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Final state interactions in the reactions He3(He3,2p)He4 and T(He3,np)He4 Blackmore, Ewart William 1967

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The U n i v e r s i t y  o f B r i t i s h Columbia  FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION. FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of . EWART WILLIAM BLACKMORE B.Sc.,(Eng.) , Queen's U n i v e r s i t y , 1963 M.Sc,  University  of B r i t i s h Columbia, 19  THURSDAY, AUGUST 17, 1967 AT 3:30 P.M. IN ROOM 301, HENNINGS BUILDING COMMITTEE IN CHARGE Chairman: JoB„ Warren B.L. White M. M c M i l l a n  I . McT. Cowan CM. Griffiths E . Vogt F.K. Bowers  Research S u p e r v i s o r : J.B. Warren E x t e r n a l Examiner: T.A. T o m b r e l l o Department of P h y s i c s C a l i f o r n i a I n s t i t u t e o f Technology Pasadena California U.S.A.  FINAL STATE INTERACTIONS IN THE He  3  (He  3  ,2p)He  4  and T(He  3  REACTIONS  4 ,np)He .  ABSTRACT F i n a l s t a t e i n t e r a c t i o n s i n the p-p p-n  and  systems c o r r e s p o n d i n g to the f o r m a t i o n of the  singlet  s t a t e s of the d i p r o t o n and the deuteron have 3 3 4 been observed i n the r e a c t i o n s He (He ,2p)He and 3 4 T(He of  ,np)He , by measuring the energy  the f i n a l  s p e c t r a of  two  state p a r t i c l e s detected i n coincidence.  These i n t e r a c t i o n s appear as r e g i o n s of h i g h d e n s i t y of  events a l o n g the k i n e m a t i c contours  i n two dimen4 s i o n a l energy space. Both p-p and p-He coincidences 3 3 4 4 from the r e a c t i o n He (He ,2p)He and p-He coincidences 3 4 from the r e a c t i o n T(He ,np)He were s t u d i e d . The dominant mechanism p r o d u c i n g the t h r e e p a r t i c l e f i n a l s t a t e s was found t o be the s e q u e n t i a l breakup through 5 5 the s t a t e s of L i  and He  , i n agreement w i t h the r e -  s u l t s of p r e v i o u s experiments. the two  nucleons  dence events energy  affects  The  i n t e r a c t i o n between  the d i s t r i b u t i o n of c o i n c i -  o n l y i n the r e g i o n of two  dimensional  space c o r r e s p o n d i n g to a breakup i n which the  two nucleons emerge w i t h low r e l a t i v e energy. The r e l a t i v e c o n t r i b u t i o n s of the d i f f e r e n t p r o c e s s e s i n 3 3 4 the r e a c t i o n He (He ,2p)He was determined f o r i n c i d e n t 3 He  e n e r g i e s from 1.15  MeV  t h a t the nucleon-nucleon  t o 5.0  MeV.  I t was  found  i n t e r a c t i o n becomes l e s s  p o r t a n t as the i n c i d e n t energy  increases.  The  im-  validity  of two approximate t h e o r i e s of f i n a l  state  t i o n s , the Watson theory and the P h i l l i p s ,  interacGriffy  and Biedenharn d e n s i t y of s t a t e s f o r m a l i s m , was checked by comparing t h e i r p r e d i c t i o n s w i t h the observed energy s p e c t r a .  GRADUATE STUDIES F i e l d of Study:  Experimental Nuclear Physics  Nuclear Physics E . Vogt, J.B. Warren Theoretical Nuclear Physics M. M c M i l l a n Cosmic Rays and H i g h Energy Physics J.B„ Warren Elementary Quantum Mechanics A. Kaempffer E l e c t r o n i c Instrumentation F.K. Bowers E l e c t r o m a g n e t i c Theory G. V o l k o f f D i g i t a l Computer Programming H. Dempster Low Temperature P h y s i c s J.B. Brown Group Theory Methods i n Quantum W Opechowski Mechanics  PUBLICATIONS AND E.W.  PAPERS  Blackmore and J.B. Warren.^ " F i n a l S t a t e a c t i o n s i n the R e a c t i o n He (He^,2p)He4" Phys. Rev. L e t t e r s 16,520 (1966).  Inter-  r  R.J.A. Levesque, R.W, O l l e r h e a d , E.W. Blackmore and J.A. Kuehner. " P r o p e r t i e s of L e v e l s a t 6.69 and 6.88-6.89 MeV i n S i & " . Can. J . Phys. 44,1087 (1966). 2  E.W.  Blackmore and J.B. Warren. " F i n a l State Intera c t i o n s i n the R e a c t i o n s He^(He3,2p)He^ and T(He ,np)He ". Can. J . Phys. ( s u b m i t t e d ) . 3  4  F I N A L STATE INTERACTIONS He (He ,2p)He 3  3  I f  I N THE REACTIONS  AND T ( H e , n p ) H e 3  l f  by EWART W I L L I A M BLACKMORE B.Sc.CEng ) Queen's U n i v e r s i t y , K i n g s t o n , . 1963 M.Sc, U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1965 A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e department o f PHYSICS We a c c e p t t h i s required  thesis as conforming  to the  standard  THE U N I V E R S I T Y OF B R I T I S H COLUMBIA J u l y 1967  In  presenting  for  an  that  advanced  thesis  shall  I further  agree  for scholarly  Department  o r by  publication  without  thesis  degree  the Library  Study.  or  this  my  Department  h.iis  make  Date  i t freely  that  may  be  thesis  of  of Columbia  the  granted  by  requirements  Columbia,  t h e Head  shall  and  copying  It i s understood  gain  I agree  for reference  for extensive  for financial  permission.  of  British  available  permission  representatives.  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, C a n a d a  fulfilment  the U n i v e r s i t y  purposes  of this  written  at  in partial  of  of  this  my  that  n o t be  copying  allowed  - i iABSTRACT Final corresponding p r o t o n and He  (He  t o the f o r m a t i o n of the  the d e u t e r o n  ,2p)He  o f two  s t a t e i n t e r a c t i o n s i n t h e p-p  and  of the f i n a l  p-n'systems  s i n g l e t s t a t e s o f the d i -  have been observed  T(He  and  i n the r e a c t i o n s  ,np)He , by m e a s u r i n g t h e e n e r g y s p e c t r a  state p a r t i c l e s detected  i n coincidence.  These i n t e r a c t i o n s a p p e a r a s r e g i o n s o f h i g h d e n s i t y o f along  the k i n e m a t i c contours  B o t h p-p and  and  p-He  dimensional  1  J  The  dominant mechanism p r o d u c i n g  s t a t e s was  found  t o be  the  the t h r e e  were particle  s e q u e n t i a l breakup through  the  *>  s t a t e s o f L i ' and  He  experiments.  i n t e r a c t i o n b e t w e e n t h e two  The  , i n agreement w i t h the r e s u l t s o f  the d i s t r i b u t i o n of c o i n c i d e n c e events dimensional  t h e two  space.  p-He* " c o i n c i d e n c e s f r o m t h e r e a c t i o n H e ^ ( H e ^ , 2 p ) H e ^  5  two  energy  c o i n c i d e n c e s from the r e a c t i o n T(He ,np)He  studied. final  i n two  events  affects  o n l y i n the r e g i o n of  energy space c o r r e s p o n d i n g  nucleons  nucleons  previous  t o a breakup i n which  emerge w i t h l o w r e l a t i v e e n e r g y .  The  relative  c o n t r i b u t i o n s o f the d i f f e r e n t p r o c e s s e s i n the r e a c t i o n 3 3 3 He (He , 2 p ) H e was d e t e r m i n e d f o r i n c i d e n t He- e n e r g i e s f r o m 3  1.15  "to 5«0  MeV.  I t was  i n t e r a c t i o n becomes l e s s increases.  The  found  important  v a l i d i t y o f two  t h a t the as  the i n c i d e n t energy  approximate t h e o r i e s of  s t a t e i n t e r a c t i o n s , t h e W a t s o n t h e o r y and and B i e d e n h a r n  nucleon-nucleon  the P h i l l i p s ,  d e n s i t y o f s t a t e s f o r m a l i s m , was  comparing t h e i r p r e d i c t i o n s w i t h the observed  checked  final Griffy by  energy s p e c t r a .  - i i i  -  TABLE OF CONTENTS  CHAPTER I  CHAPTER I I  INTRODUCTION A.  General I n t r o d u c t i o n  B.  R e v i e w o f P r e v i o u s Work  C.  P r e s e n t Work  • A.  KINEMATICS AND EXPERIMENTAL TECHNIQUE Kinematics  of three p a r t i c l e breakup  reactions B, CHAPTER I I I  CHAPTER I V  Experimental Technique EXPERIMENTAL ARRANGEMENT  A.  Introduction  B.  G e o m e t r y #1  T a r g e t Chamber  C.  G e o m e t r y #2  Target-Chamber  D.  T r i t i u m Handling System  E.  Charged P a r t i c l e  F.  Electronics .  G.  O n - l i n e Computer  -  Detectors  Techniques  EXPERIMENTAL PROCEDURE-AND RESULTS  A*  G e o m e t r y #1  B.  G e o m e t r y #2. M e a s u r e m e n t s -----  C.  The He3(He3 2p)He"+  D.  The T ( H e , n p ) H e  Measurements  ?  3  L f  Reaction  Reaction  THEORY OF F I N A L STATE INTERACTIONS  CHAPTER V A«  Introduction  -•  -  B.  A n a l y s i s of Coincidence Proton  C.  G e o m e t r y #1 A n a l y s i s o f R e s u l t s  D.  G e o m e t r y #2 A n a l y s i s o f R e s u l t s  Spectra  _ iv Contents  continued DISCUSSION  73  A.  Present Results  73  B.  F u t u r e Work  75  CHAPTER V I  APPENDIX A  Page  REACTION KINEMATICS FOR THREE F I N A L PARTICLES  78  APPENDIX B  COMPUTER PROGRAM L I S T I N G S  87  APPENDIX C  SEMI-EMPIRICAL EXPRESSION FOR ENERGY LOSS I N THIN F O I L S  REFERENCES  89 92  V -  LIST OF FIGURES; To f o l l o w P fi a  Figure 1, 2,  R e l a t i o n s h i p between v e l o c i t i e s i n l a b . and scm. coordinate systems* .. . .  17  R e l a t i o n s h i p between v e l o c i t i e s i n scm* 1?  and r c m ( i ) coordinate systems* 3»  e  Kinematic contours f o r p-p and p-He *-coin* cidences from the r e a c t i o n He^(He^,2p)He ,  20  Kinematic contours f o r p-He*" coincidences from t h e r e a c t i o n He^(He^,2p)He *  23  5#  Schematic diagram of Geometry #1 and Geometry #2*  26  6*  Kinematic contours f o r p-p, p-He^ andRe^-p coincidences from the r e a c t i o n He (He ,2p)He .  26  Kinematic contours f o r p-p coincidences from the r e a c t i o n He (He3,2p)He .  26  8,  Geometry #1 target-detector arrangement*  27  9*  Geometry #2 t a r g e t - d e t e c t o r arrangement (side-view)*  29  1  lf  *t.  1  lf  3  7*  3  10,  3  lf  lf  Geometry #2 target-detector arrangement (rear-view)*  29  11*  Diagram of pumping and gas handling system.  31  12*  Block diagram of e l e c t r o n i c s used i n o n - l i n e data a c q u i s i t i o n a t Chalk R i v e r ,  35  Block diagram of e l e c t r o n i c s used i n data a c q u i s i t i o n a t U.B.C.  35  Time d i s t r i b u t i o n spectrum of coincidences from the r e a c t i o n He^(He ,2p)He %_  35  13* Ik,  3  15,  1  Two dimensional energy spectrum taken w i t h Geometry #1 and  = 6° *  **3  - vi Figures Figure  -  continued 16.  to  Coincidence  p r o t o n s p e c t r a o b t a i n e d by-  summing e v e n t s 17.  along appropriate contour.  Coincidence proton spectra obtained summing e v e n t s  18.  along appropriate  . 1+3  by  along appropriate contour.  Coincidence proton spectra obtained  Single  V3  contour.  Coincidence proton spectra obtained  summing e v e n t s 22.  .  p r o t o n s p e c t r a o b t a i n e d by.  summing e v e n t s 21.  *+3  along appropriate contour.  summing e v e n t s 20.  by  C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by  Coincidence  ^3  along appropriate contour.  summing e v e n t s 19.  along appropriate  particle  by  ,2p)He  1+3  :  contour.  s p e c t r a . i n both deteetors  t h e r e a c t i o n He (He  a t 90° t o  *+3 from  the  i n c i d e n t beam d i r e c t i o n . 23.  Two d i m e n s i o n a l p-He  2h.  3  He (He ,2p)He 3  contour  reaction 1+5  = 152°.  2  obtained-by  l f  for A  1  2  contour f o r Single  £^  particle  reaction  summing o v e r  p-He** 1+6  = 152°.  Coincidence proton spectrum from t h e He^(He ,2p)He  26»  1  from-the  and  C o i n c i d e n c e p r o t o n spectrum from the 3  25.  at A  l f  M+  c o n t o u r p l o t o f p-p  coincidence events  He (He ,2p)He 3  follow page  obtained-by  reaction  summing o v e r  p-He  = 165°.  h-6  spectra i n both  from the r e a c t i o n T(He ,np)He 3  t h e i n c i d e n t beam d i r e c t i o n .  1+  detectors a t 90°  to 1+7  - vii Figures  Figure  -  continued  27.  to follow page  Two d i m e n s i o n a l k d-He  coincidence events  T(He3,np)He 28.  k c o n t o u r p l o t o f p - H e ~ and  at  lf  A  1 2  from-the  l^lA  =  0  ,  k8  Coincidence proton spectrum from the reaction T(He ,np)He-obtained-  by-summing  3  o v e r p-He *" c o n t o u r f o r  A - j ^ 151 A .  1  29.  Coincidence  3  over p-He^  obtained  lf  contour f o r  Excitation functions  ^9  0  proton spectrum from  r e a c t i o n T(He ,np)He  30.  reaction  A ^  for  =  the  by-summing  .165°.  states  ky  of L i ^  p r e d i c t e d b y W a t s o n and PBG t h e o r i e s . 31.  Excitation functions  for states  of  62  He^  p r e d i c t e d by W a t s o n a n d PBG t h e o r i e s . 32.  Excitation functions  for singlet  62  s t a t e of  p-p  s y s t e m p r e d i c t e d by W a t s o n a n d PBG t h e o r i e s . 33.  Excitation functions  for.singlet  state.of  n-p  s y s t e m p r e d i c t e d by W a t s o n and PBG t h e o r i e s . 3*+.  Comparison  Q  35«  1.15  for  6k  MeV.  Comparison  of experimental coincidence  s p e c t r u m w i t h W a t s o n and PBG t h e o r i e s T = Q  36.  37.  for  6k  of p r e d i c t i o n s  of  statistical  b r e a k u p w i t h W a t s o n and PBG t h e o r i e s Li  proton  5.00 MeV.  Comparison  for  excited state.  Comparison  66  of e x p e r i m e n t a l - c o i n c i d e n c e  spectra at small angles theories.  62  of experimental c o i n c i d e n c e - proton  s p e c t r a w i t h W a t s o n and PBG t h e o r i e s T=  62  w i t h W a t s o n and  proton PBG 67  Figures  viii  continued  F i g u r e 38.  to follow page  Coincidence proton-spectrum from the reaction He (He ,2p)He 3  3  l f  for A  1  2  =  152°  d i v i d e d by t h e a v a i l a b l e p h a s e - s p a c e . . . 39.  Comparison of experimental c o i n c i d e n c e p r o t o n s p e c t r a w i t h Watson t h e o r y f o r p-p  h-0.  70  final  the  state interaction.  71  Coincidence proton spectrum from the . r e a c t i o n T(He  ,2p)He  A^=-l^l h°  for  0  d i v i d e d by t h e a v a i l a b l e p h a s e - s p a c e . ^1.  Comparison  of experimental c o i n c i d e n c e  p r o t o n s p e c t r a w i t h Watson n-p Al.  final  71  theory for  the  state interaction.  71  R e l a t i o n s h i p between v e l o c i t i e s i n l a b . and scm. c o o r d i n a t e s y s t e m s .  A2.  79  R e l a t i o n s h i p between v e l o c i t i e s i n and r c m C i ) c o o r d i n a t e s y s t e m s .  CI.  Energy  loss  deuterons C2.  Energy  curves  f o r protons  79 and  in nickel foils.  loss  curves  in nickel foils.  f o r He  3  scm.  91 and  He^ 91  -  ix  -  L I S T OF TABLES To f o l l o w page T a b l e 1.  Symbols used i n d e s c r i b i n g particle  2.  a  three  breakup.  16  Commercial e l e c t r o n i c u n i t s  used i n  the  experimental arrangement. 3.  Detector  configurations  35  used w i t h  G e o m e t r y #1 m e a s u r e m e n t s . k-.  Parameters  obtained, f o r  and He* f r o m s i n g l e  *+l  states  level  of L i ^  dispersion  theory. 5»  59  E f f e c t i v e - r a n g e "theory parameters nucleon-nucleon  s c a t t e r i n g phase  for shifts.  59  ACKNOWLEDGEMENTS I Warren, f o r h i s course  am d e e p l y g r a t e f u l t o my s u p e r v i s o r , i n t e r e s t and e n c o u r a g e m e n t  of t h i s work.  The a s s i s t a n c e  G.M. G r i f f i t h s who a c t e d a s absence  throughout  of Drs.  Dr. J . the  B. L . W h i t e a n d  interim supervisors  i n Dr.  Warren's  is also greatly appreciated. The many d i s c u s s i o n s w i t h D r . E r i c h V o g t  on some  o f the t h e o r e t i c a l problems have been a tremendous h e l p . w i l l i n g assistance faculty,  B.  students  o f t h e members o f V a n de G r a a f f g r o u p , and t e c h n i c i a n s i s a c k n o w l e d g e d w i t h  R i v e r N u c l e a r L a b o r a t o r i e s f o r making i t p o s s i b l e some o f t h e e x p e r i m e n t a l m e a s u r e m e n t s Finally,  at higher  Chalk  to carry  Research  r e c e i v e d d u r i n g my  g r a d u a t e work and f o r t h e i r c o n t i n u e d f i n a n c i a l s u p p o r t studies.  out  energies.  I am i n d e b t e d t o t h e N a t i o n a l  C o u n c i l f o r a B u r s a r y and t h r e e S t u d e n t s h i p s  both  thanks.  I w i s h t o t h a n k t h e tandem g r o u p a t t h e  postdoctoral  The  in  - 1  -  CHAPTER  I  INTRODUCTION A.  General  Introduction Nuclear reactions  are produced i n the f i n a l  i n w h i c h t h r e e o r more  particles  s t a t e h a v e r e c e n t l y become t h e  subject  o f a g r e a t d e a l o f i n t e r e s t b o t h e x p e r i m e n t a l l y and t h e o r e t i c a l l y . T h i s has  come a b o u t a s a r e s u l t o f t h e d e v e l o p m e n t  dimensional pulse height analysers h a s made p o s s i b l e Although  of  multi-  and o n - l i n e c o m p u t e r s  useful experimental studies  of these  which  reactions.  these r e a c t i o n s are very complicated i n comparison  t h e u s u a l n u c l e a r r e a c t i o n w i t h two p a r t i c l e s i n b o t h t h e and f i n a l  states,  analysing  equipment,  gained  a n d h e n c e t h e n e e d f o r more t h e r e a r e a number  in their investigation.  advantages i t i s  of nuclear research a t low  initial  sophisticated  o f a d v a n t a g e s t o be  Before enumerating  worthwhile to discuss  with  these  some o f t h e p r e s e n t  aims  energies.  The f u n d a m e n t a l p r o b l e m o f n u c l e a r p h y s i c s i s understand  the f o r c e s a c t i n g between the n u c l e a r p a r t i c l e s .  the i n v e s t i g a t i o n of t h i s the obvious course systems, those They r e a s o n e d  i n t e r a c t i o n early researchers  and s t u d i e d i n t e n s i v e l y t h e s i m p l e s t  i n which only  two n u c l e o n s  t h a t a complete knowledge  are  between n u c l e o n s  evidence i n d i c a t e s  In  followed nuclear  interacting.  o f t h e two  nucleon  s y s t e m s w o u l d a l l o w one t o compute a l l n u c l e a r p r o p e r t i e s , that the forces  to  are simply a d d i t i v e .  Present  t h a t t h i s may n o t be c o m p l e t e l y t r u e  t h a t t h e n u c l e a r f o r c e may i n v o l v e t e r m s w h i c h a r i s e  i.e.  only  and when  a t h i r d or f o u r t h p a r t i c l e i s  2  -  present.  These  "many-body"  forces  h a v e n o t b e e n s t u d i e d i n g r e a t d e t a i l a s y e t due t o t h e i r m a t h e m a t i c a l c o m p l e x i t y and t o t h e d i f f i c u l t y experiments  two body f o r c e s i t . i s  simple i n t e r a c t i o n w i l l In f a c t i t w i l l standing  designing  to determine t h e i r p r o p e r t i e s unambiguously.  many f e a t u r e s o f n u c l e a r b e h a v i o u r using  in  are conveniently  explained  expected t h a t the study of  c o n t i n u e t o be p r o f i t a b l e f o r some  p r o b a b l y be n e c e s s a r y  c a n be d r a w n a b o u t  determining nuclear  to obtain a better  two n u c l e o n s , The p o s s i b l e  under-  properties. consisting  states  of these n u c l e o n - n u c l e o n systems  the concepts  of o r d i n a r y  e i t h e r p a r a l l e l corresponding  or a n t i p a r a l l e l c o r r e s p o n d i n g a n d two n e u t r o n s  with opposite identical  s p i n and  isospin.  spins  to a singlet  spin state,  s p i n s t a t e , "*"S,  on t h e o t h e r h a n d c a n e x i s t  states  i n the i s o s p i n  3  S,  The  only  as a r e s u l t of t h e e x c l u s i o n p r i n c i p l e f o r  of the t h r e e systems  t r i p l e t T=l,  w h i l e the t r i p l e t  singlet  state  In general,simple been used  to a t r i p l e t  ordinary  p a r t i c l e s and t h e r e f o r e m u s t be i n a s i n g l e t  The s i n g l e t  of  may be  The n e u t r o n - p r o t o n s y s t e m i n t h e S s t a t e c a n h a v e i t s  two p r o t o n s  in  t h e d i - p r o t o n , t h e d i - n e u t r o n , and t h e d e u t e r o n .  c l a s s i f i e d using  is  time.  t h e r o l e o f many body f o r c e s  There a r e t h r e e n u c l e a r systems  isospin  this  o f t h e two body i n t e r a c t i o n b e f o r e a n y q u a n t i t a t i v e  conclusions  spins  Since  belong t o the s t a t e of the  state same  deuteron  T=0. s c a t t e r i n g experiments  t o u n c o v e r most o f the p r o p e r t i e s o f t h e s e  have  systemso  However-j o n l y t h e p r o t o n - p r o t o n a n d p r o t o n - n e u t r o n s y s t e m s  are  S,  - 3 a c c e s s i b l e with these  -  s c a t t e r i n g experiments  of o b t a i n i n g a t a r g e t of f r e e neutrons. a target of e s s e n t i a l l y f r e e protons, bombarded w i t h a beam o f p r o t o n s  p a r t i c l e s i s monitored.  measured a r e the t o t a l c r o s s  the d i f f e r e n t i a l nucleon i s  energy  is  neutrons  The q u a n t i t i e s w h i c h  cross s e c t i o n or  the  are  s c a t t e r i n g as a  function  or the e x c i t a t i o n f u n c t i o n ,  the p r o b a b i l i t y t h a t t h e a n d i n more  incoming  recent  the p o l a r i z a t i o n or p r e f e r r e d s p i n d i r e c t i o n of  scattered nucleon. has  gas,  and t h e s c a t t e r i n g o f  scattered through a given angle,  experiments  experiments  s u c h as h y d r o g e n  section for  of the r e l a t i v e n u c l e o n - n u c l e o n  these  problem  from an a c c e l e r a t o r ^ o r  from a r e a c t o r or neutron generator incoming  In  due t o t h e  Information  about the n e u t r o n - n e u t r o n  the system  been o b t a i n e d i n d i r e c t l y from the s c a t t e r i n g of n e u t r o n s  deuterons  and f r o m t h e r e a c t i o n o f n e g a t i v e Of t h e p o s s i b l e  n e u t r o n - p r o t o n system i s  triplet force,  The s i n g l e t  a r e n o t bound p o i n t i n g spin  the  Measurements  states  of the  state,  magnetic  predominantly i n  belonging  to the  o u t one p r o p e r t y o f t h e  the  isospin nuclear  dependence. If  the n u c l e a r  of a simple p o t e n t i a l i t i s experiments  deuterons.  f o u n d t o e x i s t i n a s t a b l e bound  moment o f t h e d e u t e r o n i n d i c a t e t h a t i t i s state.  on  two n u c l e o n s y s t e m s o n l y  the ground s t a t e of the d e u t e r o n .  triplet  pions  on  interaction is  found t h a t the low energy  c a n n o t d e t e r m i n e t h e shape  of t h i s  m e r e l y two q u a n t i t i e s w h i c h d e s c r i b e i t s  f o r the s i n g l e t  states  r.  terms  scattering  p o t e n t i a l but  gross features,  s c a t t e r i n g l e n g t h a and the e f f e c t i v e range these parameters  described i n  the  The v a l u e s  are presently  of  reported  as  k -  follows: n-p a  s  r  Q S  p-p  = -23.71 ± .07 f m .  a  p  = 2 . i f + .3 f m .  r  Q p  = - 7 . 7 2 + .Ok f m . = 2.72 + .10 f m .  The s i m i l a r i t y o f t h e t w o e f f e c t i v e r a n g e s s u g g e s t s t h a t t h e n u c l e a r f o r c e s a r e charge this  independent.  Further evidence f o r  i s the f a c t t h a t the concept o f i s o s p i n ,  i n which the  n e u t r o n a n d p r o t o n a r e r e g a r d e d as two a l m o s t d e g e n e r a t e  states  o f t h e same p a r t i c l e ,  the nucleon, i s extremely successful  predicting properties  of mirror nuclei.  remains,  how good i s t h e a p p r o x i m a t i o n o f c h a r g e  The s c a t t e r i n g l e n g t h s b u t most  However  in  the question independence.  f o r t h e two systems a r e q u i t e d i f f e r e n t  o f t h i s d i f f e r e n c e c a n be a t t r i b u t e d t o t h e Coulomb  f o r e e i n the case  o f the p-p system.  Approximate  o f t h e s c a t t e r i n g l e n g t h f o r two p r o t o n s Coulomb f o r c e y i e l d s a v a l u e  calculations  i n t h e absence  of the  o f -17 f m . T h e b e s t e s t i m a t e s o f  the s c a t t e r i n g l e n g t h f o r t h e n - n system range  f r o m -17 f m . t o  -2k f m . One p r o p e r t y o f t h e n u c l e a r f o r c e w h i c h i s v e r y much i n e v i d e n c e i n t h e v a s t  amount o f e x p e r i m e n t a l  a v a i l a b l e i s i t s extremely complicated nature. of the simplest  properties  of a nuclear  moment o f t h e d e u t e r o n , i t i s n e c e s s a r y of a n o n - c e n t r a l o r tensor more c o m p l i c a t i o n s  component  such as r e p u l s i v e  system,  information  To e x p l a i n one the quadrupole  t o assume t h e p r e s e n c e  i n the nuclear f o r c e . cores  and v e l o c i t y  i n t e r a c t i o n s a r e used t o e x p l a i n t h e r e s u l t s  Even  dependent  of scattering  experiments  5 -  c a r r i e d out a t h i g h e r It  is  energies.  not expected t h a t the study immediately solve  breakup  reactions w i l l  However  t h i s a p p r o a c h s h o u l d a l l o w a more a c c u r a t e  of the n e u t r o n - n e u t r o n  of o b t a i n i n g  "many-body"  forces.  evidence f o r or a g a i n s t  the  In h i g h energy  of t h i s  t y p e has  l e d to the d i s c o v e r y  strange  p a r t i c l e i n t e r a c t i o n s , s u c h as success,  physics  h i g h energy  of n u c l e i  In low energy  reactions  short-lived  the pion resonances. has  As  l e d t h e way space  a  in  calculations  reactions.  nuclear physics,  r e a c t i o n s may be u s e d t o g i v e  about  reactions  of  o f many o f t h e  physics  of  containing  the a n a l y s i s  the c o m p l i c a t e d k i n e m a t i c and phase  a p p l i c a b l e to m u l t i p a r t i c l e breakup  remote  the presence  i n t e r a c t i o n , m u l t i p a r t i c l e breakup  many n u c l e o n s .  determining  determination  In a d d i t i o n to obtaining information  may be u s e d t o p r o b e t h e c l u s t e r e d n a t u r e  r e s u l t of t h i s  complicated s i t u a t i o n .  s c a t t e r i n g l e n g t h and i t o f f e r s  possibility  the n u c l e o n - n u c l e o n  this  of m u l t i p a r t i c l e  three p a r t i c l e  s i m i l a r i n f o r m a t i o n about  the  breakup nucleon-  n u c l e o n i n t e r a c t i o n o r any o t h e r p a r t i c l e - p a r t i c l e i n t e r a c t i o n a s scattering experiments.  Here the i n t e r a c t i o n appears  s t a t e i n t e r a c t i o n " i n f l u e n c i n g the energy and a n g u l a r of the breakup p a r t i c l e s .  If  the f i n a l  as a  distributions  state interaction is  s u f f i c i e n t l y l o n g d u r a t i o n t h e n t h e b r e a k u p may a l s o be as a s e r i e s product decays  o f two body d e c a y s .  of the f i r s t decay i s i n t o two s t a b l e  fall  this  considered  s e q u e n t i a l breakup  a v i r t u a l p a r t i c l e which  of  the  subsequently  particles.  The t y p e s these r e a c t i o n s  In  "final  of measurements  i n t o two g r o u p s .  used i n the a n a l y s i s  The f i r s t g r o u p c o n s i s t s  of of  t h o s e measurements  6  -  w h i c h a r e made b y m o n i t o r i n g  o n l y one d e t e c t o r .  These i n c l u d e d e t e r m i n a t i o n s  y i e l d as a f u n c t i o n o f the i n c i d e n t e n e r g y , distributions  of the r e a c t i o n p r o d u c t s .  t o be a m b i g u o u s u n l e s s some s o r t is  used.  Reasons f o r  this  of the r e a c t i o n k i n e m a t i c s The s e c o n d o f two d e t e c t o r s the f i n a l  chapter  total  and t h e v a r i o u s  energy tend  of p a r t i c l e i d e n t i f i c a t i o n system are  i n Chapter  II.  class  of the  g i v e n i n the  o f measurements  the energies  discussion  requires  and d i r e c t i o n s  the  A d e t a i l e d d e s c r i p t i o n of this  it will  of the r e a c t i o n k i n e m a t i c s .  be shown t h a t b y c h o o s i n g  a z i m u t h a l a n g l e s o f t h e two d e t e c t o r s  from  In  the  possible  next  polar to  and  observe  a p a r t i c u l a r i n t e r a c t i o n as a f u n c t i o n o f the r e l a t i v e energy the corresponding energy  i t is  possible  function for scattering  two p a r t i c l e s . to determine  two p a r t i c l e s as  that i t is  i n a single determine course,  with a fixed  t h e same s o r t  possible  to observe  several  the r e l a t i v e i n t e n s i t i e s  w o u l d n o t be p o s s i b l e  disadvantage  if  In  if  incident  However  final  state  the energies.  a simple matter  the three p a r t i c l e s advantage  from the v a r i o u s  i n most r e a c t i o n s  reaction  interactions  o f the i n t e r a c t i o n s .  some c a s e s t h i s  the c o n t r i b u t i o n s  c a n n o t be s e p a r a t e d .  excitation  of the three p a r t i c l e breakup  e x p e r i m e n t and t h e r e f o r e i t i s  s t a t e were i d e n t i c a l .  of  of  beam  one w o u l d o b t a i n by s t u d y i n g  b e t w e e n t h e same p a r t i c l e s a t v a r i o u s One a d v a n t a g e  is  Therefore  of  technique  appropriate  i t is  use  o f two  s t a t e p a r t i c l e s d e t e c t e d i n c o i n c i d e n c e and hence  a discussion  with  These measurements  ambiguity  to monitor  t h e same b r e a k u p . requires  the r e a c t i o n  to  This,  i n the might  of  final be a  interations  i t is  possible  to  choose d e t e c t o r c o n f i g u r a t i o n s dominates.  Another  i n which the i n t e r a c t i o n of  property of these r e a c t i o n s  is  o f mass m o t i o n o f t h e i n t e r m e d i a t e v i r t u a l s y s t e m k i n d of "energy  amplifier".  i n t h e two p a r t i c l e s y s t e m  keV m i g h t c o r r e s p o n d  to a range  energy  t h a t the  This  of  a  relative  of a few  o f a f e w MeV i n t h e  o f one o f t h e b r e a k u p p a r t i c l e s .  centre  c a n be u s e d a s  T h i s means t h a t a r a n g e  or i n t e r n a l e n e r g i e s  interest  hundred  laboratory  feature allows  a  more a c c u r a t e d e t e r m i n a t i o n o f t h e e x c i t a t i o n f u n c t i o n e x p e c i a l l y a t low e x c i t a t i o n e n e r g i e s .  From a n e x p e r i m e n t a l p o i n t o f  the f a c t t h a t a c o i n c i d e n c e experiment i s useful i n reducing At  the background the p r e s e n t  being performed  from contaminant  view,  is  reactions.  time the main problem faced  in  o b t a i n i n g u s e f u l i n f o r m a t i o n from the e x p e r i m e n t a l r e s u l t s  is  the m a t h e m a t i c a l c o m p l e x i t y o f the t h r e e body p r o b l e m .  Although  there i s  techniques  considerable  e f f o r t b e i n g made t o w a r d s  finding  t o i n c l u d e t h e t h r e e b o d y e f f e c t s e x a c t l y , and some o f t h e s e appear p r o m i s i n g ,  the s t a t e o f the e x i s t i n g  s u f f i c i e n t l y advanced experimental results for  final  w i t h much c o n f i d e n c e .  still  from  the  Several  only to a c e r t a i n type of problem.  of t h i s work i s  g i v e n i n Chapter V.  successful  results. results  to e x t r a c t n u c l e a r parameters  is  However  A general  formalisms  i n explaining certain features the p r e s e n t  situation is  t o c h e c k on t h e e x i s t i n g  important r e s u l t of studying t h i s way i s  These  that i t serves  as  theories.  Perhaps  the n u c l e o n - n u c l e o n one o f t h e m o s t  the  been  experimental experimental  the  most  interaction  stringent  being  discussion  have  of the  t o use  not  formalisms  s t a t e i n t e r a c t i o n s have been d e v e l o p e d , e a c h method  applicable  partly  theories  methods  tests  in on  the  8  -  theories. W i t h the development  inaccessible  parameters  s u c h as  of a p r e c i s e  the neutron-neutron  s c a t t e r i n g l e n g t h may be d e t e r m i n e d a c c u r a t e l y . should  also  be q u i t e u s e f u l i n h i g h e n e r g y  multiparticle actions  theory,  breakup r e a c t i o n i s  otherwise  singlet  The  theory  p h y s i c s where  q u i t e common and t h e  between the p a r t i c l e s are i n the process  the  inter-  of being  investi-  gated. B,  Review of P r e v i o u s  Work  A g e n e r a l c o n c l u s i o n w h i c h c a n be d r a w n f r o m results  the  o f the e x p e r i m e n t a l work to d a t e i s  that f i n a l  state  i n t e r a c t i o n s or t h e i r k i n e m a t i c e q u i v a l e n t ,  sequential  decays  through  intermediate states,  breakups.  This i s  p l a y a dominant  role i n multiparticle  i n d e e d f o r t u n a t e as a n o n u c l e a r  c o u l d be o b t a i n e d o t h e r w i s e .  The o t h e r p o s s i b l e  is  breakup  the d i r e c t or instantaneous  angular  distributions  This  r e a c t i o n mode  i n which the energy  of the r e a c t i o n p r o d u c t s  a v a i l a b l e phase-space.  information  and  d e p e n d o n l y on t h e  t y p e o f b r e a k u p has  a  coincidence  y i e l d d i s t r i b u t i o n c h a r a c t e r i z e d by a s l o w v a r i a t i o n w i t h p a r t i c l e e n e r g y and t h e p r e s e n c e The e f f e c t o f f i n a l  o f p e a k s a t t h e maximum p a r t i c l e  state interactions  is  energies.  to modify t h i s phase-space  d i s t r i b u t i o n and by p e r f o r m i n g a c o i n c i d e n c e e x p e r i m e n t i t usually  possible  to d i s t i n g u i s h  The p r o c e e d i n g s Correlations the best  between the r e a c t i o n  mechanisms.  of the G a t l i n b u r g Conference  of P a r t i c l e s Emitted i n Nuclear Reactions  summary a t t h e p r e s e n t  on t h e s e r e a c t i o n s .  is  time o f the work b e i n g  (1)  on contain  undertaken  In a d d i t i o n to s e v e r a l review a r t i c l e s  on  - 9 t h e e x p e r i m e n t a l and t h e o r e t i c a l t e c h n i q u e s , many experimental results of t h i s  have been r e p o r t e d .  review to give  these r e a c t i o n s .  be m e n t i o n e d a r e t h o s e w h i c h have  t i o n about reactions  the n u c l e o n - n u c l e o n 3  l f  of the l e v e l s Brookhaven  The r e a c t i o n s  been used t o g a i n  o f t h e second  i n this  t a r g e t a n d two t h r e e p a r t i c l e 3  case both H e - p 3  corresponding  b r o a d p e a k was a l s o  observed  from the  i n coincidence with a to the excited states  state of the deuteron.  3  energy being  i n several  spectrum of the t h i r d p a r t i c l e ,  systematic  survey  i n He**.  A  in  bombarding  s t a t e i n t e r a c t i o n i s r e l a t i v e l y much  t h r e e body r e a c t i o n s  t h e two n u c l e o n s .  triton  No s i m i l a r p e a k was f o u n d  The n u c l e o n - n u c l e o n i n t e r a c t i o n s h a v e a l s o observed  studied.  c o i n c i d e n c e s p e c t r a due  t h e p-T c o i n c i d e n c e s p e c t r a i n d i c a t i n g t h a t a t t h i s t h e p-p s i n g l e t  The  a n d T - p c o i n c i d e n c e s were  i n the p-He  were  two d i m e n s i o n a l  o f two c o i n c i d e n t p a r t i c l e  c o n t a i n e d two p e a k s  energy  states  o f T+p+p a n d t h e o t h e r H e + p + n .  spectrum of the protons  to the s i n g l e t  et a l at  A 31.8 MeV He3 beam was u s e d t o bombard a  (2).  of the energies  The e n e r g y  type of  1  s t a t e i n t e r a c t i o n s were o b s e r v e d u s i n g  reaction,  informa-  l f  i n He *" a t 19.9^ a n d 21.2^+ MeV b y P a r k e r  p r o d u c e d , one c o n s i s t i n g  analysis  which  i n the g e n e r a l i n t r o d u c t i o n i s the d i s c o v e r y  deuterated polyethylene  final  of the  and T ( H e 3 , n p ) H e .  One i n t e r e s t i n g r e s u l t discussed  t h e scope  i n t e r a c t i o n s , i n p a r t i c u l a r the  of i n t e r e s t He (He3,2p)He  measurement  I t i s beyond  a c o m p l e t e up t o d a t e summary  e x p e r i m e n t a l work on a l l will  interesting  weaker.  been  (3-6) by m e a s u r i n g  the  t h e o t h e r two p a r t i c l e s  T o m b r e l l o and B a c h e r  (5) h a v e made a  of s e v e r a l of these r e a c t i o n s .  The p r o t o n - p r o t o n  - 10 i n t e r a c t i o n was s t u d i e d i n t h e r e a c t i o n s H e ( d , t ) 2 p ,  He (He ,He )2p  3  and He3(p,d)2p by o b s e r v i n g of the t r i t o n ,  at forward angles  reaction He (d,He )pn. 3  the energy  w e r e t y p i c a l l y 10-12  MeV.  s p e c t r a and o n l y a t v e r y f o r w a r d a n g l e s .  used i n  end o f t h e p a r t i c l e  The g e n e r a l  the present  conclusion  s e q u e n t i a l decay  c o u l d be e x t r a c t e d .  the r e a c t i o n H e ( d , H e ) p n .  isospin  l f  In  spectra  o f any s t r u c t u r e  state is  c o n v e r s a t i o n as  zero.  This i s  the  p-n  total  convincing  e v i d e n c e t h a t t h e i n t e r a c t i o n s b e i n g o b s e r v e d a r e i n f a c t due the s i n g l e t  to  states. U s i n g a s i m i l a r e x p e r i m e n t , J a r m i e and A l l e n (6)  observed  the d i - n e u t r o n i n t e r a c t i o n i n the a l p h a p a r t i c l e  spectrum from the r e a c t i o n T(T,He )2n. if  d i - n e u t r o n s t a t e was f o u n d . c o u l d be o b t a i n e d a s superimposed measurements,  No e v i d e n c e f o r a bound  t h e p e a k due t o t h e n - n  on a c o n t i n u u m f r o m t h e s t a t e s  i n t e r a c t i o n was o f He5.  These  they i n d i c a t e t h a t  n u c l e o n - n u c l e o n i n t e r a c t i o n c a n be c o n v e n i e n t l y o b s e r v e d final  state interaction, also  energy  A g a i n no q u a n t i t a t i v e i n f o r m a t i o n  although i n t e r e s t i n g since  and  in  t h i s r e a c t i o n the s i n g l e t T = l ,  i n h i b i t e d by i s o s p i n  of the i n i t i a l  theories  The most i n t e r e s t i n g  o f t h e i n v e s t i g a t i o n was t h e a b s e n c e l f  the  these  c o u l d o n l y g i v e q u a l i t a t i v e agreement w i t h the observed no n u c l e a r p a r a m e t e r s  The  was t h a t a l t h o u g h t h e i n t e r a c t i o n s do  p l a y a p a r t i n the breakup,  interaction is  spectra  The two n u c l e o n i n t e r -  peaks a t the h i g h energy  drawn from these s t u d i e s  I f  s t u d i e d i n a s i m i l a r manner i n  The i n c i d e n t e n e r g i e s  3  a c t i o n s appeared as  result  3  a l p h a p a r t i c l e and d e u t e r o n r e s p e c t i v e l y .  p r o t o n - n e u t r o n i n t e r a c t i o n was  measurements  3  as  p o i n t o u t t h e n e e d f o r a more  the a  - 11  .' I  sophisticated  experimental  approach.  Coincidence experiments analysis  two d i m e n s i o n a l  h a v e b e e n u s e d by s e v e r a l g r o u p s i n s t u d y i n g  He (He3,2p)He .  The p o s s i b l e  (1)  Li (g.s)  l f  3  He-  using  3  + He-*  ?  (la)  Li^* + p  (2)  Ee e t a l (7)  He *"  10.892  + p + p  1  E  at Rice University  have measured  coincidences  these energy  s p e c t r a were c a l c u l a t e d u s i n g  o f h,<) MeV,  the  from t h i s  be d i s c u s s e d  i n some d e t a i l  i n t e r m e d i a t e s t a t e s w i t h the energy determined from the c o r r e s p o n d i n g  the g e n e r a l i z e d  It  o f two body d e c a y s  dependence  of the  in this  analysis  This treats  through  interaction  were  shifts. the  e x c i t e d s t a t e o f L i ^ and the s i n g l e t  The d o m i n a n t  process  be t h e s e q u e n t i a l d e c a y t h r o u g h  the ground s t a t e of L i ^ „  i n t e r a c t i o n was s e e n i n t h e  p - p and p-He* " c o i n c i d e n c e s 4  from t h i s  s t a t e t r a n s i t i o n was a g a i n  the dominant  spectra. observed  coincidences  w i t h a geometry  energy  process.  to  No good  the  r e a c t i o n a t an i n c i d e n t  They f o u n d t h a t a t t h i s  were a n a l y s e d  two  i n t h e r e a c t i o n was f o u n d  B a c h e r a n d T o m b r e l l o (9) h a v e a l s o  o f 9 . 9 1 MeV.  (8).  i n Chapter V.  for  density  e l a s t i c s c a t t e r i n g phase  The i n t e r m e d i a t e s y s t e m s c o n s i d e r e d  e v i d e n c e f o r t h e p-p  energy  The t h e o r e t i c a l p r e d i c t i o n s  the t h r e e p a r t i c l e breakup as a s e r i e s  g r o u n d s t a t e and f i r s t  MeV  reaction at  f o r m a l i s m o f P h i l l i p s , G r i f f y and B i e d e n h a r n  proton s t a t e .  = 5-10  x  12.859  energy  formalism w i l l  follow-  4  a bombarding  energy  a r e the  + p ->~ He " + p + p  s p e c t r a o f b o t h p - p and p-He  of states  reaction  + p + p  k  Aldridge  r e a c t i o n mechanisms  the  energy-  the  He  3  ground  Proton-alpha  favourable  to  observing  - 12 the p-p  -  i n t e r a c t i o n a t low r e l a t i v e energies.  Only a  small  number o f c o u n t s w e r e f o u n d i n t h i s r e g i o n o f t h e k i n e m a t i c contour i n d i c a t i n g the l a c k of importance of t h i s interaction.  The r e s u l t s  o f Z u r m u h l e (10)  final  a t an i n c i d e n t  o f 15 MeV a r e i n a g r e e m e n t w i t h t h e two p r e v i o u s l y experiments.  In  this  with a small angular statistics  e x p e r i m e n t p-p  state  mentioned  c o i n c i d e n c e s were  observed  s e p a r a t i o n o f t h e two d e t e c t o r s b u t  p r e v e n t e d any c o n c l u s i o n s  energy  from b e i n g drawn  poor  regarding  the p-p i n t e r a c t i o n . No s i m i l a r e x p e r i m e n t s u s i n g  coincidence  h a v e b e e n p u b l i s h e d f o r t h e r e a c t i o n T ( H e ,np)He ", 3  s p e c t r a of the charged p a r t i c l e s from t h i s o b s e r v e d by Moak (11) b e l o w 1 MeV. e t a l (13)  (1)  He  a t an i n c i d e n t energy  + T  for incident  o f 3.23 MeV.  The  been  energies  Q(MeV) iif.320  He *" +• d  (2a)  Li^* +  (3)  He^Cg.s.) + p  (3a)  He^* + p ^  (if)  H e ^ +• p + n  n  He " + p + n  10.128  14  He**" + p +  n  E  x  = 5-10  Be* + n + p He^ + n + p  MeV  11.138 E  x  = 2-lf MeV" 12.095  o f Moak and K u h n i n d i c a t e t h a t f o r i n c i d e n t  t h a n 1 MeV t h e r e a c t i o n c h a n n e l s  Barry  possible  1  Li^Cg.s.) + n  less  energy  r e a c t i o n have  a r e the f o l l o w i n g :  (2)  The r e s u l t s  The  L|  The n e u t r o n s p e c t r u m h a v e b e e n o b s e r v e d by  r e a c t i o n mechanisms 3  and K u h n e t a l ( 1 2 )  techniques  energies  1 and h a r e o f a p p r o x i m a t e l y  t h e same i n t e n s i t y , w i t h c h a n n e l 3 a f a c t o r o f 6 - 8 f o u n d t h a t r e a c t i o n c h a n n e l 2 has a b o u t  lower.  Barry  t h e same i n t e n s i t y a s  sum o f 3 and h f o r t h e i n c i d e n t e n e r g y 3.23 MeV.  The  the  separation  - 13  -  o f t h e r e l a t i v e c o n t r i b u t i o n s i s made d i f f i c u l t m e c h a n i s m k- p r o d u c e s breakup  through  C.  Present  p a r t i c l e s p e c t r a as  the f i r s t e x c i t e d s t a t e s  the observed energy of the s i n g l e t  similar single  by t h e f a c t the  o f L i ^ and He^.  s p e c t r a t h e r e was no e v i d e n c e f o r  that  In  the  all  formation  s t a t e of the d e u t e r o n .  Work The w o r k w h i c h w i l l  be d e s c r i b e d i n t h i s  thesis  was  o r i g i n a l l y undertaken t o determine the importance of the  p-p  i n t e r a c t i o n i n the r e a c t i o n H e ( H e , 2 p ) H e  energies  3  a r o u n d 1 MeV. measurements  events  on t h i s  d e s c r i b e d i n the a u t h o r ' s the angular  b e t w e e n t h e two p r o t o n s  p r e d i c t e d what i s  coincidence  arguments.  i n t u i t i v e l y obvious,  peaked a t an angle  possible  calculations  through  the s t a t e s  of L i 5  Also  a n i n c r e a s e i n t h e number o f  events w i t h decreasing angular  obtained  t h a t the d i s t r i b u t i o n of  of 180° between the p r o t o n s .  which produces  was  distribution  processes  These  between  perpendicular  The r e a c t i o n m e c h a n i s m  c o i n c i d e n c e s from the breakup  final  d i s t r i b u t i o n of  the v a r i o u s  f r o m k i n e m a t i c and p h a s e - s p a c e  process  thesis ( I k )  the e x p e r i m e n t a l angular  with those c a l c u l a t e d f o r  series  Masters  B o t h d e t e c t o r s were k e p t i n a p l a n e  d e t e r m i n e d by c o m p a r i n g  The f i r s t  as a f u n c t i o n of the a n g l e  t o t h e i n c i d e n t beam d i r e c t i o n .  p-p  a t bombarding  r e a c t i o n had b e e n r e p o r t e d .  of observing  the p r o t o n s .  l f  A t t h e t i m e t h e w o r k was b e g u n no c o i n c i d e n c e  of measurements, consisted  3  the  is only  coincidence  s e p a r a t i o n of the protons  is  the  s t a t e p-p i n t e r a c t i o n . The e x p e r i m e n t a l d i s t r i b u t i o n o f c o i n c i d e n c e  showed t h a t a t t h i s  i n c i d e n t energy the dominant process  is  events again  -  the s e q u e n t i a l decay through  -  11+  the ground s t a t e of L i ^ .  A more  i n t e r e s t i n g r e s u l t was t h a t t h e r e was a d e f i n i t e i n c r e a s e i n d i s t r i b u t i o n at small angles o n l y be a t t r i b u t e d t o t h e p - p  between the d e t e c t o r s w h i c h c o u l d final  state interaction.  decided to continue the i n v e s t i g a t i o n of t h i s  It  using  These e x p e r i m e n t s w e r e c a r r i e d o u t  t h a t i t w o u l d be u s e f u l energy.  3  made d u r i n g  The r e s u l t s  and w i l l  be d i s c u s s e d  that the s i n g l e t coincidence detectors  The m e a s u r e m e n t s  s t a t e p-p  at higher  o f t h e s e measurements more f u l l y i n t h i s  were  tandem  have been r e p o r t e d  thesis.  It  was  i n t e r a c t i o n was v e r y e v i d e n t i n  s p e c t r a t a k e n a t an a n g u l a r  of 6°.  the  energies  the Chalk R i v e r  first  indicated  the e f f e c t of i n c r e a s i n g  t h e summer o f 1965 u s i n g  accelerator. (15)  to study  a  the  t h e U . B . C . V a n de G r a a f f g e n e r a t o r and t h e r e s u l t s  incident He  was  reaction using  r e c e n t l y a c q u i r e d two d i m e n s i o n a l k i c k s o r t e r t o a n a l y s e proton-proton events.  the  s e p a r a t i o n of the  the proton  The c o n t r i b u t i o n o f t h i s i n t e r a c t i o n r e l a t i v e  t o the c o n t r i b u t i o n from the ground s t a t e o f L i ^ d e c r e a s e d as bombarding  energy  1+  the  increased.  The n e x t s t e p i n t h e i n v e s t i g a t i o n was p-He  found  to  study  c o i n c i d e n c e s f r o m t h e same r e a c t i o n w i t h a t a r g e t - d e t e c t o r  geometry arranged energies  to observe  o f t h e two p r o t o n s .  c a r r i e d out u s i n g 3  system a t low r e l a t i v e  The same e x p e r i m e n t was  then,  a t r i t i u m t a r g e t i n p l a c e of the H e .  reactions He (He ,2p)He 3  t h e p-p  The  3  l f  and T ( H e , n p ) H e 3  I f  have s i m i l a r  Q-values  o f 12.859 a n d 12.095 r e s p e c t i v e l y a n d t h e r e f o r e t h e same e x p e r i mental arrangement a l l o w s  the s i n g l e t d i - p r o t o n s t a t e and  s i n g l e t d e u t e r o n s t a t e t o be o b s e r v e d and  compared.  the  - 15 This  thesis  -  presents  the d e s c r i p t i o n of the  p e r i m e n t a l a r r a n g e m e n t and t h e t e c h n i q u e u s e d i n p e r f o r m i n g measurements  along with a discussion  imate t h e o r i e s of f i n a l  of the r e s u l t s .  f o r m a l i s m (8)  s t a t e i n t e r a c t i o n s , the Watson t h e o r y  are used t o f i t the observed  and t h e s u i t a b i l i t y o f t h i s parameters.  (16)  of  spectra.  S t a t e m e n t s a r e made a b o u t t h e v a l i d i t y o f t h e s e two  nuclear  the  Two a p p r o x -  and t h e P h i l l i p s , G r i f f y and B i e d e n h a r n g e n e r a l i z e d d e n s i t y states  ex-  formalisms  experimental technique i n determining  - 16  -  CHAPTER  II  KINEMATICS AND EXPERIMENTAL TECHNIQUE A.  Kinematics  o f Three P a r t i c l e Breakup Before a systematic  Reactions  i n v e s t i g a t i o n of the  state i n t e r a c t i o n s involved i n a three p a r t i c l e c a n be c a r r i e d o u t , i t i s standing  necessary  breakup  t o have a c o m p l e t e  of the r e a c t i o n k i n e m a t i c s .  final reaction under-  The r e a s o n f o r c h o o s i n g  c o i n c i d e n c e t y p e o f measurement  r a t h e r than observing  particle  e v i d e n t once t h e k i n e m a t i c s  energy  s p e c t r a becomes  the breakup are u n d e r s t o o d . c a l c u l a t i o n s are necessary t a r g e t - d e t e c t o r geometry e x c i t a t i o n energies  a t h r e e body d e c a y .  t o scan the d e s i r e d range  coordinate These  which the t a r g e t nucleus  mass ( s c m ) latter  and t h e v a r i o u s  are u s e f u l  b e f o r e one c a n c h o o s e  of the p o s s i b l e  Several  in  I n a d d i t i o n a number  In  two p a r t i c l e  at rest,  recoil  in  these  publications  system  of The  important.  The  when  general breakup recent  are given  for  A.  be d e r i v e d i n t h i s  breakup parameters and a r e  (lab)  of the breakup  The i m p o r t a n t e x p r e s s i o n s  Some o f t h e e x p r e s s i o n s  B r o n s o n (17)  describe  systems have been d e r i v e d i n s e v e r a l  reference i n Appendix  various  systems.  o f mass ( r c m ( i ) ) .  the t h e o r e t i c a l a n a l y s i s  (17?l8).  experiment w i l l  of i n t e r n a l or  kinematic formula for a three p a r t i c l e  coordinate  of  appropriate  the system c e n t r e  centres  t h e s e q u e n t i a l two body d e c a y mode i s non-relativistic  the  single  kinematic  s y s t e m s may be u s e d t o  i n c l u d e the l a b o r a t o r y is  of  the  a  chapter.  which w i l l  summarized  u s e f u l i n the d e s i g n The s y m b o l s  be u s e d a r e t h o s e  i n T a b l e 1.  The  of  for  given  the the by  relationships  TABLE 1 Symbols used i n d e s c r i b i n g relevant  coordinate  Coordinate lab.  a t h r e e p a r t i c l e breakup  systems, (reference  system  three  1 and 2 ) .  Definition  scm. kinetic  T  Figure  i n the  H  i  velocity  energy of p a r t i c l e of p a r t i c l e  i .  i .  momentum o f p a r t i c l e i . p  i  Pi  •Pi  p o l a r angle of v e l o c i t y of p a r t i c l e i r e s p e c t t o t h e beam d i r e c t i o n . azimuthal angle with respect angle  of v e l o c i t y of p a r t i c l e  b e t w e e n t h e two v e l o c i t i e s emitted  i and  ;).  first  momentum o f p a r t i c l e j i n s y s t e m angle  i  t o t h e beam d i r e c t i o n ,  rem. system f o r p a r t i c l e i  polar  with  (i).  of p a r t i c l e J w i t h respect  to  t h e beam d i r e c t i o n , LP(i)  azimuthal angle  of p a r t i c l e  with  respect  t o t h e beam d i r e c t i o n . polar angle of p a r t i c l e the r e c o i l a x i s . v e l o c i t y o f scm.  scm (i) rem  internal  3k  system i n scm.  overall  mass o f p a r t i c l e  M  t o t a l mass o f  cos  system, system.  reaction.  i .  system  relations: a  to  or e x c i t a t i o n energy of c l u s t e r  m.  Useful  system i n l a b .  v e l o c i t y of r c m ( i ) Q-value f o r  j with respect  c o s O ^ -+- s i ^ O S w \ ^ c o s ( $ - § / ) c  L  (j+k).  - 17 between t h e parameters i n Figures designate  1 a n d 2.  i n the three coordinate The s u b s c r i p t s  0, 1,  2, 3 a r e u s e d t o  t h e i n c i d e n t p a r t i c l e , t h e two d e t e c t e d p a r t i c l e s and  the undetected p a r t i c l e r e s p e c t i v e l y . different pairs the s u b s c r i p t s positions  s y s t e m s a r e shown  Since  i t i s possible  that  o f p a r t i c l e s may b e d e t e c t e d w i t h t h e two d e t e c t o r s , 2 will  1,  while l e t t e r  r e f e r s p e c i f i c a l l y t o the detector  subscripts  b, c , d w i l l  be u s e d t o d i f f e r -  e n t i a t e between t h e p a r t i c l e s . A three p a r t i c l e f i n a l state i s completely by n i n e q u a n t i t i e s ,  f o r instance  p a r t i c l e momenta o r t h e e n e r g y  the nine  a n d t h e two p o l a r  angles o f each o f the t h r e e p a r t i c l e s . five  independent  quantities  components  described  of the three  coordinate  These a r e r e d u c e d t o  by i m p o s i n g  energy  a n d momentum  conservation.  Rf  =  T -t-C{ 0  PL2  with  =  Solving the terms  t %  f F£  T,  + T2  t  2miT  equations  gives the quadratic  - 2 B P  APz where  t  P  -  /\  =  B  »  Z  (mztm  T3  2-2  L  2-1 a n d 2-2 f o r  and r e g r o u p i n g  equation  t C 3  =0  )/na  P cos i©^ c  2-1  2-3  z  FJ c o s  A  i  Z  BEAfA DIRECT I OKI F i g u r e 1.  Relationship  between v e l o c i t i e s i n l a b . and  coordinate  systems.  scm.  - 18 The s o l u t i o n s  of the q u a d r a t i c equation  P w i t h the range  (B  ±  of values  of  B2- - A C  >  2  -  ±  Coincidence breakup  (for  instance  V B  2  - A C / A  d e t e r m i n e d by t h e r e q u i r e m e n t  t h e ?^  events a s s o c i a t e d  p a r t i c l e b •»  P-j_.pl o  »  v s  the r e l a t e d T  vs.  2  plane.  with a particular  d e t e c t o r 1,  p a r t i c l e c «+  d e s c r i b e d by e q u a t i o n  A similar locus  ane  T3 Cos 0  The k i n e t i c e n e r g y  T 0  breakup,  +  0  - P oose V 2  2  only  P  2-6  3  one p a r t i c l e i n t h e  only i f  quantities.  the breakup  two body d e c a y .  occurs  then the averaging  observed. If  process  breakup  to describe be' a n  type  s e q u e n t i a l l y through  This  the  average  An experiment of t h i s  w e l l d e f i n e d i n t e r m e d i a t e s t a t e and i f  the u s u a l  used,  2-5  z  s p e c t r u m o f one p a r t i c l e w i l l  the f i r s t e m i t t e d p a r t i c l e i s to  -T  -T,  observing  o v e r t h e two u n o b s e r v e d i s meaningful  third  may be c a l c u l a t e d  three of the f i v e q u a n t i t i e s necessary  the energy  reasonably  Q  - Ff c o s O ,  Since determines  T^ o f t h e  expressions.  -  = (P  3  2-*+  c a n be c a l c u l a t e d f o r  p a r t i c l e and t h e l a b o r a t o r y p o l a r a n g l e s »Q^, from the f o l l o w i n g  that  0  d e t e c t o r 2) m u s t be on a c u r v e d l o c u s in  are  a  the spectrum  reduces  the  breakup  no p a r t i c l e i d e n t i f i c a t i o n i s tends  t o c o v e r up much o f  of  the  - 19 s t r u c t u r e w h i c h m i g h t be e x p e c t e d t o a p p e a r i n t h e s p e c t r u m i f i n t e r m e d i a t e s t a t e or s t r o n g  final  Several  h a v e b e e n made i n t h e p a s t  improper conclusions  d o m i n a n t d e c a y mode i n t h i s observe  in  two d e t e c t o r s  present. of  the  t y p e o f r e a c t i o n due t o a f a i l u r e  the above r e q u i r e m e n t s .  by u s i n g  state interaction i s  This  to observe  i n d e t e r m i n a c y c a n be  two o f t h e f i n a l  an  state  to  removed  particles  coincidence. Since  the a n g u l a r  coordinates  o f t h e two d e t e c t o r s  d e t e r m i n e t h e p o l a r a n d a z i m u t h a l a n g l e s *9< , $ 1  necessary breakup  completely.  to determine both T  This  quantity is  it  2  for  2  P , 2  o f P-j_.  the energies b,c,d  i t is  evident  two s o l u t i o n s  of  one  desirable  reasons? and  contam-  reduced.  that for c e r t a i n detector  is  a double valued  function  c a n be s e p a r a t e d by  observing  of both p a r t i c l e s .  six distinct loci  The p r o b l e m o f  energy  greatly  2  the s i x permutations  is  the energy  a r e d i s t i n c t p a r t i c l e s o f d i f f e r e n t mass  there e x i s t  locus  is  is  the  experimentally i t is  the f o l l o w i n g  and t h e r e f o r e T ,  These  usually  from a c c i d e n t a l c o i n c i d e n c e s  F r o m e q u a t i o n 2-h  If  However  two b o d y r e a c t i o n s  angles  c)  and T  x  The b a c k g r o u n d inant  b)  O^, $ ,  ?  t o d e t e r m i n e o n l y one more q u a n t i t y t o s p e c i f y  of the d e t e c t e d p a r t i c l e s .  a)  1  2  V  s,  each event w i t h the  s i m p l i f i e d by u s i n g  analysis.  T-j_ c o r r e s p o n d i n g  If  the l o c i  two  appropriate  dimensional  overlap considerably  some f o r m o f p a r t i c l e i d e n t i f i c a t i o n i s  necessary  Another  coincidence  solution is  to  o f t h r e e p a r t i c l e s w i t h two d e t e c t o r s .  associating  somewhat  T  then  to perform a t r i p l e  as  then well.  - 20 measurement with three d e t e c t o r s , together with two  dimensional  energy a n a l y s i s as has been done by Reimann i n the r e a c t i o n Li (He ,p)2He 6  3  l f  (19).  The experimental work d e s c r i b e d i n t h i s t h e s i s  uses  two d e t e c t o r s t o perform the two d i m e n s i o n a l energy a n a l y s i s .  The  parameters B.  which are determined  Experimental  are O^, $ »*^'2» ^2> 1  T  l '  a  n  "*"2*  d  Technique.  T y p i c a l l o c i of c o i n c i d e n c e events or "kinematic contours" i n the T  plane are shown i n F i g u r e 3 f o r p-p  vs. ^  2  and p-He*" c o i n c i d e n c e s from the r e a c t i o n H e ( H e , 2 p )Re* 1  3  3  .  contours have been c a l c u l a t e d f o r an I n c i d e n t beam energy MeV  These T =i.50 Q  and f o r the case w i t h the two d e t e c t o r s coplanar with the beam.  To s i m p l i f y the s i t u a t i o n d e t e c t o r 1 i s assumed t o observe o n l y protons while d e t e c t o r 2 can observe both protons and a l p h a p a r t i c l e s . D e t e c t o r 2 i s f i x e d a t *G<= 90° and d e t e c t o r 1 can be r o t a t e d i n 2  the plane of the beam w i t h the angular s e p a r a t i o n of the d e t e c t o r s +  T  *  i e  S  r a  u s i n g the U.B.C. IBM JOkO  P h shown has been computer  generated  computer and a Calcomp p l o t t e r .  A  g e n e r a l program f o r c a l c u l a t i n g kinematic contours i s l i s t e d i n Appendix B.  The number a d j a c e n t to each contour r e f e r s to the  value of A-j_2» The d i s t r i b u t i o n of c o i n c i d e n c e events a l o n g a kinematic contour i s determined  by the i n t e r a c t i o n s which take  p l a c e between the p a r t i c l e s d u r i n g breakup.  The u s u a l method  of comparing the experimental c o i n c i d e n c e y i e l d w i t h  theoretical  p r e d i c t i o n s i s t o use the t r i p l e c o r r e l a t i o n d i s t r i b u t i o n s  (20)  o o. o  He(He,2p)He " .859 MeV .50 M e V 90°  - - ODD  2.000  4.000  6.000  fl(MEV)  Figure 3.  Kinematic  He (He3,2p)He- . J  h  contour  b.oao  f o r p-p a n d p-He  10.000  12.000  14.000  16.000  c o i n c i d e n c e s from t h e r e a c t i o n  The-number a d j a c e n t t o e a c h c u r v e  i sthe corresponding value o f A  1 2  - 21 given  -  by  O-C-T,)-  2-8  ^  C^Tl)-  or  2-9  T h e s e d i s t r i b u t i o n s a r e o b t a i n e d by summing  the  coincidence events along a p a r t i c u l a r contour f o r constant case of  GTC^)  and T  i n the case of  2  (T(T ).  d i s p l a y e d i n the form of a h i s t o g r a m . is  shown l a t e r i n F i g u r e  2  in  These sums a r e  A t y p i c a l example o f  the  usually this  15«  A s m e n t i o n e d i n t h e i n t r o d u c t i o n , two r e a c t i o n mechanisms  are possible  f o r a t h r e e body d e c a y : d i r e c t breakup  t h r e e p a r t i c l e s and s e q u e n t i a l breakup In the f i r s t case, i f i t i s statistical,  that i s  (see Appendix -  assumed t h a t t h e b r e a k u p i s  then the t r i p l e  purely  o n l y on t h e  c o r r e l a t i o n has  the  form  A):  ^  where K i s  t h r o u g h an i n t e r m e d i a t e s t a t e .  the decay p r o b a b i l i t y depends  a v a i l a b l e phase-space,  into  2-io  a constant depending  on the p a r t i c l e m a s s e s .  y i e l d s a broad s t r u c t u r e l e s s d i s t r i b u t i o n which i s  This  characteristic  of s t a t i s t i c a l breakups. If  the s e q u e n t i a l decay process  takes p l a c e ,  then  there w i l l  be a n i n c r e a s e i n t h e c o i n c i d e n c e y i e l d a t p o i n t s  the T  T^ p l o t w h e r e t h e i n t e r n a l o r e x c i t a t i o n e n e r g y  2  vs.  o f t h e two p a r t i c l e c l u s t e r s ,  either E  1 2  ,  E^,  or E ^ ,  of  in one  corresponds  - 22 to a s t a t e of that p a r t i c u l a r system.  The w i d t h o f t h i s  state  will  be r e f l e c t e d i n t h e w i d t h o f t h e p e a k i n t h e c o i n c i d e n c e d i s t r i b u t i o n , A well defined state w i l l w h i l e a broad s t a t e w i l l of the c o n t o u r .  Since  appear as a p o i n t i n the T produce c o i n c i d e n c e events  the e x c i t a t i o n energies  before designing  accessible  i t is  worth-  the t a r g e t  and  chamber  any p a r t i c u l a r r e a c t i o n . Two c a s e s m u s t be c o n s i d e r e d  in this  the f i r s t e m i t t e d p a r t i c l e i n the breakup  1)  is  w i t h one o f t h e p a r t i c l e s f r o m t h e b r e a k u p iate  calculation:  detected  system.  In  the f i r s t case o r d i n a r y  If  we assume t h e i n t e r m e d i a t e s y s t e m i s  energy  r e l a t i o n s are given  T  0  — E  + Q  2  3  two b o d y k i n e m a t i c r e l a t i o n s  rearranging (  T  '  V  Solving  terms  '  Q -  c a n be  used. and  by  = T  t  +7^3  2-12  of the v i r t u a l  2  system (2,3).  system.  t h e n t h e momentum  (2,3)  where P,,^ a n d T ^ a r e t h e momentum and e n e r g y  «  along  of the i n t e r m e d -  b o t h d e t e c t e d p a r t i c l e s come f r o m t h e i n t e r m e d i a t e  2)  E  segment  out the r e l a t i o n s between the e x c i t a t i o n energy  the o t h e r breakup .parameters for  T^ p l o t  over a  which are  a l o n g a g i v e n c o n t o u r depend on the d e t e c t o r a n g l e s , while working  vs.  2  both equations  a n d 2-12  2-11  for P  and  g  gives +  ^  [  ^ ^  2  T  T (rr\o-™ -m0 0  t  A s i m i l a r r e s u l t may be o b t a i n e d f o r  -  ~  5  ^  2-13  T, NA~] b  y  interchanging  the  - 23 subscripts  1 and  -  2.  In  the second case the i n t e r m e d i a t e system i s  (1,2).  The momentum a n d e n e r g y r e l a t i o n s may be w r i t t e n =  PTZ  T  2  ^ E , z  ^  "  T  K  *  2-i^  2-15  ^ T z  w h i c h y i e l d s on e l i m i n a t i n g  P^  2  A . J 2-16  E, = - i — r r^T] • - m.Tk - 2 i ^ T * a  Curves particle  o f f i x e d e x c i t a t i o n e n e r g y i n one o f t h e two  s y s t e m s may be d r a w n on t h e T  vs.  2  plot.  If  it  is  d e s i r e d t o study a p a r t i c u l a r system a t a g i v e n e x c i t a t i o n energy then i t i s necessary  t o choose a d e t e c t o r arrangement which y i e l d s  a contour i n t e r s e c t i n g the e x c i t a t i o n c u r v e .  The c o n t o u r  should  be c h o s e n s o t h a t n o o t h e r i n t e r s e c t i o n p o i n t s o f t h e e x c i t a t i o n curves from the other p o s s i b l e interest.  F i g u r e 4- shows t h e p-He  w i t h the l o c i systems.  s y s t e m s a r e n e a r t o t h e one contours  f r o m F i g u r e 3-  along  of constant e x c i t a t i o n i n the three i n t e r m e d i a t e  The c u r v e s m a r k e d  E  2  3  =  M  e  V  a  n  d  B  i2  M  =  e  V  pond t o t h e g r o u n d s t a t e o f L i ^ a n d a b r e a k u p p r o c e e d i n g this  of  s t a t e would produce events along these c u r v e s .  hatched area represents  t h e r e g i o n where e v e n t s  o f a two p r o t o n s y s t e m w i t h r e l a t i v e e n e r g y l e s s be e x p e c t e d t o a p p e a r .  The  from the  corresthrough crossbreakup  t h a n ^00 keV w o u l d  o o  o o  He (He^2p)He' T « 1.5 0.MeV. 3  0  o o o CO  2  « 90°  o o o  UJ  E . ^ < 5 0 0 kcV  ( M o  i<  .97  E  o  I 2  L  9  MeV  7  D O  -.000 F i g u r e k.  2.0O0 Kinematic  6.000 contours  f o r p-He  A l s o shown a r e some o f t h e c o r r e s p o n d i n g  8.000  10.000  16.000  L2.0DQ  c o i n c i d e n c e s f r o m t h e r e a c t i o n He- (He--*,2p)He . , 5  excitation  e n e r g i e s i n t h e two p a r t i c l e  systems.  - 2h CHAPTER  III  EXPERIMENTAL ARRANGEMENT A.  Introduction As h e l i u m - 3 and t r i t i u m a r e b o t h gases a t  temperature, i t i s particular angular  an obvious  experiment.  c h o i c e t o u s e a gas  target i n  Gas t a r g e t s h a v e s e v e r a l a d v a n t a g e s  d i s t r i b u t i o n measurements  t h a n one d e t e c t o r .  room  or measurements  Target u n i f o r m i t y i s  in  r e q u i r i n g more  inherent except f o r  beam h e a t i n g e f f e c t s and t h e r e a r e no p r o b l e m s w i t h t a r g e t C o n t a m i n a n t r e a c t i o n s c a n be h e l d t o a minimum by u s i n g t o d e t e r m i n e the a c t i v e volume o f the t a r g e t gas. be d i v i d e d i n t o two t y p e s :  this  small  backings.  collimators  Gas t a r g e t s  t h o s e i n w h i c h t h e beam e n t e r s  may  from  t h e h i g h vacuum r e g i o n t h r o u g h a t h i n w i n d o w and t h o s e i n w h i c h t h e beam e n t e r s first  t h r o u g h a d i f f e r e n t i a l l y pumped c a p i l l a r y .  t y p e was u s e d i n t h i s  as l i t t l e tritium.  t a r g e t gas  as p o s s i b l e ,  Nickel f o i l  window b e c a u s e availability  e x p e r i m e n t as  The  i t was d e s i r a b l e t o  p a r t i c u l a r l y i n the case  was c h o s e n a s  the m a t e r i a l f o r the  use  of entrance  o f i t s h i g h m e c h a n i c a l s t r e n g t h and t h e c o m m e r i c a l  of high q u a l i t y vacuum-tight  f o i l s of the r e q u i r e d  thicknesses. The c h a r g e d p a r t i c l e s f r o m t h e r e a c t i o n a r e with solid state detectors. are l i n e a r response  The r e q u i r e m e n t s  for protons  over a range  on t h e s e  of energies  monitored  detectors from  500 keV t o 1*+ MeV and f o r a l p h a p a r t i c l e s f r o m 500 keV t o 5 MeV along w i t h an i n t r i n s i c r e s o l u t i o n of l e s s barrier detectors using  t h a n 35 k e V .  h i g h r e s i s t i v i t y (12,000 ohm=cm)  s i l i c o n were f o u n d t o meet t h e s e r e q u i r e m e n t s .  Surface n-type  Two m e t h o d s  of  - 25 d e t e c t i n g the r e a c t i o n products employed. a series  The d e t e c t o r s may be i m m e r s e d of collimators  t a r g e t volume cell. very  are possible  and d e f i n i n g  i n t h e t a r g e t gas u s i n g  slits  t o determine  In the l a t t e r thin foils  the energy  case  through  t h e gas c e l l  loss  i n traversing  concern than the energy  very  small quantities  arrangement.  particles  target  the t a r g e t  of target  The  gas p r e s s u r e s a r e u s e d gas may t h e n be o f In  addition  this  were u s e d i n c o u r s e  of  these  t h a t gas t a r g e t s  i n t h e chamber d e s i g n and s o l i d  state  be u s e d i s t h e a n g u l a r v a r i a t i o n o f t h e d e t e c t o r s . a z i m u t h a l a n g l e s o f t h e two d e t e c t o r s  variable  i n s u c h a way t h a t t h e d e s i r e d  energies  of the intermediate t h e r e i s more  present,  configuration  t o be  In which can  the intermediate  reason  f o r choosing  one  The d e c i s i o n c a n t h e r e f o r e be made  o f s i m p l i c i t y i n chamber Two r e a c t i o n chambers  i n determining  are required  s y s t e m s c a n be o b t a i n e d .  and t h e r e i s no a p r i o r i  The f i r s t t a r g e t - d e t e c t o r  detectors  The p o l a r  t h a n one d e t e c t o r c o n f i g u r a t i o n  over another.  other  range of e x c i t a t i o n  be u s e d t o y i e l d t h e same i n f o r m a t i o n a b o u t  on t h e b a s i s  of  measurements.  than the requirement  states  pass.  gas may be u s e d w i t h  The p r i m e c o n s i d e r a t i o n  general  t h e gas  e x i t windows  l o s s i n the e x i t f o i l .  Both arrangements  experimental  must have  which the charged  more  and/or  the a c t i v e  o r t h e y may be p l a c e d i n t h e vacuum o u t s i d e  s e c o n d method i s p r e f e r a b l e i f l a r g e as  when gas t a r g e t s a r e  construction. were e m p l o y e d i n t h e e x p e r i m e n t .  configuration  c a l l e d G e o m e t r y #1 was u s e d  the r e l a t i v e contributions  a n d t h e two p r o t o n s y s t e m i n t h e r e a c t i o n  of the s t a t e s Ee^(Ee^  ^2^)Ee^  of L i ^ by  studying  26  -  proton-proton coincidences.  schematically i n Figure  In  this  5a, t h e p o l a r a n g l e s  a r e k e p t a t 90° w i t h t h e a n g u l a r  geometry,  of both  s e p a r a t i o n of the  detectors  detectors  v a r i a b l e i n t h e a z i m u t h a l d i r e c t i o n f r o m 180° t o 6 ° . shows t h e k i n e m a t i c c o n t o u r s from t h i s angular  f o r p-p,  p-He  r e a c t i o n at an i n c i d e n t energy  separations  ^  = 1  °  6  2  a  n  ^ i 2  d  Figure  and He - p  o f 1.15 •  =  T  n  shown  coincidences  MeV and  e  6  for  and  V-Re*  LL  He  - p c o i n c i d e n c e s may be removed by p l a c i n g a f o i l  of each d e t e c t o r to degrade This  results  The r e g i o n s  i n only a s l i g h t  region which w i l l  t h a n 500 k e V .  evident  contributions  G e o m e t r y #2  i n t h e two p r o t o n s y s t e m  MeV c o r r e s p o n d i n g geometry  the  coincidence events  l y i n g along  contours  coincidences  area indicates  corres-  of  t h e two  r e p r e s e n t a r e l a t i v e energy  less  lines  i n t h e p-He " 14  to the ground s t a t e o f L i ^ .  g i v e s good s e p a r a t i o n b e t w e e n  from both intermediate The s e c o n d  particles.  T. p l o t o f p - p  The c r o s s h a t c h e d  Coincidence events  that this  of the a l p h a  front  t o the p r o t o n - p r o t o n  be p o p u l a t e d b y p - p  and E ^  s y s t e m o f 1.97 is  7»  t o a r e l a t i v e energy  m a r k e d E-^  change  o f i n t e r e s t i n t h e T^ v s .  a r e shown i n F i g u r e  ponding  the energy  in  the  systems.  target-detector configuration  called  was u s e d i n t h e i n v e s t i g a t i o n o f t h e p - p and p - n  s t a t e i n t e r a c t i o n s i n the r e a c t i o n s  It  He (He ,2p)He 3  3  i +  and  final  T(He ,np)He 3  LL  As  i t was n e c e s s a r y  interactions,  coincidences  t o compare  G e o m e t r y #1 d i d n o t a l l o w t h e d e s i r e d r a n g e  e x c i t a t i o n energies Figure  t o u s e p-He  t o be s t u d i e d .  I n G e o m e t r y #2  as  the of  shown i n  5h b o t h d e t e c t o r s a r e k e p t i n t h e p l a n e o f t h e beam w i t h  one d e t e c t o r f i x e d a t a n a n g l e  o f 90° w i t h r e s p e c t  t o the  beam  DETECTOR 2.  9 0 ° (FIXED)  BEAM DIRECTION  DETTECTOR I  (a)  GEOMETRY  *  I  DETECTOR 2  9  % « 9 o ° (FIXEt})  Dl RECT»OKJ t>€TEfi-TOR. | ("b) Figure  5.  GEOMETRY  # £  S c h e m a t i c d i a g r a m o f G e o m e t r y #1 a n d G e o m e t r y  #2,  o o o  •3  «2  H e { H e ,2p)He .l5.-MeV 3 CD  ' -',000 Figure-6.  2*000 Kinematic  He^CHe^ap^Ie^.  ij'.OOO contours  c'.OOO  8>0O0  TKMEVJ  f o r p - p , p-He  10.000  ~  12.000  a n d He -p c o i n c i d e n c e s f r o m  14.000  16.003  the reaction  The number a d j a c e n t t o e a c h c u r v e I s : t h e c o r r e s p o n d i n g , v a l u e o f ^ \ * ?  o a o  C-'i.  3,  3  H e ( H e ,2p)He  O o t_>  TQ  MeV  = 1.15  ©. = 9 0 ° In  A  a o o  j  2  -  «  4  2  €> * 9 0 ' . * ,  jo '  a  o o  U-l  • 1.97  E < : 5 Q 0 keV  l—CO  UeV  r  o  o o o  o o a  -.000 Figure; 7 . <-i ,•  2.000 Kinomatic  4.000  6.000  8.000  Tl (MEV)  ID.000  iB.ooa  14-000  12.000 0  'D  LL  c o n t o u r s f o r p-p c o i n c i d e n c e s f r o m . t h e r e a c t i o n H e ( H e , 2 p ) h e . A l s o i-ho r>opi>P«nnnriinVexcitation'ener'eies i n t h e two. p a r t i c l e s y s t e m s . J  J  - 27  -  direction.  The o t h e r d e t e c t o r i s v a r i a b l e i n t h e p o l a r  for angular  separations  kinematic  contours  been d e s c r i b e d  o f t h e d e t e c t o r s f r o m 180°  and e x c i t a t i o n curves  dences i n which the a l p h a  I n studying  t o d i s c r i m i n a t e a g a i n s t He^-p particle  e n t e r s d e t e c t o r 1.  d i s c r i m i n a t i o n i s made w i t h t h e u s e o f a t h i n The d e t a i l s  chapter.  The  both  coinci-  Again the  foil.  o f t h e two t a r g e t c h a m b e r s a n d a  d e s c r i p t i o n of the t r i t i u m handling part of this  t o 135°.  f o r t h i s geometry have  p r e v i o u s l y i n F i g u r e s 3 a n d k.  reactions i t i s necessary  direction  system i s g i v e n i n the f i r s t  The r e s t o f t h e c h a p t e r  contains a  d i s c u s s i o n o f t h e e l e c t r o n i c s u s e d i n t h e two d i m e n s i o n a l  energy  a n a l y s i s and t h e use o f an o n - l i n e computer t o s i m p l i f y t h e d a t a handling B.  and a n a l y s i s .  G e o m e t r y #1  T a r g e t Chamber The t a r g e t chamber i s shown i n F i g u r e  8.  The  e x t e r n a l beam, d e f i n e d by a s e r i e s o f c o l l i m a t o r s ( A ) , e n t e r s t h e chamber t h r o u g h a t h i n brass  tube ( B ) .  nickel  f o i l mounted on a r e m o v a b l e  The d e t e c t o r h o l d e r s  ( C ) a n d ( D ) a r e mounted o n  r a d i a l a r m s , one o f w h i c h i s f i x e d and t h e o t h e r may be r o t a t e d i n the plane  perpendicular  t o t h e beam d i r e c t i o n .  s e p a r a t i o n o f the d e t e c t o r s i s read o u t s i d e o f t h e chamber.  The  angular  on t h e s c a l e ( E ) on t h e  The d e t e c t o r h o l d e r s may be p o s i t i o n e d  a t a n y r a d i a l d i s t a n c e f r o m t h e beam a x i s , w i t h i n t h e c o n f i n e s o f the  c h a m b e r , a n d t h e y may a l s o be r o t a t e d a b o u t a n a x i s  t o t h e beam d i r e c t i o n .  This r o t a t i o n serves  parallel  two p u r p o s e s ?  to  i n c r e a s e t h e e f f e c t i v e d e p l e t i o n t h i c k n e s s o f the d e t e c t o r s and t o a l l o w the detectors  t o be p o s i t i o n e d c l o s e r t o g e t h e r  f o r measurements  at small angular  separations.  6° were made u s i n g  28  -  The m e a s u r e m e n t s a t a n a n g l e o f  two r e c t a n g u l a r d e t e c t o r s mounted  i n a l u c i t e block.  The d e t e c t o r s were u s u a l l y p l a c e d a t a  d i s t a n c e o f 5«0 t o 5.5 em. f r o m t h e beam a x i s .  The a c t i v e v o l u m e  of t h e gas t a r g e t i s d e t e r m i n e d by a c y l i n d r i c a l width  5 nun. a t a d i s t a n c e o f 12.7 mm.  entrance  apertures,  slit  (F) of  f r o m t h e beam a x i s a n d by  adjustable s l i t s i n f r o n t of the d e t e c t o r s . the  together  The a l i g n m e n t o f  the d e f i n i n g s l i t s and the a n g u l a r  was done o p t i c a l l y w i t h t h e a n g u l a r  readings  accurate  scale  to better  than + 1°. The i n c i d e n t beam i s s t o p p e d i n a b r a s s  cup ( G )  i n s u l a t e d f r o m t h e r e s t o f t h e chamber t o a l l o w t h e beam to  be m o n i t o r e d .  T h i s m e a s u r e m e n t was u s e d o n l y a s a means o f  o p t i m i z i n g t h e beam f o c u s a s t h e t a r g e t g a s s u r r o u n d i n g stop prevented  any a c c u r a t e  0.050 m i l s t h i c k .  These f o i l s  square, obtainable  W a t e r bury., C o n n e c t i c u t . to  their  technique  brass  holders  window a r e t y p i c a l l y  a r e Grade C ( w h o l l y  f r o m Chromium C o r p o r a t i o n  O r i g i n a l l y the f o i l s  0.025 t o  light-tight) of America,  were s o f t = s o l d e r e d  stress to the f o i l s  A s i m p l e r method o f a t t a c h i n g t h e f o i l s ,  u s i n g a n e p o x y r e s i n HYSOL t y p e  V3O7 w i t h t y p e  ( o b t a i n a b l e f r o m HYSOL C o r p o r a t i o n , considerably better success. between t h e f o i l  The  using a high t e n a c i t y f l u x but t h i s  was f o u n d t o c a u s e c o n s i d e r a b l e  due t o t h e h e a t i n g .  t h e beam  beam c u r r e n t d e t e r m i n a t i o n .  n i c k e l f o i l s used i n the entrance  x  current  hardener  O l e a n , New Y o r k ) gave  The l o s s o f a good h e a t  and i t s h o l d e r  maximum beam c u r r e n t t h e f o i l  3h0k  contact  d i d n o t seem t o l i m i t t h e  could withstand  indicating  that  a good p o r t i o n o f t h e f o i l the t a r g e t  -  heating  i s removed by c o n d u c t i o n  w i t h a W a l l a c e and  t a r g e t gas  Hg).  generally used.  The  Research Corporation l e s s t h a n 3•  6x10"^%  G e o m e t r y #2  pressure  Tiernan Absolute  FA-160 ( O - ^ I O mm.  A He  Pressure  and  had  was  monitored  I n d i c a t o r Type  o f 100-150 mm.  target pressure t a r g e t gas  3  i s continuously  obtained  The  of t h i s  a s p e c i f i e d p u r i t y o f 99.8$ H e  in  cell  and  the f i l l i n g  c e l l was  designed  so t h a t i t c o u l d be  intended  t o d i s c a r d the  was  as p o s s i b l e w o u l d b e ' u s e d . easily installed,  low  The  gas  as i t  Two  views of the  target  The  gas  is  side flanges using  event  cell  t a r g e t gas  lengthwise  enters  the c e l l  through the  T e f l o n w a s h e r s (H)  t h r o u g h a 1/16"  s t e m o f t h e gas  A  c l i p attached  is  the  t o a K o v a r s e a l on t h e r e a r f l a n g e ( C )  stem o f the c e l l a f t e r  c u r r e n t t o be  i n s t a l l a t i o n t o a l l o w the  and  a  the diameter  cell  a l i g n e d w i t h a s i m i l a r h o l e i n the mounting f l a n g e .  to  of  (A)  Neoprene 0 - r i n g s e a l t o keep i t i n s u l a t e d from the r e s t of  hole d r i l l e d  was  or e x i t f o i l s . 10.  i n the  kept  cell  shown i n F i g u r e s 9 and of the  manifold  gas.  c o n t a m i n a t e d gas  breakage of the entrance  The  the  chamber t o a l l o w i t t o be u s e d w i t h t r i t i u m  t a r g e t gas  chamber.  with  3  tritium.  so t h a t a s l i t t l e  mounted on one  was  T a r g e t Chamber  v o l u m e o f t h e gas  assembly are  Hg  from Monsanto  S e v e r a l s a f e t y f e a t u r e s were i n c o r p o r a t e d design  through  gas. The  C.  29  and  spring attached beam  monitored. F o i l s are attached  t o the  gas  cell  on  three  sides.  The  f o i l s f o r the entrance window and alpha p a r t i c l e e x i t window  are t y p i c a l l y 0,025 m i l s t h i c k and the f o i l c o v e r i n g the p r o t o n e x i t window i s 0,200 m i l s t h i c k .  The p r o t o n window has a  r e c t a n g u l a r c r o s s s e c t i o n so t h a t the protons  can be observed a t  p o l a r angles from 90° t o ^5° with r e s p e c t t o the beam d i r e c t i o n . These f o i l s were a t t a c h e d u s i n g the epoxy r e s i n p r e v i o u s l y mentioned and the gas c e l l was vacuum t e s t e d before i n s t a l l e d u s i n g a d i f f e r e n t i a l pressure o f 200 mm,  being Hg o f hydrogen,  50$ was obtained i n mounting the  A success r a t i o o f approximately foils.  The p r o t o n d e t e c t o r (B) i s mounted on a brass arm (I)  which a l s o c o n t a i n s a p a i r o f c o l l i m a t o r s t o d e f i n e the s o l i d  angle. of  This arm can be r o t a t e d i n the plane o f the beam by means  a s t e e l rod (F) vacuum coupled  through  the remaining  side flange  A p o i n t e r (G), a t t a c h e d t o the end o f t h i s rod r o t a t e s over an angular to  s c a l e ( n o t shown) mounted on the o u t s i d e o f the chamber  allow the angular s e p a r a t i o n o f the d e t e c t o r s t o be  determined.  The alpha p a r t i c l e d e t e c t o r (D) i s f i x e d a t an angle o f 90° w i t h r e s p e c t to the beam d i r e c t i o n .  The p o s i t i o n i n g • o f the two d e t e c t o r  i s accurate to + The a c t i v e volume of the gas t a r g e t i s determined by a ^,75 mm. diameter  a p e r t u r e ( J ) a t a d i s t a n c e o f 16 mm.  the a x i s o f the t a r g e t and by a r e c t a n g u l a r s l i t each d e t e c t o r . to prevent  from  (K) i n f r o n t o f  An a n t i s c a t t e r i n g c o l l i m a t o r ( L ) i s a l s o p r o v i d e d  the h i g h energy protons  from e n t e r i n g the d e t e c t o r s  a f t e r s c a t t e r i n g from the chamber w a l l s .  The i n c i d e n t beam enters  the chamber through a s e r i e s o f s t a i n l e s s s t e e l c o l l i m a t o r s ( E ) ,  - 31 The  e n t i r e a s s e m b l y was a l i g n e d o p t i c a l l y u s i n g a l i g h t beam  a helium-neon D.  from  laser.  T r i t i u m Handling  System  F i g u r e 11 i s a d i a g r a m o f t h e pumping a n d g a s h a n d l i n g s y s t e m u s e d i n c o n j u n c t i o n w i t h t h e t r i t i u m and h e l i u m gas  targets.  The s y s t e m c a n be i s o l a t e d f r o m  t h e vacuum s y s t e m  o f t h e beam h a n d l i n g e q u i p m e n t by u s i n g a C.V.C. p n e u m a t i c a l l y operated  gate v a l v e .  T h i s v a l v e c a n be o p e r a t e d m a n u a l l y  a c t u a t e d by a p r e s s u r e r i s e i n t h e t a r g e t c h a m b e r . has  i t s own a i r s u p p l y and i s o p e r a t e d  so t h a t a n e l e c t r i c a l f a i l u r e w i l l  or  The v a l v e  i n t h e n o r m a l l y c l o s e mode  leave the valve c l o s e d .  The  s i g n a l t o a u t o m a t i c a l l y a c t u a t e the v a l v e i s o b t a i n e d from a n i o n i z a t i o n gauge w i t h t y p e UBC-NP-12 c o n t r o l u n i t s i t u a t e d i n front of the target c o l l i m a t o r s .  Normally  the pressure i n the  —6 vacuum s y s t e m i s 3x10  D  mm.  Hg.  The a d j u s t a b l e t r i p - o u t o f t h e  gauge i s s e t t o o p e r a t e when t h e p r e s s u r e r i s e s t o 10"^ mm. In  order t o prevent any gas from  the target c e l l  from  Hg.  entering the  beam l i n e b e f o r e t h e v a l v e i s c o m p l e t e l y c l o s e d , a s e r i e s o f b a f f l e s i s p l a c e d i n t h e l i n e b e t w e e n t h e i o n i z a t i o n gauge a n d t h e gate v a l v e . The  vacuum s y s t e m c o n s i s t s o f a n E d w a r d s H i g h Vacuum  2M*+A m e r c u r y d i f f u s i o n pump w h i c h pumps i n t o a r e s e r v o i r o f one litre  capacity.  operate  T h i s b o o s t e r pump was c h o s e n b e c a u s e i t c a n  i n t o a b a c k i n g p r e s s u r e o f 30-35 mm.  r e s e r v o i r may be e v a c u a t e d mechanical  Hg.  The p u m p i n g  u s i n g a W e l s h t y p e l*+05 D u o - s e a l  pump when n o n - c o n t a m i n a t i n g  gases a r e being used.  If  GAS TARGET CELL BO0f?DON TYPE PRESSORS 3Ai  TRITIUNS GONTAIMER OFT STAINLESS STEEL, DlAPWRA&M  ACTIVATED T R A P  TO  EDWARDS 2.M4-A MERCURY DIFFUSION POV\P UMTH. COL.D T R A P  CHARCOM-  Pi RAMX  Figure 11.  VAN D E SRAAPF  ACCELERATOR.  PUhAPlNG RESERVOIR  Diagram  o f pumping a n d g a s h a n d l i n g  system  - 32 t r i t i u m i s present c h a r g e d w i t h 225 liquid  -  t h e r e s e r v o i r i s opened t o a c h a r c o a l  gms  o f a c t i v a t e d c h a r c o a l and  nitrogen bath.  The  immersed i n a  a d s o r p t i o n r e l a t i o n f o r hydrogen i n (21)  c h a r c o a l a t l i q u i d n i t r o g e n t e m p e r a t u r e s i s g i v e n by \ where V per  = 1.6xl0~  P  2  u  i s t h e v o l u m e o f h y d r o g e n i n c c . a t S.T.P. a d s o r b e d  Q  gram o f c h a r c o a l and The  gas  diaphragm s e a l v a l v e s to  trap  a brass  block.  P^  i s the e q u i l i b r i u m p r e s s u r e  handling manifold  in  c o n s i s t s o f f o u r HOKE  of a l l metal c o n s t r u c t i o n s i l v e r  The'tritium container  ORNL t y p e  soldered  HoH-50-3  c o n t a i n i n g l O c c . of t r i t i u m i s connected t o the m a n i f o l d v a l v e A.  Valves  B and  evacuated simultaneously e n t i a l across  the f o i l s .  c o n t a i n e r , as w e l l as detector.  C a l l o w b o t h s i d e s o f t h e gas to maintain  The  gas  Valve  The  volume of the  t a r g e t s y s t e m and  t h e gauge a c c o u n t i n g Hg,  pressure  w i t h 1/8"  vacuum).  A pressure  entire  system i s enclosed  with  o f 50  used d u r i n g  t h i c k l u c i t e and  i n an a i r - t i g h t  exhausted to the  u s i n g a s m a l l a e r o f o i l f a n of approximately  Ports are  leak  mm.  the  measurements. The  covered  He^  gauge i s 20 c c .  f o r most of the volume.  be  continuously  gauge ( 0 - 3 0 " Hg  e q u i v a l e n t t o a b o u t k- c u r i e s o f t r i t i u m , was  experimental  air  pressure  is  to  differ-  D i s used to a t t a c h the  i n the t a r g e t c e l l  monitored w i t h a Bourdon type  through  cell  a minimum p r e s s u r e  f o r leak t e s t i n g using a helium  pressure  microns.  cut i n the l u c i t e  manipulated  and  t h e gas  cell  of personal  contamination.  200  to a l l o w the necessary t o be Tests  replaced  outside  box open  c.f.m. c a p a c i t y . valves  to  be  w i t h a minimum d a n g e r  were c a r r i e d  out  on t h e  tritium  - 33 handling  system u s i n g  -  o r d i n a r y hydrogen  t a i n e r was c o n n e c t e d .  before the t r i t i u m c o n -  The t r i t i u m l e v e l  inside  t h e box  c o n t i n u o u s l y measured w i t h a t r i t i u m - i n - a i r m o n i t o r d e t e c t i n g l e v e l s down t o 5 m i c r o - c u r i e s No p r o b l e m s system d u r i n g  r e q u i r e d w i t h t h e t r i t i u m as  E.  resistivity  (10,000 - 12,000 ohm-cm)  rectangular  and t o t h e n -  e f f e c t i v e depletion thicknesses  resolution for  ments.  Counter Development  through bias  a r e o b t a i n e d by t i l t i n g  the  particles.  10 mm. d i a m e t e r and  5 MeV a l p h a p a r t i c l e s i s  of  o f 1000 m i c r o n s .  the  a b o u t 35  The p a i r o f r e c t a n g u l a r d e t e c t o r s were f a b r i c a t e d by t h e River  high  film  A reverse  t o the d i r e c t i o n of the incoming  The a c t i v e a r e a o f t h e s e d e t e c t o r s i s  con-  Electrical  type wafer  g i v e s the r e q u i r e d d e p l e t i o n t h i c k n e s s  d e t e c t o r s a t an angle  River  of a s l i c e of  through a t h i n gold  a n o n - r e c t i f y i n g c o n t a c t on t h e b a c k s u r f a c e .  intrinsic  at Chalk  n - type s i l i c o n .  type l a y e r  e v a p o r a t e d on t h e f r o n t s u r f a c e ,  Larger  entire  b a r r i e r type  j u n c t i o n formed a t the s u r f a c e  c o n t a c t i s made t o t h e p -  1  the  t y p e PH-8-35~10 o b t a i n e d f r o m N u c l e a r  These d e t e c t o r s a r e t h e s u r f a c e  350- +00 v o l t s  was  Detectors  state detectors are  of a p-n  cell  i t remained i n t a c t f o r  d e t e c t o r s employed i n the s m a l l a n g l e measurements  sisting  meter.  O n l y one gas  With the e x c e p t i o n of the p a i r of  Diodes Inc.  of  measurements.  Charged P a r t i c l e  the s o l i d  capable  were e n c o u n t e r e d w i t h t h e t r i t i u m  the e x p e r i m e n t a l runs.  d u r a t i o n of the  per cubic  is  keV.  Chalk  G r o u p t o be u s e d i n p o l a r i z a t i o n  measure-  These d e t e c t o r s h a v e a n a c t i v e a r e a o f 1^ mm. by 1*+ mm.  - 3h but  t h i s was r e d u c e d t o 6 mm.  b y k mm.  u s i n g a n aluminum  arrangement f o r t h e measurements r e p o r t e d h e r e . were mounted t o g e t h e r  w i t h a s e p a r a t i o n o f 1 mm.  These  slit detectors  between t h e  a c t i v e a r e a s t o a l l o w t h e m e a s u r e m e n t s t o be made a t a s m a l l angular F.  separation.  Electronics The  use o f a charge s e n s i t i v e , p r e a m p l i f i e r i n con-  junction with a solid  state detector results i n a voltage  pulse  from the a n p l i f i e r which i s l i n e a r l y p r o p o r t i o n a l t o the p a r t i c l e energy, assuming the d e p l e t i o n depth o f the d e t e c t o r maximum r a n g e o f t h e c h a r g e d p a r t i c l e s  being  detected.  e l e c t r o n i c a r r a n g e m e n t u s e d i n t h e two d i m e n s i o n a l of the pulses described  i n this  section.  to p a r t i c l e energies  Briefly,  T  ±  energy a n a l y s i s  the f u n c t i o n of t h i s  from both d e t e c t o r s ,  i n d e t e c t o r 1 and T  s t o r e t h e e v e n t i n a T-^ v s . T  2  2  arrange-  corresponding  i n d e t e c t o r 2, a n d t o  array i f c e r t a i n requirements a r e  These r e q u i r e m e n t s f o r t h e measurements r e p o r t e d h e r e a r e  t h a t t h e two p u l s e s the corresponding values. being  The  f r o m two s u c h d e t e c t o r - p r e a m p l i f i e r s y s t e m s i s  ment i s t o a m p l i f y t h e p u l s e s  met.  exceeds the  be c o i n c i d e n t i n t i m e w i t h i n 50 n s e c . a n d t h a t  energies  The c o i n c i d e n c e  analysed  T-|_ a n d T  2  be w i t h i n a g i v e n r a n g e o f  r e q u i r e m e n t e n s u r e s t h a t t h e two p a r t i c l e s  come f r o m t h e same b r e a k u p a n d t h e e n e r g y  e l i m i n a t e s random c o i n c i d e n c e s Two c o i n c i d e n c e  requirement  due t o t h e s c a t t e r e d i n c i d e n t beam. systems were employed I n t h e c o u r s e  o f t h e e x p e r i m e n t a s t h e measurements were c a r r i e d  out using  both  t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 3 MeV V a n de G r a a f f a c c e l e r a t o r  -  and  R i v e r 12 MeV tandem a c c e l e r a t o r .  the Chalk  the f a s t - s l o w c o i n c i d e n c e F i g u r e 12.  35 -  A block diagram o f  s y s t e m u s e d a t C h a l k R i v e r i s shown i n  T h i s a r r a n g e m e n t has been d e s c r i b e d a t l e n g t h by  T o m l i n s o n and Brown (22).  I t i n c o r p o r a t e s a 100 c h a n n e l k i c k s o r t e r  to provide a time d i s p l a y o f the c o i n c i d e n c e events. dimensional  data a c q u i s i t i o n i s c a r r i e d  A description of this  _ The two  o u t u s i n g a PDP-1 c o m p u t e r .  o n - l i n e system i s g i v e n i n the f o l l o w i n g  section. The F i g u r e 13.  coincidence  s y s t e m u s e d a t U.B.C. i s shown i n  T h i s a r r a n g e m e n t i s made up o f s t a n d a r d  commercial  u n i t s ( s e e Table  2) w i t h t h e e x c e p t i o n o f t h e c h a r g e  preamplifiers.  The p r e a m p l i f i e r s , d e s c r i b e d b y W h a l e n ( 2 3 ) ,  produce a l i n e a r  output  and  a slow decay time  p u l s e w i t h a f a s t r i s e t i m e o f 10-15  The o u t p u t s  o f the double delay  c l i p p e d a m p l i f i e r s a r e f e d i n t o s i n g l e channel produce an output  pulse a t the zero-crossover  input pulse f a l l s  w i t h i n t h e r e q u i r e d window.  are used.as the s t a r t and stop p u l s e s  t h e 128 c h a n n e l  mode.  events  time  coincidences  line  which  These  outputs  t o pulse  height  by 50 n s e c . t o  This d i s p l a y i s  D a t a ND 1 2 0 k i c k s o r t e r o p e r a t i n g i n A f u r t h e r s i n g l e channel  t o s e t a window o n t h e t i m e coincidence  line  point only i f the  f o r a time  spectrum i n the d i s p l a y .  obtained using a Nuclear  A typical  analysers  The a l p h a p a r t i c l e p u l s e i s d e l a y e d  centre the time  nsec.  o f 100 usee, s u i t a b l e f o r use i n d e l a y  c l i p p e d main a m p l i f i e r s .  converter.  sensitive  spectrum t o minimize  and t o remove t h o s e  events  a n a l y s e r i s used t h e random  w i t h no s t o p  pulse.  s p e c t r u m i s shown i n F i g u r e lh f o r p-p a n d p-He  from t h e r e a c t i o n He^(He^,2p)He^.  The window  ENCODER  ENCODER  To  POP-1  TO  PDP-1  ENCODER.  ©ATE  T D SEQUENCE  DELAYS  BREAK DETECTOR PREAMP 41  D.D.L  POP-I  P0OR-FOL.D PROMPT  P°6T  PELAYED  FAST OUTPUT  4  D D L AMP.  PR3mPT  SINGLE CHANNEL ANALNSd  TIMETO- AV\P«-»TU0E CONVERTER. ST&P  Low LEVGJ  DISPLAV  UKliT tOO CHAMWEL  FAST COINCIDENCE FAST AMPuRE«  UNIT  5-50  kiacsoers? HIGH U S V E U  F i g u r e 12. B l o c k diagram o f e l e c t r o n i c s used i n o n - l i n e Chalk  T1»A£ SPECniUK SATS,  data a c q u i s i t i o n a t  River.  f  1  OF  TABLE  2  Commercial E l e c t r o n i c U n i t s used i n the E x p e r i m e n t a l Arrangement 1)  (see F i g u r e  13).  C o s m i c M o d e l 901 A L i n e a r (Cosmic R a d i a t i o n Labs.  Amplifier Inc.,  Bellport,  2)  C o s m i c M o d e l 901 SCA S i n g l e  3)  LRS M o d e l 108H A n a l o g S t o r a g e Time t o H e i g h t ( L e c r o y R e s e a r c h Systems C o r p . , I r v i n g t o n ,  h)  CI  Timing S i n g l e  Converter N.Y.).  Inc.,  Middletown,  Conn.).  ORTEC M o d e l ^30 S c a l e r s (Oak R i d g e  6)  Analyser.  Channel Analyser  (Canberra Industries 5)  Channel  N.Y.).  Technical Enterprises,  Oak R i d g e ,  N u c l e a r D a t a ND 160 D u a l P a r a m e t e r A n a l y s e r (Nuclear Data I n c . ,  Palatine,  111.).  70  N u c l e a r D a t a ND 120 512 C h a n n e l A n a l y s e r  8)  D a t a p u l s e 106A P u l s e (Datapulse  Inc.,  Generator  Inglewood,  Calif.).  Term.).  PULSE ( 8  PUISE ( 8  SCALER.  SENEKATog.  TEST"  4  ®  AMR  SCALER  3 TIME-TO  TEST  HE\OHT  ^ETECrt)!?  PREftM*  sc.  D . D L © /AMP.  DUAL.  ©  PARAMETER N\efY\o£ Y D O  PlNftUVSSR - <  :  —  :  —  STOP  50nsac  ©  TIM I MS S.C.A  ^ INGLE  FAft/>iMETER K'CK«ORTei? SATE  MP*  S  Figure  13•  Block-diagram  o f e l e c t r o n i c s used i n data a c q u i s i t i o n a t U.B.C  1600 WINDOW SETTING  TIME  u r e Ik.  DISPLAY  (\  OSec/CHMslKjEL)  Time d i s t r i b u t i o n s p e c t r u m o f c o i n c i d e n c e s f r o m t h e reaction  He^CHe^,2p)Re*.  - 36 setting is response  also  shown.  of the s o l i d  particles.  -  The two p e a k s  arise  state detectors to protons  The r e s u l t i n g p u l s e  The two l i n e a r p u l s e s a r e f e d i n t o the F and M s i d e s operating  •a n e g l i g i b l e is  time of  pulses.  from the main a m p l i f i e r s  channel analyser. was u s e d as  this  with  coinci-  resulted  in  kicksorter pre-  analysis.  linearity  system and  the  o f t h e a m p l i f i e r s w e r e t e s t e d by f e e d i n g p u l s e s  two D a t a p u l s e By v a r y i n g  generators  i n t o the t e s t i n p u t s  the d e l a y between the p u l s e s  of the  set to give  the d e s i r e d window.  channel analyser  the s i n g l e s  O n - l i n e Computer  channel analyser and c o i n c i d e n c e  of. t h e  analyser-  single  are connected to  2)  scalers  rates.  Techniques  The u s e and u s e f u l n e s s "data-simulation"  techniques  breakup  has  reactions  channel  resolving  from the alpha p a r t i c l e d e t e c t o r ( d e t e c t o r  and t h e t i m i n g s i n g l e to monitor  The o u t p u t s  from  preamplifiers.  the c o i n c i d e n c e  t i m e c o u l d be d e t e r m i n e d a n d t h e t i m i n g s i n g l e  analysis  Dual  each run f o r  The t i m i n g o f t h e c o i n c i d e n c e  G.  A  The memory o f t h e ND 160  t r a n s f e r r e d i n t o a PDP-8 c o m p u t e r a f t e r  liminary  nsec.  i n t h e 6^x6^ mode and g a t e d  50 n s e c .  random r a t e .  alpha  o f a N u c l e a r D a t a ND 160  the output of the t i m i n g s i n g l e dence r e s o l v i n g  and  s h a p e s p r o d u c e t h e 10  t i m e d i f f e r e n c e b e t w e e n t h e s t a r t and s t o p  Parameter Analyser  from the d i f f e r e n t .  o f an o n - l i n e  i n the a n a l y s i s  computer  of three  b e e n d e s c r i b e d by D o n o v a n ( 2 ^ - ) .  s y s t e m was s e t up u s i n g  the o n - l i n e computer  and  particle A  similar  facility  - 37 a t the Chalk R i v e r  tandem a c c e l e r a t o r .  a PDP-1  ( D i g i t a l Equipment  modules  o f ^096, 18 b i t w o r d s .  output devices  s u c h as  there i s  Cathode r a y  a 16"  This f a c i l i t y  Corporation)  Along w i t h the standard  tape readers,  of pulse  for  break, u s u a l l y  the purpose triggered  i n d i c a t i n g a d e s i r e d e v e n t has  particular  time.  In data a n a l y s i s  is  a g e n e r a l purpose  might  be d i s p l a y i n g  causes a t r a n s f e r deals  A.D.C. u n i t s  The  which  as  the k i n e m a t i c contours was d i s p l a y e d  the events  from p-p  appear as contour.  A g e n e r a l program  coinci-  display  T2 v s . for  T^  generating  was a l s o w r i t t e n and t h e a p p r o p r i a t e ' c o n t o u r  simultaneously  mentioned p r e v i o u s l y  the  on t h e r e a c t i o n He^(He^,2p)He  t h e y a c c u m u l a t e d e i t h e r on a c o n t o u r  p l o t o r on a n i s o m e t r i c d i s p l a y .  of  locations.  i n a two d i m e n s i o n a l 6 0 x 6 0 c h a n n e l a r r a y a n d t o  these events  it  interrupt  routine  t h e p r o p e r memory  to store  that  interrupted  the a p p r o p r i a t e b u f f e r s  D u r i n g the measurements  dences  the  r o u t i n e where  of c o n t r o l to a data storage  t h e c o m p u t e r was programmed  pulse  the program t h a t i s  some s p e c t r u m o f i n t e r e s t .  and i n c r e m e n t i n g  analysis.  performing at  spectrum h a n d l i n g  w i t h t h e e v e n t by r e a d i n g  eight  height  taken p l a c e , i n t e r r u p t s  from the o p e r a t i o n i t i s  display.  system are  by a c o i n c i d e n c e  computer p r o c e s s o r  memory  punch,  t u b e and l i g h t p e n f o r v i s u a l  ^fOO c h a n n e l A . D . C . u n i t s  on  input-  t y p e w r i t e r and c a r d  break  usually  based  computer w i t h f o u r  Connected t o the computer v i a a sequence  The s e q u e n c e  is  w i t h the e x p e r i m e n t a l e v e n t s .  i n Chapter  II,  r e g i o n s of h i g h d e n s i t y  the f i n a l of events  state  along  interactions  the  kinematic  To g i v e a n i m m e d i a t e i d e a o f t h e i n t e r a c t i o n s  a r o u t i n e was w r i t t e n t o sum t h e c o i n c i d e n c e e v e n t s  As  along  present, either  - 38 energy a x i s side  and w i t h i n a s p e c i f i e d number  of channels  of the p r e d i c t e d k i n e m a t i c c o n t o u r .  The number  summed o v e r c o u l d be v a r i e d t o c h e c k t h e e f f e c t few counts  l y i n g w e l l o f f the c o n t o u r .  and t h e s p e c t r u m o b t a i n e d by a d d i n g were d i s p l a y e d as  o n t h e 16"  It  these  CRT a s w e l l .  was f o u n d  s u b t r a c t i n g a background. of performing  the  spectra  together  The s p e c t r a may be a d d e d of the experiment o f random a n d  with  con-  so t h a t no p r o v i s i o n was made  This  time consuming  channels  of i n c l u d i n g  two s p e c t r a  t h a t t h e number  t a m i n a n t e v e n t s was n e g l i g i b l e  of  The two summed  t h e y a r e i d e n t i c a l due t o t h e symmetry  G e o m e t r y #1.  on e i t h e r .  facility  off-line  e l i m i n a t e d the  analysis  for  necessity  and removed  the  g u e s s w o r k o f d e t e r m i n g when s u f f i c i e n t s t a t i s t i c s had b e e n a c c u m ulated. The p u l s e h e i g h t of B r i t i s h Columbia c o n s i s t s  analysis  system at the  of s e v e r a l conventional  i n c l u d i n g a ND 160 d u a l p a r a m e t e r a n a l y s e r o f *+096 w o r d memory w i t h a m a g n e t i c  University kicksorters  and a PDP-8  computer  tape system f o r data  and k  program the case  storage.  The c o i n c i d e n c e e v e n t s ,  of the r e a c t i o n He^(He^,2p)He  lf  b o t h p-p  a n d G e o m e t r y #2,  a c c u m u l a t e d w i t h t h e ND 160 k i c k s o r t e r o p e r a t i n g mode.  and p-He  converters  for  the purpose  was made, h o w e v e r ,  i n t e r f a c e d t o any a n a l o g of pulse height  f o r the r a p i d t r a n s f e r  L  the computer.  The r e m a i n i n g  1  PDP-8  to  analysis.  digital Provision  of i n f o r m a t i o n from  memory o f t h e ND 160 t o t h e c o m p u t e r memory. w r i t t e n t o t r a n s f e r a 6^x60 c h a n n e l a r r a y  were  i n t h e 6 fx6 +  A t t h e t i m e t h e e x p e r i m e n t was p e r f o r m e d t h e  c o m p u t e r was n o t d i r e c t l y  in  A short  program  from the k i c k s o r t e r  256 l o c a t i o n s  i n the computer  the was to  were  - 39 used to s t o r e  the t r a n s f e r  i n f o r m a t i o n i n memory  p r o g r a m and a p r o g r a m  e i t h e r as  numbers o r s i x 6*+xl0 a r r a y s  seen i n the a r r a y s  s e n t a t i o n of the data proved p r e l i m i n a r y c h e c k on t h e  to type out  t h r e e 6^x20 a r r a y s  o f two  of f o u r d i g i t numbers.  Zero  s u p p r e s s i o n was u s e d i n t h e t y p e o u t be e a s i l y  -  so t h a t t h e c o n t o u r s  of numbers.  This form of  t o be q u i t e u s e f u l  experiment.  the  digit  could pre-  in obtaining  a  - ho  -  CHAPTER  I¥  EXPERIMENTAL PROCEDURE AND RESULTS In  the p r e v i o u s  chapters  and d a t a a c c u m u l a t i o n systems  t h e two r e a c t i o n  chambers  have been d e s c r i b e d a l o n g w i t h the  k i n e m a t i c c a l c u l a t i o n s f o r b o t h t h e G e o m e t r y #1 and G e o m e t r y #2 target-detector the  configurations.  In  chapter an o u t l i n e  e x p e r i m e n t a l procedure w i t h both arrangements  o f the measurements using  are given.  using  a well  tandem a c c e l e r a t o r . studying  c o l l i m a t e d He^  target, after  entrance f o i l ,  The n i c k e l f o i l  +  o f 1.15  lf  used  to incident  f o r p, d , H e  J  for  energies  c o r r e c t i n g f o r the energy l o s s  in  2 . 0 MeV a n d 5.0 MeV r e s p e c t i v e l y . k  of a l l f o i l s used i n the course  source.  Several curves  the energy k  loss  of  the  o f t h e 5.^77  A computer program  t o c a l c u l a t e the energy  i n the f o i l s . showing o  River  u s e d i n t h e e n t r a n c e w i n d o w was n o m i n a l l y 0.050 m i l s  The t h i c k n e s s e s  i n Appendix C i s  incident  w e r e 1.90 MeV, 3.00 MeV  correspond  MeV,  a l p h a p a r t i c l e s f r o m a n Am  Appendix  first.  w h i c h were c h o s e n  e x p e r i m e n t were d e t e r m i n e d f r o m t h e e n e r g y l o s s 2l+i  particles  w h i c h w e r e 'made  beam f r o m t h e C h a l k  The beam e n e r g i e s  These e n e r g i e s  t h e gas  thick.  results  were c a r r i e d o u t a t t h r e e  the r e a c t i o n He^(He^,2p)He  a n d 5.^0 MeV. inside  of  Measurements. These m e a s u r e m e n t s  energies  and the  The m e a s u r e m e n t s  t h e G e o m e t r y #1 a r r a n g e m e n t a r e d i s c u s s e d  A . G e o m e t r y #1  the  this  loss  are also  MeV described  of the d i f f e r e n t included i n  as a f u n c t i o n o f p a r t i c l e  this  energy  a n d He . F i g u r e 6 shows t h a t t h e p r o t o n - a l p h a a n d  proton kinematic contours  proton-  f o r G e o m e t r y #1 do n o t o v e r l a p f o r  a  -1+1 particular  angular  angles  s e p a r a t i o n o f t h e two d e t e c t o r s , a l t h o u g h  a r o u n d 180° t h e c o n t o u r s  together This  -  lie sufficiently  t h a t some a l p h a p a r t i c l e d i s c r i m i n a t i o n i s  was o b t a i n e d by p l a c i n g a 3 . 0 mg/cm  f r o n t of each d e t e c t o r . observe  the p-p  geometry,  i t is  From F i g u r e  o f t h e two d e t e c t o r s a s tion,  =  required.  t o use as  possible.'  in  evident that,  i n t e r a c t i o n at low r e l a t i v e energies necessary  close  aluminium f o i l  7 i t is  for  with  s m a l l an a n g u l a r  to  this  separation  The minimum a n g u l a r  6 ° , w h i c h was u s e d ' i n t h e m e a s u r e m e n t s ,  separa-  was  deter-  m i n e d by t h e d e t e c t o r s a v a i l a b l e a n d t h e c o i n c i d e n c e c o u n t i n g  rate.  To s c a n t h e e n t i r e r a n g e  6°  of angles  from  three d i f f e r e n t detector configurations listed about  = 180° to were e m p l o y e d .  i n T a b l e 3 a l o n g w i t h some o f t h e r e l e v a n t the s o l i d angles  involved.  b o t h d e t e c t o r s were a p p r o x i m a t e l y The s i n g l e  A^  These  thickness  and  The s o l i d a n g l e s  subtended  by t h e d e t e c t o r . imately  is  is  t a r g e t the G f a c t o r i s  the  subtended  given  approx-  by G  where  the e f f e c t i v e s o l i d angle  F o r a gas  by  equal.  p a r t i c l e y i e l d i n each d e t e c t o r  SL  are  information  p r o p o r t i o n a l t o t h e g e o m e t r i c a l f a c t o r G = LSI w h e r e L i s target  =  2  =  sA/Rh  *f-l  s  is  the w i d t h of the f i r s t d e f i n i n g  slit,  A  is  the a r e a of the second d e f i n i n g  slit,  R  is  the d i s t a n c e  t h e beam h  is  of the second d e f i n i n g  slit  from  rate  therefore  axis,  t h e d i s t a n c e b e t w e e n t h e two  slits.  The r a t i o o f t h e c o i n c i d e n c e r a t e t o t h e s i n g l e s  TABLE ^ Detector  Detector conf .  configurations  Angular range  Slit  u s e d w i t h G e o m e t r y #1  shape  in front  of  Angular of  measurements.  width  detectors  G  G  l 2 cm.xlCV  G  + G  covered  detectors  #1  180°-22°  Circular  11°  11° '  9.50  #2  22°-13°  Elliptical  11°  6°  5.01  7°  h°  3.60  #3  6°  Rectangular  A O  Foil  1 2 v  in  front  of  detectors 2 3 . 0 mg/cm aluminum none •• none  - 1+2 depends  on t h e f a c t o r  G  G 1  2  ^  G  + 1  G  ?)  where G  1  and G  g e o m e t r i c a l f a c t o r s f o r t h e two d e t e c t o r s .  This  the  f a c t o r was  d e t e r m i n e d f o r d e t e c t o r c o n f i g u r a t i o n #1 by u s i n g g i v e n above and the a p p r o p r i a t e d i m e n s i o n s .  are  2  the  expression  The v a l u e s  for  c o n f i g u r a t i o n s #2 and #3 were d e t e r m i n e d r e l a t i v e t o c o n f i g u r a t i o n #1 by p l a c i n g a n a l p h a s o u r c e ( T h C ) a t t h e c e n t r e o f  the  !  r e a c t i o n chamber t o s i m u l a t e t h e a c t i v e v o l u m e o f t h e t a r g e t  gas,  and c o m p a r i n g t h e c o u n t i n g r a t e s f o r t h e d i f f e r e n t c o n f i g u r a t i o n s . These r e s u l t s a r e l i s t e d i n t h e s e c o n d l a s t c o l u m n o f T a b l e 3» the  same q u a n t i t i e s e v a l u a t e d f o r d e t e c t o r c o n f i g u r a t i o n s #2 and  #3 u s i n g  e x p r e s s i o n *+-l a n d t h e s l i t  dimensions  agree w i t h i n  The n o r m a l i z a t i o n b e t w e e n r u n s a t d i f f e r e n t a n g u l a r and w i t h d i f f e r e n t d e t e c t o r c o n f i g u r a t i o n s i s the  singles  r a t e i n b o t h d e t e c t o r s and u s i n g  s o l i d angle r a t i o .  separations  o b t a i n e d by m o n i t o r i n g the  corresponding  The c o r r e c t i o n t o t h e s i n g l e s  i n s e r t i o n - of- t h e a l u m i n u m f o i l  r a t e due t o t h e  was d e t e r m i n e d by m a k i n g r u n s  = 22° b o t h w i t h a n d w i t h o u t t h e  10%,  at  foil.  A n e n e r g y c a l i b r a t i o n o f 250 k e V / e h a n n e l was u s e d the  two d i m e n s i o n a l p u l s e h e i g h t a n a l y s i s .  adjusting  the a m p l i f i e r gains u n t i l  in  T h i s was o b t a i n e d by  the p r o t o n peak  corresponding  t o t h e t r a n s i t i o n t h r o u g h t h e g r o u n d s t a t e o f L i 5 was c e n t e r e d a b o u t c h a n n e l 38 f o r a n i n c i d e n t e n e r g y o f 1.15 e n e r g y and a n g l e ,  O  MeV.  For  = 9 0 ° , t h i s p e a k s h o u l d a p p e a r a t 9.^6  The l o w e r l e v e l d i s c r i m i n a t o r o f t h e S . C . A . ' s was s e t t o pulses  corresponding  this  to less  t h a n 1.25  MeV.  reject  MeV d e p o s i t e d i n t h e  detectors.  T h i s was n e c e s s a r y  t o remove t h e s c a t t e r e d H e  when no f o i l  was p l a c e d i n f r o n t o f t h e d e t e c t o r s .  J  events  The window  - >f3 s e t t i n g o f t h e S . C . A . ' s was opened t o a c c e p t p u l s e s The c o u n t i n g an i n c i d e n t energy  for  the s i n g l e s  MeV.  rates with detector configuration  o f 1.15  a target pressure  up t o 15  #3,  MeV, a beam c u r r e n t o f 0.5 uamps and  o f 100 mm. Hg w e r e t y p i c a l l y 100-150  r a t e and 5-10  counts/min.  for  counts/sec.  the c o i n c i d e n c e  The r u n s l a s t e d u n t i l a t l e a s t 1000 c o i n c i d e n c e e v e n t s a l o n g  the  d e s i r e d k i n e m a t i c c o n t o u r were a c c u m u l a t e d .  A typical  two  dimensional  The s o l i d  curve  represents angle  spectrum i s  the k i n e m a t i c contour  and e n e r g y  well off  specified.  t h e p-p  The e v e n t s  shown i n F i g u r e f o r p-p  The e v e n t s  coincidences  t h e p-p  a n d He - p  contour  time of  approximately 8 events/hour  50 n s e c . in  energy histograms  or c o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d  events  l y i n g w i t h i n a nine  the k i n e m a t i c c o n t o u r . these  o f t h e symmetry  detectors Figures  o f 10  16 - 21.  of counts t h e number  normalized to a t o t a l  events  of the  of counts  G e o m e t r y #2  singles  equal t o or l e s s  i n that particular  two by  error  along  experiment the  count i n  f o r d e t e c t o r c o n f i g u r a t i o n #1,  In a l l cases the s t a t i s t i c a l  per channel i s  the  channel i n t e r v a l  two c o i n c i d e n c e s p e c t r a may be a d d e d t o i m p r o v e  Similar histograms, 6  B.  Because  15 a r e  the  agreement  rate.  t h e p-p  shown i n F i g u r e  lying  coinci-  w i t h the observed  summing  Also  the  coincidences.  a r e random  With a coincidence resolving  e x p e c t e d random r a t e i s  for  b e l o w c h a n n e l 10, k k  c o n t o u r a r e due t o p-He  l y i n g w e l l above  dence e v e n t s .  15.  rate.  statistics. both  a r e shown i n i n the  than the square  number  root  of  channel.  Measurements  These m e a s u r e m e n t s were c a r r i e d o u t u s i n g a 1.88 MeV TT 3 + he beam f r o m t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n de G r a a f f  He CHe 2 ") H e 3  3  >  T  F i g u r e 15. and  0  = !.!5  Two d i m e n s i o n a l e n e r g y A-^2 6 ° . =  Also  4  P  MeV  s p e c t r u m t a k e n w i t h G e o m e t r y #1  shown a r e t h e e n e r g y  o b t a i n e d by summing  events along  histograms  contour.  To - 1.16 A,,Zoo  MeV  180°  -  A  I 2  »I35  C  J  2o CHANNEL Figure  16.  4. 30 NUMBER  4o  1  C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by events  along appropriate  contour.  _l so  summing  To -  O  1.15 M e V  |0  20 CHAN MEL  F i g u r e 17.  Coincidence  30  40  50  NUM&ER.  p r o t o n s p e c t r a o b t a i n e d by  e v e n t s a l o n g a p p r o p r i a t e contour,,  summing  Me (He ,2p)HeT T « 2.40 MeV 3  3  0  10  Figure  18.  20  30 KIUM8ER  40  So  CHANNEL. C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by summing events along a p p r o p r i a t e  contour.  Figure  19.  C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by events  along appropriate  contour,,  summing  Figure 20.  C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by events along, a p p r o p r i a t e  contour.  summing  To - 5 . 0 0 MeV A ,  2  - 9 0  e  CHANNEL  ure 21,  KI0M6ER.  C o i n c i d e n c e p r o t o n s p e c t r a o b t a i n e d by summing events, along a p p r o p r i a t e  contour,  - hk  accelerator.  -  The i n c i d e n t e n e r g y  t h e gas  target after  correcting  f o r the energy  1.50 MeV.  From t h e k i n e m a t i c c a l c u l a t i o n s t h e d e t e c t o r a n g l e s  are r e q u i r e d to observe est possible <&  loss  inside  i n t h e 0.025 m i l n i c k e l window was  the s i n g l e t  r e l a t i v e energies  two n u c l e o n s y s t e m s  for this  - 90.0° f o r t h e r e a c t i o n H e ^ ( H e , 2 p ) H e  '•9* = 90.0° f o r t h e r e a c t i o n T ( H e ^ , n p ) H e . l f  2  the  3  Coincidence events  and  The d i f f e r e n c e i s  due  12.859 MeV f o r  and 12.095 MeV f o r t h e r e a c t i o n  1+  and  62.0°  and ' 6 ^ = 6 l A °  I f  s l i g h t d i f f e r e n c e i n the r e a c t i o n Q-values,  r e a c t i o n He^(He ,2p)He  at the l o w -  geometry a r e =  3  2  which  to  the  T(He^,np)He . I f  i n which the alpha p a r t i c l e enters  d e t e c t o r 1 and t h e p r o t o n e n t e r s d e t e c t o r 2 a r e removed f r o m t h e r e g i o n o f i n t e r e s t by t h e 0.200 m i l n i c k e l f o i l e x i t window and a 0.100 m i l n i c k e l f o i l The a l p h a p a r t i c l e e x i t window i s s i o n s of the s l i t measurements the  is  1/8"  by 1/H-"  These  4  angles C.  used,  corresponding  s o l i d angles  of running  thick.  3  I f  of  width  allowed s u f f i c i e n t s t a t i s t i c s  a t a p a r t i c u l a r p a i r of angles time.  This  in  to in  t i m e d e p e n d e d on t h e and t h e t a r g e t  p a r t i c l e spectra i n both detectors  t h i s r e a c t i o n a r e shown i n F i g u r e  through  series  gas.  Reaction.  The s i n g l e  end o f b o t h s p e c t r a i s  The d i m e n -  t o an a n g u l a r  t h e beam c u r r e n t , t a r g e t p r e s s u r e  The H e ( H e 3 . 2 p ) H e  breakup  0.025 m i l s  1.  h° and i n t h e a z i m u t h a l d i r e c t i o n  be o b t a i n e d f o r m e a s u r e m e n t s three to s i x hours  proton  i n f r o n t of d e t e c t o r  i n f r o n t of both d e t e c t o r s f o r t h i s  polar d i r e c t i o n A O =  A <|) = 30  over the  22.  The p e a k a t t h e h i g h  from energy  due t o t h e f i r s t e m i t t e d p r o t o n f r o m t h e  the ground  s t a t e of L i  .  This  peak was  used  CHANNEL. DETECTOR  2 SPECTRUM  CHANNEL. Figure  22.  Single  NUMBER  NUMBER  p a r t i c l e s p e c t r a i n both d e t e c t o r s from the  r e a c t i o n He^(He^ 2p)He 5  !+  a t 90° t o t h e beam d i r e c t i o n .  - i+5 t o s e t t h e g a i n s o f b o t h m a i n a m p l i f i e r s so t h a t t h e c a l i b r a t i o n was 200 k e V / c h a n n e l . spectrum from d e t e c t o r 2 i s  energy-  The l o w e n e r g y p e a k i n  due t o a l p h a p a r t i c l e s and  from the breakup of the L i ^ ground s t a t e .  This  the  protons  peak does  a p p e a r i n t h e d e t e c t o r 1 s p e c t r u m due t o t h e n i c k e l f o i l s f r o n t of t h i s d e t e c t o r . is  not in  The b r o a d c o n t i n u u m i n b o t h  spectra  made up o f c o n t r i b u t i o n s f r o m t h e s e q u e n t i a l d e c a y  through  the f i r s t  e x c i t e d s t a t e o f L i - ' and t h e s i n g l e t d i - p r o t o n  and f r o m t h e d i r e c t t h r e e p a r t i c l e b r e a k u p .  The s m a l l  a b o u t c h a n n e l 32 i n t h e d e t e c t o r 2 s p e c t r u m i s from the contaminant r e a c t i o n He^CdypjHe^.  due t o  Although  peak  protons these  t o n s h a v e a n e n e r g y o f 15»0 MeV a t 90° o n l y a b o u t 6 MeV d e p o s i t e d i n the a l p h a d e t e c t o r because ness.  This  peak i s  is  the  d e t e c t o r has a l a r g e e n o u g h d e p l e t i o n  t o s t o p a 1*+ MeV p r o t o n and t h e r e f o r e t h e p e a k  a b o v e c h a n n e l 6*+. were b o t h ' s e t 12.8  this  pro-  depletion thick-  n o t o b s e r v e d i n t h e same p l a c e i n  d e t e c t o r 1 s p e c t r u m as thickness  of I t s  state  The windows  of the s i n g l e  channel  to accept p a r t i c l e s w i t h energies  appears  analysers  f r o m 1 MeV  to  MeV. A two d i m e n s i o n a l c o n t o u r p l o t o f t h e  events  observed  f o r the case o f =  62° a n d ^  coincidence  = 90° i s  shown Li.  i n Figure  23.  The e v e n t s a l o n g  contour A are the d e s i r e d  coincidences.  The e v e n t s a l o n g  c o n t o u r B a r e due t o p - p  dences  p--He coinci-  and i n t h e r e g i o n m a r k e d C due t o He - p c o i n c i d e n c e s  x^hich t h e a l p h a p a r t i c l e f r o n t o f d e t e c t o r 1. LL  f r o m p-He  e n e r g y has  in  been degraded by the f o i l s  The f e w e v e n t s  in  i n the r e g i o n marked D a r e "5 LL c o i n c i d e n c e s from the contaminant r e a c t i o n He^CdjpjHe .  T o - /.SO MeV  5b  10-25  •  24- 100  A  |ol-5oo  x»»x x««x x«*x x«»* x»» X •• XX  ^46 a: UJ (0  •X XX, x»x  XX  xZ x«x* x»xx x*xx xxxxx n X»xxx ^  J bl "2  p D »X *x xx  X»X  y  o  XX •* ** *x **  XXXXX  < 4:  o  X  20  x  **  xyx ** »** *2. X X x xx •• X X X X X X x X X X X X » X X X X X X X X x • • • • • • • ••XX $xxxxxxxx«»»««»xxvxx xxxx««»*«»t«;««»xxx xx •>< A i a y a y s j yJuxKX XX X X VV AO • • • • • • • • • • • • X X X*X TN xxxxxxxx • A xxx*xx#«*»»aa**»xxx,«*«xx yw X XXX«»«A&^*»«* X x vvv XX«*^AA«X - •* X«( •A4A«X x»»*««* D  A  >  XX.XX X  »©  20  30  CHANNEL.  NOMBER  40  5o  60  T,  k Figure  23.  Two d i m e n s i o n a l  coincidence  contour  events from the *!2=  plot  of  p-p  and  r e a c t i o n He^(He^ 2p)He 152". s  p-He at  - i+6 Iii t h i s  case  of the He^  the deuterium i s beam a n d b e c a u s e  +  p r e s e n t as a HD  -fr-  of the h i g h c r o s s  component section for  this  •h  r e a c t i o n a f e w nanoamps o f HD rate.  produces  Although t h i s r e a c t i o n leads  a significant  coincidence  t o a two p a r t i c l e  final  state  and t h e r e f o r e o n l y a p a r t i c u l a r c o n f i g u r a t i o n o f t h e two d e t e c t o r s will  observe  both p a r t i c l e s simultaneously,  i t is  found t h a t  this  c o n f i g u r a t i o n i s a l m o s t e x a c t l y t h e same c o n f i g u r a t i o n r e q u i r e d observe  the p-p  interaction.  F o r t u n a t e l y t h e s e p a r a t i o n c a n be  made by u s i n g  the p r o t o n e n e r g y as  r e a c t i o n have  energies  T  some o f t h e p r o t o n s  the events  = 16.0 MeV and T&= p «•*  geometry and t h e r e f o r e l i e  to  from the  contaminant  3.3 MeV f o r  this  w e l l o f f the d e s i r e d c o n t o u r .  l o s e p a r t o f t h e i r e n e r g y by s l i t  However  scattering  and t h e s e p r o d u c e t h e c o i n c i d e n t e v e n t s i n t h e r e g i o n D.  Measure-  ments w e r e made w i t h a p u r e d e u t e r i u m beam t o s i m u l a t e t h e HD component i n t h e He events  beam a n d t h e s e showed t h a t no  from t h i s r e a c t i o n produce events  A where t h e p - p  Interaction is  with alpha p a r t i c l e s i n detector 2 i s coincidence events  i n the p o r t i o n o f  expected to  The s p e c t r u m o f p r o t o n s  coincidence contour  appear.  from d e t e c t o r 1 i n  coincidence  o b t a i n e d by summing  the  l y i n g w i t h i n an e i g h t c h a n n e l i n t e r v a l o f  c a l c u l a t e d p-He^ c o n t o u r .  This  s p e c t r u m was c o r r e c t e d f o r  c o n t r i b u t i o n f r o m t h e r e a c t i o n He ( d , p ) H e  by u s i n g  the the  the r e s u l t s  t h e r u n w i t h t h e p u r e d e u t e r i u m beam t o o b t a i n t h e s h a p e  of  contribution.  similar  This  spectrum i s  r u n was made f o r d e t e c t o r a n g l e s  shown i n F i g u r e ^  2*+.  A  of  the  = 75° a n d *Q* = 90° a n d  the k  c o i n c i d e n c e p r o t o n s p e c t r u m o b t a i n e d by summing contour i s  shown i n F i g u r e  25.  over the  Both these spectra are  p-He normalized  T  6o»-  0  « 1.50 MeV  5od-  l-  2 4O0U  id >  UI  0 300| ui Q O Z O  *0  1  200  /  X  I  -J-  10  20  CHANNEL. NUMBER  i  F i g u r e 2 *. 1  50  3©  -6I  8i _  I 10  Coincidence p r o t o n spectrum from the r e a c t i o n  He3(He3,2p)He\-obtained for ^  by summing o v e r p-He 1 2  =  152°.  contour  60  To= 1.50 MeV  Oh  500  jo^oo  2  UJ >  1U 2  300  a  8  200 I I  100  l  l J  n-rurL  20 J  CHAN fOCL.  3^T _l  NUMBER  4-0  6  8  T, (MeV) Figure  25.  IO  Coincidence p r o t o n spectrum from the r e a c t i o n  He~'(He' ,2p)He :3  50  T  k  o b t a i n e d by summing o v e r p-He" for ^  1 2  =  !65°  contour  1  Go  12  - h  7  t o t h e same number o f s i n g l e detector. events  For the angles  counts  -  6 (2,5 x 10 ) i n the f i x e d  •O^ = 75° and t6< = 90° t h e c o i n c i d e n c e 2  from the contaminant r e a c t i o n a r e n e g l i g i b l e as  this  geometry-  d o e s n o t p e r m i t t h e a l p h a p a r t i c l e and p r o t o n t o be o b s e r v e d taneously i n both detectors unless  simul-  one o r b o t h o f t h e p a r t i c l e s  have b e e n s c a t t e r e d . D.  The T ( H e ^ . n p ) H e  Reaction  I f  The s i n g l e p a r t i c l e  s p e c t r a from t h i s r e a c t i o n are  shown i n F i g u r e 26 f o r b o t h d e t e c t o r s a t 90° t o t h e i n c i d e n t beam d i r e c t i o n . is  The same e n e r g y c a l i b r a t i o n o f 200  used f o r these measurements.  keV/channel  The p o s s i b l e p r o c e s s e s  b u t i n g t o these s p e c t r a are the f o l l o w i n g ! * k (1)  He  0  + H —  contriQ(MeV)  He " + d  l .320  4  k  (2)  —>» L i ^ + n  —»- He^ + p + n  10.128  (3)  —*• H e  —*• H e ^ + n + p  11.138  (If)  — ^ He *" + n + p  (5)  5  + p  12.095  1  He  3  + D* —*• He* " + p  18.352  1  The p o s i t i o n s  of the peaks expected from the v a r i o u s  and p o s s i b l e f i n a l  s t a t e s a r e shown a b o v e e a c h s p e c t r u m .  number r e f e r s t o t h e p r o c e s s  and t h e s u b s c r i p t t o t h e  detected.  The p a r t i c l e  energy l o s s  i n the n i c k e l f o i l s .  nickel  particles  from being observed.  particle  e n e r g i e s have been c o r r e c t e d f o r The 0.300 m i l t h i c k n e s s  i n f r o n t of d e t e c t o r 1 prevents  the low energy  The c o n t i n u u m i n b o t h s p e c t r a  The  the of  structure consists  mainly of c o n t r i b u t i o n s from the s e q u e n t i a l decay through 5 5 f i r s t e x c i t e d s t a t e o f L i ^ a n d He .  the  To - /:50 MeV bereCTOK  I  SPECTRUM  2 o  o o  ^200h  o 2  ZJO CHANNEL,  DETECTOR  soq-  2. SPECTROKA  ZO 30 40 CHANNEL. NUMBER  ro Figure  26.  Single  r e a c t i o n T(He  30 NUMBER.  50  GO  p a r t i c l e s p e c t r a i n both d e t e c t o r s from the 3 s  n p ) H e ^ a t 90° t o t h e beam d i r e c t i o n .  -  1+8  -  A two d i m e n s i o n a l c o n t o u r p l o t o f t h e c o i n c i d e n c e events  for ^  = 61.M  before,the events  and 0  5  = 9Q° i s  2  l y i n g along  shown i n F i g u r e  As  27.  contour A are the d e s i r e d  p-He  LL  1+ coincidences.  The e v e n t s  i n r e g i o n B a r e f r o m He - p  i n w h i c h t h e a l p h a p a r t i c l e e n e r g y has  coincidences,,  b e e n d e g r a d e d by t h e  foils LL  i n f r o n t o f d e t e c t o r 1 and the peak i n t h i s c o i n c i d e n c e s f r o m t h e two . p a r t i c l e f i n a l events d-He  i n r e g i o n C and a l o n g  s t a t e T(He  a particular detector configuration.  The e v e n t s  along  events as  lost  is  2  this  a r e due t o  for the  coincidences  e n e r g y by s l i t  state consisting  scatterin  coincidence  of the  particle spectra.  deuteron  some t h r e e o r d e r s  The p e a k c h a n n e l  of magnitude above  the  e f f o r t was made t o r e d u c e t h e e f f e c t  i n g by u s i n g  a c c u r a t e l y m a c h i n e d s l i t s b u t i t was f o u n d  t o remove i t c o m p l e t e l y .  is  a  the n-p i n t e r a c t i o n .  Considerable  chapter.  is  approximately  c o n t r i b u t i o n per channel from the t h r e e p a r t i c l e f i n a l  dence s p e c t r a .  The  t h e d o m i n a n t d e c a y mode o f t h e r e a c t i o n .  may be s e e n i n t h e s i n g l e  be u s e d t o remove t h i s  -d  are  an a p p r e c i a b l e c o n t r i b u t i o n to the  and a l p h a p a r t i c l e i s  is  T  some o f i t s  t h e two p a r t i c l e f i n a l  t h i s process  This  the l i n e of constant  e f f e c t produces  .  o n l y be o b s e r v e d  t h a t r e q u i r e d to observe  i n w h i c h t h e d e u t e r o n has  ,d)He  A g a i n as  state both p a r t i c l e s w i l l  same c o n f i g u r a t i o n a s  due t o He  t h e . l i n e of c o n s t a n t energy  c o i n c i d e n c e s f r o m t h e same r e a c t i o n .  two p a r t i c l e f i n a l  This  region i s  Thi from  average  states.  of s l i t  scatter-  impossible  P a r t i c l e i d e n t i f i c a t i o n techniques  may  c o n t r i b u t i o n t o t h e two d i m e n s i o n a l c o i n c i -  These i m p r o v e m e n t s  F o r the purpose  are discussed  i n the  final  of the experiment c o n s i d e r e d h e r e ,  t h e o b s e r v a t i o n o f t h e two n u c l e o n i n t e r a c t i o n s , t h i s  that  contri-  T(W. ;np")Ue s  T  50-  4  » /.50 MeV  0  X * A 4 A * « X  26-loo  A  lO| - 5 o O  *  Sco-leoo  •  • • • * • • • • • A « X *»*A»»X.  _*l  •  > IOOC5  _  •••A*X  CD  X » » » X  5  XX  3C-  2  *  XXX  J  X  T  X  V  s  <  *  6 C  *  - *  •  X X X x x x x x x x x x x vx xx xx xxyxx xx*x xxv xx xX%x>* X»4BA • x x x x x x y y x xxxxx x x x x « y x ^ X x x x x x x > x x . x x x x x x x x * x x x x x * A S « A  O _  X X XX  XX  XX X  O  XX  X X X X X X  X  X  XXKX XXX X****X*X'KX X X XXXXXXyXXKM«««MM*«««X«XXXX X  X  * ^ * 0  xxxxxxxxxxv«xxxxxxxxXXXXX«AA^X  X X XX XM • • • * A A * A • XXX XXX*(*" AAAMAA<S^AAM»(|tXX  A  X  10  J  A  u  20  30  CHANNEL.  •  K I C M 8 E R  xx*'***A«A*»a«»«*«XXX -XXX X*••••••••X © X XXXXXXX X •••••xxx XXX» «»A«X V •••« XX «« «*X •a  40  50  T,  •4h F i g u r e 27, Two d i m e n s i o n a l c o n t o u r p l o t o f p-He a n d d - H e o Lj. c o i n c i d e n c e e v e n t s f r o m t h e r e a c t i o n T(He , n p ) H e a t A = 151.lf«> 1  2  60  - if9 b u t i o n does n o t a f f e c t the  results.  The c o n t a m i n a n t r e a c t i o n D C H e ^ j p ) ! ^ a l s o a problem i n these measurements. p r e s e n t i n t h e t r i t i u m gas  This  target.  time the deuterium  lf  is  There i s not s u f f i c i e n t  He^ i n t h e t r i t i u m t o p r o d u c e a n y s i g n i f i c a n t p - p from the He^(He^,2p)He  presents  r e a c t i o n so i t i s  coincidences  unlikely that i t is  the  + HD  component i n t h e beam p r o d u c i n g  Although  t h e p-He  the contaminant r e a c t i o n .  coincidence events  a p p e a r i n t h e r e g i o n where t h e n - p  f r o m t h i s r e a c t i o n do n o t  interaction is  observed  they  do p r e s e n t a p r o b l e m i n d e t e r m i n i n g t h e c o n t r i b u t i o n f r o m t h e 5 states  I n He .  The t e c h n i q u e u s e d t o remove t h e c o n t r i b u t i o n  f r o m t h i s r e a c t i o n was of angles  t o make t h e same m e a s u r e m e n t s  f o r two s e t t i n g s  of the b i a s  peak f r o m the h i g h energy p r o t o n s  level  at this  o f d e t e c t o r 1.  from the contaminant  pair The  reaction  t h u s a p p e a r e d a t d i f f e r e n t p l a c e s i n t h e s p e c t r u m a n d c o u l d be subtracted  out. The c o i n c i d e n c e p r o t o n s p e c t r u m o b t a i n e d by  summing  k  o v e r a n e i g h t c h a n n e l i n t e r v a l a l o n g t h e c a l c u l a t e d p-He ^ k and s u b t r a c t i n g the c o n t r i b u t i o n f r o m t h e D(He-',p;He shown i n F i g u r e positions  6^  28.  reaction  The s i m i l a r s p e c t r u m o b t a i n e d f o r  = 75° a n d  = 90° i s  shown i n F i g u r e  contour is  the d e t e c t o r In  29.  case the contaminant r e a c t i o n does n o t p r e s e n t a p r o b l e m .  this  Again  both  6 t h e s e s p e c t r a a r e n o r m a l i z e d t o 2.5 x 10  single  counts  i n the f i x e d  detector. The t h e o r e t i c a l i n t e r p r e t a t i o n o f t h e s e t h e s p e c t r a f r o m t h e r e a c t i o n He (He  ,2p)He  is  spectra  discussed  in  and the  TTH^npJH*  4  To = /.50 MaV  2 ul  Q U  z  300,-  8  :r i a.  \oo[ .  0 0  IO  c3  a  .  1  Figure  28»  1  20  CHANNEL  1 «•  .  30  NUMBER  I 6  .  v  T, ( MeV^  |  _J 40  1 5o  Ssj-  1 8  i  1 12  Go  C o i n c i d e n c e p r o t o n spectrum from the r e a c t i o n  T(He3,np)He  lf  o b t a i n e d by summing  o v e r p-He " c o n t o u r f o r 11  A ^ l ^ l .  L  T * 0  1.50 MeV  250P  2 „ , > 2ocUJ  Ul  UJ  O  z  o o  n l  I) 100-  X  I  CL 50-  10  ^CHANNEL  4  Figure T(He  29.  30  20  T,(  6 MeV)  40  50  60  _l  8  C o i n c i d e n c e p r o t o n spectrum from the r e a c t i o n  ,np)He  o b t a i n e d b y summing  o v e r p-He  contour f or ^  = l65c  next chapter.  50 -  In Chapter VI,improvements  technique are considered which w i l l resulting  f r o m t h e two p a r t i c l e  to the e x p e r i m e n t a l  remove some o f t h e  final  ambiguity  s t a t e s , both from the  c o n t a m i n a n t r e a c t i o n a n d t h e d e c a y mode  T(He jd)!^. 3  -  51  -  CHAPTER ¥ THEORY OF F I N A L STATE INTERACTIONS A.  Introduction The t e s t o f a good n u c l e a r  first  theory i s  of a l l i n e x t r a c t i n g n u c l e a r parameters  its  usefulness  from e x p e r i m e n t a l  i n f o r m a t i o n and t h e n i n p r e d i c t i n g w h a t t o e x p e c t f r o m f u r t h e r experiments  on t h e b a s i s o f t h e s e r e s u l t s .  no r e a l l y good t h e o r y e x i s t s  for  t h e t h r e e body p r o b l e m  much o f t h e m a t h e m a t i c a l g r o u n d w o r k development  of such a t h e o r y .  low energy  nuclear physics  t h r e e body  theory are  and e f f o r t b e i n g  A t the present  has  been l a i d f o r  and p a r t i c l e p h y s i c s  on t h i s  problem.  of the mathematical techniques  t h r e e body p r o b l e m w i l l i m a t e methods particle  be g i v e n .  of a  As  this  two o f t h e  be d i s c u s s e d  a l o n g w i t h some o f t h e r e c e n t d e v e l o p m e n t s a c c u r a c y o f t h e two t h e o r i e s w i l l  3  l f  and  Watson (16)  enhance  transitions  His  the approxthree  chapter  of the t h e o r y .  be c h e c k e d by c o m p a r i n g  3  in  The their  the  2  l f  i n t r o d u c e d the term  that these  where two n u c l e o n s  of low r e l a t i v e energy.  is  T(He ,np)He' .  i n 19 5  s t a t e i n t e r a c t i o n " and showed  of  in this  p r e d i c t i o n s w i t h the e x p e r i m e n t a l s p e c t r a measured He^(He ,2p)He  time  complete  used i n t a c k l i n g  However  in  precise  thesis  developed to e x p l a i n c e r t a i n features  breakup r e a c t i o n s w i l l  reactions  the  The i m m e d i a t e a p p l i c a t i o n s  i n t e n d e d t o be m a i n l y e x p e r i m e n t a l i n c o n t e n t , no history  although  s u f f i c i e n t to warrant considerable  spent  time  "final  i n t e r a c t i o n s can  emerge  in a singlet  a p p r o a c h was t o s e p a r a t e  the  greatly state  -  r e a c t i o n process  the energy  In  the case  s t a t e , i . e . a r e a c t i o n of the A •+ B — * -  the i n t e r a c t i o n o p e r a t o r i n t o two t e r m s , v+ V ,  particular  and a n g u l a r  distributions  be w r i t t e n  in  XL +  0f"^  equation i s  t h e two n u c l e o n  separated  interaction  section for  the  The t r a n s i t i o n . . ' a m p l i t u d e may  . .  is  the f i n a l  a c t i o n of v a l o n e .  ._, .  5-1  s t a t e wave f u n c t i o n u n d e r  W a t s o n ' s main assumption  r e l a t i v e n u c l e o n momentum, t h e same k - d e p e n d e n c e  as  the  2M,  v - < * r i v i i r > where  range  type  to the c o r r e c t s c a t t e r i n g c r o s s p a i r of p a r t i c l e s .  the  o f two n u c l e o n s  i n the Schrodinger  where v i s  final  state  p a r t i c l e s before they can get o u t s i d e  of t h e i r mutual f o r c e s .  which leads  i n w h i c h the  no i m p o r t a n t p a r t and a " f i n a l  i n t e r a c t i o n " which d i s t o r t s  final  -  i n t o a " p r i m a r y mechanism"  state i n t e r a c t i o n plays  of the outgoing  52  is  the  inter-  t h a t f o r k,  s m a l l , the t r a n s i t i o n amplitude  (p^  has  .  R . J . N . P h i l l i p s (25)  uses the e x a c t o u t s i d e  wave  f u n c t i o n f o r t h e two n u c l e o n c a s e and shows t h a t t h e s p e c t r u m p a r t i c l e X i n t h e b r e a k u p may be a p p r o x i m a t e d  .•  the  of  by  = Wo [FlkQcesS* G(kb)sc^Sl 5-2  where F a n d G a r e  the r e g u l a r  and i r r e g u l a r  wave e q u a t i o n e v a l u a t e d a t a r a d i u s  'V,  w h i c h a r e n o t momentum d e p e n d e n t and £ i s n u c i e o n s c a t t e r i n g phase  shift.  solutions  Wo c o n t a i n s t h e S-wave  of the the  radial  factors  nucleon-  - 53 A somewhat d i f f e r e n t a p p r o a c h i s u s e d b y G . C . P h i l l i p s , G r i f f y and B i e d e n h a r n ( 8 ) .  They e x p r e s s  the cross  section f o r the  process a + A —>- b + B where B i s f o r m e d i n a s t a t e u n s t a b l e B  to p a r t i c l e emission, i . e .  —*- c + C , b y  T^-^^;|<Btfc EjH lA«;E >|%(E ^  5-3  ,  J  a  B  where H ' i s t h e i n t e r a c t i o n H a m i l t o n i a n , | A + a E ^ r e p r e s e n t s t h e s  initial  s t a t e v e c t o r and |B+b,E^^ t h e f i n a l  initial  and f i n a l wave numbers  the  generalized density  B having  are k  of states  only a s e t of sharp  a  state vector.  a n d k^, a n d ^ ( B ) i s c a l l e d e  a  f u n c t i o n f o r B.  states  The  at energies E  F o r t h e case o f this  n  f u n c t i o n may  be e x p r e s s e d a s  The d e n s i t y  of states  f u n c t i o n f o r a system B which i s  unstable  t o d e c a y i n t o two p a r t i c l e s c+C i s o b t a i n e d b y e v a l u a t i n g the, number o f d i s c r e t e s t a t e s w i t h i n two s p h e r e s ,  per u n i t energy  interval, of B l y i n g  one w i t h t h e i n t e r a c t i o n r a d i u s  other with an a r b i t r a i r i l y large radius  'R'.  This  'b  !  and t h e  leads, to the  result  ? l  where  fE ) = B  $^ i s t h e p h a s e  scattering  o f c+C a n d  ( S,(E ) + 4>/E ,b)) B  s h i f t f o r the corresponding ($> i s t h e h a r d  5-5  B  elastic  sphere phase  shift  eval-  5k uated a t the radius It Phillips,  'b'.  i s e a s y t o show t h a t t h e r e s u l t s  G r i f f y and B i e d e n h a r n ( h e r e a f t e r r e f e r r e d t o as t h e  PBG t h e o r y )  lead to a similar expression  t h e e a s e where t h e s c a t t e r i n g p r o c e s s shifts  o f Watson and  f o r the cross s e c t i o n f o r  has a resonance  w h i c h may be d e s c r i b e d b y s i n g l e  w i t h phase  level dispersion  theory.  Then t h e s c a t t e r i n g p h a s e s h i f t may be w r i t t e n a s  where  A  wi t h  L £ P  ^  m  £  .  £  T  ^  e  (  r A G / )  ^ - - [ ^ V e ] [ U / A  and  ]  Pi  =  i  5-6  ?  * / / A /  K ^ / a  ?  ) + ^ ) J  x2 with  ^  = kb.  bj^ a n d E  a r e r e s p e c t i v e l y t h e reduced w i d t h and  the c h a r a c t e r i s t i c energy used t o d e s c r i b e Watson's theory as expressed  the p a r t i c u l a r  resonance.  i n e q u a t i o n 5-2 may a l s o  be w r i t t e n a s ... tab)  =  WATSON  This  relationship  and  4^ d e f i n e d a s  and  fa  1  L  St +  fy)  5-7  i s t r u e f o r any form o f t h e phase s h i f t s  with P  followss  =  -fa/n"' - L i  5-9  If approximation  t h e p h a s e s h i f t s a r e d e s c r i b e d by t h e s i n g l e  t h e n e q u a t i o n .5-7 becomes •  C5(E) Similarily  level  _ const,  on d i f f e r e n t i a t i n g  ~% Pjl  5-io  the resonant  5~6 "the  phase s h i f t  cross s e c t i o n obtained from the d e n s i t y of s t a t e s formalism i s g i v e n by  5-11 "The two . r e s u l t s a r e e q u i v a l e n t i f e n e r g y and  is  a linear  i s independent of energy.  Barker  have shown t h a t t h i s  i s approximately  f u n c t i o n of• (26)  and T r e a c y  t r u e f o r e n e r g i e s w e l l above  t h r e s h o l d b u t f o r e n e r g i e s n e a r t h r e s h o l d o r f o r p h a s e s h i f t s note x h i b i t i n g a r e s o n a n c e t h e two f o r m a l i s m s This w i l l  be shown i n t h e n e x t  used t o f i t the e x p e r i m e n t a l  results. method h a s b e e n u s e d b y  e x p l i c i t l y f o r the. t h r e e a l p h a and t h r e e n u c l e o n  Duck (27)  results.  s e c t i o n where b o t h f o r m a l i s m s , a r e  Another approximation  and  produce d i f f e r e n t  f o r a c o i n c i d e n c e m e a s u r e m e n t o f two o f t h e t h r e e  systems  final  state  12 particles.  I n the ease o f the t h r e e alpha, decay o f C  the t r i p l e  c o r r e l a t i o n c r o s s s e c t i o n has t h e form  P,FL  d cr 3  AP +P[ Z  where t h e f i r s t  a25A - FJcosOz (g  m  'JT'  5-u  t e r m i s the. p h a s e - s p a c e f a c t o r d e s c r i b e d i n .  A p p e n d i x A a n d / T L ,1s the. s q u a r e o f t h e m a t r i x e l e m e n t f o r C" "*" 1  ( s p i n J.) t o b r e a k u p t h r o u g h B e ' ( s p i n J ' )  and c o n t a i n s a l l  the  angular  dependence.  Breit-Wigner  56 -  T h i s m a t r i x e l e m e n t was e v a l u a t e d u s i n g  resonance  theory,  the Watson t h e o r y of f i n a l  state  i n t e r a c t i o n s a n d t h e PBG d e n s i t y  of s t a t e s  p r e d i c t the d i s t i n c t i v e f e a t u r e s  of the e x p e r i m e n t a l s p e c t r a a l -  though peak w i d t h s  a r e n o t p r e d i c t e d w i t h any  and p o s i t i o n s  A similar expression triple  has  also  c o r r e l a t i o n by u s i n g  formalism.  the  All  b e e n o b t a i n e d f o r t h e p-D  a modified impulse approximation.  The  that  theory.  A more " e x a c t " has  accuracy.  inelastic  form of the i n t e r a c t i o n s i n c l u d e d i n the approximation i s o b t a i n e d from the Watson  theories  t r e a t m e n t of the t h r e e n u c l e o n  b e e n made b y Amado and h i s  co-workers  system  (28,29) based on the  f u n d a m e n t a l t h e o r y o f F a d e e v and L o v e l a c e .  The t h r e e body  effects  are taken completely i n t o account i n c l u d i n g i n e l a s t i c processes the couplings and s t i l l t o use  between c h a n n e l s .  In order  keep the problem t o manageable  separable  is  interactions, in this  i s o s p i n zero s t a t e .  the i n t e r a c t i o n s requires  taken to a r i s e  case  one i n t h e s p i n z e r o , i s o s p i n  s p i n one,  i t is  effects necessary  interaction. f r o m a sum  two S-wave i n t e r a c t i o n s  t h e e x a c t t r e a t m e n t o f t h e t h r e e body  speed  n + D  computer.  The  the  for  which  differential  scattering 2n + p  b e e n c a l c u l a t e d and t h e g e n e r a l f e a t u r e s  d a t a a r e r e p r o d u c e d by t h e t h e o r y .  are  effects  the s o l u t i o n of a set of coupled i n t e g r a l equations  p r o t o n spectrum f o r the i n e l a s t i c  of  one s t a t e and t h e o t h e r i n  Even w i t h the s i m p l i f i e d form  c a n o n l y be o b t a i n e d w i t h a h i g h  has  proportions  a s i m p l i f i e d form f o r the n u c l e o n - n u c l e o n  The f o r c e b e t w e e n t h e n u c l e o n s  used,  to include these  and  of the  The m a g n i t u d e s  experimental a r e n o t so  well  reproduced but the agreement this  57  -  does i n d i c a t e c o n s i d e r a b l e  t y p e o f t r e a t m e n t o f t h e t h r e e body p r o b l e m .  (29) a l s o  compare t h e i r t h e o r y w i t h t h e  rfatson  promise  Amado and  theory f o r  in  Aaron  final  s t a t e i n t e r a c t i o n s i n the r e g i o n of low r e l a t i v e  neutron-neutron  momentum.  u s e d by  They show t h a t a l t h o u g h  that i n this  not v a l i d I f  one c o n s i d e r s  Watson t h e o r y g i v e s r e s u l t s  slightly larger  this  resemblance  p r e s e n t l y under i n v e s t i g a t i o n . Amado's work i s  is  is  the  of the Watson  t h e e x p e r i m e n t a l i n f o r m a t i o n on t h i s  r e a c t i o n , are not  precise  scattering lengths  -2h  B.  Analysis  theory.  evident  time t h e t h e o r y , and  t o d i f f e r e n t i a t e between n-n  a  a c c i d e n t a l or not  One r e s u l t w h i c h i s  t h a t a t the present  the  exact  o b t a i n e d by u s i n g  s c a t t e r i n g l e n g t h i n the case  The q u e s t i o n o f w h e t h e r  is  the exact treatment,  which c l o s e l y resemble  The s i m i l a r i t y i n t h e r e s u l t s  and  Watson,  r e g i o n o n l y the i n t e r a c t i o n between the neutrons  important, is  theory.  the assumption  Is  from  probably sufficiently o f -17  fm.  fm. of Coincidence Proton  Spectra  The q u a n t i t y w h i c h h a s  been d e t e r m i n e d i n  measurement  of the c o i n c i d e n c e p r o t o n s p e c t r a i s  correlation  distribution  the  the  triple  5-13 If  the r e a c t i o n proceeds  v i a a s e q u e n t i a l decay through an i n t e r -  m e d i a t e two p a r t i c l e s t a t e , t h e n t h e c o o r d i n a t e i n deriving a theoretical expression o f mass s y s t e m  of the corresponding  s e c t i o n i n the r c m ( i )  for  5-13  is  system  interest  the r e c o i l  two p a r t i c l e s .  system f o r a breakup  of  involving  The the  center  cross cluster  (j+k)  58 -  i s g i v e n by d <r s  5~ik  rem  where  i s the i n t e r n a l or e x c i t a t i o n energy  (j+k)  a n d i , j , k i s some p e r m u t a t i o n o f 1 , 2 , 3 .  required to transform this  of the c l u s t e r The J a c o b i a n  cross s e c t i o n to the l a b o r a t o r y  system  is j  ^ ( £ j ; J2j>cm) ; f l j  The J a c o b i a n f o r t h i s  transformation i s c a l c u l a t e d i n Appendix A.  Several approximations quantity 0 ^ ^ » system this  (rem))  k  a r e made i n d e t e r m i n i n g t h e  The f i r s t i s t h a t t h e b r e a k u p  c e n t e r o f mass.  F o r the purpose  is isotropic  of the c a l c u l a t i o n s  i s n o t a bad a p p r o x i m a t i o n a s i n t h e f i r s t s e r i e s  ments w i t h G e o m e t r y #1 t h e p o l a r a n g l e s constant  and i n t h e second  i n polar angle  i s less  series  of  measure-  of both detectors  Since  the l a b o r a t o r y  remain  velocities  of the f i n a l s t a t e p a r t i c l e s a r e i n general c o n s i d e r a b l y than the i n c i d e n t v e l o c i t y the scm. p o l a r angles d i f f e r e n t from the l a b . p o l a r angles  are not too  and t h e r e f o r e remain  o f t h e range  of  larger  approx-  measurements.  The s e c o n d a p p r o x i m a t i o n i s t h a t t h e b r e a k u p intermediate This  requires  s t a t e i s i s o t r o p i c i n i t s own c e n t e r o f mass t h a t the i n t e r m e d i a t e system l a s t s  lost  before i t decays  preferred d i r e c t i o n of breakup.  of the system.  sufficiently  t h a t any s p a t i a l l o c a l i z a t i o n of i t s c o n s t i t u e n t p a r t i c l e s from i t s f o r m a t i o n ^ i s  here  w i t h G e o m e t r y #2 t h e v a r i a t i o n  than 15°«  i m a t e l y t h e same o v e r most  i n the  long  resulting  s o t h a t t h e r e i s no  The t h i r d a p p r o x i m a t i o n i s  that  the c o n t r i b u t i o n s  59 -  from the v a r i o u s  intermediate states  are  considered  t o be s i m p l y a d d i t i v e , i . e . t h e r e a r e no i n t e r f e r e n c e e f f e c t s . is  r e a l i z e d t h a t t h e r e a r e no good a r g u m e n t s  approximations.  However  to provide a comparison final  the purpose  of the p r e d i c t i o n s  0" ^  take.  the e x c i t a t i o n energy  p-He  system depends  s e c t i o n i n d i c a t e s how t h e s e q u a n t i t i e s a r e  as  studied mainly  on a c c o u n t  a polarization analyser.  quite w e l l .  of the use  Therefore  The P-wave p h a s e  to the f i r s t  two s t a t e s  f i t t e d using  single  phase  p r e d i c t e d by t h i s  shifts  parameters  shifts  the phase  6^  level dispersion  shifts  and 5 ^ w h i c h  theory.  theory i s  the s t a t e s  shifts  the parameters  for  either shifts  been targets  are  known  correspond  adequately  The f o r m o f  given i n equation et a l  the 5-6. (30)  of L i ^ are o b t a i n e d w i t h the s e t S i m i l a r i l y the experimental  o f Hoop and B a r s c h a l l the f i r s t  has  of helium  o f t h e mass 5 s y s t e m may be  l i s t e d i n Table  P-wave p h a s e  on  The  by He  1  for  only  evaluated.  From t h e d a t a on p-He *- s c a t t e r i n g r e p o r t e d by B a r n a r d the b e s t f i t s  cross  Shifts.  The e l a s t i c s c a t t e r i n g o f n u c l e o n s extensively  the  I n b o t h c a s e s the phase  e l a s t i c s c a t t e r i n g must be k n o w n .  and n-He^ Phase  two s t a t e s  (3D  o f He .  of  that a  o f t h e s y s t e m and may be e v a l u a t e d u s i n g  the corresponding  following  mainly  experimental  With these approximations  t h e W a t s o n t h e o r y o r t h e PBG t h e o r y . for  of the  f o r a p a r t i c u l a r two p a r t i c l e  r  is  of the simple t h e o r i e s  w i t h t h e hope o f i n d i c a t i n g t h e d i r e c t i o n s  more p r e c i s e t h e o r y must section  these  of these c a l c u l a t i o n s  s t a t e i n t e r a c t i o n s w i t h the r e s u l t s  measurements,  to support  It  are used t o These  also  of  n-He obtain are  TABLE h Parameters o b t a i n e d f o r s t a t e s of L i l e v e l dispersion theory.  State J  f  f  Phase s h i f t .  L i ^ ground state 3/2"  Si  5 L i ^ excited state 1/2" He^ ground state 3/2" He excited state 1/2"  5  and He^ from s i n g l e  (MeV)  b.(fm.)  2  (MeV)  3.0  lf.60  8.15  3.0  19.79  15.28  2.9  3.10  8.50  16,0  2.9  i  \  12.5  TABLE 5 E f f e c t i v e range theory parameters f o r nucleon-nucleon s c a t t e r i n g phase  State  shifts.  Phase  shift  n-p s i n g l e t state  So  p-p s i n g l e t state  So  a (fm.)  r  Q  (fm.)  -23.71  2 AO  -7.75  2.78  P  0.0^1  - 60 l i s t e d i n T a b l e k.  It  s h o u l d be p o i n t e d o u t t h a t t h e  d i f f e r e n c e between the v a l u e of E and the r e s o n a n c e d e f i n i t i o n of n-p Phase  energy of the p a r t i c u l a r l e v e l  Z^,  the energy  shift, i n this  is  energy,  due t o  the  analysis.  Shifts The p h a s e  scattering is  discussed  shift analysis  of  i n most t e x t b o o k s  f o r example P r e s t o n (32). phase  , the c h a r a c t e r i s t i c  large  The s i n g l e t  nucleon-nucleon on N u c l e a r  or t r i p l e t  Physics,  state  s h i f t s may s e p a r a t e l y be e x p a n d e d i n a T a y l o r ' s  momentum, f o r w h i c h t h e l o w e s t two t e r m s =  korth  +  £ r  o  n  k  n-p  series  in  are 5-i6  z  where k i s  t h e r e l a t i v e n u c l e o n momentum, a _ i s c a l l e d t h e n s c a t t e r i n g l e n g t h and r i s c a l l e d the e f f e c t i v e range. The on 7  to  &  to  v a l u e o f a „ and r which b e s t f i t the p r e s e n t e x p e r i m e n t a l d a t a n on a r e g i v e n i n T a b l e 5» from the s o l u t i o n s radial  The h a r d s p h e r e p h a s e  o f t h e r a d i a l wave e q u a t i o n .  f u n c t i o n s f o r t h e n-p F (o)  =  0  and u s i n g given  s h i f t s are  singlet  obtained  The a p p r o p r i a t e  s c a t t e r i n g a r e as  follows  ^  r e l a t i o n 5=9 t h e h a r d s p h e r e  phase  shift is  simply  by ^ o  where b i s evaluated.  =  ^  =  5-17  feb  the r a d i u s a t w h i c h the h a r d sphere phase  shift  is  - 61 -  p-p Phase  Shifts The p h a s e  is  shift analysis  o f p-p e l a s t i c  c o m p l i c a t e d b y t h e e f f e c t o f t h e Coulomb  dependence  of the singlet  s t a t e phase  shifts  field.  scattering  The momentum  i s g i v e n by t h e  f o l l o w i n g g e n e r a l i z a t i o n o f 5-16 5-18 R  3p  where  Q2 _  £ir^ e  X =  R and  2  ^  - /  0.577£  2.8815 x Id' " con.  *>?. .  The l e a s t for  =  2  2  Z,Z^e  z  squares f i t t o the experimental data gives the values  the parameters  a , r a n d P l i s t e d i n T a b l e 5* The Coulomb P op f u n c t i o n s a p p r o p r i a t e here a r e g i v e n a p p r o x i m a t e l y as f o l l o w s v  G . ^ } =_/_!"/ where  + 2 - » j f (-fci 2 ^ + 2 * - / +- K / 7 } ) )  <p .= k b a s b e f o r e a n d It  ence o f t h e c r o s s  {fy i s o b t a i n e d u s i n g o  i s now p o s s i b l e section  r e l a t i o n 5-9.  t o determine the energy  f o r a n y o f t h e two p a r t i c l e  dependsystems  rem consisting  of a proton, neutron or alpha p a r t i c l e .  numerical constants theory has the form  the cross  Apart  from  s e c t i o n p r e d i c t e d by t h e Watson  ~ 62  -  5-19  WATSOW  a n d by t h e PBG t h e o r y ,  the  form  The r e s u l t s  of the e v a l u a t i o n of these  quantities  u s i n g t h e p h a s e s h i f t s d e s c r i b e d p r e v i o u s l y a r e shown i n 5 30 and 31 f o r t h e two s t a t e s 33 f o r t h e s i n g l e t is  of L i  Figures  5 a n d He  and i n F i g u r e s  32 and  two p r o t o n s t a t e and t h e s i n g l e t d e u t e r o n .  evident that there i s  o f t h e two t h e o r i e s .  c o n s i d e r a b l e d i f f e r e n c e i n the  Even i n the case of the s t a t e s  He^ where t h e p h a s e s h i f t s  follow single  predictions 5  of L i  level dispersion  the d i s t r i b u t i o n s a r e s i m i l a r o n l y near the ground s t a t e The g r e a t e s t d i f f e r e n c e i s  It  and  theory peak.  i n the c o n t r i b u t i o n t o the e x c i t a t i o n  d i s t r i b u t i o n w e l l o f f r e s o n a n c e , w i t h the Watson t h e o r y p r e d i c t i n g a much l a r g e r c o n t r i b u t i o n . is  only a s l i g h t  For  the n u c l e o n - n u c l e o n systems  s i m i l a r i t y i n the shape o f t h e e x c i t a t i o n f u n c t i o n ' s  p r e d i c t e d by b o The t h t choei on cr ii dees n. c e p r o t o n s p e c t r u m i n t h e l a b . is  o b t a i n e d by m u l t i p l y i n g t h e r c m ( i )  possible  cross sections  for  system the  i n t e r m e d i a t e s t a t e by t h e a p p r o p r i a t e J a c o b i a n and by a  constant which determines i t s intermediate states.  . In  c o n t r i b u t i o n r e l a t i v e t o the  the measurements  c o n t r i b u t i o n from the v a r i o u s  w i t h G e o m e t r y #1  the  the  c o i n c i d e n c e p r o t o n s p e c t r a a r e s e p a r a t e d k i n e m a t i c a l l y so  the  of these  spectra is  final  other  state i n t e r a c t i o n s to  analysis  there  somewhat  simplified.  For t h i s  reason  o o  CD  Figure o o o  o o o  30.  Excitation functions by W a t s o n and PBG  for  states  theories.  of L i  predicted  o o o  Figure  31.  Excitation functions  for states  o f He  predicted  by W a t s o n and PBG t h e o r i e s .  -.000  1.000  2.0O0  3.000  4-000  E N-FUMEV)  5.000  6.000  7.000  8.000  *C  °  F i g u r e 32.  Excitation functions  for singlet  p r e d i c t e d by VJatson and PEG  s t a t e of p-p  theories.  syst  - 63 this analysis  is  considered  G e o m e t r y #1 A n a l y s i s  C.  For  this  the d e t e c t o r s  -  first.  of  Results  g e o m e t r y and f o r a n a n g u l a r  180° o r 135°  the c o n t r i b u t i o n from the  s t a t e i n t e r a c t i o n between the protons events  observed  with this  separation  i s n e g l i g i b l e as  c o n f i g u r a t i o n correspond  e x c i t a t i o n s i n t h e p-p s y s t e m .  of  final  coincidence  to very  high  The l a b . c r o s s s e c t i o n may be  written  <jJ /) - ( T  a+  where E _ system,  ,E  +cC(j crJE^ f J (T-(E ))  J\iGjEe*> -H4_CT  +  both correspond  N  p - * l , p  lL  to e x c i t a t i o n energies  2 and H e - * - 3 .  Since  whether d e t e c t o r 1 or d e t e c t o r 2 observes 5 from the breakup  through L i  The q u a n t i t i e s U" a n d <r  using  not  sities  and f i r s t e x c i t e d s t a t e (-)  f o r the t r a n s f o r m a t i o n of these The q u a n t i t i e s a  o f t h e two s t a t e s  t h e i n c i d e n t He  of L i  ^23  a n c  * ^13  * ° ^ ,  r  5-21 e  a  make t h i s  calculation is  sections  O  +  (E 2)j 2  are  the  c.Li  sections  to  lab.  a r e the r e l a t i v e i n t e n -  followed i n determining is  only  on  r  r  a  e  detector angles  and  J-^L  ^^23  The r e m .  cross 7  incident  The c o m p u t e r p r o g r a m K I N J A C u s e d  l i s t e d i n A p p e n d i x B.  (T+CE-J^),  the l a b .  to evaluate the q u a n t i t i e s  PP °P 'i 't  energy as a f u n c t i o n of T^.  R  obtained  and J  cross  the  energy.  s e c t i o n from e x p r e s s i o n J  and a  for  a n d a r e a s s u m e d t o be d e p e n d e n t  The p r o c e d u r e  ^2L  proton  , b o t h c o n t r i b u t i o n s must be i n c l u d e d .  1JL  coordinates.  known  the f i r s t e m i t t e d  e i t h e r t h e W a t s o n o r PBG t h e o r y and J  Jacobians  i n the L i ^  a r e the rem. c r o s s s e c t i o n s  +  g r o u n d s t a t e (+)  i t is  5-21  I3  2L  to  cross  CT.CE^) are then determined  - 6h from  t h e e x c i t a t i o n f u n c t i o n s shown i n F i g u r e 3 «  The  U  i n t e n s i t i e s were c h o s e n t o g i v e t h e b e s t f i t t o t h e for A  spectrum  1  180°.  =  2  The  relative  observed  r e s u l t s of these c a l c u l a t i o n s  t h e e x p e r i m e n t a l s p e c t r a a r e shown i n F i g u r e 3+ f o r t h e energy  1,15  T = Q  and  The  solid  TQ=  5»00 MeV.  and  the dashed curves  e x c i t a t i o n energies energy  T  i n F i g u r e 35  MeV  curves correspond  t o t h e PBG E ^  and  2  f o r the i n c i d e n t  theory.  E-^  incident  energy  to the Watson t h e o r y A l s o shown a r e  as a f u n c t i o n o f the  the  proton  1 #  I n order t o o b t a i n the b e s t f i t t o the 5»00 MeV  experimental  spectrum  f o r TQ=  to set a  =0,  The  of the e x c i t a t i o n d i s t r i b u t i o n f o r the L i ^ ground  tail  and  i . e . no  p r e d i c t e d by t h i s  u s i n g the Watson t h e o r y i t i s n e c e s s a r y  c o n t r i b u t i o n from  the e x c i t e d  state of L i .  t h e o r y i s more t h a n e n o u g h t o a c c o u n t  continuum between the ground s t a t e peaks.  The  state  f o r the  Watson t h e o r y does  p r e d i c t t h e p o s i t i o n o f t h e g r o u n d s t a t e p e a k more a c c u r a t e l y t h a n t h e PBG  theory. An  obvious  shortcoming  of t h i s  simple a n a l y s i s i s  t h a t i t does n o t produce the r e q u i r e d v a r i a t i o n w i t h the A  1  2  a s may  be  for A  seen i n F i g u r e  =  1  ^5°  •  angle  These  curves  + a r e c a l c u l a t e d w i t h t h e same i n t e n s i t i e s a the spectrum  a t 180°.  This indicates  the i n t e r m e d i a t e s t a t e breaks o f mass s y s t e m  up  and  a  used to f i t  t h a t the assumption  i s o t r o p i c a l l y i n i t s own  must n o t be v a l i d .  The  a n g l e i n t h e rem.  b e t w e e n t h e r e c o i l v e l o c i t y o f t h e L i ^ and b r e a k u p p r o t o n ( e i t h e r 1\ S}"^ o r ~<\  the v e l o c i t y  that center system  of  the  i n the d i s c u s s i o n of  the  H^(He ,2p)We 1.15 MeV 3  —  -  WATSOW  PBG.  4  C^/cL \.2. a  CCVa.-aO.28  IS  o 2  4 Figure  3^.  Comparison  6  8  of experimental coincidence  w i t h Watson and PEG t h e o r i e s , f o r T  Q  proton  = 1.15 M e V . '  spectra  T o =5.00 MeV  T, gure 35.  Comparison  (MeV)  of experimental c o i n c i d e n c e proton  w i t h W a t s o n and PBG t h e o r i e s f o r  = 5.00  MeV.  spectrum  - 65 -  k i n e m a t i c s i n A p p e n d i x A ) may be e v a l u a t e d a t e a c h p r o t o n T^. and  F o r the case  ' ?2 r  1 ) =  cases  7  °*°°  f  o  i s fairly  r  emitted proton entering detector 1  of the f i r s t  T = 9 . 5 MeV, t h e a n g l e A  i 2  =  1  ^°  t  T J ^ ^ 23.3° f o r 1  T  h  e  angular  ±2  180° a n d  difference i n T ^ ^  are seen f o r t h e l a r g e r breakup angle 5  direction.  & =  c o n s t a n t f o r a l l v a l u e s o f T^.  from the breakup o f the L i  f o r t h e two  1 )  Since fewer  emerges p r e f e r e n t i a l l y  of the.type  events  i t appears t h a t the proton i n the r e c o i l  T h i s i s n o t a n u n e x p e c t e d r e s u l t a s i n most  correlations  energy  Ca,b^) i n i t i a t e d  triple  by d i r e c t  r e a c t i o n s the p r e f e r r e d a x i s i s the r e c o i l d i r e c t i o n o f the i n t e r m e d i a t e p a r t i c l e (33) • A n o p p o s i t e e f f e c t h a s b e e n o b s e r v e d f o r t h e 5 6 3 ' k Li g r o u n d s t a t e by R e i m a n n (19) i n t h e r e a c t i o n L i (He ,p)2He • Here a n a x i a l asymmetry i s found 5 Li  about the r e c o i l d i r e c t i o n o f the  i n the breakup o f the ground s t a t e .  of the proton i s p r e f e r e n t i a l l y  I n t h i s case  the emission  i n the forward d i r e c t i o n  with  r e s p e c t t o t h e beam a x i s when a l l k i n e m a t i c e f f e c t s a r e t a k e n  into  account. A n o t h e r i n t e r e s t i n g f e a t u r e o f t h e measurements shown h e r e i s t h e r a p i d d e c r e a s e  i n t h e amount o f c o n t i n u u m b e t w e e n  the ground s t a t e peaks as t h e i n c i d e n t energy i n c r e a s e s . -t- _ PBG t h e o r y t h e r a t i o  a /a  r e q u i r e d t o f i t the observed  i n c r e a s e s by a f a c t o r  o f 5.*+ f r o m T = 1.15 Q  W a t s o n t h e o r y r e q u i r e s a n e v e n more d r a s t i c T = Q  5.00 MeV.  the L i  Regardless  Using the spectra  MeV t o 5.00 MeV. change as  The  a"= 0 f o r  o f t h e t h e o r y , i f i t i s assumed t h a t o n l y  s t a t e s c o n t r i b u t e t o the coincidence events  the r a t i o o f t h e ground s t a t e i n t e n s i t y  i n this  t o the e x c i t e d s t a t e  region,  - 66 i n t h e r e a c t i o n He (He- ,2p)He  intensity  J  >  o f a t l e a s t f o u r f r o m T = 1.15  MeV t o 5.00 MeV.  Q  uniform T= Q  m u s t i n c r e a s e by a f a c t o r This increase i s  w i t h i n c i d e n t e n e r g y a s may be s e e n i n t h e s p e c t r u m f o r  2.1+0 MeV i n F i g u r e  18.  A t t e m p t s were made t o e x p l a i n t h i s c o n s i d e r i n g t h a t the ground s t a t e preferentially angular  1  m i g h t be  J ^ - 1/2"  to the excited state  momenta i n t h e i n c o m i n g beam.  duces a change i n t h e r e l a t i v e it  J = 3/2  populated  by h i g h e r  Although  this  i n t e n s i t y i n the r i g h t  c a n a t m o s t a c c o u n t f o r a n i n c r e a s e o f 30$.  obtained  i n c r e a s e by  order  effect  pro-  direction  This r e s u l t i s  by a s s u m i n g t h e l o w e n e r g y beam i s p u r e S-wave a n d t h e  h i g h e n e r g y beam i s P-wave.  Another p o s s i b l e explanation i s that  t h e e f f e c t i s due t o t h e p r e f e r e n t i a l b r e a k u p o f t h e p r o t o n 5 the L i i n t h e r e c o i l d i r e c t i o n .  The b r e a k u p a n g l e  (l ) i  rj£  1  from s  found t o i n c r e a s e s l i g h t l y w i t h i n c r e a s i n g e x c i t a t i o n energy i n the L i  y  system but i t i s found t h a t t h i s  increase i s p r a c t i c a l l y  the  same f o r t h e d i f f e r e n t i n c i d e n t e n e r g i e s .  not  seem l i k e l y  sities  i s due t o some k i n e m a t i c  effect.  i t does n o t appear t h a t the s t a t e s o f L i c a n  account f o r the observed coincidence that there  only other  spectra the obvious  process  which can produce coincidence  The  events i n t h i s  three p a r t i c l e breakup i n which t h e  s t a t e i n t e r a c t i o n s do n o t p l a y a p a r t .  three curves,  conclusion  i s some c o n t r i b u t i o n f r o m a n o t h e r d e c a y mode.  region i s the instantaneous final  i t does  t h a t t h e o b s e r v e d change i n t h e r e l a t i v e i n t e n -  Since  is  Therefore  one i s t h e c o i n c i d e n c e  proton  F i g u r e 36 shows spectrum f o r a  statis-  T  0  -I.  15  MeV  T,  F i g u r e 36,  (MeV)  Comparison of p r e d i c t i o n s  w i t h W a t s o n a n d PBG  theories  of s t a t i s t i c a l  f o r the L i ^ e x c i t e d  breakup  state.  - 67 tical  breakup  obtained from e q u a t i o n A-28  and t h e o t h e r two a r e  the  s p e c t r a p r e d i c t e d by t h e W a t s o n a n d PBG t h e o r i e s f o r t h e f i r s t 5 e x c i t e d state of L i , These d i s t r i b u t i o n s a r e q u i t e s i m i l a r i n the r e g i o n  Tj= k MeV t o 8 MeV so i t w o u l d be d i f f i c u l t 5  the c o n t r i b u t i o n of the L i breakup.  If  to  separate  e x c i t e d s t a t e from the s t a t i s t i c a l  i t i s assumed t h a t p a r t o f t h e c o n t i n u u m b e t w e e n t h e  ground s t a t e peaks  f o r T^= 1.15  M  ©  v  is  due  t o the s t a t i s t i c a l 5  b r e a k u p and t h a t t h i s ground s t a t e as to account f o r  c o n t r i b u t i o n decreases  the i n c i d e n t energy the observed The f i n a l  important i n explaining at small angular metry. to  In  &j.2  tical  t  ^  breakup  processes  i e  is  will  possible  s t a t e i n t e r a c t i o n between the protons the c o i n c i d e n c e p r o t o n s p e c t r a  separations  c o r r t  then i t i s  Li  spectra.  rlbution  o  neglected.  f  of the s p e c t r a f o r  the  states  geo-  &2_2 ^° =  o f L l ^ and the  Reasons f o r not i n c l u d i n g  be g i v e n l a t e r .  is  measured  o f t h e two d e t e c t o r s w i t h t h i s  the p r e l i m i n a r y a n a l y s i s  =  increases  r e l a t i v e to the  statis-  these  The l a b . c r o s s s e c t i o n may  then  be w r i t t e n  TgJ.T,) where E is (T  12  is  the c o r r e s p o n d i n g  the J a c o b i a n f o r is  = a" J <r (E ) SL  o  e x c i t a t i o n i n t h e p-p  s e c t i o n f o r the s i n g l e t  determined from the e x c i t a t i o n f u n c t i o n s  As  two p r o t o n  shown i n F i g u r e  o f t h e e v a l u a t i o n o f e q u a t i o n 5-22  shown i n F i g u r e 37 s u p e r i m p o s e d  spectra.  system. J . _ 3L  the t r a n s f o r m a t i o n to l a b . c o o r d i n a t e s  the rem. cross  results  5-22  lz  and state  32.  The  f o r t h e two t h e o r i e s  on t h e c o r r e s p o n d i n g  b e f o r e the s o l i d curve corresponds  is  experimental  t o the Watson  Me ( Ufa*) He T - LIS MeV (a) ^ , a t 3  4  0  f  4  0.024  0500  °-oo  E .(M©v)  s  l2  -  WATSON  - PBG  0.323  i-oo 0 u>  I  0.500  T  l.oo 0. "~ r  a *-T15fr*. p  a «-nSfm p  E (MaV) ia  '  U IU  o  BlooL. WATSON WATSOKJ  4 F i g u r e 37,  6  Ti CMeV)  9  cy»-lO.Ofm. O.p»-6.0firv>  10  Comparison of experimental c o i n c i d e n c e proton s p e c t r a  at small angles  w i t h W a t s o n a n d PBG t h e o r i e s .  68 t h e o r y a n d t h e d a s h e d c u r v e t o t h e PBG t h e o r y . constant a for  0  was c h o s e n t o f i t t h e o b s e r v e d s p e c t r u m a t A-j_2  12  are  ^°  =  e a c h t h e o r y a n d t h e same c o n s t a n t i s u s e d f o r t h e c a l c u l a t i o n  of the spectrum a t E  The n o r m a l i z a t i o n  t  ^  i e  t v r a  P  r  o  t  2  o  n  2  °  e  S  o  m  e  o  f  "the e x c i t a t i o n e n e r g i e s  system corresponding  shown a b o v e e a c h s p e c t r u m .  t o the l a b . energy  The minimum e x c i t a t i o n e n e r g y  reached w i t h t h i s geometry ( n e g l e c t i n g the w i d t h o f the d e t e c t o r s ) is  2h  keV. From t h e s e c u r v e s  theory gives the  i t i s e v i d e n t t h a t the Watson  t h e b e s t f i t t o t h e o b s e r v e d c o i n c i d e n c e s p e c t r a when  p-p f i n a l  state interaction i s important.  However i t d o e s  p r e d i c t t h e peak i n t h e p-p e x c i t a t i o n f u n c t i o n a t t o o l o w a n energy.  The e f f e c t o f c h a n g i n g  the s c a t t e r i n g l e n g t h  a  is P  shown i n F i g u r e 3 7 c . theory gives  A s m a l l e r s c a t t e r i n g l e n g t h i n t h e Watson  a b e t t e r f i t but i t s t i l l  does n o t a c c o u n t f o r t h e  r a p i d decrease a t low e x c i t a t i o n energies. the  This i s opposite to  o b s e r v a t i o n o f Amado and A a r o n (29) who f o u n d t h a t i n t h e c a s e  of the s i n g l e t d e u t e r o n the Watson t h e o r y resembles theory i f a l a r g e r  s c a t t e r i n g length i s used.  o f t h e PBG t h e o r y f a i l the  t h e i r exact  The p r e d i c t i o n s  t o a c c o u n t f o r b o t h t h e peak p o s i t i o n s and  change w i t h a n g l e . The e f f e c t o f i n c l u d i n g t h e c o n t r i b u t i o n s f r o m t h e  5  states  of L i  a n d t h e s t a t i s t i c a l b r e a k u p w o u l d be t o a d d a  s t r u c t u r e l e s s background. In the L i ^ system f o r A peak i s n o t p r e s e n t .  n  Id  The minimum e x c i t a t i o n e n e r g y  flat  reached  = 6° i s a b o u t 3.0 MeV so t h e g r o u n d  The maximum amount t h a t t h e s e p r o c e s s e s  state can  - 69 contribute is  d e t e r m i n e d by t h e d i p a t V . 5 Me?  clusions  reached i n t h i s a n a l y s i s  ing this  contribution.  so t h a t t h e  con-  w o u l d n o t be a f f e c t e d by i n c l u d -  The c o i n c i d e n c e s p e c t r a o b s e r v e d f o r t h e s e a n g l e s the h i g h e r Figures  i n c i d e n t e n e r g y a r e v e r y s i m i l a r a s may be s e e n  19 and 21.  the s i n g l e t  However  by B a c h e r  i n importance r e l a t i v e to  the i n c i d e n t energy  t h i s reason t h a t the study  increases.  of t h i s r e a c t i o n a t higher  (9) and A l d r i d g e (7)  dence f o r the p r e s e n c e  o f t h e p-p  in  apparent t h a t the f o r m a t i o n of  two p r o t o n s t a t e d e c r e a s e s  the L i ^ ground s t a t e as  energies  i t is  final  It  is  for  incident  d i d n o t r e v e a l good  evi-  state interaction.  The  k i n e m a t i c c a l c u l a t i o n s show t h a t t h i s d e c r e a s e i s n o t a  phase-  space e f f e c t ,  as  the r a t i o of the a v a i l a b l e phase-space  for  two p r o c e s s e s  is  approximately constant for incident energies  1.15  MeV t o 5»00 MeV,  cal analysis D.  of t h i s  G e o m e t r y f2  One o f t h e a i m s breakup  Analysis  of  The a n a l y s i s w i t h G e o m e t r y #2 i s of both the s t a t e s  should  o f a more a c c u r a t e  be t o e x p l a i n t h i s  be c o n s i d e r e d t o g e t h e r .  theoreti-  Results o f the c o i n c i d e n c e s p e c t r a  obtained  o r He"' and t h e two n u c l e o n s y s t e m  c o n t r i b u t i o n was  must  The p r o c e d u r e u s e d i n t h i s a n a l y s i s  the r e g i o n o f the s p e c t r u m where t h i s  process  is  was  fitting  predominant.  t h e n s u b t r a c t e d from the measured  spectrum,  h o p e f u l l y l e a v i n g t h e p o r t i o n due o n l y t o t h e two n u c l e o n state.  from  effect.  t o d e t e r m i n e t h e c o n t r i b u t i o n f r o m t h e mass 5 s y s t e m s by  This  the  c o m p l i c a t e d by t h e f a c t t h a t t h e c o n t r i b u t i o n of L i  at  The PBG t h e o r y was u s e d t o d e t e r m i n e t h e shape  singlet 5 of the L i  - 70 -  and He^ c o n t r i b u t i o n s a s  i t g i v e s a b e t t e r e s t i m a t e of the  t o be i n c l u d e d f o r e x c i t a t i o n e n e r g i e s p a r t of the e x c i t a t i o n f u n c t i o n . istical  t h r e e p a r t i c l e breakup  l y i n g w e l l o f f the  amount resonant  The c o n t r i b u t i o n f r o m t h e  is  stat-  i n c l u d e d as p a r t o f the c o n t r i -  b u t i o n f r o m t h e e x c i t e d s t a t e o f t h e mass 5 n u c l e i .  The  a /a  determined  for  = 0.33 f o r t h e i n c i d e n t e n e r g y 5 the L i ^ s t a t e s  by f i t t i n g  are obtained simultaneously  T =  the p-p  Q  1.50  MeV was  coincidence spectra,  obtained for  by t h e a v a i l a b l e p h a s e - s p a c e  as  = 62° and  with this  t i o n a t the h i g h  geometry,  energy  intensities  G e o m e t r y #1 a s  to g r e a t l y magnify  the  Removing  g i v e s a more a c c u r a t e p i c t u r e o f  i n the case  divided A-28. spectra  contributhis  o f the measurements  the observed  the  This  made w i t h  calculated for  spectra  purely  the r e l a t i v e  c o n t r i b u t i n g to the spectrum.  the a v a i l a b l e phase-space  geometry does n o t d i s t o r t  0  the r a t i o o f the observed y i e l d t o  of the processes  was n o t n e c e s s a r y  = 9O  on t h e c o i n c i d e n c e  end o f t h e s p e c t r u m .  k i n e m a t i c e f f e c t by u s i n g a v a i l a b l e phase-space  is  coincidence  c a l c u l a t e d from e q u a t i o n  The e f f e c t o f t h e a v a i l a b l e p h a s e - s p a c e measured  which  i n t h e r e a c t i o n He^( H e ^ , 2 p ) H e ^ .  F i g u r e 38 shows t h e c o i n c i d e n c e p r o t o n s p e c t r u m ( i n with alpha p a r t i c l e s )  ratio  this  to such an e x t e n t .  5 The c o n t r i b u t i o n f r o m t h e s t a t e s subtraction, is  also  i n L i ^ used i n the  s i m i l a r i l y c o r r e c t e d f o r the a v a i l a b l e  shown i n F i g u r e  the c o r r e s p o n d i n g  38.  The c u r v e s  e x c i t a t i o n energies  marked. E ^  background phase-space, and E ^  i n the Li-^ system.  are A  s i m i l a=r 9 s°p° e u m was . c t rThe s p e cct ar al c uo lbattaei nd e df o rby t hseu bctar saec t»0 i»n g = t 75° h e s e and background  T  0  -  1.50  e« = &20  MeV e2=  SO  0  T, (MeV) F i g u r e .38•  C o i n c i d e n c e p r o t o n spectrum from the r e a c t i o n  He (He ,2p)He 3  3  l f  for  ^= ±2  p h a s e - s p a c e . A l s o shown i s states  152° d i v i d e d by t h e a v a i l a b l e the c o n t r i b u t i o n from the  o f L i ^ c a l c u l a t e d w i t h t h e PBG  theory.  - 71 e s t i m a t e s from the measured  -  s p e c t r a a r e shown i n F i g u r e 39 a l o n g  w i t h some o f t h e e x c i t a t i o n e n e r g i e s s o l i d and d a s h e d c u r v e s  gives  the c l o s e s t It  t h e r e a c t i o n T(He  f m . and  f i t t o the measured i s more d i f f i c u l t  ,np)He  between the  t h a t the s m a l l e r  value  spectrum.  to determine the c o n t r i b u t i o n  t o the c o i n c i d e n c e p r o t o n s p e c t r a from as b o t h the L i  and He  y  . Two q u a n t i t i e s a r e r e q u i r e d f o r t h i s  being the r a t i o  Watson  a j= - 6 . 0 0 f m . P  s i m p l e t o choose  but i t does a p p e a r  f r o m t h e mass 5 s y s t e m s  present.  a = -7.75 P  Here i t i s n o t as  two s c a t t e r i n g l e n g t h s  The  r e p r e s e n t the p r e d i c t i o n s o f . t h e  theory f o r s c a t t e r i n g lengths respectively.  i n t h e p-p s y s t e m .  states  are  c a l c u l a t i o n , one  a / a " f o r t h e He^ s y s t e m and t h e o t h e r t h e r a t i o  of the cross  s e c t i o n f o r the breakup through L i to the c r o s s 5 + „ s e c t i o n f o r t h e b r e a k u p t h r o u g h He The same r a t i o a / a = 0.33 5 5 found f o r the s t a t e s of L i i s assumed t o a p p l y f o r He a s w e l l . 5 The c r o s s s e c t i o n f o r t h e b r e a k u p t h r o u g h L i i s t a k e n t o be t w i c e 5 a s l a r g e as t h e c r o s s s e c t i o n f o r t h e b r e a k u p t h r o u g h He . This y  e  estimate i s  o b t a i n e d from the r e s u l t s  of Barry  (13).  F i g u r e h-0 shows t h e c o i n c i d e n c e p r o t o n o b t a i n e d f o r " © ^ = 6l,k° 5  and  0  2  spectrum  - 90° a n d t h e c o n t r i b u t i o n f r o m  5  the L i  and He  states determined using  ratios.  Again  the a v a i l a b l e phase-space  t h e PBG t h e o r y a n d has  b o t h t h e m e a s u r e d and c a l c u l a t e d s p e c t r a . was made f o r t h e o t h e r m e a s u r e d The r e s u l t s  of the background  spectrum a t  b e e n removed  these from  The same c a l c u l a t i o n .0  = 75° a n d =  s u b t r a c t i o n a r e shown i n F i g u r e  a l o n g w i t h some o f t h e e x c i t a t i o n e n e r g i e s  i n t h e n-p  system.  90°. *+l The  He (He Z )l-U+ 3  3  3  P  To - I.50 MeV 2  IVATSOW  a  IVAT50NJ  a »  - - 7  f  p  75  -6LOO  fry,  E.-(MeV)  5oo 4  5 °0  4  6 "Tj (MeV)  \ ID O  2 ai  o  (b)  o z  0,=  75°  WAjTBoM a =»-7.T5fm WATSON ap =• -6.00  •%=30°  P  6 u  LOO 1  i  i.oo  •530  E, (Mev) 3  ^-1-  0-  6 T(MeV) Figure  39.  Comparison  8  lO  of experimental coincidence proton  w i t h Watson theory  f o r t h e p-p f i n a l s t a t e  12.  spectra  interaction.  T, ( MeV) Figure  ^fO.  Coincidence proton spectrum from the r e a c t i o n  ile^CHe^ , 2 p ) H e phase-space. states  i+  for Also  151»^° d i v i d e d by t h e a v a i l a b l e shown i s  the c o n t r i b u t i o n from the  o f L i ^ and He^ c a l c u l a t e d w i t h t h e PBG  theory.  T(He. ,np) H e * 3  To =  1.50  .500 .100 0 .|Q0 4  4  4  500  E| CMeV) 3  4  WATSON  Q - -23.71 P *  WATSON  a  n  - -30.0  n  fro  o z 1.0  4  :567  l.oo  4  4  H, CMeV) 3  I  WATSON  0.  O --23.7/pv> n  £1 8  12.  10  T, (MeV) Figui-3 ^ 1 .  Comparison  of experimental coincidence  w i t h Watson theory  f o r the n-p f i n a l  state  proton  spectra  interaction.  s o l i d and d a s h e d c u r v e s  is  spectrum (a)  represent  the p r e d i c t i o n s  the Watson t h e o r y f o r n-p  singlet  scattering lengths  and a  t h e n-p  excitation function calculated  = -30.0 fm.  Since  u s i n g t h e PBG t h e o r y i n c r e a s e s decreases  r a p i d l y as  As for it  t h e two c u r v e s  t h e two v a l u e s i s apparent  fits  theory  p r e d i c t e d by t h e W a t s o n  depend v e r y c r i t i c a l l y  contribution subtracted.  similar  e v a l u a t i o n o f t h e c o n t r i b u t i o n f r o m t h e He^ and L i  has  b e e n done  somewhat  states.  a r b i t r a r i l y due t o t h e l a c k o f A more a c c u r a t e a n a l y s i s  theory of f i n a l  analysis states  information  would r e q u i r e  e x p e r i m e n t a l e f f o r t t o l e a r n more a b o u t  a more p r e c i s e  these  state interactions.  The e f f e c t  s t a t e d e t e c t o r s , w h i c h has  b e e n c o n s i d e r e d h e r e , \-rould h a v e  t o be i n c l u d e d i n a more  analysis  A discussion  o f some o f t h e r e s u l t s  and o f t h e improvements  mental technique i s  of  this  chapter.  not  careful  preliminary  w h i c h c a n be made t o t h e  contained i n the next  con-  states,  of t h e f i n i t e w i d t h of the s o l i d  analysis.  best  5  the  and  theory  on t h e  In t h i s  5  siderable  would  = 0,  scattering length are quite  spectrum w i l l  of background  about these  energy  t h a t the c h o i c e of the s c a t t e r i n g l e n g t h which  the measured  amount  o f the n-p  = -23.71 f m .  n  the e x c i t a t i o n  t h e c o i n c i d e n c e s p e c t r u m p r e d i c t e d by t h i s  be a l m o s t a d e l t a f u n c t i o n a t E  a  of  experi-  CHAPTER  VI  DISCUSSION A,  Present  results One i m p o r t a n t r e s u l t  clear  evidence  t h a t the s i n g l e t  may be o b s e r v e d a s  final  o f t h i s work i s  states  o f t h e p-p and n - p  state interactions  3 3 1+ 3 h He (He ,2p)He and T(He ,np)He . A l t h o u g h has b e e n o b s e r v e d  previously  r e c e n t l y by C o h e n e t a l (35)? the s i n g l e t  that i t  by P a r k e r  i n the  systems  reactions  the s i n g l e t  (2),  deuteron  S i m p s o n (3*+) and more  no s u c h good e v i d e n c e e x i s t s  two p r o t o n s t a t e .  gives  for  A c o m b i n a t i o n o f two f a c t o r s ,  p u r e l y k i n e m a t i c a l and t h e o t h e r t h e Coulomb f o r c e a c c o u n t s  for  this difference.  Kinematics  particle  i n w h i c h two o f t h e p a r t i c l e s emerge w i t h l o w  breakups  r e l a t i v e momentum. factor  This  p l a y an i m p o r t a n t r o l e i n  one  type of breakup  i n w h i c h the dominant  term i s  r e l a t i v e momentum,  i n the case singlet  together  The Coulomb f o r c e p r e v e n t s  more p r o m i n e n t  i n these  r e p o r t e d h e r e and p r e v i o u s been u s e d .  measurements  Although  reason  the in  low  may t a k e a d v a n t a g e  o f t h e two p r o t o n s y s t e m and f o r t h i s  deuteron i s  has  o n l y systems  i n a s t a t e of  of  this  the  reactions.  The m a i n d i f f e r e n c e b e t w e e n t h e  energy  proportional to  However  or low i n t e r n a l energy,  t h i s k i n e m a t i c a l enhancement.  g r e a t l y e n h a n c e d by a  inversely  r e l a t i v e momentum o f t h e two p a r t i c l e s . w h i c h t h e two p a r t i c l e s c a n e x i s t  is  three  measurements  i n that a lower  the r e a c t i o n s  are found  incident to  pro5  eeed l a r g e l y v i a s e q u e n t i a l d e c a y s He 5  ?  through  corresponding, to a nucleon-alpha  the states  particle  final  of L i state  or inter-  action,  i t is  singlet  s t a t e o f t h e two n u c l e o n s y s t e m i n e a c h r e a c t i o n .  contribution,  possible  t o s e p a r a t e out the c o n t r i b u t i o n from the  i n the case  o f t h e p-p  system,  is  found to  This decrease  5 relative energy  to the c o n t r i b u t i o n from the L i  increases,  states  as  the i n c i d e n t  i n d i c a t i n g that low i n c i d e n t energies  t h e b e s t i n f o r m a t i o n t o be g a i n e d a b o u t t h e  allow  nucleon-nucleon  interactions. Several  conclusions  may be d r a w n f r o m a  o f t h e p r e d i c t i o n s o f t h e W a t s o n and PBG t h e o r i e s i n t e r a c t i o n s w i t h the e x p e r i m e n t a l r e s u l t s . the Watson t h e o r y d e s c r i b e s better  of f i n a l  The f i r s t i s  However i t i s  that  apparent that n e i t h e r  can account f o r a l l the observed  the e x p e r i m e n t a l s p e c t r a . t h a t the r e a c t i o n process  state  t h e n u c l e o n - n u c l e o n i n t e r a c t i o n much  t h a n t h e PBG t h e o r y .  of these formalisms  comparison  The b a s i c a s s u m p t i o n  features  of both  theories,  c a n be s e p a r a t e d i n t o a p r i m a r y  w h i c h h a s no e f f e c t on t h e e n e r g y final  p a r t i c l e s , and a f i n a l  valid  for short-lived f i n a l  and a n g u l a r  of  mechanism  d i s t r i b u t i o n s of  state interaction, is state interactions.  obviously This  is  the  not  shown t o  5 be t h e c a s e f o r  the s t a t e s  of L i  as  i t is  necessary  t o assume  5 t h a t the L i  system r e t a i n s  which r e s u l t e d i n i t s dependence  mechanism  f o r m a t i o n , t o e x p l a i n the observed  angular  of the e x p e r i m e n t a l s p e c t r a . How b e s t  theory i s  some memory o f t h e p r i m a r y  a difficult  t o i n c l u d e t h e s e e f f e c t s i n a more a c c u r a t e  question.  One method m i g h t  be t o  extend  the d i r e c t r e a c t i o n t h e o r i e s  to p r e d i c t angular  t h e t y p e ( a , be) where a , b , c  are a l l p a r t i c l e s i n contrast  t h e (d,n^f)  type of r e a c t i o n .  Another  correlations  p o s s i b l e approach i s  of  to to  - 75  -  t r e a t , t h e t h r e e body e f f e c t s e x a c t l y a s Amado ( 2 0 ) the case of a f i n a l particle B.  state consisting  rather than three  Future  has done,  o f two n u c l e o n s  for  and an a l p h a  nucleons.  work The m o s t u s e f u l i m p r o v e m e n t t o t h e e x p e r i m e n t a l  t e c h n i q u e used i n t h e measurements  r e p o r t e d h e r e w o u l d be  in  particle  of t h i n f o i l s f o r t h i s  purpose,  identification.  The u s e  a l t h o u g h e x t r e m e l y s i m p l e and e f f e c t i v e i n t h e s e p a r a t i o n protons  and a l p h a p a r t i c l e s , p r o d u c e s  sufficient loss  r e s o l u t i o n t o make t h i s method u n s u i t a b l e f o r p r e c i s e Two s o l u t i o n s  are p o s s i b l e :  one method i s  of  energy  measurements.  to place a t o t a l l y  d e p l e t e d d e t e c t o r i n f r o n t o f one o r b o t h o f t h e p r e s e n t  detectors  and t o d i f f e r e n t i a t e b e t w e e n t h e p a r t i c l e s w i t h d E / d x v s . analysis;  the other i s  on t h e r e s p o n s e  t o use p u l s e  of  E  shape d i s c r i m i n a t i o n , r e l y i n g  of the d e t e c t o r - p r e a m p l i f i e r arrangement  t o be  s u f f i c i e n t l y d i f f e r e n t f o r the d i f f e r e n t p a r t i c l e s to a l l o w i d e n t i f i c a t i o n of the p a r t i c l e s . the s e p a r a t i o n of protons to separate protons is  i t is  l a t t e r method i s  i n t h i s way.  necessary  to i d e n t i f y low these are  stopped i n the t o t a l l y d e p l e t e d d e t e c t o r .  However  difficult  energy completely f o r the  study  of i n t e r e s t h e r e , p a r t i c l e i d e n t i f i c a t i o n i n  one o f t h e d e t e c t o r s i s proton detector.  for  The f i r s t method  e s p e c i a l l y a l p h a p a r t i c l e s , as  of the r e a c t i o n s  possible  and a l p h a p a r t i c l e s b u t i t i s  from deuterons  preferable unless  particles,  This  necessary  and t h i s d e t e c t o r c a n be t h e  P a r t i c l e i d e n t i f i c a t i o n using  u s e f u l not only i n separating  only  this  technique  out the c o n t o u r of i n t e r e s t  and  is  - 76 p r o v i d i n g b e t t e r energy particle final reactions.  r e s o l u t i o n but a l s o i n removing  s t a t e c o i n c i d e n c e s which a r e a problem  The c o n t a m i n a n t  r e a c t i o n He ( d , p ) H e  t h e two  i n these  i s character-  i z e d by v e r y h i g h p r o t o n e n e r g i e s and t h e s e p r o t o n s c a n be e a s i l y removed by d i s c r i m i n a t i n g dE/dx d e t e c t o r . 3  a g a i n s t v e r y low energy  Similarily  c o i n c i d e n c e events from  + c a n be r e m o v e d by e l i m i n a t i n g t h e d e u t e r o n s  dE/dx v s . E a n a l y s i s . One o f t h e p r o b l e m s f o u n d  with  i n determining the s i n g l e t  c o n t r i b u t i o n t o the c o i n c i d e n c e p r o t o n s p e c t r a from the  I  k  r e a c t i o n T(He ,np)He  i s t h e l a c k o f k n o w l e d g e a b o u t t h e He  and a b o u t t h e r e l a t i v e i n t e n s i t i e s • o f a t the i n c i d e n t energy  used.  the competing  5  states  r e a c t i o n modes  A systematic study of the coincidence  s p e c t r a from t h i s r e a c t i o n , s i m i l a r V 3 . if He'CHe  the r e a c t i o n  ]  mode T(He ,d)He  deuteron  p u l s e s from t h e  t o t h a t done f o r t h e r e a c t i o n  ,2p)He , w o u l d be v e r y u s e f u l i n s u p p l y i n g t h i s i n f o r m a t i o n .  T h i s i n f o r m a t i o n t o g e t h e r w i t h a more a c c u r a t e t h e o r y o f t h e breakup would improve t h e a c c u r a c y w i t h which the d e t e r m i n i n g t h e n-p i n t e r a c t i o n c a n be o b t a i n e d .  parameters  A f u r t h e r refinement t o the experimental w o u l d be t h e d e t e c t i o n o f t h e n e u t r o n s 3 T(He  from  technique  the r e a c t i o n  *+ ,np)He .  S i n c e one o f t h e d e s i r e d r e s u l t s o f t h e s t u d y o f  the n u c l e o n - n u c l e o n  i n t e r a c t i o n by means o f two d i m e n s i o n a l  a n a l y s i s o f a three p a r t i c l e breakup i s t o determine  energy  the para-  m e t e r s d e s c r i b i n g t h e n-n i n t e r a c t i o n , i t i s a p p a r e n t  t h a t some  type of neutron d e t e c t i o n i s r e q u i r e d t o achieve t h i s  result.  if The  r e a c t i o n T(T,2n)He  which  i s t h e a n a l o g o f t h e two r e a c t i o n s  s t u d i e d h e r e , w o u l d be t h e r e a c t i o n o f i n t e r e s t i n d e t e r m i n i n g  -  77 these  parameters.  delay  between the a r r i v a l  detector placed  The n e u t r o n e n e r g y may be m e a s u r e d by t h e t i m e of the charged p a r t i c l e  c l o s e t o t h e t a r g e t and t h e a r r i v a l  i n a n e u t r o n d e t e c t o r , s u c h as a n o r g a n i c f u r t h e r away.  i n a solid  o f the neutron  scintillator,  placed  The r e s o l u t i o n o f t h e n e u t r o n e n e r g y m e a s u r e m e n t s  d e p e n d s o n t h e d i f f e r e n c e i n t h e two f l i g h t p a t h s . from the r e a c t i o n Her(He ,2p)He J  The r e s u l t s  i n d i c a t e that the best  t i o n a b o u t t h e p-p i n t e r a c t i o n i s g a i n e d coincidences  state  w i t h t h e two d e t e c t o r s  by s t u d y i n g  a t as s m a l l an  informa-  t h e p-p angular  s e p a r a t i o n as p o s s i b l e .  This  t h e r e a c t i o n T(He ,np)He  i f t h e n e u t r o n e n e r g y c a n be m e a s u r e d .  T h e r e i s no p r o b l e m i n t h i s  same e x p e r i m e n t i s p o s s i b l e i n  case i n o b t a i n i n g a s m a l l  s e p a r a t i o n as t h e n e u t r o n d e t e c t o r the p r o t o n d e t e c t o r .  c a n be p l a c e d d i r e c t l y  I t w o u l d be a c o n s i d e r a b l y more  e x p e r i m e n t t o p e r f o r m two d i m e n s i o n a l coincidences of f l i g h t  s y s t e m s w o u l d be r e q u i r e d .  particle  i n a. s o l i d  be t h e s t u d y  could  o f n-He  coincidences  difficult  a s two n e u t r o n t i m e  The s t a r t p u l s e  be o b t a i n e d  state detector.  behind  e n e r g y a n a l y s i s o n n-n  f r o m t h e r e a c t i o n T(T,2n)He  neutron time o f f l i g h t  angular  f o r the  by d e t e c t i n g t h e a l p h a  A simpler from t h i s  experiment would  reaction.  Although  I t i s c l e a r t h a t more p r e c i s e t h e o r i e s a r e r e q u i r e d t o o b t a i n parameters such as s c a t t e r i n g l e n g t h s  from these  reactions, a 3  d i r e c t c o m p a r i s o n o f t h e r e s u l t s f r o m t h e r e a c t i o n s T(He and  T(T,2n)He  should  n-n  interaction.  give considerable  h  ,np)He  i n f o r m a t i o n about the  - 78  -  APPENDIX A REACTION KINEMATICS FOR THREE F I N A L P A R T I C L E S The s y m b o l s are l i s t e d  for  the v a r i o u s  i n Table 1 of Chapter II.  For  breakup the sake  parameters of complete-  n e s s some o f t h e r e l a t i o n s d e t e r m i n i n g t h e b r e a k u p i n laboratory  s y s t e m w h i c h were d e r i v e d i n C h a p t e r ' I I w i l l  g i v e n h e r e as w e l l . momentum and  and  »» 2  where  Tj +  the requirement of c o n s e r v a t i o n  of  - 2&P  2  Z  A  =  B  =  T  -T T"  z  A-2  3  2^1^  sa  both equations  AP^ where  Using  be  energy  TQ+ Q  and s o l v i n g  the  f o r P^ y i e l d s  the q u a d r a t i c  + C = O  equation  A-3  i^s/m^  I  P CoS 0 0  - P, CoS  2  A  i a  z o  The  2 P P, cos B, 0  2r^ Q  "  i  3  s o l u t i o n s o f A-3 a r e  Pz  -  ±  (B  subject to the requirement  B  2  - A C  ± / S - A C )/A 2  A  that  > 0  A-^f  - 79 By i n s e r t i n g forming  the s o l u t i o n  simple  for^ ^ i ^  ^ ^ n  e q u a t i o n A-3 and p e r -  0  a l g e b r a i c manipulation the quadratic equation f o r  as a f u n c t i o n o f t h e a n g l e s *©^  DP,  ^3/^,) A  F - (l - m K ) AP 3  From t h e s e r e l a t i o n s  2 0  § I> $ 2  3  P, + F  - 2 E  Z  D * (l +  where  -  l  s  o b  "  1 : a i n e ( 3  ••  -O  -  COS A 2  (2L  - P C05 e - 2nnAGJ 2  2  0  2  a l l the necessary  3  parameters i n the l a b o r a t o r y  s y s t e m may be e v a l u a t e d . The p a r a m e t e r s i n t h e scm. s y s t e m , t h e c e n t r e o f mass s y s t e m o f t h e t h r e e f i n a l using the v e l o c i t y  triangle  t h e c e n t r e o f mass V  s t a t e p a r t i c l e s , a r e determined  shown i n F i g u r e A l .  The v e l o c i t y o f  i s g i v e n by scm  The l a w o f c o s i n e s i s u s e d t o d e t e r m i n e  Tl  -  ( V * L  + v ^ 2  s  ~ 2\J  L  t h e scm. v e l o c i t i e s .  V s ^ c o s a ^  2  A-7  The a z i m u t h a l a n g l e s do n o t c h a n g e f r o m t h e l a b . t o t h e scm. system as p o l a r c o o r d i n a t e s a r e used w i t h t h e z - a x i s along t h e beam  direction.  •Pi-  h  Dl RECTION  Figure A l .  Relationship  between v e l o c i t i e s i n l a b . and  coordinate  Figure A2.  Relationship  systems.  b e t w e e n v e l o c i t i e s i n scm, a n d  coordinate  scm.  systems.  rqm(i)  80 The p o l a r a n g l e s cos  Qi  i n t h e scm, system a r e o b t a i n e d from F i g u r e A l  -Vscm)/Vi  (VLCOS&I  =  -  Using  these r e l a t i o n s  A-8  t h e scm. k i n e t i c  energies  and momenta may be c a l c u l a t e d f o r t h e t h r e e p a r t i c l e s . meters  o f t h e t h i r d p a r t i c l e may a l s o  The p a r a -  be d e t e r m i n e d f r o m  o f p a r t i c l e 1 a n d 2 by u t i l i z i n g momentum a n d e n e r g y  those  conservation  i n the scm. system. Thus  -*  I  p.  *t  and  and  4-  cos  &  =  3  -t  -  o  - E  L  ~(p OSe {C  The c o o r d i n a t e theoretical analysis  + p  i  2  0069^ p  system  of the breakup  A 3  "  1  0  o f i m p o r t a n c e as f a r a s t h e i s concerned i s the rem.  s y s t e m , t h e c e n t r e o f mass s y s t e m o f t h e two p a r t i c l e  clusters.  The n o t a t i o n u s e d h e r e i s t o s p e c i f y t h e c l u s t e r ( j + k ) b y t h e s u p e r s c r i p t ( i ) where I j k i s some p e r m u t a t i o n , o f 1 , 2 , 3 . 9  s  Thus  (i) v ' i s t h e r e c o i l v e l o c i t y o f t h e c l u s t e r ( j + k ) a n d i s g i v e n by rem  ~$rcl  -  -_J*±_  nf  L  A - i i  The r e l a t i o n s h i p b e t w e e n t h e s c m . s y s t e m and t h e r c m ( i ) shewn i n F i g u r e A 2 . breakup  system  is  The v e l o c i t y o f one o f t h e p a r t i c l e s f r o m t h e  of the c l u s t e r (j+k) i s  w i t h the i n t e r n a l energy E  =  of the c l u s t e r g i v e n  l a t e d from F i g u r e  oaftf-qf)» The o t h e r a n g l e  -i . the c l u s t e r  o-u  ^  w h i c h measure  t o t h e beam a x i s  the  may be c a l c u -  0  '  (u^e^s^-^+^^vaO  of i n t e r e s t i s  (i) t h e o r i e n t a t i o n o f v^ the breakup  A-13  Q ^\  with respect A2  by  mj(rtji-rV)  The p o l a r and a z i m u t h a l a n g l e s o r i e n t a t i o n of v ^ ^  81  5  A  the p o l a r angle V J ^ . ^ which  .  15  measures  t h e v e l o c i t y o f one o f t h e p a r t i c l e s  of the c l u s t e r ( j + k ) , w i t h r e s p e c t  from  to the v e l o c i t y  of  i) v C<> rcm  COS  -T\f - - (  *  e « Sy  V  if*  A-16  Jacobians In general s u c h as e n e r g y  t h e o r e t i c a l expressions  distributions  or c r o s s  o b t a i n e d i n a r e f e r e n c e frame o t h e r This  necessitates  transforms ical  sections  for  quantities  a r e mos t  than the l a b o r a t o r y  the d e t e r m i n a t i o n of the c o n v e r s i o n  to the l a b o r a t o r y  system.  In  system.  factor  q u a n t i t i e s i n the r e f e r e n c e frame used i n the  analysis  easily  which  theoret-  the t h r e e p a r t i c l e  b r e a k u p v i a t h e s e q u e n t i a l d e c a y mode t h e i m p o r t a n t t h e o r e t i c a l distribution is particle  the t r i p l e  c o r r e l a t i o n which i s  o b t a i n e d w i t h one  i n t h e scm. s y s t e m and t h e o t h e r two i n r e m .  coordinates.  82  This quantity  called  for particle i  emitted f i r s t i s  given  by ( 7  rcm  ~  The c o r r e s p o n d i n g <km  remembering  i n t h e s c m . and l a b . s y s t e m s  is  the K.E.  =  /  J  -  i L  A-19  a r e r e l a t e d by t h e f o l l o w i n g  systems a r e d e f i n e d  J  i n the scm.system of p a r t i c l e 1  £L£Z  and J ^ ^ t h e J a c o b i a n s  coordinate  «  connecting as  o(t| : coso,,*fi;  >(T,  the  expressions  appropriate  CO Aii\ cose^vpj  e v a l u a t i o n of the a p p r o p r i a t e  between the c o o r d i n a t e  A  Jacobians  partial derivatives systems g i v e n  A-20  A-21  i C o a e ^ j o O ^ O  The. d e t e r m i n a t i o n o f t h e s e  relations  are  A-18  that t  These q u a n t i t i e s  and  quantities  -  (7*.  where  A-17  involves  using  i n the  "  2  2  the  the  preceeding  83 section. yield  -  These c a l c u l a t i o n s a r e g i v e n i n B r o n s o n ' s t h e s i s a n d  the following j-  t  results =  M^LEZ.  !  A-23  A-2lf  P. P^ ( A P + ^ C o s - P o O K ^ O 2  T  m  MF?P/  LL  I  (Is  /'  .^  A-25  1  The d e r i v a t i o n o f t h e s e q u a n t i t i e s f r o m t h e p a r t i a l derivatives, although  straightforward, involves the manipulation  o f many l o n g a n d c o m p l i c a t e d determining  the Jacobians  expressions.  A s i m p l e r method o f  i n v o l v e s the e v a l u a t i o n o f the t r i p l e  c o r r e l a t i o n f u n c t i o n s f o r the case o f a s t a t i s t i c a l the t h r e e c o o r d i n a t e systems. phase space Phase  breakup i n  This r e q u i r e s a knowledge o f  calculations.  space The t r a n s i t i o n p r o b a b i l i t y f o r a r e a c t i o n h a s t h e  form  -> _  ,  ,2.  1_ \  " h  where H i s t h e m a t r i x e l e m e n t c o n n e c t i n g  the i n i t i a l  s t a t e s and ^ ( E ) i s t h e d e n s i t y o f f i n a l  s t a t e s o r phase  factor. to  For s t a t i s t i c a l  be c o n s t a n t  and f i n a l  b r e a k u p s t h e m a t r i x e l e m e n t i s assumed  so t h a t t h e breakup p r o b a b i l i t y depends  the a v a i l a b l e phase s p a c e .  space  The n o n - r e l a t i v i s t i c  phase  o n l y on space  - 83+ •factor for a n-particle  final  where E  is  the t o t a l  P 3  is  t h e t o t a l momentum o f t h e  d P., i s  energy  state is  available  to the  (36)  system,  system  t h e momentum v e c t o r d i f f e r e n t i a l and c a n be  .L  2 w r i t t e n as p ^ d p - d J l -  8 functions  The  d e f i n e d as  and e n e r g y  i n polar  coordinates.  a r e used to i n c l u d e the requirements  conservation.  of  The p h a s e s p a c e d i s t r i b u t i o n s  momentum are  d e t e r m i n e d by r e s t r i c t i n g t h e i n t e g r a t i o n o f e q u a t i o n A-26 the a p p r o p r i a t e  variables. To i l l u s t r a t e an e x p l i c i t c a l c u l a t i o n o f  consider*  the case  w i t h momenta  the angular  r a t i o n over  of a f i n a l  p^" a n d  i n t e g r a t i o n over If  p  2  state  consisting  the s o l i d a n g l e  [ 3U)  is  Sl^  E  n  particles  Since  P]_ ~P2 =  „  Q  p^ u s i n g  this  desired  the  integ-  omitted.  a & function is  =  over  ^ ^ )  gives  d i s t r i b u t i o n of p a r t i c l e 1 i s  where  o f two  pt, i n t h e c e n t e r o f m a s s .  The r u l e f o r i n t e g r a t i o n o v e r  Integrating  to  rule  gives  the  following  - 85 -  cL ?i.ie) =  no, f m  dfL  l  p,2  with These r e s u l t s  -  2  A-27  t  L  n^z.  E  show t h a t t h e s t a t i s t i c a l p r o b a b i l i t y o f a two  p a r t i c l e breakup Is is  z. p  m  p r o p o r t i o n a l t o t h e p a r t i c l e momentum and  i s o t r o p i c i n t h e c e n t e r o f mass  system.  By e x t e n d i n g t h e s e c a l c u l a t i o n s t o t h e c a s e o f a three p a r t i c l e f i n a l  state i t is  correlation functions  (7% ,* lab  C„  s  A-17,  A-18  and A-19  possible  9 and ( T ^ ^ d e f i n e d by scm? rem 1  J  and e q u a t i o n A-26 f o r n = 3 i s  H  given  by  constant  f (E) 3  over ?  2  (77 ,  cx  The  integration  yields  dP.di^dSl^ and  equations  is  where t h e s y m b o l s h a v e b e e n d e f i n e d p r e v i o u s l y . of  triple  f o r a purely s t a t i s t i c a l breakup.  I n t h e l a b . s y s t e m t h e momentum e q u a t i o n  For  to e v a l u a t e the  JS&CE)  ( A f J + Picas'- P cos& ) 0  ^  fYi,nQ  3  F?Fj  z  A-28  -  86  -  The same q u a n t i t y i n t h e s c m . s y s t e m i s  cr^oi d ? (e) 3  3  A p  + P, cos  2  S  /a  that  which i s  t h e same a s  e q u a t i o n A-2.1+.  The t r i p l e o b t a i n e d by c o n s i d e r i n g  c o r r e l a t i o n function rcm(i)  system  shown p r e v i o u s l y  tional  i n e q u a t i o n A-27  t o t h e p a r t i c l e momenta.  particle  i n the breakup  these breakups  If  i  is  are  the  system.  propor-  the f i r s t e m i t t e d  then  and s i m i l a r i l y f o r t h e b r e a k u p  ot flj [Tew)  of the c l u s t e r  pr\ [tftijj i  (j+k)  J  For a s t a t i s t i c a l breakup a l l i n t e r n a l energies so  is  t h e b r e a k u p as a two p a r t i c l e d e c a y i n  s c m . s y s t e m f o l l o w e d by a two p a r t i c l e d e c a y i n t h e r c m ( i ) As  0.  A-29  nn,m p,  9  cM, dQftu^cfojticn so  o b t a i n e d by s e t t i n g P^=  are equally  probable  that  NA  P,  P  a  and which agrees  w i t h e q u a t i o n A-25.  A l i s t i n g of the computer  w r i t t e n t o c a l c u l a t e the breakup parameters along w i t h the Jacobians  is  i n a l l three  g i v e n i n A p p e n d i x B. .  program  systems  - 87  -  APPENDIX E COMPUTER PROGRAM L I S T I N G S In  this  a p p e n d i x two FORTRAN IV  u s e f u l i n c a l c u l a t i n g the q u a n t i t i e s particle breakup  breakup, are l i s t e d . parameters  possible, V12  are i n  particles.  various where  i . e . VSCM c o r r e s p o n d s  to  a r e i n MeV,  ^2?  $2'  a  n  d  S  the k i n e m a t i c  the l a b o r a t o r y e n e r g i e s  I n a two d i m e n s i o n a l  Q  w  h  e  r  e  d e s c r i b e d i n T a b l e 1. mining plot  t  facilities  T^ u s i n g  o f t h e U»B.C„  i e  SF i s  t h e f u n c t i o n T^iT^) „  o f T^ v s .  ^  energy  the energy  e x c e p t SF  i n the t h r e e c o o r d i n a t e  the J a c o b i a n s coordinates.  for  are  output  systems,  para-  l a b . , s c m . , and r e m . a n d  the t r a n s f o r m a t i o n from rem. c o o r d i n a t e s  r e p l a c e d by t h r e e q u a n t i t i t e s T I ,  o f one o f t h e f i n a l  deter-  contour  a l l the breakup  p a r t i c l e s w i t h TI  to  lab.  f o r CONTOUR TF and  The c a l c u l a t i o n s a r e c a r r i e d o u t as a f u n c t i o n o f t h e energy  a  one o f t h e  The i n p u t q u a n t i t i e s a r e t h e same as  e x c e p t t h a t SF i s  Q  Center.  The p r o g r a m KINJAC e v a l u a t e s meters  T ,*9^,  The f o r m o f t h e o u t p u t i s  Computing  The  increment used i n  the Calcomp p l o t t e r ,  the  analysis  2  quantities  contours  o f two o f  a r e t h e f o l l o w i n g % Q, m , m^, m , m^, F  scm  masses  t h e s e w o u l d be t h e two p a r t i c l e s d e t e c t e d i n c o i n c i d e n c e . input quantities  v >  degrees.  CONTOUR e v a l u a t e s  w h e r e T^ and T^ a r e  three f i n a l  been c h o s e n ,  A l l i n p u t and o u t p u t e n e r g i e s  The p r o g r a m TgCT-^),  of i n t e r e s t i n a t h r e e  g i v e n i n A p p e n d i x A have  a r e i n a , m , u . and a n g l e s  programs  The FORTRAN names f o r t h e  t o be s e l f - e x p l a n a t o r y ,  to v ^ ^ e t c .  computer  DT.  laboratory  the i n i t i a l  value  of t h i s  energy,  -  TF t h e f i n a l v a l u e and DT t h e e n e r g y  The o u t p u t q u a n t i t i e s a r e energies  88  the t h r e e c o r r e s p o n d i n g  E. . o f t h e two p a r t i c l e s y s t e m s ,  increment.  excitation  the t h r e e  Jacobians  (i) J  L  this  and t h e b r e a k u p a n g l e s calculation is  statistical  PSF,  1~[ . t h e phase  .  Another  space  quantity obtained  f a c t o r , which allows  e n e r g y d i s t r i b u t i o n t o be d e t e r m i n e d .  the  in  S I B F T C CONTOUR " ' C KINEMATIC CONTOURS T2 ( T 1 ) FOR A THREE P A R T I C L E BREAKUP DIMENSION T H 6 0 0 ) * T2<600> CALL PLOTS CALL A X I S ( 2 . 0 * 2 . 0 » 7 H T 1 ( M E V ) * - 7 * 8 . 0 * 0 . 0 * 0 . 0 * 2 . 0 ) CALL"AX I S ( 2 . 0 * 2 . 0 * 7 H T 2 ( M E V ) * 7 * 6 . 0 * 9 0 . 0 * 0 . 0 * 2 . 0 ) 50 READ(5»1) Q,AM0,AM1,AM2»AM3 READ ( 5 * 1 ) T 0 » T H 1 i T H 2 i P H 1 i P H 2 » S F IF ( S F ) 1 2 0 * 4 5 , 4 5 7 45 SW1 = 1.0 SW = 0.0 "Tl'SW = 0 . 0 ~ . c C ] ; T 0 U H  ;  i  v  A = (AM2+AM3)/AM2 PO = S O R T ( 2 . 0 * A M 0 * T 0 ) CTH1 = C O S ( . 0 1 7 4 5 3 2 * T H 1 ) CTH2 = C O S ( , 0 1 7 4 5 3 2 * T H 2 ) STH1 = S I N ( , 0 1 7 4 5 3 2 * T H 1 ) STH2  CPH KD12 D12 D = G = E =  =  SIN ( .0174532*TH2 )  COS(.0174532*(PH2-PH1)) = CTH1*CTH2 + STH1*STH2#CPH = ARCOS(CD12)/.01745 ( AM1+AM3 )/AMI -• (AM0-AM3)/AMO _ P0*CTH1  ~  =  " __-  F = G*P0**2 - 2.0*AM3*Q P I I NT = (E + S Q R T ( E * * 2 - D * F ) ) / D T1 I NT = PI I N T * * 2 / 2 . 0 / A M l ' " ~\[  40  35 "30 29 28 20 18  '  1 = 1 T I ( I ) = 0.0 PI = ' S Q R T ( 2 . 0 * A M l * f l ( I ) ) " " . * B = P0*CTH2 - P1*CD12 ' C = D*P1**2 + G*P0**2 - 2 . 0 * P 0 * P 1 * C T H 1 D I F F = B**2 - A*C ; IF ( D I F F ) 20,35,35 I F CSW1) 28,30,30 P 2 = (B + SQRT ( DI F F ) ) / A * T 2 ( I ) = P2**2/2.0/AM2 GO TO 15 P2 = (B - S Q R T ( D I F F ) ) / A GO TO 29 I F (SW1 ) lOOt.100* 18 SWT = -1.0 ~ ' "  ------  " -  2.0*AM3*Q  '  -  _ "  _ -  -  T1SW = T 1 U - 1 ) C0RT0UI-W2 T2SW = T 2 ( 1 - 1 ) GO TO 14 15 I = 1+1 14 T1 ( 1 ) = T l ( I - l ) + SW1*SF I F ( T l ( I } . G T . T l I N T . A N D . 0 1 2 . L E . 9 0 . 1 ) GO TO 100 IF ( T l ( I ) . L E . T l I N T . A N O . S W l . E O . l . O ) GO TO 40 I F ( T l ( I ) . L E . T 1 I N T . A N D . S W 1 . E Q . ( - 1 . 0 ) ) GO TO 10 IF ( T l ( I ) . G T . T l I N T . A N D . S W . E Q . O . O ) GO TO 12 GO TO 40 12 SF = 0. 1*SF _ -v.., . "sw = 1 . 0 " GO TO 40 100 KMAX = 1 - 1 WRITE ( 6 , 2 ) Q , A M 0 » A M 1 , A M 2 » A M 3 ~ WRITE ( 6 , 3 ) T 0 , T H 1 , T H 2 , P H 1 , P H 2 DO 110 .1 = 1, KMAX _ • T l ( I ) = T l ( I ) / 2 . 0 + 2.0 "" ' \ 110 T2 ( I ) = T 2 ( I ) / 2 . 0 + 2.0 -. I-F ( AMI-AM 2 ) 1 1 2 . 1 1 8 , 1 1 2 112 I F "(T1SW) 1 1 8 , 1 1 8 , 1 1 5 115 T1SW = T1SW/2.0 + 2.0 T2SW = T2SW/2.0 + 2.0 . ..' GO TO 119 118 KM ID = KMAX/2 T1SW = T l ( K M I D ) T 2 SW = T 2 ( K M I D ) 119 CALL LINE ( T 1 , T 2 » K M A X , 1 ) GO TO 50 : _•_ : 120 C A L L PLOTND STOP 1 FORMAT (6F10.5) 2 FORMAT ( 2 0 H Q-VALUE $ MASSES = , 5 F 8 . 3 , / ) 3 FORMAT ( 2 4 H I N C . ENERGY .$ ANGLES = , 5 F 8 . 2 , / ) 5 FORMAT ( 2 0 H Tl T2 ,/) 6 ' "FORMAT ( I X , 2F10.3) END SENTRY  SIBFTC KINJAC iUfWat-JC THREE P A R T I C L E 3REAKUP K I N E M A T I C S AND J A C O B IANS 5 READ ( 5 , 9 9 ) A M O , A M 1 » A M 2 , A M 3 » Q WRITE ( 6 , 1 0 0 ) AMO,AM1,AM2,AM3,Q -'• ^ READ ( 5 » 9 9 ) TO , SL 1 , SL2 , CPH2 " " W R I T E (6,101) T0,SL1,SL2,CPH2 " ' " A = (AM3 + AM2 J/AM2 AM = AMI+AM2+AM3 . T = 2.0 RAD = 0 . 0 1 7 4 5 3 2 UL1 = C 0 S ( R A 0 * S L 1 ) _ _ ' S L 1 = S I N ( R A D * S L 1 ) " ' *~" UL2 = C O S ( R A D * S L 2 ) ' SL2 = SIN<RAD*SL2) CPH2 = C 0 S ( C P H 2 * R A D ) UL12 = UL1*UL2 + SL1*SL2*CPH2 10 READ ( 5 , 9 9 ) T I , T F , D T ; T l ' '=" T l ' " "' " " • ~ WRITE ( 6 , 1 0 2 ) ..WRITE ( 6 , 1 0 3 ) C LAB V A L U E S 15 PO = S O R T ( T * A M 0 * T 0 ) PI = SQRT(T*AM1*T1) C"= (AM1+AM3 ) / A M l * P l * * 2 + '(AM0-AM3 )/AM0*P0**2 - T*AM3*Q 1 - T*P0*P1*UL1 B = P0*UL2 - P1*UL12 IF (B) 2 5 , 20,20 ' 20 DIFF = (B**2 - A*C) IF . ( D I F F ) 5,22,22 _ . 22 " P2 = (B + S Q R T ( D I F F ) ) / A GO TO 30 :  25  B = -B ' D I F F = (B**2 - A*C) I F ( D I F F ) 5,27,27 27 P2 = (-B + SQRT ( D I F F ) ) /A _ _ I F (P2> 5, 30,30 •30 T2 = P-2**2/T/AM2 '. " • T3 = Q + T 0 - T 1 - T 2 " P3 = SQRT ( T*AM3*T3 ) UL3 = (PO - P 1 * U L 1 - P 2 * U L 2 ) / P 3 IF ( U L 3 ) 3 5 , 4 0 , 4 0 ;r  _ _ - _ _ _ ' - .  _  "  1  ..  v  _  GO  TO  SL3  =  SL3  =  45  KIHJAC-2  UL 3 SORT(1,0  CPH3  =  VI  =  P1/AM 1  V2  =  P2/AM2 " .  V3  =  SCM  -  SL3**2 J  -'(Pl*Sll  + "  P2*SL2*CPH2)/P3/SL3 "  P3/AM3 VALUES  VSCM  =  PO/AM  •"*"  •  '.*"  VSQ  =  VSCM**2  SV1  =  SQRT(V1**2 +  VSQ  -  SV2  =  S Q R T ( V 2 * * 2 '+  VSQ  -'"f * V 2 * V S C M * U L 2 )  SQRT(V3**2  VSQ  -  ' SV3  = =  Ul  (V1*UL1  +  T*V1#VSCM*UL1)  -  VSCM)/SV1  U2  =  (V2*UL2  -  VSCM)/SV2  U3  =  (V3#UL3  -  VSCM)/SV3  T*V3*'VSCM*UL3) "  '  U12  =  U1*U2  +  V1/SV1*V2/SV2*SL1*SL2*CPH2  "0*31  =  U3*U1'+'  V3/SV3*V1/SV1*SL3*SL1*CPH3  X  RCM  VALUES  RV1  =  RV2  =  RV3  =  V21  AM1*SV1/<AM2+AM3>  SV2**2  ' = "SV1**2  V13  "  AM3*SV3/(AM1+AM2)  =  V12  j  A M 2 * S V 2 / (AM1+AM3  SVl-**2  =  +  RV1**2  +  +  RV3**2  T*SV2*RV1*U12  +  + ' T * S V 1 * R V 2 * U 1 2:'  RV2**2  AM2*(AM2+AM3)/T/AM3*V21  E23  =  E13  =  E12  =  V12  =' S Q R T ( V 1 2 )  A M1  *  _  V2i  = " S O R T < V 2 i f " =  "  =  -(RV1  +  SV2*U12)/V21  CN12  =  - (RV2  +  S V 1 * U 1 2 )/ V 1 2  CN13  =  -(RV3  +  SV1*U31)/V13  JACOBIANS =  "  SQRT(V13)  CN21  B  V 1 2 "  ( A M1 + A M 3 ) / T / A M 3 *  AM1*(AM1+AM2)/T/AM2*V13  V13  "PSF"=  "  T*SV1*RV3*U31  +  _  "• _  P 1 * P 2 * * 2 / ( P 2 * A ~+" Pl*uCi2~-~'P0*liL2 V :  AM*PSF/AM1/AM2**2  AJ1  =  AJ2  =  B/SV2/V12  AJ3  =  B/SV3/V13*AM2/AM3  WRITE WRITE  B/SV1/V21  (6,104) (6,105)  "  ~ — -  .  1H**£23tE13»E12»CN24.i.CN12.CN13 AJ1 » ' A J 2 » A J 3 » P S F  T 1 •= T l + D T KINJAC-3 IF ( T I - T P ) 1 5 , 1 5 , 5 99 FORMAT ( 5 F 1 0 . 5 > 100 FORMAT ( 1 H 1 , 5H M 0 = » F 6 . 3 » 4 H K 1 = , F 6 . 3 » 4 H M 2 = » F & . 3 » 4 H M3=,F6.3, 1 3H 0 = » F 7 . 3 ) ' 101' FORMAT (/,/,6H T0 = , F6 • 2 »8H THET A1= » F6 • 2* BH " THET A2 = » F 6 • 2 , 1 7H P H I 1 2 = , F 6 . 2 ) 102 FORMAT (/,/,70H TI E23 E13 E12 CN21 1 CN12 CN13 ) • 103 FORMAT (BOH J l 1 J2 J3 PSF ) 104 FORMAT "(/»7F10.3) " " ' " 105 FORMAT (40H . 4 F 1 0 . 3 ) .' END ' _ • •. SENTRY " - - - - -  - 89 APPENDIX  C  S E M I - E M P I R I C A L EXPRESSION FOR ENERGY LOSS IN As  t h i n f o i l s are used e x t e n s i v e l y i n t h i s  m e n t , b o t h i n t h e e n t r a n c e and e x i t windows to provide analysis, energy  THIN F O I L S  o f t h e gas  experi-  cell  p a r t i c l e d i s c r i m i n a t i o n i n t h e two d i m e n s i o n a l i t is  loss  necessary  t o have  energy  some means o f e v a l u a t i n g  of the d i f f e r e n t p a r t i c l e s i n t r a v e r s i n g  and  the  the  foils.  A s e m i - e m p i r i c a l r e l a t i o n was d e v e l o p e d f o r t h e s p e c i f i c  energy  l o s s f o r protons (Al) cross  where  by f i t t i n g  t o Z = 79 ( A u ) . section  N  is  is  The u s u a l  t h e number  o f atoms  t h e a t o m i c number the charge  m  is  the e l e c t r o n mass.  is  the average  I  for  C(E,Z) i s  of the s t o p p i n g  stopping  m a t e r i a l per  of the stopping m a t e r i a l .  of the p a r t i c l e moving w i t h v e l o c i t y  energy  corrections  a reasonably  account and  energies.  o f C ( E , Z ) and I were c h o s e n e m p i r i c a l l y t o  good f i t t o t h e d a t a .  been found p r e v i o u s l y  into  at low energies  the p o l a r i z a t i o n c o r r e c t i o n s a t h i g h The f u n c t i o n a l f o r m s  v.  ionization potential.  a c o r r e c t i o n term which takes  the b i n d i n g  give  the  volume.  ze i s Q  expression  f r o m Z = 13  is  unit Z  t h e a v a i l a b l e d a t a (37)  (38)  to decrease  Z w i t h the form of the decrease  The q u a n t i t y I/Z slightly with  given approximately  has  increasing by  - 90 -  1/2  '3.5 - 0.04-H ev.  c  _  2  C ( E , Z ) was c h o s e n t o h a v e t h e f o l l o w i n g v a r i a t i o n w i t h E and Z  OfE,£) = a, + a /z-h(a -tci^/Z z  T h e r e i s no t h e o r e t i c a l b a s i s for  + a /Z )E  + « E  z  3  s  f o r choosing  c-3  2  6  t h i s p a r t i c u l a r form  the c o r r e c t i o n term, although i t i s evident that a simpler  form o f C(E,Z) cannot g i v e  the necessary  On i n s e r t i n g t h e v a l u e s  v a r i a t i o n w i t h E and Z.  of the numerical  i n t o e x p r e s s i o n C - l the s p e c i f i c energy l o s s  The b e s t l e a s t s q u a r e s protons  constants  f o r protons  f i t t o the s p e c i f i c energy l o s s  becomes  data f o r  i n A l , Cu and A u f r o m 1 0 0 keV t o 1 0 MeV (37) i s  obtained  w i t h the f o l l o w i n g parameters % & %  1  = 0.976  a  = -23.1+0  a ^ = -226.0  The c a l c u l a t e d e n e r g y l o s s  2  =  a ^ = 0.239 a  w i t h these parameters  6  = -0.057  i s w i t h i n 10$  of the t a b u l a t e d data over the e n t i r e energy range w i t h the agreement 1 MeV.  c o n s i d e r a b l y b e t t e r f o r Z a b o u t 29 and e n e r g i e s The s p e c i f i c e n e r g y l o s s  f o r the other p a r t i c l e s  i n the experiment i s determined from the f o l l o w i n g ^(deuteron)  a§(triton)  E  E  =  =  ^ ( proton)  E / 2  f~(proton) ^ E /  above involved  relationships:  - 91  ^(He^  p a r t i c l e )g  ^(proton)^^  =  | § ( alpha p a r t i c l e ) =  Z  E  where  -2 Z is  ^-CprotorOg/^  2  t h e e q u i l i b r i u m h e l i u m i o n c h a r g e and i s a -2  of the p a r t i c l e energy.  The f u n c t i o n a l  c h o s e n e m p i r i c a l l y by f i t t i n g following  -  the data  form f o r  of W h a l i n g  E < 2.0 Mel/ where  ^ b  3  2  2  determined  -z _ Z - 4.0 + b/fc. + b / £ + ^ / £ 2  a  = 0.757  b  =  -1.83  = 0.722  b^ =  -0.08  £  ^/E  +  "  5  of  The f i r s t  as  energy l o s s  are  obtained  into four  energy l o s s f o r  intervals  integration.  experiment  are  calculations  for  the  five The  previously the  particle  iteration  a r e w i t h i n 1/2%. the PDP-8  the p a r t i c l e s  shown i n t h e F i g u r e s C I  and  loss  energy.  and e v a l u a t i n g  c a l c u l a t i o n was w r i t t e n f o r  of these  t o the energy  by d i v i d i n g  u n t i l successive approximations  Typical results  loses  a t the entrance  the corresponding  using a Simpson's rule  p r o g r a m t o do t h i s  the p a r t i c l e  approximation  energy l o s s evaluated  Subsequent approximations  mean s p e c i f i c  energy l o s s  of f i n i t e  4  by u s i n g a n i t e r a t i v e c a l c u l a t i o n t o t a k e a c c o u n t  specific  determined  C 3  is  energy i n the f o i l .  in this  the  thickness  the change i n the s p e c i f i c  continues  with  (39)  4.0  -  The e n e r g y l o s s i n a f o i l  energies  also  was  result:  B > 2.0 MeV  uses the  Z  function  C2,  A computer.  of  interest  4.  _l  6 .  PARTICLE  Figure CI.  Energy l o s s  —I  I  ENERGY  8  1  1  10  12.  (MeV)  curves f o r p r o t o n s and deuterons i n n i c k e l foils.  PARTICLE  \.oo\.800  A  He  B  He,  C  Me  FOIU THICKNESS  0.050 mils  3  aoas  4  3  r*,lS  O.0Z5 mils  >  1  8-600  > Ui .400  z  111  •200h  O  Figure 02.  2  4  G '  8  10  PARTICLE ENERGY (Me^  Energy l o s s  c u r v e s f o r He^ a n d He** i n n i c k e l  foils.  - 92 REFERENCES Minutes  1.  o f t h e T o p i c a l C o n f e r e n c e on C o r r e l a t i o n s o f P a r t i c l e s  Emitted i n Nuclear Reactions, R e v . Mod. P h y s . 3 2  Phys. 3.  DoB.  Rev.  196 *-, 1  (1965).  RD. P a r k e r , P.F. D o n o v a n ,  2.  G a t l i n b u r g , Tennessee,  J . V . Kane and J . F .  L e t t e r s l )-, 15 1  Mollenauer,  (1965).  S m i t h , N. J a r m i e and A . M . L o c k e t t , P h y s .  Rev.  129  785 (1963). h.  H.E. Phys.  C o n z e t t , E. Rev.  Shield, R.J.  S l o b o d r i a n a n d S.  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