exchanger and a r e s e r v o i r .  The c o o l a n t a l s o removes  heat from the whole h i g h v o l t a g e t e r m i n a l .  A cut-off  switch  removes a l l power from the source i f the c o o l a n t p r e s s u r e or f l o w r a t e f a l l below p r e s e t v a l u e s . B.1.2.  The A c c e l e r a t i n g Tube The  to  i o n source E i n z e l l e n s system was  an a c c e l e r a t i n g tube.  The  beam.  F i g . B-2  directly  purpose of the tube i s to c o n v e r t  a g e n e r a l l y d i v e r g e n t low energy h i g h e r energy  coupled  beam i n t o a w e l l c o l l i m a t e d  shows a beam d i v e r g i n g from P  and t r a v e l l i n g through a z e r o - f i e l d r e g i o n u n t i l i t reaches  the  R1  ig.  B-2  :  Schematic units  diagram  shown  in  of  this  I  the  1  accelerator  diagram  by  the  showing  numbered  the  beam t r a j e c t o r y .  squared  boxes  are  The  listed  in  electronic Table  B-1.  -112-  first  electrode  o f the tube where i t i s converged.  The beam  then t r a v e l s through an approximately c o n s t a n t - f i e l d r e g i o n f o l l o w i n g a n e a r l y p a r a b o l i c path throughout the l e n g t h of the tube.  F i n a l l y i t i s diverged  enters  a second z e r o - f i e l d  a t the e x i t o f the tube as i t  region.  T h i s k i n d o f a c c e l e r a t i n g s t r u e t u r e k n o w n a s , a three t  element system (EL 53)» has a converging a c t i o n as the beam passes from the f i e l d  f r e e r e g i o n i n t o the uniform f i e l d  the tube and a d i v e r g i n g a c t i o n as the beam leaves enter a second f i e l d f r e e r e g i o n .  the tube.to  The t o t a l e f f e c t i s t o con-  verge the beam s i n c e the beam enters energy and leaves  inside  the tube a t low k i n e t i c  a t a higher k i n e t i c energy, so t h a t the  p o s i t i v e a c t i o n o f the i n p u t l e n s i s g r e a t e r  than the negative  a c t i o n o f the output l e n s . A s e c t i o n of an o l d a c c e l e r a t i n g tube from the Chalk R i v e r Van de G r a a f f a c c e l e r a t o r was used. teen saucer shaped e l e c t r o d e s  I t consists of s i x -  with uniformly  increasing  inside  diameter separated by one i n c h t h i c k g l a s s i n s u l a t i n g r i n g s . The  electrode  shape prevents the beam from "seeing"  thus m i n i m i z i n g the b u i l d - u p  the g l a s s ,  on the g l a s s of any contamination  s c a t t e r e d by the beam and p r o t e c t s  the metal to g l a s s vacuum  s e a l s from exposure t o s c a t t e r e d beam. For p r a c t i c a l reasons i t was d e s i r a b l e to have the tube as s h o r t as p o s s i b l e .  Because the column had some cracks  g l a s s i n s u l a t o r s , 1 2 KV was c o n s i d e r e d  i n the  to be the maximum safe  -113-  potential mum  d i f f e r e n c e between i n d i v i d u a l e l e c t r o d e s .  a c c e l e r a t i n g voltage  sixteen electrodes. e l e c t r o d e was The  8  The  of 180 KV  then r e q u i r e d a t o t a l of .  diameter of the hole i n the  first  cm.  d i s t a n c e between the f i r s t  e r a t i n g tube and  A maxi-  e l e c t r o d e of the a c c e l -  the l a s t e l e c t r o d e of the E l n z e l l e n s was  to be not too c r i t i c a l , because the f o c a l d i s t a n c e  (exit  thought point)  of the E i n z e l l e n s c o u l d be changed by v a r y i n g the p o t e n t i a l in  the l e n s .  first  However, there i s a maximum d i s t a n c e a t which the  e l e c t r o d e can be p l a c e d , t h a t i s , when the diameter of  beam equals  the i n s i d e diameter of the e l e c t r o d e .  d i v e r g i n g from the of 4-°  With a beam  e x i t p o i n t o f the E i n z e l lens a t a h a l f angle  the maximum d i s t a n c e f o r an e l e c t r o d e , 8 cm  i s approximately 60 cm. t r i a l and  the  i n diameter,  To a r r i v e a t the optimum d i s t a n c e  e r r o r method was  used.  Due  to the f a c t t h a t i t was  d e s i r a b l e to have the whole assembly as s h o r t as p o s s i b l e , t e n t h of the maximum d i s t a n c e was  a  chosen.  one-  A l s o there i s appre-  c i a b l e a b e r r a t i o n i f the whole diameter i s used. The  a c c e l e r a t i n g tube was  t e s t e d w i t h the  and E i n z e l l e n s o p e r a t i n g under normal c o n d i t i o n s .  i o n source In  the  energy range 100  to 180 KeV  a n e a r l y p a r a l l e l beam, 3 to 6  i n diameter, was  obtained.  However, below t h i s energy i t was  mm  necessary to reduce the e f f e c t i v e number of e l e c t r o d e s to o b t a i n similar focusing c h a r a c t e r i s t i c s . f a c t t h a t by s h o r t e n i n g  T h i s can be e x p l a i n e d  by  the  the e f f e c t i v e l e n g t h of the tube, the  g r a d i e n t between the r e m a i n i n g e l e c t r o d e s was  i n c r e a s e d to a  -Up-  value s i m i l a r to the one used i n the h i g h energy range.  The  s h o r t e n i n g can be done on e i t h e r s i d e of the tube, but i t was found t h a t b e t t e r r e s u l t s can be obtained i f i t i s done on the ion  source s i d e . The  h i g h v o l t a g e was  d i s t r i b u t e d u n i f o r m l y along  a c c e l e r a t i n g tube by means of 15 (20 Mn,  the  5 W each) h i g h v o l t a g e  r e s i s t o r s a t t a c h e d to the e l e c t r o d e s i n a z i g - z a g f a s h i o n and p l a c e d above the tube.  To prevent  corona from the somewhat  irre-  g u l a r r e s i s t o r c h a i n , f i v e f l a t aluminium r i n g s were e v e n l y : d i s t r i b u t e d a l o n g the tube.  With the maximum h i g h v o l t a g e  a p p l i e d to the tube, no corona was  observed.  Because of the s h o r t l e n g t h of the a c c e l e r a t i n g tube and the r e l a t i v e l y l a r g e i n s i d e diameter the conductance of the tube was  of the e l e c t r o d e s , ,  adequate f o r the gas  l o a d from  the i o n source. A s h o r t " e x t e n s i o n tube" couples the a c c e l e r a t i n g tube to the a n a l y z i n g magnet and provides a c o n n e c t i o n to the vacuum system.. T h i s tube a l s o holds a p a i r of water c o o l e d tantalum istics B.l.3.  beam choppers which are used to check the c h a r a c t e r -  of the beam before i t i s analyzed. High V o l t a g e A d.c. UNIVERSAL VOLTRONICS Model BAL-130-14 power supply  was  used to p r o v i d e the main a c c e l e r a t i n g v o l t a g e .  a c o n v e n t i o n a l s o l i d s t a t e C o c k r o f t & Walton v o l t a g e  I t contains doubler  -115-  i n one tank and a double LC f i l t e r u n i t i n a second tank. The power supply i s a b l e t o d e l i v e r 5 mA a t 150 KV, o r lk mA maximum a t 130 KV w i t h a 3$ R.M.S. r i p p l e . a t t e n u a t e d by a f a c t o r o f 1/100 by the f i l t e r The to  The r i p p l e i s  unit.  h i g h v o l t a g e was l a t e r i n c r e a s e d t o 180 KV i n order  cover the f i r s t resonance i n the r e a c t i o n  B(p,tf)  C which  occurs a t a p r o t o n energy o f 163 KeV i n the l a b o r a t o r y frame. The  e x t r a 30 KV was p r o v i d e d by a UNIVERSAL VOLTRONICS Model  BPE-32-5.5 power supply.  I t was p l a c e d i n the a c c e l e r a t o r  t e r m i n a l i n s e r i e s w i t h the main h i g h v o l t a g e s e t . This power supply c a n d e l i v e r 5.5 mA w i t h 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  s u p p l i e s a.c. power t o the e l e c t r o n i c  equip-  ment i n the a c c e l e r a t o r t e r m i n a l . A c h a i n o f h i g h v o l t a g e low temperature  coefficient  r e s i s t o r s R2 ( F i g . B-2) t o t a l i n g 2000 Mil i s used t o determine the a c c e l e r a t i n g v o l t a g e  (beam energy).  The r e s i s t o r s ,  placed  under o i l i n a PIREX tube, a r e connected between the anode e l e c t r o d e o f t h e i o n source and the ground through a 20 y*A, 0.5$ t r a c k i n g microammeter. Fig.  The whole assembly was c a l i b r a t e d t o 1$.  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 e l e c t r o n i c u n i t s shown i n t h i s diagram  by the numbered square boxes a r e l i s t e d i n Table B - l .  -116-  Table B - l :  B.1.4.  Accelerator's electronic units  1.  F i l a m e n t a.c. supply  2.  Magnet d.c, supply  3c  Arc  4.  E x t r a c t i o n d . c supply  5»-  E i n z e l l e n s d.c. supply  6.  Booster d.c. supply  7.  High v o l t a g e d.c. supply  8.  I s o l a t i o n transformer 1 : 1  9.  Main i s o l a t i o n transformer 1 : 1  d„Co  supply  ( 0 - 3 0 A) ( 0 - 3 A) A)  (0-3  ( 0 - 3 0 KV) ( 0 - 6 KV)  ( 0 - 3 0 KV) ( 0 - 1 5 0  KV)  ( I s o l . 40 KV) ( I s o l . 2 0 0 KV)  The Vacuum System A 7 0 0 1/sec (@ 10"-> mm o f Hg) o i l d i f f u s i o n pump  p r o v i d e s vacuum to the machine.  I t i s coupled, through a water-  c o o l e d chevron r i n g "baffle and a l i q u i d n i t r o g e n t r a p , d i r e c t l y to the " e x t e n s i o n tube".  The f o r e - p r e s s u r e i s p r o v i d e d  a b a l l a s t tank, by an 80 l / s e c  through  (@ 1 0 " ^ mm of Hg) mechanical  pump.  The p r e s s u r e , under normal c o n d i t i o n s , w i t h t h e . i o n ,  source  "OFF", i s about 7 x 1 0 ' mm of Hg measured a t the  "extension B.1.5.  tube".  The S h i e l d i n g The components i n the a c c e l e r a t o r t e r m i n a l were assembled  on two s t e e l frames,  one i s o l a t e d a t the e x t r a c t o r p o t e n t i a l ( 3 0 KV)  w i t h r e s p e c t to the o t h e r . ceramic  Both frames a r e supported by f o u r  i n s u l a t o r s a t t a c h e d to another  tential .  s t e e l frame a t ground po-  -117-  To a v o i d corona the whole h i g h v o l t a g e enclosed  i n an aluminium s h i e l d i n g box.  assembly was  The c o n t r o l s , s i t u a t e d  i n s i d e the box, are manipulated e x t B r n a l l y by means o f LUCITE rods.  A s e r i e s of meters, mounted i n s i d e the box behind a LUCITE  window, a r e used t o I n d i c a t e  the o p e r a t i n g  was observed when the f u l l v o l t a g e  conditions.  No corona  was a p p l i e d .  An aluminium f e n c e , supporting  a 1/8 i n c h t h i c k l e a d  sheet, was b u i l t around the a c c e l e r a t o r and a c c e l e r a t i n g tube, for  protection against  the high v o l t a g e  and to s h i e l d the room  from X - r a y s .  B.1.6.  Characteristics A t y p i c a l s e t of c o n d i t i o n s  under normal o p e r a t i n g  conditions  f o r a 160 KeV p r o t o n beam  i s shown i n Table B-2.  An  e x t r a c t o r channel 0.008 i n c h i n diameter was used throughout the experiment.  The machine was operated f o r continuous p e r i o d s  to 76 hours without o b s e r v i n g performance. imately  up  any s i g n i f i c a n t change i n i t s ,  The f i l a m e n t was found t o have a l i f e  400 hours w i t h hydrogen gas.  of approx-  A p i c t u r e o f the a c c e l e r -  a t o r i s shown i n F i g . B-3 and the a c c e l e r a t i n g column i s shown i n F i g . B-4. B.2,  The Magnetic A n a l y z e r I n order t o a n a l y z e the n e a r l y p a r a l l e l beam produced  by the a c c e l e r a t o r , a 45° d e f l e c t i o n magnetic a n a l y z e r designed and b u i l t by the author.  was  38  I  FIG. B - 3 : VIEW OF THE ACCELERATOR. THE MAGNETIC ANALYZER IS SHOWN AT THE LEFT.  -120-  T y p i c a l a c c e l e r a t o r c o n d i t i o n s f o r a 160 KeV proton beam.  Table B-2 >:  0.66 A (approx. 0.2 mm of Hg  Thermal l e a k  i n the a r c chamber) Filament  26.0  A (approx. 30 W)  Arc v o l t a g e  88.0  V  Arc c u r r e n t  1.4  A  30.0  V  0.6  A  Intermediate  electrode  Magnet c u r r e n t  10.2  Extraction voltage  0.0  E i n z e l lens  V  300 0 y«AA  H* beam c u r r e n t  o  -6  8.7 x 10~  Vacuum  B.2.1.  KV  mm o f Hg  The Magnet The magnet can t r a n s m i t a ^He e b  a m  o f 200 KeV.  yoke has a c o n v e n t i o n a l C-shape w i t h two i d e n t i c a l c o i l s a t both s i d e s o f the magnet gap.  The placed  The pole t i p s were designed to  have a double f o c u s i n g e f f e c t on the beam i n the manner d i s c u s s e d by W. Cross  (CR 51).  The  c o n d i t i o n s f o r double " l i n e f o c u s i n g " ( t h a t i s ,  f o r c o n c e n t r a t i n g to a p o i n t a p a r a l l e l beam o f p a r t i c l e s which has a f i n i t e c r o s s s e c t i o n ) can be expressed  by the f o l l o w i n g  geometrical r e l a t i o n s h i p s : t<x* t  z  =  I [ t o - v ^ - S i ] 4. i / ( $ - C o t 6 i ) ]  ![M$- o - v(* -^m £  (B.2.1.  - 1)  ( 3 . 2 . 1 . - - 2)  -121-  where, f o l l o w i n g C r o s s ' n o t a t i o n , 1£ i s the image d i s t a n c e ( i n u n i t s o f the r a d i u s o f c u r v a t u r e 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 o f the pole t i p i i s the angle between the i n c i d e n t p a r t i c l e s to the edge o f the pole t i p ; s i m i l a r l y £ mean p a r t i c l e ; and $ i s the d e f l e c t i o n i n the uniform f i e l d .  The equations  i  s  2  f  o  and the normal r  t  n  e  emerging  angle of the mean p a r t i c l e  (B.2.1.  - 1) and ( B . 2 . 1 .  - 2)  are v a l i d p r o v i d e d the pole gap i s s m a l l compared to the l e n g t h and r a d i u s of c u r v a t u r e o f the p a r t i c l e ' s magnetic f i e l d . and of  path i n the uniform  F i g . B-5 shows the shape of the p o l e t i p chosen  the t r a j e c t o r y  of the mean p a r t i c l e , where f i s i t s r a d i u s  curvature.  F i g . B-5 s  View o f the pole t i p I n the h o r i z o n t a l plane o f d e f l e c t i o n , (B p e r p e n d i c u l a r t o the page), and t r a j e c t o r y of the mean p a r t i c l e .  -122-  mlnimum i n to +12°.  I t was d e s i r a b l e to have 1" as l a r g e as p o s s i b l e . o the e q u a t i o n B-2 occurs f o r 6^ approximately Taking t h i s value f o r 6 ; 1  The  equal  the f i n a l d e s i g n parameters  were:  45° +12° +11° 9» 2.3 15.0 d B.2.2.  The Power  cm  3.175 cm ( a i r gap) Supply  A r e g u l a t e d d.c. power supply was b u i l t .  The  circuit  i s a m o d i f i e d v e r s i o n of the 100 A power supply used to d r i v e the U.B.C. spectrometer  (SM 6 l ) .  I = 20 A (max.) ; E = 9 0 V ; r i p p l e  I t s main c h a r a c t e r i s t i c s a r e : = 0.05$ (R.M.S.),  i t y was b e t t e r than 0,3$ over an 8 hour p e r i o d .  The  stabil-  APPENDIX C THE ENERGY OF THE GAMMA-RAYS FROM THE REACTION D ( p , t f ) % e AND THE COORDINATE SYSTEM TRANSFORMATIONS The energy o f the gamma-rays i n the c e n t e r of mass system i s g i v e n by;  where E  i s the energy  of the incoming protons i n the l a b o r a t o r y  system.  Using the r e l a t i v i s t i c  t r a n s f o r m a t i o n e q u a t i o n s , the  gamma-ray energy i n the l a b o r a t o r y system i s found to be:  1 - |2> cos 6  U  ie e m i t t e d ggamma-ray w i t h r e s p e c t to where 6^ i s the angle o f the the Incoming p a r t i c l e i n the l a b o r a t o r y system and  '  M +ho h  V  ripe  3  T h i s r e a c t i o n has a Q = 5.4-9 MeV.  At E  = 160 KeV  the t h i r d term i n the e q u a t i o n ( C - l ) , which corresponds to the n u c l e a r r e c o i l energy, i s n e g l i g i b l e .  The e n e r g i e s o f the  gamma-rays as a f u n c t i o n of the i n c i d e n t proton energy and as a f u n c t i o n o f the angle of o b s e r v a t i o n , computed f o r t h i s experiment,  a r e shown i n Table C - l .  The v a r i a t i o n o f the gamma-ray energy a t E  = 160 KeV  over the observed angles Is l e s s than 1.1$ (and l e s s than 1% a t  -123-  -124-  E  = 90 KeV).  In the computation  of the gamma-ray  (Chapter I I I ) t h i s v a r i a t i o n was Table C - l :  not taken i n t o  D(p TO^He gamma-ray e n e r g i e s a t E 0  and E  = 90 KeV  intensity  account, = 160  KeV  f o r d i f f e r e n t ang?es of o b s e r v a t i o n .  E*  E  (MeV)  P (KeV)  e =o°  e =90°  e =i35°  160  5.63  5.60  5.57  90  5.58  5.55  5.53  L  u  L  In order to o b t a i n the angular d i s t r i b u t i o n i n the c e n t r e of mass system (Chapter I I I ) the experimental data (Tables IIT-1 and I I I - 2 )  were a c c o r d i n g l y transformed u s i n g  the f o l l o w i n g equations:  Q'  =  tan"' (  \  SI*  Qt-  f^P *  cose -/2> L  and  1 (4-/2>co6 9,.) \ E  A P P E N D I X N U C L E A R  I N S T R U M E N T S  A N DM E T H O D S  D  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  CO.  LOW COST DEUTERATED P O L Y E T H Y L E N E TARGETS OF C O N T R O L L E D THICKNESS FOR HIGH CURRENT ACCELERATORS M. A . O L I V O and G . M. B A I L E Y  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) He 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 titaniumdeuteride, 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 polyethylene on carbon have been developed in this labora-. tory by Tripard and White ). We have applied their technique to prepare solid backed deuterated polyethylene targets and found them to have a number of advantages. These targets are relatively stable, have a well defined composition ( C D ) , and for the same 3  1  2  4  n  energy loss give less multiple scattering and a higher y-ray yield than deuteride targets. Targets were prepared by dissolving a weighed quantity 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 atmosphere. Tn the present case targets of about 40 /(g/cm were prepared on a 15 cm copper backing by dissolving 600 fig of the polyethylene in 1 g of xylene. Target performance has been compared with commercial 2  * Deuterated polyethylene ( > 9 8 % D ) obtained from Merck, Sharp and Dohme of Canada Ltd., Montreal, Canada.  100  160  100 BOMBARDMENT  TIME  IN  MINUTES  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 10 atoms/cm . Targets A and B correspond to commercial deuteride targets of equal thickness (nominally 280,ug/cm 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/cm 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 . 18  2  2  2  2  353 -125-  -126354  M.  A. O L I V O  A N D G. M.  BAILEY  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 <0>* Thickness Energy loss Target (,ug/cm ) (keV) (dea) 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. 71 10 2.8 x 10 280 ZrDi.s The present tests at 60 correspond to a beam current 40 32 2.8 x 10 (C2D )n li density of 0.3 mA/cm at the target. . . . The polyethylene targets are extremely simple to * The rms multiple scattering angle <8> has been calculated make and with practice one can judge a good target from the work of Williams ). from the uniformity of the surface. A reject target would have a noticeable shrinkage pattern on its surdeuteride targets by monitoring the 90° y-yield from the face. We have made as many as 30 targets in a day and D(p,y) He reaction with a 12.5 c m x l O cm Nal(Tl) had only two failures. Thickness variation across the crystal. In all cases the targets were clamped to a 1.6 mm surface (excluding the edges) of a target is typically 10% thick water cooled copper plate which was an integral but this could be improved with careful attention to the part of the target rod assembly. Protons of 160 keV, surface flatness and horizontal mounting of the backing collimated to give a target spot of 20 m m were used to and a controlled drying environment. A characteristic check target deterioration. The beam current variation of these targets is that they rapidly show a dark spot was less than 5% for these tests and a number of target even when bombarded with quite small beams. This spots were run to allow for possible bad thermal contact deposit, presumably carbon from breakdown of the with the cooled mount. The result of these tests are polymer, does not seem to affect the performance of the summarized in fig. 1. target, and has in fact proved useful in determining the The difference between curves A and B illustrates the profile of the beam spot. uncertainty in the composition of deuteride targets, Targets made by this technique are quite inexpensive which can contain anything from one to two atoms of compared with the commercial deuteride targets and deuterium per atom of zirconium. From these curves it can be made to any physical size. Further tests to reduce can be inferred that the deuteride targets give superior target deterioration are planned using a rapidly rotating yield and stability for a given deuterium content. How- target holder. ever, if the energy loss or the multiple scattering of the protons is of prime concern, the polyethylene targets References are superior. This is indicated in table 1. !)G. E. Tripard and B. L. White, Rev. Sci. Instr. 38(1967) 435. The rapid initial deterioration of the polyethylene ) E. J. Williams, Rev. Mod. Phys. 17 (1945) 217. TABLE 1  Deuterium content (atoms/ cm )  2  2  18  4  18  2  2  3  2  2  APPENDIX E MULTIPLE SCATTERING The mean square m u l t i p l e s c a t t e r i n g angle o f charged massive p a r t i c l e s i s g i v e n i n the centre  o f mass system by  (MO 6 5 ) :  <e > = * « «* U£-)  (E - i i  l  where K = <?T Nt Z  2  Z  e^ (K  2  + M g ) M~ 2  ±  of s c a t t e r i n g nuclei/cm , Z  and M  2  2  2  E~  ; Nt being the number  2  the atomic number and mass  of the s c a t t e r i n g n u c l e i , and Z^ and M^ the corresponding quant i t i e s f o r the i n c i d e n t p a r t i c l e s , which possess an energy E i n the l a b o r a t o r y -2.1  z£  /3  frame. Q j _ m  i  n  s  d e f i n e d by:  * (M +M ) / (a M y2M E). 1  2  Q  2  1  ( ! Z  Z  e 2  V ^ E M ^ O . ) (a).  0 min" ...«< 3.8 a  Q  (E -.2) Z2 e (M +M )/(2a M E) /3  ( Z ^ e / • n ^ 2 E M j ^ > l ) (b)  2  1  2  o  2  2  being the Bohr o r b i t r a d i u s , For the  (CD ) 2  n  compound the t o t a l R.M.S. m u l t i p l e  t e r i n g angle was c a l c u l a t e d u s i n g the f o l l o w i n g  scat-  expression:  [e] -V<2>-*<i> e  where  e  and ( © Q ^ are the mean square m u l t i p l e s a c t t e r i n g an-  g l e s due t o the deuterium and carbon atoms, r e s p e c t i v e l y .  To c a l c u l a t e  [QJ \ ^ 6 * ^ s  -127-  a  program was w r i t t e n u s i n g a  .-.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 test i s included  i n the program t o d e t e r m i n e w h i c h o f the two c o n d i t i o n s t o i n e q u a t i o n (E-2), (a) wave o r (b) c l a s s i c a l , The v a l u e s o f the m u l t i p l e  referred  applies.  s c a t t e r i n g a n g l e 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 o f t h e ' i n c i d e n t p a r t i c l e s remains  c o n s t a n t as t h e y t r a v e r s e  the  target.  The v a l u e s i n column 2 were o b t a i n e d a t an energy e q u a l t o the i n c i d e n t energy.  The e q u a t i o n ( E - l ) i n d i c a t e s t h a t the s c a t t e r -  i n g a n g l e i n c r e a s e s as the p a r t i c l e energy d e c r e a s e s .  Thus a  more r e l i a b l e e s t i m a t e f o r the m u l t i p l e s c a t t e r i n g a n g l e i s o b t a i n e d (column 6) a t an energy w h i c h i s the average thickness  of the t a r g e t .  That i s a t E  = E  -  AE/2.  over the  APPENDIX F THE REACTIONS  1 2  C (p, &") N AND 1 3  1 3  C(p tf J^N f  The maximum a v a i l a b l e energy f o r the gamma-ray s i t i o n s i n the r e a c t i o n  1 2  tran-  C(p.tf) N i s 1 3  which i s below the 2.95 MeV d i s c r i m i n a t i o n l e v e l used i n the computation o f the gamma-ray i n t e n s i t y (Chapter I I I ) . 12 cross  s e c t i o n , f o r 160 KeV protons, i s CT(  In the ^ C ( p , $ ) ^ N  The t o t a l 3  C)=4.6 x 10" yub. J  r e a c t i o n the maximum a v a i l a b l e energy f o r  the gamma-ray t r a n s i t i o n s i s  E* The t o t a l c r o s s  J ^ , , \  + Q = 77 0.160 + 7.546 = 7.  s e c t i o n , f o r 160 KeV p r o t o n s , i s i n t h i s case  G"( C)=2.5 x 1 0 " y ^ b (which i s comparable 13  for  5 heV  2  to the C(D)=8 x 10~ ^b 2  the i s o t r o p i c component i n the D(p,tf)^He r e a c t i o n a t the  same bombarding  energy).  The f i n i t e v a l u e of the c r o s s  i n d i c a t e s the p o s s i b i l i t y o f having gamma-rays o f t h a t  energy 1  or lower (due t o cascades to the v a r i o u s  l e v e l s i n the  which w i l l be p r e s e n t as an i n d i s c r i m i n a t e d  beam  section  lk \ N)  dependent  background t o g e t h e r w i t h the 5.6 MeV from the D(p,l$) He r e a c t i o n . 13 3  Because only  1.11$ of  J  0 i s p r e s e n t i n the n a t u r a l carbon  the t o t a l gamma-ray c o n t r i b u t i o n from the r e a c t i o n i n v o l v i n g t h i s i s o t o p e w i l l be p r o p o r t i o n a l  t o <T( C)x 1. llxK/100=2.8<K.10"" 13  compared with<T(D)«2,K=l6«K-129from the D(p,tf)^He, ( i n K were  2  -130-  i n c l u d e d the a p p r o p r i a t e u n i t s ; the f a c t o r 2 a r i s e s from the composition  of the t a r g e t ) .  T h i s means t h a t i n the gamma-ray C ( p . t f ) o n l y 0.1?#  y i e l d a r i s i n g from D(p,tf) He  and  due  I t s c o n t r i b u t i o n can t h e r e f o r e be  3  to the second r e a c t i o n .  1 3  will  be  neglected. The  t o t a l c r o s s s e c t i o n s f o r the r e a c t i o n s  " ^ C ( p . u " ) w e r e evaluated at 160 KeV  and  by H a i l and Fowler (HA 50). s e c t i o n was 12  and  128 KeV  data.  l6l  KeV  The  which was  value of 0"(  by B a i l e y and  used.  The  1 2  C ) = ( 5.0  126 KeV  to f i t the. 88: KeV  x 10~ y^b obtained 3  For the second  ~ C ) = a E~— 1exp(b, E~—.)  13 J  2  parameters a and b were found by f i t t i n g  by Lamb and Hester  obtained may  - 0.3)  S t r a t t o n (BA 50).  e x p r e s s i o n to the experimental and  found  52)  (LA 57).  The  was  found  KeV  c r o s s s e c t i o n so Woodbury  u s i n g the s i n g l e l e v e l B r e i t - W i g n e r , d i s p e r s i o n  formula determined the c o n t r i b u t i o n of the 554 KeV MeV  this  c r o s s s e c t i o n o b t a i n e d a t 114  be somewhat out from the a c t u a l v a l u e .  and Fowler (W0  broad 1.25  expression  e x t r a p o l a t i o n i s i n good agreement w i t h  r e a c t i o n the same energy dependance CT( was  given  In the f i r s t r e a c t i o n the c r o s s  exp(-6 E~^)  1  the experimental at  from the r e s u l t s  extrapolated using t h e i r semi-empirical  (T( C) =0.0024 E""  C(p,tf) -%  and  the  resonances to the c r o s s s e c t i o n a t 129 KeV.  t h a t n e a r l y 75% was  due  to these resonances.  It  However.  we  are here o n l y i n t e r e s t e d i n knowing the order of magnitude  of  the c r o s s s e c t i o n .  because:  The  e x t r a p o l a t e d v a l u e i s then  acceptable  -131-  the e x t r a p o l a t i o n was obtained  based on c r o s s  experimentally,  thus they i n c l u d e  c o n t r i b u t i o n from the resonances the e x t r a p o l a t i o n was only 30$ higher mental data was  sections the  and  done to an energy which i s  than the one obtained.'  i n which the  experi-  APPENDIX G CORRECTION DUE TO THE GAMMA-RAY ABSORPTION IN THE TARGET HOLDER Assume a p o i n t source per u n i t o f s o l i d angle  of gamma-rays whose i n t e n s i t y  i s I., Fig. G - l .  BEAM  ii  !  Pig.  G-l :  t d  v  Target h o l d e r a b s o r p t i o n c o r r e c t i o n t  1^ i s the t r a n s m i t t e d gamma-ray i n t e n s i t y i n t e g r a t e d over the s o l i d angle absorber.  of the d e t e c t o r and d the t h i c k n e s s of the  F o r s i m p l i c i t y i t i s assumed t h a t the cone subtended  by the d e t e c t o r cuts a t the t a r g e t h o l d e r i n SS». Then c =  COS  Q;  and  r = — cos  -I32-  p  r = cos  cos p  -133-  where  i s the t o t a l l i n e a r a t t e n u a t i o n  target holder  where  i s made o f d i f f e r e n t m a t e r i a l s ,  i s the t o t a l mass a t t e n u a t i o n  material,  ^  -  J  l  / Z  c o e f f i c i e n t f o r a given We have f i n a l l y  i  where the c o r r e c t i o n f a c t o r  The  I f the  then  i t s d e n s i t y and d^ i t s t h i c k n e s s .  h  holder  coefficient.  is  T a r g e t Holder "TA":  A c r o s s s e c t i o n of the t a r g e t  "TA" i s shown below:  WATER COOLING TARGET BACKING  1 0.3^ cm  (0.030 cm copper)  v//;///////;////////T777\ O  Q  Q  0  0.25 cm  O  O  Q  O  O  0.21 cm  O  O  O  TARGET HOLDER (copper)  -134-  T h i s was assumed t o be e q u i v a l e n t t o :  ^ — WATER l  !  IIIIIIIIIJ  III COPPER  The Target Holder "TB" :  A c r o s s s e c t i o n of the t a r g e t  h o l d e r "TB" i s shown below:  TARGET BACKING  (0.030 cm copper)  V/////////////////?////A  0.16 cm  TARGET HOLDER  (copper)  The d a t a used f o r D(p,^) He and B(p,o') C a b s o r p t i o n 3  c o r r e c t i o n s a r e shown i n T a b l e G - l .  11  1 2  An average gamma-ray  energy  of 5^58 MeV f o r the D ( p , l $ ) % e r e a c t i o n was chosen t o determine the mass a t t e n u a t i o n c o e f f i c i e n t s .  These v a r y over the energy  range o f the gamma-rays shown i n Table G - l by l e s s than 0 . 5 $ .  -135-  For the  B(p,"tf)  Efl = l l o 7  MeV.  C the c o e f f i c i e n t s were determined f o r  The mass a t t e n u a t i o n c o e f f i c i e n t s were obtained  from the work of G.W. Table G - l :  Grodstein  (GR 5 7 ) .  Target h o l d e r c o r r e c t i o n parameters f o r the D(pVtf) He and B(p,'S) C r e a c t i o n s . 3  11  1 2  "TB"  "TA" WATER D(M) H  COPPER  COPPER  D(p,*) H 3  3  e  e  (r>(cm /g)  0.0286  0 . 0206  0.0312  0.0308  0.0312  ^(g/cm )  1.0  1.0  8.92  8.92  8.92  0.124  0.124  0.2^9  0.249  0.189  2  3  d (cm) The  t a r g e t h o l d e r a b s o r p t i o n c o r r e c t i o n f o r h o l d e r "TA" 11  was checked w i t h  1 1 . 6 8 MeV gamma-rays from the r e a c t i o n  The r e s u l t s obtained are summarized i n Table Table G-2  : Q  ?  MEASURED FRACTION TRANSMITTED  0.9358  0.94  45°  0.9219  0.93-0.02  60°  O.8914  0.90 i 0.02  experimental  the c a l c u l a t e d a b s o r p t i o n s .  C.  G-2.  30°  The  B(p 0)  Target h o l d e r a b s o r p t i o n measurements f o r E^=11.7 CALCULATED FRACTION TRANSMITTED  12  v  - 0.02  r e s u l t s are i n good agreement w i t h  MeV.  • 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 t a r g e t or from the a c c e l e r a t o r d u r i n g the D ( p , t f ) % e experiment was  c o n s i d e r e d s i n c e 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 s u r r o u n d i n g m a t e r i a l s g i v i n g r i s e t o an e x t r a gamma-ray y i e l d .  Because  the gamma-ray  y i e l d from the r e a c t i o n D(p,"tf) He i s very s m a l l , s p e c i a l l y a t 3  0°,  a c a r e f u l check f o r such neutron c o n t r i b u t i o n s was  out.  At the bombarding  carried  e n e r g i e s c o n s i d e r e d here no d i r e c t neu-  t r o n s can a r i s e from the r e a c t i o n D(p,n)2p which has a t h r e s h o l d of 3.3 H. l ,  MeV. Neutrons A r i s i n g from the A c c e l e r a t o r The hydrogen used i n t h i s experiment was  I. 5 x 1 0 "  3  p a r t s of D;,o t h e r e f o r e deuterium was  n a t u r a l with  p r e s e n t i n the  mass two beam which s t r u c k i n s i d e of the a n a l y z i n g 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 g i v e r i s e to neutrons from the r e a c t i o n D(d,n) He. 3  A t h i r t y hours angular d i s t r i b u t i o n r u n was w i t h a 160 KeV beam h i t t i n g a c l e a n copper t a r g e t .  performed  This run  was made i n order to check whether a neutron background up a f t e r a long p e r i o d of r u n n i n g .  -136-  built  The c o u n t i n g r a t e was  found  -137-  to be independent of the p o s i t i o n of the d e t e c t o r #1, and e q u a l to  the c o u n t i n g r a t e without the beam,, so w i t h i n the accuracy of  the  D(p 'i)^Ee  the  deuterium h i t t i n g the magnet box.  H.2.  t  measurement no s i g n i f i c a n t c o n t r i b u t i o n came from  Neutrons A r i s i n g i n the Deuterated P o l y e t h y l e n e Targets As was mentioned  i n Chapter I I , neutrons may a r i s e  :  from the r e a c t i o n D(d,n) He caused by the deuterohs i n the p o l y 3  ethylene t a r g e t which have p i c k e d up energy by c o l l i s i o n s w i t h i n c i d e n t protons.  Neutron c o n t r i b u t i o n s of t h i s k i n d have been  observed f o r p r o t o n e n e r g i e s below 500 KeV when heavy i c e t a r g e t s  bombarding  (SE 59).  A d i r e c t d e t e r m i n a t i o n of the number o f neutrons produced would not g i v e 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 N a l c r y s t a l f o r d e t e c t i n g neutrons was  not  known.  Furthermore, because the neutrons w i l l  be-scattered  i n the s u r r o u n d i n g m a t e r i a l s i t would be d i f f i c u l t t o e v a l u a t e how many w i l l enter the c r y s t a l .  A f u r t h e r d i f f i c u l t y -is - t o  e v a l u a t e how many of those gamma-rays which a r i s e from the i n t e r a c t i o n of the neutrons i n s u r r o u n d i n g m a t e r i a l s a r e s c a t t e r e d i n t o the c r y s t a l . Because  o f these d i f f i c u l t i e s  the shape o f the-spectrum  from the d e t e c t o r when bombarded w i t h neutrons was measured and compared to the gamma-ray s p e c t r a from the r e a c t i o n D(p,^) He. 3  The neutrons were o b t a i n e d from the r e a c t i o n D(d,n)^He,  -138-  by bombarding  a deuterium gas t a r g e t w i t h 876 KeV deuterons from  the U.B.C. Van de G r a a f f a c c e l e r a t o r . and s h i e l d i n g geometry  U s i n g the same c o l l i m a t o r  as f o r the D(p,tf) He runs the d e t e c t o r 3  was p l a c e d a t 0° w i t h r e s p e c t to the incoming beam, w i t h the f r o n t f a c e of the c r y s t a l 20 cm from the c e n t r e o f the gas target.  The t a r g e t c o n t a i n e d a O.83 cm beam path i n deuterium  gas a t 200 mm of Hg p r e s s u r e w i t h a 127 micron N i window. The spectrum shown i n P i g . H - l was o b t a i n e d a f t e r s u b t r a c t i o n f o r a t o t a l charge of 30  background  d e l i v e r e d to "the t a r g e t  i n a f o u r minute r u n a t an average c u r r e n t o f about 135 nA. The maximum k i n e t i c energy a v a i l a b l e f o r the knockon deuterium atoms i s E (max.) = 8/9 E D  T h e r e f o r e , f o r 160 KeV protons we have E  (head on c o l l i s i o n ) . D  = 142 KeV.  The  angular d i s t r i b u t i o n o f the neutrons from the r e a c t i o n D(d,n) He 3  a t a bombarding  energy o f E ^ = 142 KeV Is a p p r o x i m a t e l y i s o t r o p i c .  The c r o s s s e c t i o n f o r the i s o t r o p i c component i n the r e a c t i o n D(p,T£) He 3  to 0.07 yub a t E  p  ranges from approximately 0.08 M.b a t E =£60 KeV  = 90 KeV (GR 62 ; GR 63) w h i l e the c r o s s  section  f o r the r e a c t i o n D(d,n) He v a r i e s from approximately 27 mb a t 3  E„ = 142 KeV t o 12 mb a t E~ = 80 KeV (AR 54).  Because  the c r o s s  s e c t i o n f o r the r e a c t i o n D(d,n) He f a l l s more r a p i d l y than the 3  D(p,*tf) He the comparison was made w i t h the D(p,lJ) He d a t a 3  3  o b t a i n e d a t 160 KeV w i t h the d e t e c t o r a t 0° where the gammar a y y i e l d i s minimum.  I f the neutron background does not show  any e f f e c t a t t h 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-  -140-  at  90 KeV. I t should be mentioned here t h a t the energy of the  neutrons from the gas t a r g e t a t 0° f o r E energy of 3 . 9 9 MeV, the  D  = 8?6 KeV,  have an  while the energy of the neutrons l e a v i n g  p o l y e t h y l e n e t a r g e t s a t 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 d e t e c t o r does not change a p p r e c i a b l y w i t h neutron energy over t h i s range. Pig.  H-2  shows the gamma-ray spectrum from the r e a c t i o n  D(p,tf) He taken a t 0° f o r E 3  Fig.  H-3  shows the 0°  p  = 160 KeV  (Table I I I - 2 ,  i=3)..  spectrum w i t h the background removed.  I t was o b t a i n e d by s u b t r a c t i n g the background spectrum shown i n Fig.  I I I - 2 when i t was n o r m a l i z e d to the same r u n n i n g time as  f o r - t h e 0° r u n .  The s t a t i s t i c a l e r r o r s i n the low energy chan-  n e l s look v e r y l a r g e .  However, t h i s i s due to the f a c t  that  they correspond to s m a l l d i f f e r e n c e s between l a r g e numbers. I t i s more convenient to remove t h i s  statistical  s c a t t e r b e f o r e comparing t h i s spectrum w i t h the D(d,n) He 3  one.  The method used to f i l t e r out the s t a t i s t i c a l  f o l l o w s the technique  d e s c r i b e d by H.P.  fluctuations  Yule (YU 67).  It i s  based on the l e a s t squares f i t t i n g of the e x p e r i m e n t a l , p o i n t s (number of counts i n each channel) to a power f u n c t i o n over a s m a l l r e g i o n o f the o r i g i n a l d a t a . Let  N. be the number o f counts i n the channel i .  X ID D(p,tf) He 3  9 = 0°  o o o  1  d-l  E = P  160 KeV  CM  o ,  +  1  — o  + 1—  ~ZL  ZD  C_Jg o 11  + 4  .  +  +  + LA  OZ LU CO  + + + +.  210  +  O I  LA II  +  to  o.  o o o iiiiimiimiiuiiiiiiiii "1  -.000  Fig.  1.000 H-2  :  T 2.000  3.000  ENERGY LRB  D ( p , ^ ) ^ H e gamma-ray  spectrum.  U.OOO  (MEV]  5.000  6.000  7.000  o  X 1  (N_|  D(p,*) He 3  8 = 0 °° 1  O o o  a  Q .  E 160 KeV E = = U P P  (BACKGROUND  CO  r  (Ej -0.511) MeV  O o o  "1 + + +  +  ZD  + +  +  o Li_o +  LU  +  +  +  + +  +  +  E,  =  SUBTRACTED)  5-6  MeV  + +  + +  +  +  g o ZD<=> i  o o Q  o  03. I  i.oao  -.000 Fig.  H-.3  :  D(p,tf)^He  z.oao 3.000 ENERGY LRB gamma-ray  u.ooo (MEV)  s p e c t r u m shown  5.00Q  i n F i g . H-2 w i t h  6.000 the background  7.000 removed.  -143-  The  smoothed v a l u e of  g The constants a  i s d e f i n e d as S^,  (  V j  where  "  1^,1  (H-l)  . and the n o r m a l i z a t i o n constant N depend m, j m  upon the power of the f u n c t i o n chosen to which the raw i s to be f i t t e d .  data  Tables of these constants f o r d i f f e r e n t degree  of p o l y n o m i a l s are g i v e n by A S a v i t z k y and M. Golay The  ' •  e q u a t i o n (H-l) then g i v e s a new  (SA  64),  value f o r  which i s found by f i t t i n g m lower channels and m h i g h e r  channels  ( i n c l u d i n g the channel to be smoothed) to a power f u n c t i o n n f. = > b, i . T h i s process i s r e p e a t e d f o r a l l the channels k  1  k=0  *  e x c l u d i n g the f i r s t and the l a s t m T h i s technique was i n F i g . H-3. was  channels.  a p p l i e d to the spectrum  The r e s u l t i s shown i n F i g . H-4.  This  shown spectrum  o b t a i n e d under the f o l l o w i n g c o n d i t i o n s ; a.  1 9 p o i n t smooth was  used  (m=9)  b.  A q u a d r a t i c f u n c t i o n was  c.  The smoothing process was not c a r r i e d out f o r channels above approximately 4 MeV.  d.  The process was r e p e a t e d twice; t h a t i s , the o r i g i n a l p o i n t s were smoothed and the new p o i n t s were smoothed a g a i n .  used  (n=2)  A computer program, w r i t t e n by B a i l e y (BA 6 8 ) , was  used t o c a r r y  out the smoothing o p e r a t i o n . I n order to assess the s i g n i f i c a n c e of a c o n t r i b u t i o n which may  be p r e s e n t , the D(d,n) He 3  neutron  neutron  -144-  spectrum, shown I n F i g . H - l was normalized so that the number of counts i n the energy range 2.95 to 6.1 MeV was e q u a l to 2% of the number of counts i n the same energy range o f the gammaray  system shown i n F i g . H-3.  Then the n o r m a l i z e d neutron spec-  trum was s u b t r a c t e d from the smoothed gamma-ray spectrum shown i n F i g . H - 4 t o g i v e the curve shown i n F i g . H-5.  S i n c e the r e -  s u l t i n g curve i s n e g a t i v e i n the lower energy range i t i s c l e a r t h a t too much has been s u b t r a c t e d .  T h e r e f o r e the neutron con-  t r i b u t i o n to the c o u n t i n g r a t e i n the energy range used f o r e v a l u a t i n g the gamma-ray f l u x i s s i g n i f i c a n t l y l e s s than 2% and to the  accuracy of these measurements i t can be s a i d t o be i n s i g -  nificant.  O Q  CD CM.  X 1 D(p,«)  O o o  ; 5  He  (SMOOTHED)  •  o. CO  o o o +  -H-H+  o o  A/ % £  LL.O  o r -  CO  nun mini +^  1  J  LU  2-0  ZD a I  RAW  SPECTRUM  o o o o  CO.  I  i  -.000  1.000  3.000  ENERGY LRB Fig  H-k  :  D(p,tf)  He  1  I  2-000 gamma-ray  spectrum  4.000  5.000  6-000  7.0O0  (MEV) of  Fig.  H-3  with  the  first  1^5  channels  smoothed.  o a CD fM.  X I  o a o CO  D(p,tf) He  -  3  2% D ( d , n ) H e 3  O O O  o o  +  LL.C3  O  •ft  CO  LU  +  2 D a*. i  a o o a  CD. i  -.000 Fig.  I-000 H-5  :  2.000  4-000  ENERGY LRB (MEV)  Gamma-ray from  3.0O0  the  spectrum spectrum  obtained shown  in  by Fig.  subtracting \\-k.  5.000 the normalized  6.000 neutron  7.000 spectrum  APPENDIX I LIST OF COMPUTER PROGRAMS USED IN THIS THESIS Function  Program Name  IBM 7040/7044 ND-160  TALLY paper tape decoder  SPECTRA  Energy c a l i b r a t i o n , energy s h i f t and i n t e g r a t i o n of the s p e c t r a  NORABS  Background s u b t r a c t i o n , absorption corrections  POLYLS  I n i t i a l estimate o f the parameters f o r the i t e r a t i v e l e a s t squares f i t  MLKH1F  Iterative  COMPSC '  Compton s c a t t e r i n g  DE-WFC  D e t e c t o r e f f i c i e n c y and f i n i t e s o l i d angle c o r r e c t i o n s (smoothing f a c t o r s )  NDPTHE  Spectra p l o t t i n g  SMOOTH  Gamma-ray smoothing  KONRAS  N o n - r e l a t i v i s t i c k i n e m a t i c s two body break-up used f o r the r e a c t i o n D ( d j n ) H e  n o r m a l i z a t i o n and  l e a s t squares f i t and p l o t t i n g calculation front  collimator  spectra  3  PDP-8 RMSAMS  R.M.S. M u l t i p l e  -147-  scattering  angle  calculations  

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