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Polarization in p-p elastic scattering Keeler, Richard Kirk 1978

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POLARIZATION  IN P-P E L A S T I C SCATTERING by  RICHARD KIRK KEELER B.Sc,  McGill  University,  1976  THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE  STUDIES  (PHYSICS)  We  accept t h i s to  thesis  the required  as c o n f o r m i n g standard  THE UNIVERSITY OF BRITISH COLUMBIA MARCH 197 8  ©Richard  Kirk  Keeler,  197 8  In  presenting  an  advanced degree  the I  Library  further  for  shall  agree  scholarly  by  his  of  this  thesis  in  at  University  the  make  that  partial  freely  permission  for  It  financial  is  for  gain  PHYSICS  University  of  British  2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  April  24 , 1978  of  of  Columbia,  British  Columbia  for  extensive by  the  understood  permission.  of  fulfilment  available  p u r p o s e s may be g r a n t e d  thesis  Department  Date  it  representatives.  written  The  this  shall  requirements  reference copying  Head o f  that  not  the  of  I  agree  and this  be a l l o w e d  or  that  study. thesis  my D e p a r t m e n t  copying  for  or  publication  w i t h o u t my  ABSTRACT The  absolute normalization  proton-proton e l a s t i c by the  a double energy  double  scattering range  energy  beam e n e r g i e s , first  experiment  250-520 MeV.  scattering  variable  scattering  experiment  cyclotron.  of the p o l a r i z a t i o n i n  a t 24° l a b has b e e n  t o an a c c u r a c y o f ± 2 % o v e r  The f i r s t  energy  has been p e r f o r m e d  was u s e d  dependant a t the Triumf  D a t a were t a k e n a t f i v e  500, 467, 425, 367, and 307 MeV,  time hydrogen  determined  b o t h as p o l a r i z e r  primary  and f o r t h e and a n a l y s e r .  iii CONTENTS I.  I n t r o d u c t i o n and Formalism  II.  Apparatus  III.  Execution  IV. V. VI.  1 12  of Double S c a t t e r i n g Experiment  Data A n a l y s i s Conclusions Bibliography  25 34  •  49 51  iv TABLES 1-1.  Tensors Making Up t h e S c a t t e r i n g M a t r i x .  .4  1-2.  B e h a v i o r o f R o t a t i o n I n v a r i a n t s under Space R e f l e c t i o n , Time R e v e r s a l , and The P a u l i Exclusion Principle  5  1- 3.  T a b l e o f P r e v i o u s Measurements  10  2- 1.  P r o p e r t i e s o f t h e Secondary T a r g e t s Used i n t h e Double S c a t t e r i n g Experiment .17  2-2.  Energy l o s s i n P r i m a r y Beam, Energy l o s s i n Secondary Beam  21  2-3.  The F a c t o r X/LRAD i s T a b u l a t e d f o r each Element i n the Secondary Beamline; w i t h and w i t h o u t Helium Gas Bags 22  2- 4.  Coulomb S c a t t e r i n g RMS A n g u l a r D i v e r g e n c e o f Secondary Beam  24  Solenoid Currents Calculated t o Precess P r o t o n s t o ±90°  28  3- 1. 4- 1.  T a b l e o f Times o f F l i g h t f o r E l a s t i c and I n e l a s t i c P r o t o n s , and f o r P i o n s 36  4-2.  Asymmetries f o r CP^ T a r g e t , Carbon T a r g e t , and L i q u i d Hydrogen T a r g e t Empty, Averaged f o r each Energy  4-3.  38  Rates f o r Carbon and L i q u i d Hydrogen T a r g e t Empty Data N o r m a l i z e d t o Rates f o r CH2 Data  38  4-4.  G e n e r a l i z e d Carbon Background..  41  4-5. 4-6.  F i n a l Asymmetries 41 T a b l e o f Background Asymmetries and R a t e s ; Smoothed and Unsmoothed 44  4-7.  F i n a l Asymmetries w i t h Smoothed Parameters  4-8.  R a t i o s o f P(24 )/P (24.79 )  4-9.  Added World Data  0  0  42 45 45  V  4- 10.  Values  o f P ( 2 4 ° ) Lab Between  200  and 500' MeV....47  5- 1.  Comparison of E x p e r i m e n t a l R e s u l t s t o P r e v i o u s Phase S h i f t P r e d i c t i o n  49  vi FIGURES 1-1. K i n e m a t i c  Diagram  2-1. A S c h e m a t i c  f o r Proton-Proton  Diagram o f t h e E x p e r i m e n t a l  Configuration 2- 2. F o u r  Fold  Scattering.... 3  ,  Coincidence Polarimeter  3- 1. D i s t r i b u t i o n o f P r o t o n s on t h e S e c o n d T a r g e t , C a l c u l a t e d by t h e Monte C a r l o P r o g r a m REVMOC 3-2. Optimum q u a d r a p o l e c u r r e n t ( a r b i t r a r y u n i t s ) v e r s u s momentum 3-3. S e n s i t i v i t y 3- 4.  Electronic  (MeV/c)  o f p o l a r i m e t e r t o beam s t e e r i n g L o g i c Diagram  . .13 19  27 29 31 32  4- 1. Times o f F l i g h t (ns) 35 4-2. L i n e a r F i t s t o C a r b o n and Empty T a r g e t A s y m m e t r i e s and R a t e s V e r s u s Beam E n e r g y 43 4-3. P o l a r i z a t i o n  a t 24° L a b v e r s u s E n e r g y  48  vii ACKNOWLEDGEMENT I t h a n k my c o l l e a g u e s this  experiment  L.P.  D. S t r a t f o r d ,  L. Felawka,  the this  their  like  t o thank  long hours o f h e l p  like  t o thank  J.R. R i c h a r d s o n ,  J a c k B e v e r i d g e and Tony  i n setting  results,  Clough  up t h i s e x p e r i m e n t , and  technical  Claude Amsler  assistance.  I would  for h i saidi n interpreting  and C h r i s Oram f o r h i s g u i d a n c e  i n completing  thesis. My s p e c i a l  supervisor, the  D.V. Bugg, R. D u b o i s , J .  D. G i b s o n , G. L u d g a t e ,  Graham W a t e r s f o r h i s e x c e l l e n t also  A. C l o u g h ,  R o b e r t s o n , R. G i b s o n and N. S t e w a r t . I would  for  i n completing  - D. Axen, J . B e v e r i d g e , C. A m s l e r ,  C. Oram, G. W a t e r s , Edgington,  f o rt h e i r help  thanks  t o P r o f e s s o r Dave A x e n , my  f o r h i s leadership  experiment  and t h e w r i t i n g  and e n c o u r a g e m e n t of this  thesis.  throughout  1 I N T R O D U C T I O N AND F O R M A L I S M The subject  of  elastic  numerous  papers  Wolfenstein"'" proposed dependence  of  scattering  spin  states  and s c a t t e r i n g  This  thesis  is  preparing  concerned  P(E,9).  on t h e  interaction.  beams o f  of  spin  These  nucleons  the polarization  reviews  the  I n 1954  in  them from u n p o l a r i z e d  with  Excellent  has been  of measurements  the nucleon-nucleon  involved  nucleons  and e x p e r i m e n t s .  a series  experiments  denoted  of  certain  targets.  parameter,  the derivation  of  this  2 3 parameter  exist.  calculations  in  '  is  A synopsis  given  of W o l f e n s t e i n ' s  here.  For  a description  of  the centre  o f mass frame  the incident  labelled  k and t h e s c a t t e r e d  conservation |k| = two  elastic  proton's  o f momentum may t h e n  |k"| = k.  The s c a t t e r i n g  parameters,  proton-proton proton's  be w r i t t e n  is  particle  in  angle.  The wave  the asymptotic  limit,  as  as k and 6  the  function  as r  of  the  state  the  n  spinor.  particle r  t  e  t  spin  state  r  relationship  c a n be w r i t t e n X  F  the amplitude  i n a convenient  between  matrix  the incident  larger  given  f  Bv e x p r e s s i n g  n  e  by, ... (D  final  f(k,8  ) f o r each cm n o t a t i o n M(k,8 ), ' cm '  and s c a t t e r e d  spin  as,  = M  X  i  centre  scattered  becomes much  the range of the i n t e r a c t i o n ( - 1 . 5 f m ) , i s <# \ ^ ik •r . ikr iMrlX-j^e X + e x r w h e r e x^ i i n i t i a l s t a t e s p i n o r and Xf i s s  by  cm.  than  i  is  The  kinematically determined  w h i c h may b e c h o s e n -  mass s c a t t e r i n g  scattering  momentum  m o m e n t u m .k'.  1  of  original  (2)  function  where x  i  F  s  the f i n a l s t a t e s p i n o r .  Determining  the s p i n dependence i s now  e q u i v a l e n t t o f i n d i n g the m a t r i x of s c a t t e r i n g M(k,0  ).  The most c o n v e n i e n t way  mathematically amplitudes  t o f o r m u l a t e t h i s problem i s  t o use the d e n s i t y m a t r i x r e p r e s e n t a t i o n .  In t h i s  r e p r e s e n t a t i o n the beam o f i n c i d e n t p r o t o n s i s c h a r a c t e r i z e d i n s p i n space as. a weighted p.  1  =  EOJ  a  Y. A  a ia  YA  average of pure s t a t e d e n s i t y m a t r i c e s ,  i" .  ,  (3)  Zbi  ia / a a  where co^ i s the p r o b a b i l i t y of the system b e i n g i n the pure state x •  The  s c a t t e r e d p a r t i c l e ensemble i s then d e s c r i b e d  by the f i n a l s t a t e d e n s i t y m a t r i x p  f  =  Mp.M  (4)  +  Three o r t h o n o r m a l  b a s i s v e c t o r s may  from the k i n e m a t i c q u a n t i t i e s as:<P = (k + k^) £  =  be c o n s t r u c t e d / (|k  +^k^|),  ~ }l) / l k / - - k | ) , and-N = (~k x-k") / ( | k x k / | ) , (  ( f i g u r e 1-1).  The m a t r i x of s c a t t e r i n g a m p l i t u d e s depends on  the s p i n s and momenta of the i n c i d e n t and s c a t t e r e d p r o t o n s . The most g e n e r a l s c a t t e r i n g a m p l i t u d e  i s a linear  combination  of a l l the p o s s i b l e p r o d u c t s of the t e n s o r s formed from the s p i n v e c t o r s of each proton, o}^  and o}^  , and the t e n s o r s  formed from the c o - o r d i n a t e vectors<PyK, and N (Table S i n c e a n g u l a r momentum i s conserved  1-1).  the system, and  hence the s c a t t e r i n g a m p l i t u d e s , must be r o t a t i o n a l l y  invariant.  Hence a c c e p t a b l e p r o d u c t s of the s p i n and k i n e m a t i c t e n s o r s are s c a l a r s or pseudoscalars.  S i m i l i a r l y v a r i o u s combinations  e l i m i n a t e d by the c o n s e r v a t i o n of p a r i t y , time i n v a r i a n c e , and the P a u l i e x c l u s i o n p r i n c i p l e  are  reversal (Table 1-2).  An  F I G U R E 1-1  KINEMATIC DIAGRAM FOR PROTON PROTON SCATTERING.  4  TABLE  1-1  T e n s o r s m a k i n g up t h e S c a t t e r i n g  Rank  0  Tensors of the Spin Vectors  .a >V (1  Amplitude  Kinematic  Tensors  1 K«P  2)  N •K  £ •£  a  ( 1 )  -  ( 1 )  a. i  ( 1 )  £  xV of 3  (2)  •K  ( 2 )  2 )  2 ) +  P  a  a )  3  a.  K. K . i 3  ( 2 ) 1  P.P. i 3 N.N . K.P . + 3  K.P. 3 i  K.N. + 3  K.N. 3 i  P.N.  P.N.  1  1  I D  +  D  1  5  TABLE 1-2  B e h a v i o r o f R o t a t i o n I n v a r i a n t s Under Space R e f l e c t i o n , Time R e v e r s a l , and The P a u l i E x c l u s i o n P r i n c i p l e Y i s Invariance N i s no I n v a r i a n c e  Rotation Invariant  Space Reflection  Time Reversal  Exclusion Principle  y  Y  Y  Y  y  Y  ..K  N  N  Y  •N  Y  Y  Y  •P  N  Y  Y  1 £  U )  -£  p_ + U)  ( 2 )  a  £  a  ( 1 )  a.  (  1  x  )  (  a  af  2  (  2  2  )  ( 2 )  ) +  )  N  *K  N  N  •N  Y  •P  N  -K  N  *N  Y  N  N  •P  N  N  N  olUo™  K  i j K  Y  Y  N N  Y  Y  N  Y  Y  NN.  Y  Y  Y  P.P. ID  Y  Y  Y  K.P.+K.P. i 3 J i K.N.+K.N. i 3 3 i P.N.+P.N. l 3 3 l  Y  N  Y  N  N  Y  N  Y  Y  ±  =  expression  for  M = a (k , 9 ) ' cm  the matrix  of  + ic(k,6 ) (a ' cm — + m(k,9 + g(k,9  + h(k,9 The  two  c m  cm cm  ( 1 )  (  —  «N +- a — —  ( 1 )  ) (a ) ( a  scattering  1  )-(a —  ( 2 )  -Na « P  )  ( 2 )  c  ( 1 )  -P-a — —  experiments  4  is,  «N) —  -N)  (  — —  amplitudes  2  )  ( 2 )  of  - P  _  +  _  -P —  a  (  a —  concern  (  « K  1  )  1  )  _  in  a  _  - K - a — —  (  (  2  2  this  )  - K )  _  vK) —  )  (5)  thesis  are: 1)  The  -da  dH  for  in  1  of  is  the a  2)  = I  o  ( l )  >a  ( l )  by,  I <o > is  following  an u n p o l a r i z e d  > = P^u,  the  the  form,  The  (  for  an  unpolarized  power, is  to  F  expectation  determine beam i s value  the  of  the  two r e s u l t s . beam s c a t t e r s  of  from  final  spin  (9)  polarizing  properties  final  scattered  \MM1")_  known as t h e  From the  section  an u n p o l a r i z e d  = T r (a  {f)  Q  <a^>  cross  second experiment  given  (i)  (8)  The  state  be  (1 + P P ) l a  after  is  (7)  analyzing  target.  can  )  the  an u n p o l a r i z e d  there  giving  differential  polarization  Since  matrix  in  and P  the  density  t h e m e a s u r e m e n t c a n be e x p r e s s e d  beam,  where  the  target.  <a  I  is  (6)  a polarization  where  state  spin vector,  beam h a v i n g  1(0,<j))  section,  1  beam on a n u n p o l a r i z e d  2  cross  +  = 1(1 + < £  an i n c i d e n t  result  differential  = T r (Mp . M ) / T r (p . )  Pauli matrices  p.  the  1  one r e l e v a n t  expaned  For  = 1(6,4))  a polarized  only  measurement of  power.  the M m a t r i x ,  First,  the  Wolfenstein  polarization  from an u n p o l a r i z e d  induced  target  is  shows when  7  perpendicular t o the s c a t t e r i n g plane.  T h i s i s a consequence  of t h e c o n s e r v a t i o n o f p a r i t y . The second theorem s t a t e s t h a t t h e p o l a r i z i n g power i s e q u a l t o t h e a n a l y z i n g power.  T h i s can be proved  u s i n g time r e v e r s a l i n v a r i a n c e and i m p l i e s t h a t , P  = <a  ( f )  >  = P(E,9)  (10)  cl  where P ( E , 0 ) i s d e f i n e d as t h e p o l a r i z a t i o n parameter, cm ^ e  T h i s r e l a t i o n i s t h e fundamental p r i n c i p l e upon which double s c a t t e r i n g e x p e r i m e n t s a r e based. In a double s c a t t e r i n g experiment an u n p o l a r i z e d beam i s d i r e c t e d a t an u n p o l a r i z e d t a r g e t .  The r e s u l t i n g ,  p o l a r i z e d , s c a t t e r e d beam i s then s c a t t e r e d from a second target.  The d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e second  s c a t t e r i s g i v e n by, I  2  = I  ( + PfE-^O )P(E_,e )cos<|> )  (11)  1  0  2  2  2  where t h e s u b s c r i p t s a r e i n c l u d e d t o note t h e d i f f e r e n c e i n energy and s c a t t e r i n g a n g l e f o r t h e two s c a t t e r s , and <f> i s measured from t h e K a x i s .  The l e f t - r i g h t asymmetry i n  the number o f p a r t i c l e s s c a t t e r e d from t h e second t a r g e t i s I (6,(j) 2  e  ='  i  2  = 0) - I(e,<f> • 2  =  TT)  (12)  (e<p = o) + i (e,<j> = TT) r  2  T h i s asymmetry i s a l s o g i v e n by e = P(E ,9 )P(E ,9 ) 1  1  2  (13)  2  T y p i c a l l y the s c a t t e r i n g angles 0^, 0  2  t o be e q u a l and i d e a l l y i f t h e e n e r g i e s E^ and E  a r e chosen 2  are equal  t h e n e q u a t i o n (12) reduces t o t h e p a r t i c u l a r l y s i m p l e  8 expression  e = P Previous techniques;  double  (14)  2  measurements o f P have i n v o l v e d  s c a t t e r i n g and p o l a r i z e d t a r g e t s .  s c a t t e r i n g measurements have p r e v i o u s l y the  p o l a r i z a t i o n parameter  beryllium. ' ' ' ' ' 5  small  6  7  8  a n g l e s have o n l y  9  f o r e x p e r i m e n t s where  small  energy  polarized  angles  Protons scattered  1 0  Double  been used t o n o r m a l i z e  beams were p r o d u c e d by s c a t t e r i n g a t s m a l l and  two d i f f e r e n t  from  carbon  e l a s t i c a l l y at  l o s s e s , and r e a s o n a b l e  polar-  izations  (-30% f o r c a r b o n - p r o t o n s c a t t e r i n g a t 6° and 400 MeV  incident  k i n e t i c energy).  differential as  cross  a function  extremely  Spin  o f a n g l e and as a r e s u l t t h e measurements a r e i n t h e measurement o f t h e  o f t h e p o l a r i z a t i o n measurements have u s e d  to eliminate  been t o f l i p  scatter.  rapidly  angle. All  has  angular range both the  s e c t i o n and t h e p o l a r i z a t i o n v a r y  sensitive to inaccuracies  scattering  technique  In t h i s  This  flipping  instrumental  asymmetries.  some  One method  the spin of the proton a f t e r i t s i n i t i a l  eliminates  false  was a c c o m p l i s h e d  asymmetries  to f i r s t  by p r e c e s s i o n  order.  of the spin i n  5 6 a solenoid,' o r by c h a n g i n g t h e d i r e c t i o n o f t h e f i r s t  scatter  (ie,  angle).  changing  from  left  Other groups decided  t o r i g h t s c a t t e r i n g a t t h e same  not to r i s k  altering  7  t h e beam d i r e c t i o n 9 11  and  instead  the  final  elected  to f l i p  asymmetry, t h u s r e v e r s i n g  However i t i s d i f f i c u l t precisely  the polarimeter left  '  u s e d t o measure  and r i g h t  t o b u i l d and a l i g n a d e v i c e  about t h e a x i s o f the s c a t t e r e d  beam.  detectors. that  rotates  9 Polarized  targets  are free  of these  12 13 14 difficulties. polarized  '  target  '  Scattering  and m e a s u r i n g  an u n p o l a r i z e d  beam f r o m  t h e r e s u l t i n g asymmetry,  a  given  by e = P(E,9)P(Target) is  t h e same a s p e r f o r m i n g  scattering.  (15)  the second  The p o l a r i z a t i o n o f t h e t a r g e t  i n d e p e n d e n t l y by n u c l e a r m a g n e t i c and  spin  flipping  o f t h e R.F. f i e l d  technique  f o r measuring  Due t o n o n u n i f o r m i t y target  overall  previous double (see  Table  i s reduced scattering  technique  i n the  The N.M.R.  time  t o 6%.  t h e volume o f  of the p o l a r i z a t i o n , the  T y p i c a l l y the errors have a l s o  on  b e e n 6%  of previous p o l a r i z a t i o n  described  i n this thesis  Five  solenoid  scattering  change a f t e r t h e f i r s t s c a t t e r  , e = P  2%,  beam e n e r g y P ,  (E)P  2  was The  double  elastic  measurements were made between  A superconducting  formula^ , e -  than  using free proton-proton  the case o f a primary  formula  shift  to the target.  experiments  f l i p p i n g . . I n pp e l a s t i c  simple  by a s l i g h t  t o e v a l u a t e P a t 24° t o b e t t e r  200 and 500 MeV.  energy  (N.M.R.) t e c h n i q u e s  ).  s c a t t e r i n g was c h o s e n .  spin  i s measured  of the p o l a r i z a t i o n over  The measurement  scattering  i n double  the p o l a r i z a t i o n i s accurate t o ±4%.  1-3 f o r a l i s t  measurements  designed  applied  and t h e v a r i a t i o n w i t h  accuracy  resonance  c a n be a c c o m p l i s h e d  frequency  the  scatter  was u s e d f o r  a t 24° t h e r e i s a ( e g . 100 MeV  o f 500 MeV).  i s no l o n g e r v a l i d .  ( f (E)) i s n e c e s s a r y .  large  i s lost i n  Thus t h e  The  complete  I f n measurements  10 TABLE 1-3  TABLE OF PREVIOUS MEASUREMENTS  Energy MeV  Angle C M . deg  Experimental V a l u e o f Ppp  Total Error +  Ref  276  49.9  0.295  0.027  15  307 + 11  50.1 ± 2.7  0.362  0.016  7  328 ± 6  52.2 ± 1  0.349  0.038  14  334 . 5 ± 5.8  51.68  0.27  0.05  13  415 ± 7.8  51.5 ± 1.  0.382  0.037  418 ± 6.6  52.41 ± 1.81  0.34  0.03  13  312 ± 11  56 ± 6  0.26  0 .05  11  315 ± 6.4  53.4 ± 2.95  0.303  0.025  15  394 ± 12  48.0 ± 3.6  0.419  0 . 017  429 ± 7  45 ± 1.7  0.40  0.06  439 ± 6  44.8  0 ,335  0.030  8  498 ± 11  48.7 ± 3.1  0.452  0.020  7  500 ± 8 . 3  53.13  0.46  0.03  13  500 ± 4.2  52.4 ± 2.6  0.435  0.04  12  520 ± 20  58 ± 10  0.403  0.038  17  ± 1.83  ± 11.5  ± 1.79  5  7 16  are  made, t h e r e  Triumf v a r i a b l e polarization energy  a r e 2n unknown p o l a r i z a t i o n s . energy c y c l o t r o n  be i n t e r p o l a t e d ( i e . /2  This  the  f i t was  Now  t h e unknown  primary  As a g e n e r a l i z a t i o n used  of t h i s procedure a  to f i t the p o l a r i z a t i o n .  on t h e measurement  physical  polarizations  t h e a c c u r a c y o f t h e measured  The r e s u l t i n g  d e p e n d s on t h e s t a t i s t i c a l  s e t o f e ' s , t h e number o f p o i n t s ,  actual  each  r e d u c e s t h e number o f unknowns  to within  POp-a^).  non^linear error  t o measure t h e  s e t e q u a l t o t h e s e c o n d a r y beam e n e r g y , f ( E ) , f r o m t h e  t o n + 1 f o r n_ m e a s u r e m e n t s .  e  i t i s possible  at a s e r i e s of d i f f e r e n t energies,  p r e v i o u s measurement.  can  Using the  variation P  (E).  error i n  and t h e smoothness o f t h e  This  method  proved  highly  2 h  successful. The d e t a i l s o f t h e measurement  of P  (E) a r e g i v e n 2 k  in  the next chapters.  The a p p a r a t u s  a r r a n g e m e n t and u s e i s d i s c u s s e d . is  described  and t h e a n a l y s i s  measured v a l u e s o f P  (E) a r e t a b u l a t e d prediction.  and i t s  The d a t a c o l l e c t i o n p r o c e d u r e  of the data  2 h  p r e v i o u s phase s h i f t  i s outlined  i s c a r r i e d out.  and compared w i t h  The a  CHAPTER I I Apparatus The are reviewed  important i n this  chapter.  t o downstream o r d e r . given  i n figure  features of the experimental They a r e g i v e n i n an  A schematic  view  Beam  designed  a monitor of  of  theses.  f o r u s e i n t h e Basque p o l a r i z e d  '  F o r t h i s measurement i t was u s e d as  5 0 ym t h i c k  each.  mounted a t ±26 d e g r e e s  between t h e f o r w a r d  The d e v i c e  consisted  i n t h e beam p i p e .  i n four  t e l e s c o p e s composed  The two " f o r w a r d " t e l e s c o p e s were  t o t h e beam a x i s  arms were a t t h e c o n j u g a t e  and t h e two  a n g l e o f 60 d e g r e e s .  recoil  Coincidences  arms and t h e c o m p l e m e n t a r y r e c o i l  arms  scaled. Liquid The  by  suspended  p r o t o n s were o b s e r v e d  two s c i n t i l l a t o r s  were  beam  20  o f p r i m a r y beam i n t e n s i t y .  a CE'2 t a r g e t  Scattered  t h e r e was a p o l a r i m e t e r  I t has a l r e a d y b e e n d e s c r i b e d e x c e l l e n t l y i n 19  previous  o f the experiment i s  Monitor  In t h e p r i m a r y beamline  experiments.  upstream  2-1. Primary  originally  apparatus  liquid  5 cm d i a m e t e r  Hydrogen T a r g e t  hydrogen  flask.  target  from  o f a 20 cm l o n g  The t a r g e t w a l l s a r e 250 ym and t h e  end windows a r e 50 ym o f s t a i n l e s s separated  consisted  the beamline  steel.  The a s s e m b l y  vacuum by 120 ym s t a i n l e s s  was steel  windows. The by  a Phillips  hydrogen  t a r g e t was l i q u i f i e d  A-20 c r y o g e n e r a t o r .  and r e f r i g e r a t e d  The maximum power o f t h e  FIGURE  2-1  SCINTILLATORS  B1 V« ^VERTICAL B  A  SCHEMATIC  EXPERIMENTAL  DIAGRAM  OF  THE  POLARIMETER AND  CONFIGURATION  CH2  / C  TARGET STEERING MAGNET QUADRAPOLE DOUBLET COLLIMATOR  LIQUID HYDROGE TARGET  PRIMARY BEAM MONITOR  BENDING MAGNET  Stirling  engine  250-300 nA,  limited  because  protons t r a v e r s i n g hydrogen.  t h e p r i m a r y beam r a t e  a t h i g h e r c u r r e n t s the energy t h e t a r g e t was  T h i s was  sufficient  resevoir, The  and  target  in  roughly twelve.  of  this  target  and  components.  c a n be  i n one  Design d e t a i l s  are d e s c r i b e d  and  B e n d i n g Magnet  through  hydrogen 35°.  t a r g e t , was  The  deflection  d i p o l e magnet c a n be  used  hour  and  filled  characteristics  (21).  (4AB2)  T h i s d i p o l e magnet, p o s i t i o n e d liquid  the  the  operating  i n reference  by  p r e s s u r e of the  other relevant emptied  lost  to b o i l  c o n t i n u a l l y monitored during  e x p e r i m e n t by o b s e r v i n g t h e t e m p e r a t u r e flask,  t o between  directly  after  the  t o sweep u n s c a t t e r e d p r o t o n s  angle f o r charged p a r t i c l e s  calculated  using  in a  the e x p r e s s i o n ,  9 = e J B«dl  (.1)  where e i s t h e c h a r g e , and p i s t h e momentum o f t h e  incident  particle. It  has b e e n c a l c u l a t e d  that protons scattered were d e f l e c t e d  by  degrees  right.  to the  by  from a magnetic  24 degrees  the f r i n g e  field  field  survey  from the hydrogen  target  of t h i s m a g  n e  t  0.82  ±  0.16  a  large  Collimator Following collimator, use  3 0 cm  the l i q u i d  thick  and  i n neutron experiments.  bearing  steel plates,  t o t a l weight  50 mm  i s 25 t o n s .  hydrogen  r o u g h l y 3.5 I t was thick,  There  t a r g e t was m  long, designed f o r  constructed filled  f r o m two  with lead.  a r e 11 e q u a l l y  spaced  load  The ports  15 from The  -3° t o 2 7 ° .  Each p o r t i s d i v i d e d  u p s t r e a m end i s 10 cm i n d i a m e t e r  into  two e q u a l  sections.  and t h e downstream end i s  12.5 cm i n d i a m e t e r . The in  this  beam.  nominally  experiment  24° p o r t , a c t u a l l y  insert  scattering.  used  t o d e f i n e t h e d i r e c t i o n o f the secondary  inflated  with helium  The  capable of producing  a uniform  with  steel  at the Rutherford  a 14 cm warm b o r e . 6 t e s l a magnetic  when o p e r a t e d w i t h  plugs.  Solenoid  s o l e n o i d was d e s i g n e d  l a b . and i s 1 m l o n g w i t h  bore  gas t o reduce m u l t i p l e  Unused p o r t s were f i l l e d Superconducting  entire  was  T h i s p o r t was 3.54 m l o n g and was l i n e d w i t h a 130 ym  plastic  Energy  23.97°,  High  It is  field  over t h e  t h e maximum r a t e d c u r r e n t ,  212A. The magnetic  angle  field  of precession of the proton  c a n be c a l c u l a t e d  spin  using the expression,  a = ey_ \ B ' d l P  (2)  J  where e i s t h e p r o t o n c h a r g e ,  y i s the magnetic  t h e p r o t o n , and p i s i t s momentum. magnetic  field  0.028187  T-m-A  through  The l i n e  moment o f  integral  t h e s o l e n o i d was c a l c u l a t e d  , where t h e l i m i t s  t o 0.7% by a m a g n e t i c  of the  t o be  o f i n t e g r a t i o n were  -294 cm t o +294 cm a l o n g t h e beam a x i s . confirmed  ina  from  T h i s was e x p e r i m e n t a l l y  survey.  Q u a d r u p o l e Magnets A quadrupole  d o u b l e t was b o r r o w e d  from  the U n i v e r s i t y  22 of  Alberta.  apertures,  This  r  i s of standard design, having  and 0.5T maximum m a g n e t i c  field  10 cm  a t the pole  tips.  16  S t e e r i n g Magnets T h i s i s a s t a n d a r d Triumf beamline element.  I t has  a 100 mm p o l e gap and can be r u n a t a maximum c u r r e n t o f ±7A. The  l i n e i n t e g r a l o f t h e magnetic f i e l d was measured as  0.0272 T-m a t 5A. S c i n t i l l a t o r s and Second  Target  Two s c i n t i l l a t o r s were used t o d e f i n e t h e secondary beam and t o make time o f f l i g h t d e t e r m i n a t i o n s . s c i n t i l l a t o r , l a b e l l e d B l , was 10 cm d i a m e t e r was mounted on a perspex l i g h t g u i d e .  The f i r s t  by 0.3 cm, and  The second  scintillator,  B2, measured 2 cm ( h o r i z o n t a l l y ) by 1 cm ( v e r t i c a l l y ) and was 1.5 mm t h i c k .  I t was g l u e d t o t h e i n s i d e o f an aluminum  cone o r " a i r l i g h t g u i d e . "  foil  This e l i m i n a t e d the d i f f i c u l t y of  h a v i n g a l a r g e mass o f p e r s p e x ( c o n t a i n i n g hydrogen)  adjacent  t o t h e second t a r g e t . The  s c i n t i l l a t o r , B2, and a b l o c k o f CE^ o r carbon  j u x t a p o s e d , formed a u n i t t h a t was t h e second t a r g e t .  The  l a r g e s t C I ^ t a r g e t measured 2 cm ( h o r i z o n t a l l y ) by 1 cm ( v e r t i c a l l y ) and was 2.5 cm t h i c k .  A s i m i l i a r piece of C H ^  was made w i t h 0.5 cm h e i g h t f o r use a t secondary beam e n e r g i e s between 200 and 3 00 MeV.  This allowed the r e c o i l protons t o  escape from t h e t a r g e t w i t h s u f f i c i e n t energy t o be d e t e c t e d . Two carbon t a r g e t s were a l s o c o n s t r u c t e d .  They were  designed  t o have r o u g h l y t h e e q u i v a l e n t amount o f carbon as t h e corresponding  CE^ t a r g e t s and have r o u g h l y t h e same s i z e .  was accomplished  by u s i n g 2.5 cm by 2 cm carbon sheets  This  25 ym  t h i c k ; and g l u e i n g t h e i r edges t o f o u r s m a l l carbon s l a t s which h e l d them, e q u a l l y spaced, i n a s t a c k .  Table 2-1 g i v e s t h e s i z e s ,  17  TABLE 2-1 PROPERTIES OF THE SECONDARY TARGETS USED IN THE DOUBLE SCATTERING EXPERIMENT Material Type  Dimensions LxWxD CM  Mass grams  CH2  2.5 x 2.0 x 1.0  4 . 825  CH2  2.5 x 2.0 x 0.5  2.4125  CARBON  2.5 x 2.0 x 1.0  4.2672  CARBON  2.5 x 2.0 x 0.4  2.0648  materials  and masses o f e a c h All  them on to  o f t h e t a r g e t s were s u p p o r t e d  a 2 cm  t h e end  target.  by  2.5  cm  by  25  ym  by  resting  sheet of carbon  of a length of t h i n w a l l s t a i n l e s s  attached  steel  tubing.  Polarimeter A p o l a r i m e t e r was asymmetry o f e l a s t i c to  the  plane  proton  i s horizontal, However t h e  the h o r i z o n t a l .  vertical  solenoid  telescopes.  See  figure  nomenclature  The  2-3  with  protons  arm  forward  a scattering  by  event  four  were two  each,  mounted i n t h e  arms were two  f o r the  scintillator "forward"  aligned  at  ±24°.  recoil  telescopes  scintillators  chosen  i n the  The  i s shown i n  i n the  lab of  forward  and  designed w h o l l y by  proton-proton  approximately  arms, U F ( D F ) , must  400  scattering  MeV  so t h a t the  forward  and  opening  (84'5° ^ 89°) . the s o l i d  be  i n the r e s p e c t i v e  a n g l e between t h e r e c o i l  as t h e e l a s t i c  between 200  determined  angle  an o b s e r v a t i o n o f an e v e n t  UR(DR).  p o l a r i m e t e r was was  s p i n s ±90°  arrangement d e t e c t e d o n l y e l a s t i c  elastic  accompanied  arms was  vertical  also. This  Any  There  scintillators  at  ±62°.  basically  2-2.  t o the  recoil  scattering  the proton  Thus t h e p o l a r i m e t e r was  Complementary  24°.  first  i s i n the  precesses  p o l a r i m e t e r was  t e l e s c o p e s o f two  events  i n a plane perpendicular  Because the  the p o l a r i z a t i o n  left-right  plane. The  figure  t o measure  scattering  incident polarization.  plane. into  designed  angle f o r  The  angle  arms, and  forward  was  acceptance about  16  msr.  FIGURE FOUR  FOLD  1  s t  2-2  COINCIDENCE  LETTER  2  n d  POLARIMETER  LETTER  NUMBER  U  UP  F  FORWARD  1  FRONT  D  DOWN  R  RECOIL  2  REAR  20  The s c i n t i l l a t o r s i n t h e f o r w a r d arms were each 4 cm by 8 cm and 0.3 cm t h i c k .  They were l o c a t e d  of 25 cm and 45 cm from t h e t a r g e t c e n t r e .  at r a d i a l distances Thus t h e a n g l e s  of acceptance were ±2.58° about 24° and ±5.08° i n t h e h o r i z o n t a l plane.  The r e c o i l s c i n t i l l a t o r s had t h e f o l l o w i n g  d i m e n s i o n s . R l was 8 cm by 10 cm and 1.5 mm t h i c k , w h i l e R2 was 14 cm by 16 cm and 1.5 mm t h i c k .  They were l o c a t e d a t r a d i a l  d i s t a n c e s o f 15 cm and 35 cm r e s p e c t i v e l y . Helium Bags The d i v e r g e n c e o f p r o t o n beams i s i n c r e a s e d coulomb s c a t t e r i n g .  by  The mean square s c a t t e r i n g a n g l e was 23  estimated using the expression, < 6 > = Z (21.2 MevV -X ^ pv } LRAD 2  2  (3)  Where; Z i s t h e charge o f t h e i n c i d e n t p a r t i c l e , p i s i t s momentum, v i s i t s v e l o c i t y , and LRAD i s t h e r a d i a t i o n of t h e m a t e r i a l  i n t h e beam.  length  Therefore the s u b s t i t u t i o n of  h e l i u m gas f o r a i r t h e o r e t i c a l l y r e s u l t s i n a r e d u c t i o n o f a f a c t o r of/L~ 1 RMS by J He = 1.53.  O-.-r,  V  H e l i m nags ^ were used from  LAir  the upstream end o f t h e c o l l i m a t o r t o t h e second t a r g e t . were i n two s e c t i o n s , t h e downstream end h a v i n g a l a r g e r  They radius.  The upstream s e c t i o n had 125 ym CH_ end windows and t h e downstream s e c t i o n had 100 ym m y l a r end windows. In t a b l e 2-2 t h e v a r i o u s beam elements a r e l i s t e d 24  and and  t h e energy l o s s by t h e beam i s g i v e n f o r each element each p r i m a r y beam energy. I n t a b l e 2-3 t h e f a c t o r X/LRAD 25  i s l i s t e d f o r each element o f t h e secondary beam w i t h and  21 TABLE Energy Energy of Machine MeV  loss  2-2  in primary  beam Energy 24.79° MeV  Energy at Centre of LH„ Target _ MeV »*  TT  *^  after Scatter  500  496  391  467  463  366  425  422  334  367  362  288  3 07  302  242  Energy Initial Energy MeV  LH„  loss  in  s e c o n d a r y beam  Amount o f E n e r g y L o s t i n Mylar CH Air He  CH  2  Energy Centre Target MeV  Target MeV  MeV  MeV  MeV  Mev  Mev  391  2.70  .499  .617  . 0433  1.35  3.62  382  366  2.77  .518  .638  . 0481  1.40  3 .75  357  334  2.83  .539  .670  .0503  1.57  4.21  324  288  2.99  . 590  .727  . 0514  1.61  4.30  278  242  3.5 8  .652  . 805  .0576  1.80  4.82  230  at of  22  TABLE 2-3 The f a c t o r \ X i s t a b u l a t e d f o r each ERAD element i n t h e secondary b e a m l i n e ; w i t h and w i t h o u t Helium Gas Bags. Air  Helium Gas Bags i n c l u d e d Case  Case  Material  X LRAD  Material  X LRAD  L i q u i d Hydrogen  7.02 x 10  L i q u i d Hydrogen  7.02 x 10 -3  Stainless steel  3.49 x 10 -4  Stainless steel  3.49 x 10 -4  Air  4.22 x 10 -2  Air  9.95 x 10 -3  Mylar  3.54 x 10  Helium  1.17 x 10  CH (scintillator)  1.11 x 10 -2  Mylar  3.54 x 10  CH,  5.29 x 10 -4  CH (scintillator)  1.11 x 10 -2  w i t h o u t h e l i u m bags. t h a t t h e use scattering  by  1.44.  i n table The  exhaust  from  gas  The  {£<©?>} , i 2  are t a b u l a t e d  t h e n one  t h e coulomb  v a l u e s o f 6_„_ RMS  sees  multiple  calculated with  f o r each  primary  the  beam  2-4. f o r t h e h e l i u m bags was  the superconducting s o l e n o i d .  t o r o u g h l y 30,000 1 p e r day. bags was  Q^jyjq -  o f h e l i u m bags d e c r e a s e s  h e l i u m bags i n c l u d e d energy  Taking  r o u g h l y 610  1,  s u p p l i e d by This  amounted  S i n c e t h e volume o f t h e  t h e gas was  changed e v e r y  the  30  gas minutes.  24  TABLE 2-4 Coulomb s c a t t e r i n g  Energy o f P r i m a r y Beam MeV  RMS a n g u l a r d i v e r g e n c e o f secondary beam  8RMS t o t a l f o r Secondary beam milli-radians  500  5.5  467  5.9  425  6.4  367  7.4  307  8 .8  25 CHAPTER I I I E x e c u t i o n o f Double S c a t t e r i n g The two  discussion  subtopics;  Experiment  of t h i s experiment  i s divided  t h e beam d y n a m i c s and t h e p r o c e d u r e  into  f o r taking  data. The incident the  final  proton  beamline c o n f i g u r a t i o n  maximized the  f l u x onto the second t a r g e t w h i l e  e f f e c t s of f l i p p i n g  minimizing  the p o l a r i z a t i o n of the secondary  beam. The less  t h a n 1 s q . cm a t t h e l i q u i d  illuminated 1 cm  i n c i d e n t p r i m a r y beam had a c r o s s  hydrogen target?  cm  p r e s e r v e d by c o n v e n t i o n a l the polarimeter  (horizontal).  the spin  the solenoid  Locating  the polarimeter  spin  systems.  random r a t e ?  moreover t o  w o u l d have t o be u s e d w i t h no  o r w i t h enough c u r r e n t  solenoid  shape i s  i n t h e h o r i z o n t a l p l a n e , where t h e  current,  scintillators  This  beamline f o c u s s i n g  beam i s w i d e s t , w o u l d c a u s e a h i g h flip  to precess  i n the v e r t i c a l  the spin 180°.  p l a n e removes t h e  f r o m t h e h o r i z o n t a l l y s p r e a d beam, and t h e  i s u s e d i n t h e s y m m e t r i c mode o f p r e c e s s i n g  the  ±90°. Two computer c o d e s were u s e d t o a n a l y z e  beamline c o n f i g u r a t i o n s  before  t h e a p p a r a t u s was  ,It was l e a r n t t h a t  to gain  quadrupole doublet  s h o u l d be p l a c e d  as  thus the  t a r g e t , v i e w e d a t a 24° a n g l e , a p p e a r e d t o be  ( v e r t i c a l ) by 8.2  Placing  section of  possible.  various installed.  maximum a c c e p t a n c e and r a t e t h e as n e a r t o t h e c o l l i m a t o r  To m i n i m i z e beam image r o t a t i o n t h e s o l e n o i d  s h o u l d be u p s t r e a m f r o m t h e q u a d r i p o l e s .  A sample  distribution  26 generated figure  by t h e Monte C a r l o  3-1. T h i s  output  p r o g r a m REVMOC  shows t h e c a l c u l a t e d d i s t r i b u t i o n o f  protons over t h e secondary t a r g e t . configuration  was u s e d  p r o t o n s were s t a r t e d  i s given i n  as i n p u t  The f i n a l  t o REVMOC a n d 2 5,0 00  from t h e p o s i t i o n o f t h e l i q u i d  t a r g e t with'a" u n i f o r m h o r i z o n t a l d i s t r i b u t i o n ±15  mr a n d a u n i f o r m v e r t i c a l  ±7.5  mr.  The o u t p u t  peaked a t t h e t a r g e t The The  shows t h a t  beam e n e r g i e s was c a l c u l a t e d centre  F o r each o f t h e f i v e  t o correspond  beam d e f i n i n g  The c u r r e n t s  Bl«B2/Bl  This  aretabulated i n by m a x i m i z i n g t h e  f o r both p o l a r i t i e s  the quadrupole  i sillustrated  t o be 3 cm ( h o r i z o n t a l )  fields  i nfigure  p r i m a r y beam e n e r g y t h e beam p r o f i l e  by  1.6 cm ( v e r t i c a l ) The  scaled  of the linearly  3-2. A t 500 MeV  a t t h e second  t a r g e t was  b y 2.4 cm ( v e r t i c a l )  when t h e u p s t r e a m q u a d r u p o l e was h o r i z o n t a l l y configuration  current  (where B1,B2 a r e t h e c o u n t s i n  scintillators)  As e x p e c t e d  reverse  primary  t o t h e e n e r g y o f t h e beam a t  of therates,  The  aligned.  (500,467,425,367,307 MeV) t h e s o l e n o i d  ratio  determined  o f ±0.5 cm and  and c a r e f u l l y  3-1. The q u a d r u p o l e s were o p t i m i z e d  w i t h momentum.  o f ±5 cm and  and beam s c i n t i l l a t o r s were p l a t e a u e d a t  o f t h e magnet.  solenoid.  hydrogen  the proton d i s t r i b u t i o n i s  table  the  initial  centre.  42 5 MeV p r i m a r y beam e n e r g y .  the  distribution  b e a m l i n e was i n s t a l l e d  polarimeter  beamline  gave a beam s p o t  defocussing.  6 cm  (horizontal)  FWHM and was r e j e c t e d .  sensitivity  of the polarimeter  FWHM  to vertical  S ! S T " ! B U T I O N DF P A R T I C L E S F I N A L L Y A C C E P T E D sSPACE » o : D I S T R I B U T I O N OF P A R T I C L E S AS A F U N C T I O N OF Y I X  AT 0 6 AT 0 6  (ELFMFNT (ELEMENT  » «  -0,9000  •0,7000  -0,5000  •0,3000  •0,1000  0,1000  0,3000  -1,30  0.0  0,0  0,0  0,0  0,0  0,0  0,0  - 1 , '1 0  O'.O  0,0  0,0  0,0  0,0  0,0  0,0  -  »1,U0  0,0  0,0  <l,000  11,000  11,000  (ALONG HORIZONTAL A X I S ) (ALONG V E R T I C A L A X I S )  11J II)  SUM OF ROWS  0,7000  0,9000  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,5000'  0,0  17,000  17,000  9,000  0,0  0,0  75,000  lb,000  0,0  0,0  113,000  -0,oO  0.0  0,0  15,000  23,000  33,000  27,000  30,000  -0,20  0.0  0,0  11,000  30,000  31,000  31,000  27,000  15,000  0,0  0,0  1S1,000  0,20  O'.O  • 0,0  12,000  33,000  21,000  31.000'  23,000  12,000  0,0  0,0  113,000 131,000  0,o0  0.0  0,0  13,000  26,000  29,000  37,000  17,000  12,000  0,0  0,0  1,00  0.0  0,0  11,000  13,000  17,000  13,000  10,000  6,000  0,0  0,0  70,000  1,10  0.0 •  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  0,0  06,000  139,000  151,000  162,000  121,000  69,000  0,0  0,0  I,SO O'.O SUMS OF COLUMNS! 0,0  FIGURE Distribution the  Monte  of  Carlo  protons  on  program  REVMOC.  the  3-1 second  target,ca1culated  by  28  TABLE  Solenoid  Primary Energy MeV  currents calculated  Beam  3-1  to precess protons  ±90°  i  Solenoid Current Amps  500  62.0  467  59.9  425  57.2  367  52.3  307  47.1  29  FIGURE 3 - 2 Optimum quadrapole current (arbitrary units) versus momentum ( MeV / c ) 9501 upstream  quad  9004  downstream quad  i  8501  f  % 800  7504 7004 i  i  6504 '  I  f—i  50  r—i  1  1  100  Arbitrary  1  1  1  j  1  150  1  1  1  1  200  1  1  1  1  1  r-  250  Units (Current)  30 s t e e r i n g o f t h e beam was checked a t 425 MeV.  F i g u r e 3-3 i s a  graph showing t h e r e l a t i o n s h i p between t h e c u r r e n t i n t h e s t e e r i n g magnet and t h e asymmetry e measured i n t h e p o l a r i m e t e r . The  r e s u l t i s t h a t e changes by o n l y 0.27% ± 0.8% p e r mm. V e r t i c a l s t e e r i n g by t h e s o l e n o i d was measured by  a d j u s t i n g t h e c u r r e n t i n t h e s t e e r i n g magnet t o maximize t h e i n c i d e n t f l u x on t h e second t a r g e t .  The d i f f e r e n c e between t h e  optimum c u r r e n t s f o r o p p o s i t e s o l e n o i d p o l a r i t i e s gave a d i r e c t measure o f t h e beam s t e e r i n g .  I t was l e s s than 0.33  m i l l i r a d o r 1.1 mm a t t h e second t a r g e t . 27 Image r o t a t i o n by t h e s o l e n o i d was c a l c u l a t e d be ±17° depending on t h e s o l e n o i d p o l a r i t y .  to  The p e r c e n t a g e  change i n f l u x on t h e second t a r g e t was measured f o r d i f f e r e n t s o l e n o i d p o l a r i t i e s and was found t o be a p p r o x i m a t e l y  8%.  An event t r i g g e r , produced u s i n g s t a n d a r d Nim l o g i c u n i t s , was d e f i n e d by (U + D)»B1«B2 = (U + D)«B. of t h e l o g i c i s g i v e n i n f i g u r e 3-4.  A diagram  The event t r i g g e r was  s c a l e d a l o n g w i t h t h e s i n g l e s r a t e s f o r U,D, and B t h e coincidences  i n t h e arms o f t h e p r i m a r y beam m o n i t o r  (denoted  L and R ) . Beam b u r s t s o f 5 ns d u r a t i o n a r r i v e d every the p e r i o d o f t h e r a d i o f r e q u e n c y ,  4 4 ns,  RF, o f t h e Triumf c y c l o t r o n .  T h i s f e a t u r e was e x p l o i t e d by d e l a y i n g one i n p u t o f each c o i n c i d e n c e by 44 ns and then s c a l i n g them (see f i g u r e 3-4). The  r a t e o f "delayed"  c o i n c i d e n c e s d i r e c t l y measured t h e  31  FIGURE 3 - 3 Sensitivity steeri ng  -3.0  of polarimeter  -2.0  -1.0  0.  Current in Steering ( Amps)  to  1.0  beam  2.0  Magnet  UF 1  SCALER  S C A L E R  UD  26 ns S C A L E R  UF 2  E  UR1  |UR2  LD=?  UR  DF 2 DR1  FP  T R I G G E R  !1>D.  S T A R T  B  T D C  RF'  O S C A L E R  S T O P T D C  5 5 ns  D-B 1)  VjO  L A T C H •  S C A L E R  SCALER  If  27ns  DR2  D S C A L E R  ^B1B2y a2  H  S C A L E R  -o S C A L E R D  DR  TDC L A T C  S C A L E R  B  n;  U-B  SCALER  F A N O U T  [DFjJ  S T O P  -{54  D E L A Y  — O  S C A L E R  JO—"  FIGURE 3 - 4 ELECTRONIC LOGIC DIAGRAM  T O  F A N O U T S  ho  random r a t e  i n the undelayed c o i n c i d e n c e s .  Timesof  flight  i n the secondary  beamline  were  m e a s u r e d w i t h an L.R.S.  (2228) t i m e t o d i g i t a l c o n v e r t e r ;  started  by  and  and  These t h r e e t i m e s o f f l i g h t -  B.  w r i t t e n on of  every  RF«(U + D)«B  target,  2  and  a t the  runs.  At each 2  target.  second w i t h the  c u r r e n t was  energy  target,  33  end  events  6 events per second w i t h  the  liquid to  sixty  reversed for  a p p r o x i m a t e l y 400,000 e v e n t s  70,000 e v e n t s w i t h a  2000 e v e n t s w i t h t h e L H  the second  of about  Runs were r o u g h l y t h i r t y  the s o l e n o i d  were t a k e n w i t h a C H and  target,  and- 1 an e v e n t p e r 2  l o n g and  alternate  in  were h i s t o g r a m m e d  d a t a were r e c o r d e d a t a r a t e  h y d r o g e n t a r g e t empty.  target  U,D,  run.  per second w i t h the CH  minutes  s t o p p e d by  computer t a p e , a l o n g w i t h t h e s c a l e r s ,  The  carbon  three channels  2  carbon  t a r g e t empty and  CH  2  CHAPTER IV Data  Analysis  The d a t a a n a l y s i s was performed o f f l i n e .  An IBM  370/16 8 was used t o r e a d t h e d a t a tapes and p r i n t t h e s c a l e r information •run.  and time o f f l i g h t  (T.O.F.) h i s t o g r a m s f o r each  The RF t o Up and RF t o Down time o f f l i g h t s p e c t r a were  searched f o r t h e i r peak c h a n n e l s .  A c u t was made ±24 c h a n n e l s  from t h e maximum and t h e n t h e peak was i n t e g r a t e d t o y i e l d t h e t o t a l counts.  The asymmetry and i t s u n c e r t a i n t y was then  c a l c u l a t e d as e  A £  R  = B*U-- B'D B»U + • B«D =(B-U  + B-D)~ (l h  (1) -  e^)*  A t y p i c a l time o f f l i g h t spectrum i s shown i n f i g u r e 4-1. The c u t w i d t h was chosen t o i n c l u d e t h e e n t i r e peak f o r every spectrum.  The a c t u a l w i d t h o f t h e peaks v a r i e d  6.5 t o 20 c h a n n e l s FWHM.  from  There were 0.2 ns p e r c h a n n e l , thus  the f u l l w i d t h o f t h e c u t was 9.2 n s . T h i s c o r r e s p o n d s t o an o v e r a l l momentum b i t e o f about 200 MeV/c. c a l c u l a t e d f o r each energy a r e t a b u l a t e d  Timesof  flight  i n t a b l e 4-1. The  time o f f l i g h t d i f f e r e n c e f o r i n e l a s t i c p r o t o n s , + pp->-pnTT  v e r s u s e l a s t i c p r o t o n s , and f o r p i o n s from t h e r e a c t i o n pp->TT d  are a l s o t a b u l a t e d  i n t a b l e 4-1.  I n e l a s t i c events a r e c l e a r l y  s e p a r a t e d from t h e e l a s t i c e v e n t s . The s e n s i t i v i t y o f t h e d a t a t o t h e time o f f l i g h t c u t  35  ENERGY DIFFERENC 0  )  50  100  UJ  < o  if) >•  cc <  tr  cr < CD  5 Z  to •I—  z  ZD  o o  2  0  2  E OF FLIGHT ( n s ) FIGURE  4-1  4  36  TABLE 4 - 1  Table and  of  for  Primary Beam Energy MeV  time  of  flights  for elastic  and i n e l a s t i c  protons,  pions.  T.O.F. for e l a s t i c protons T ns  Difference in T.O.F. for i n e l a s t i c protons AT n s  Difference in T.O.F. for pions AT n s  500  59.75  11.47  -12.75  467  60.86  H.8  -12.85  425  62.67  17.90  -12.90  367  65.68  31.56  -10.89  307  69.69  Possible  +10.12  None  37 was c h e c k e d . channels error No  The a s y m m e t r i e s  calculated  a n d ±18 c h a n n e l s w e r e  o f t h e asymmetry  statistically  a l lwithin  calculated  significant  c h a n n e l was c h a n g e d b y ±2.  were  checked  some d a t a r u n s these  runs  into  no d i f f e r e n c e s were  shifts.  i n an event  i n widths  opposite  solenoid e,  asymmetry,  1  where  - e~) R  of flight by  spectra  collecting  After  dividing  channel, indicating  i n the R.F.  R  time  when t h e  r e s p e c t t o t i m e , one  o r peak  was c a l c u l a t e d  statistical  was o b s e r v e d  b y e v e n t mode.  excitations  c+Ae = K e J  the  T h i s was done  raw asymmetries  c u t s o f ±30  a ±24 c h a n n e l c u t .  Broad  subsections with  no sudden jumps The  with  difference  peak  f o r R.F.  with  found that  there  timing.  from  sequential  were  paired  runs  with  and t h e t r u e  from  ± 1 2  (2)  %  i s g i v e n by e q u a t i o n  (1) a n d t h e ^  refer  to  the  R  solenoid  polarity.  polarity  were  mean.  T £  final  paired  R = ^  data table  ^  +  R  V  '  h a v i n g t h e same  one r u n by t a k i n g  +  ^  2 /  '  1 1  /  ^  solenoid  the weighted  -2  +  ^  ( 3 )  = {E (Ae*)T2}"% i=l  asymmetry  (4)  was t a k e n a s t h e w e i g h t e d  mean  of the  asymmetries. The  full"  combined i n t o  n  Ae* The  Adjacent runs  data,  previous procedure  "carbon" d a t a , and " l i q u i d  at a l lenergies. 4-2.  was r e p e a t e d f o r " t a r g e t  The f i n a l  hydrogen target  results  empty"  are tabulated i n  38 TABLE  4-2  A s y m m e t r i e s f o r C H t a r g e t , c a r b o n t a r g e t , and l i q u i d h y d r o g e n t a r g e t empty, a v e r a g e d f o r e a c h e n e r g y . 2  Primary beam Energy MeV  CH  500  0.1337 + 0.0014  2  target £  Carbon target  L i q u i d hydrogen t a r g e t empty  e  G  CH„  MT  0.0781 + 0.0027  .1222  +  .0183  +  .0063  467  .1238  +  .0018  .0821  +  .0039  .1091  425  .1252  +  .0014  .0734 +  .0034  .0827 + .0204  367  .1115  +  .0018  .0733 +  .0037  .1592  +  .0369  307  .0966 +  .0019  .0713  +  .0042  .1040  +  .0237  TABLE 4-3 R a t e s f o r C a r b o n and L i q u i d H y d r o g e n t a r g e t normalized t o rates f o r CH data.  empty d a t a  2  Primary beam Energy MeV  Carbon rate r °  L i q u i d hydrogen t a r g e t empty r  500  0.247 ± 0.004  0.039 ± 0.001  467  0.239 ± 0.010  0.046 ± 0.008  425  0.215 ± 0.013  0.020 ± 0.004  367  0.261 ± 0.005  0.022 ± 0.001  307  0.225 + 0.003  Unreliable  The background asymmetry from carbon and t h e hydrogen t a r g e t f l a s k was s u b t r a c t e d  from t h e CH,, d a t a  t o y i e l d t h e asymmetry due t o f r e e e l a s t i c p r o t o n - p r o t o n scattering.  This involved c a l c u l a t i n g the r e l a t i v e c o n t r i b u t i o n  of carbon and t a r g e t empty events t o e l a s t i c p r o t o n e v e n t s . r a t i o s UB + DB, UB + DB, and B were used. L + R B L + R  The  The f i r s t two  r a t i o s s p e c i f y t h e r a t e a t which t h e beam s c a t t e r s - from t h e second t a r g e t i n t o t h e p o l a r i m e t e r flux."  f o r a p a r t i c u l a r "incident  Thus any o f t h e s e n o r m a l i z e t h e r e l a t i v e r a t e s f o r  d i f f e r e n t secondary t a r g e t s , ( i . e . , carbon and C H ) . 2  v e r s u s empty.  The f i r s t  The c o i n c i d e n c e s BU, BD, B, and L + R were s c a l e d  as m o n i t o r s f o r e v e r y r u n . Each r a t i o was c o r r e c t e d f o r randoms and averaged over a l l t h e runs f o r a p a r t i c u l a r s o l e n o i d p o l a r i t y , t a r g e t , and energy.  The e r r o r was a s s i g n e d as t h e maximum observed  f l u c t u a t i o n from t h e mean, t h i s b e i n g l a r g e r t h a n t h e s t a n d a r d deviation.  The r a t e from carbon n o r m a l i z e d t o CH (1) (±)  UB + DB~ L + R'  /  7  2  was t a k e n as  UB + DB" L R CH,  (5)  UB + DB~ CH, B -  (6)  or (2)(±)  UB + DB~ r B  7  /  which e v e r had t h e s m a l l e s t u n c e r t a i n t y . r a t e f o r t a r g e t empty i s g i v e n by + "MT = B B CH, L + R MT L + R  The n o r m a l i z e d  (7)  The e r r o r on each n o r m a l i z e d r a t e i s t h e e r r o r on t h e m o n i t o r r a t i o s added i n q u a d r a t u r e .  The r a t e s were then averaged over  40 the  solenoid  table  polarities.  The r e s u l t i n g r a t e s  are l i s t e d i n  4-3. The  number o f c a r b o n n u c l e i i n t h e c a r b o n  must be n o r m a l i z e d target.  Define  t o t h e number o f c a r b o n n u c l e i  target  i n the CH  2  the r a t i o  mass o f C i n C H mass o f C i n C  2  target  = k  (8)  target  One g e t s k = 0.970 f o r p r i m a r y beam e n e r g i e s o f 500, 467, and 425  MeV  (i.e.,  f o r 1x2x2.5 cm  3  targets)  and k = 0,939 f o r 367,  3 and  307 MeV  ( i e . 0.5x2x2.5 cm  r a t e w o u l d be n o r m a l i z e d by  multiplying  targets).  Usually  the carbon  t o t h e same number o f s c a t t e r i n g  by k.  C a r e was t a k e n t o i n c l u d e scintillator.  t h e e f f e c t o f t h e B2  I t i s p r i m a r i l y composed o f CH, and as n o t e d  in  Chapter  I I , i t i s an i n t e g r a l p a r t  It  contributes  of  0.077 r e l a t i v e t o t h e CH.,, d e n o t e d  a<  small  background  o f the second  i n t h e second  2  Thus t h e r a t e CH  2  target.  at a l l energies with r  B  2  •  This  was  f r o m a measurement o f t h e asymmetry a t 42 5 MeV w i t h carbon nor CH  centres  a rate  determined neither  target.  o f s c a t t e r i n g from t h e hydrogen i n  i s g i v e n by r = r„„ - r_,„ (1 - k) + k r p CH„ B2 c (9)  Z  = CH r  where one d e f i n e s which i n c l u d e s  2  "  R  c  a generalized  t h e e f f e c t o f B2.  carbon background r a t e , R , The v a l u e s o f R  are: c  TABLE 4-4 Generalized  Carbon  Background  P r i m a r y Beam E n e r g y MeV  R c  500  0.242 ± 0.004  467  0.234 ± 0.010  425  0.211 ± 0.019  367  0.250 ± 0.005  307  0.216 ± 0.003  The  final  corrected  was t h e n c a l c u l a t e d £  =  e  CH  R  "  1  where t h e e r r o r { A £  CH  +  The  (  £  + 2  +  G  R  C  MT  final  A  £  C  ) 2 A r  +  energy  from  " c c  2  asymmetry f o r e a c h  " MT MT  £  r  £  (  1  Q  )  " MT  R  r  c  i s g i v e n by r  MT MT A E  MT )/ }  { 1  +  (  £  +  £  C  )  " c - MT R  r  2  A  R  C  (11)  +  }  asymmetries a r e : TABLE 4-5 Final  Asymmetries  P r i m a r y Beam E n e r g y MeV  e ± Ae  500  0.1530 ± 0.0024  467  0.1383 ± 0.0030  425  0.1405 ± 0.0026  367  0.1232 ± 0.0030  307  r  At  MT  re  ^-^ ^ ^3i  >  3 07 MeV p r i m a r y beam e n e r g y , t h e h y d r o g e n  d a t a were u n r e l i a b l e .  The parameters  e  target  e , e „ , R , and r . , c MT c MT m  m  were l i n e a r l y f i t t e d The f i t s  and the v a l u e s a t 307 MeV e x t r a p o l a t e d .  are p l o t t e d i n f i g u r e 4-2.  o r i g i n a l parameters and the smoothed  A t a b l e summarizing the parameters i s g i v e n i n  t a b l e 4-6. The f i n a l asymmetries were r e c a l c u l a t e d u s i n g the "smoothed" are  parameters.  They a r e g i v e n i n table.'. 4-6,  and  l i s t e d here. TABLE 4-7 F i n a l Asymmetries  w i t h Smoothed Parameters  P.B.E. MeV  final  500  0.1527 ± 0.0024  467  0.1390 ± 0.0030  425  0.1409 ± 0.0026  367  0.1228 ± 0.0030  307  0.1309 ± 0.0028  These smoothed  asymmetries  asymmetry e  agree w i t h the o r i g i n a l  calculation  to w i t h i n quoted e r r o r s and are used i n the remainder of the analysis. One can now deduce the p o l a r i z a t i o n parameter from the  f i n a l asymmetries by u s i n g equation  (1-13), g i v e n  e x p l i c i t l y as, £  i  =  p  ( i » 2 4 . 7 9 ° ) P ( K ( E ) ,24°)  (1-13)  E  i  where K(E^) i s the energy of the secondary beam, d e r i v e d from two body kinematic c a l c u l a t i o n s .  (A t a b l e o f the energy  c a l c u l a t i o n i s g i v e n i n t a b l e 2-3). The e q u a t i o n  (1-13) can  be r e w r i t t e n as, e P(E ,24°) i  i  = P(E ,24°)P(K(E ) ,24°)  P(E ,24.79°) i  i  i  (12)  43  FIGURE 4-2 LINEAR FITS TO CARBON AND EMPTY TARGET ASYMMETRIES AND RATES VERSUS " BEAM ENERGY A  0  m  T  >LU  Ti.  1  T  f?.05 00  <  C 1  300  !eV I  id  T  Rc  .15  < r  .5 0  3  400  rnt  r  «1eV  500  TABLE 4-6 T a b l e o f b a c k g r o u n d a s y m m e t r i e s and r a t e s ;  smoothed and unsmoothed  UNSMOOTHED PARAMETERS Primary Beam Energy MeV  r'  f  £  CH  £ 2  c  £  MT  R  c  MT  Final  e  500  .1337±. 0014  ,0781±.0027  .12221 .0183  .242 + .004  .039±.001  .15301 .0024  467  .1238+. 0018  .0821+.0039  .1091± .0063  .234± .010  .046±.008  .1383± .0030  425  .1252±. 0014  .0734+.0034  .0827± .0204  .211± .019  .020±.004  .1405± .0026  367  .1115±. 0018  .0733+. 0037  .15921 .0369  .250± .005  .022±.001  .12321 .0030  307  .0966±. 0019  .0713±.0042  ,1040± .0237  .216± .003  Unreliable  SMOOTHED PARAMETERS P.B.E. MeV  £  c  £  MT  ^MT  Final  500  .0796±. 0027  .11181. 0183  .2361.004  .0421 .001  .15271 . 0024  467  .0781±. 0039  .11321. 0063  .2341.010  .0361 .008  .13901 .0030  425  .07631. 0034  .11491. 0204  .2311.019  .0291 .004  .14091 .0026  367  .07351. 0037  .11741. 0369  .2271.005  .0191 .001  .12281 .0030  307  .07081. 0042  .11991. 0237  .2241.003  .0091 .001  .10391 .0028  This  form has t h e advantage  variable,  , on t h e r i g h t  o f h a v i n g o n l y one i n d e p e n d a n t hand  side of the equation.  r a t i o o f the p o l a r i z a t i o n parameter  The  a t 24° v e r s u s 24.79° i s  28 known f r o m p h a s e table  gives  shift  analysis  the energies  t o 0.3%.  and p o l a r i z a t i o n  The ratios  following used i n  equation (12). TABLE Ratios  of  4-8  P ( 2 4 ° ) / P ( 2 4 .79°)  PBE MeV  E. M£V  K (E ) MeV  500  496  391  0.9546  467  463  366  0.9567  425  422  334  0.9588  367  362  288  0.9630  307  302  242  0.9668  P ( E . ,24°)/P(E. ,24.79°)  1  In a d d i t i o n t o t h e p o i n t s measured t h e v a l u e s o f P(24°) added  at 98  1 0  , 140.7 , 2 9  601  7  i n this and 7 0 2  from w o r l d d a t a t o f i x t h e p o l a r i z a t i o n  t h e e n e r g y r a n g e measured  ?  experiment MeV,  parameter  were  outside  here. TABLE 4-9  Added W o r l d Energy MeV  Data P(24°)  98  0.110 ± 0.010  140.7  0.200 ± 0.010  601  0.465 ± 0.021  702  0.511 ± 0.027 The p o l a r i z a t i o n p a r a m e t e r was w r i t t e n  as a f o u r t h  o r d e r power s e r i e s .  4 P(E,24°) = E a ( E - 4 0 0 ) n=o asymmetry i s t h e r e f o r e g i v e n by, n  The  (13)  e.P(E.,24°) = I  I  The e n e r g i e s were s h i f t e d 400 MeV so as t o reduce of t h e f i t t i n g parameters, nonlinearly  a^.  the covariance  E q u a t i o n ( 1 4 ) was used t o  f i t t h e d a t a by m i n i m i z a t i o n o f t h e c h i - s q u a r e .  A n o n s t a t i s t i c a l e r r o r e q u a l t o t h e s t a t i s t i c a l e r r o r was added i n q u a d r a t u r e t o t h e e r r o r o f each asymmetry t o account for  small i n s t a b i l i t i e s  rate monitors.  i n t h e time o f f l i g h t s p e c t r a and t h e  The c h i - s q u a r e o f t h e f i t was 1.01,  c o r r e s p o n d i n g t o a 40% c o n f i d e n c e  level.  There i s another s y s t e m a t i c e r r o r o f ±0.004 common t o a l l t h e measured e n e r g i e s due t o t h e u n c e r t a i n t y i n t h e f i r s t s c a t t e r i n g angle. e r r o r on t h e c a l c u l a t e d  T h i s was added i n q u a d r a t u r e t o t h e polarizations.  A table of the f i n a l values f o r the p o l a r i z a t i o n parameter a t 24° over t h e range o f k i n e t i c e n e r g i e s  from  200 t o 520 MeV i n 20 MeV s t e p s i s g i v e n i n t a b l e 4-10.  A  graph showing t h e e n t i r e f i t t i n g range i n c l u d i n g t h e w o r l d d a t a i s g i v e n i n f i g u r e 4-3. p l o t t e d as e  2  The d a t a from t h e experiment i s  a t t h e average energy  (E^ + K ( E ^ ) ) / 2 .  i n analogy t o p r e v i o u s s i n g l e energy double 2 experiments where e = P .  This i s  scattering  47 TABLE Values Energy MeV  o f P(24°)  4-10  l a b between  2 0 0 a n d 5 0 0 MeV  P(2 4 ) 0  200  0.278 ± 0 . 0 0 9  220  0.298  240 _  0 . 3 1 5 ± 0.007  260  0 . 3 2 9 ± 0.006  280  0.341 + 0.005  300  0.351 + 0.005  320  0.360 ±  340  0.367  360  0.374 ± 0.005  380  0.380 ± 0.005  400  0.386  420  0 . 3 9 2 ± 0.006  440  0.398 ± 0.006  460  0.404  480  0.410 ± 0.006  500  0.417  520  0.425 ± 0.010  ± 0.008  0.006  + 0.005  + 0.005  ± 0.006 ± 0.008  0.6-  ® Added  World Data  0.5 -z.  o < 0.4 cr <  o a.  V  0.3  Phase Shift Error Envelope  0.2 0.1 100  200  POLARIZATION  300  400  500 MeV  600  AT 24° LAB VERSUS FIGURE 4 - 3  700  ENERGY  CHAPTER V CONCLUSIONS The absolute  p o l a r i z a t i o n parameter was measured w i t h an  normalization  o f b e t t e r than 2% i n t h e energy  between 250 MeV and 500 MeV.  region  The most p r e c i s e v a l u e s have an  e r r o r o f about 1.5% i n t h e neighbourhood o f 42 5 MeV. The  r e s u l t s p r e s e n t e d i n t h i s t h e s i s agree w e l l  w i t h phase s h i f t p r e d i c t i o n s , based on t h e w o r l d d a t a s e t of p-p measurements.  However we have s u b s t a n t i a l l y r e d u c e d ,  from 6% t o 2%, t h e n o r m a l i z a t i o n  uncertainty.  This i s c l e a r l y  demonstrated i n t h e f o l l o w i n g t a b l e . TABLE 5-1 Comparison o f E x p e r i m e n t a l R e s u l t s Prediction.  t o P r e v i o u s Phase S h i f t  Energy Mev  P(24°) Experiment  P(24°) Phase S h i f t ( P r e v i o u s )  200 250 300 350 400 450 500  .278 .323 .351 .371 .386 .401 .417  0.280 0.314 0.340 0.361 0.380 0.398 0.414  The  ± ± ± ± ± ± ±  .009 .007 .005 .005 .005 .006 .008  ± + ± ± ± ± ±  envelope o f e r r o r from t h e phase s h i f t  i s p l o t t e d on f i g u r e 4-3.  .017 .019 .020 .022 .023 .024 .049 analysis  I t i s f e l t t h a t a new phase s h i f t  c a l c u l a t i o n w i l l show s u b s t a n t i a l l y reduced e r r o r s as a r e s u l t of t h e s m a l l e r r o r on t h e d a t a p r e s e n t e d i n t h i s t h e s i s .  One  s h o u l d a l s o see some s m a l l changes i n t h e phase s h i f t p r e d i c t i o n for  P(24°) as t h e e x p e r i m e n t a l l y  determined p o l a r i z a t i o n s d i f f e r  i n a number o f cases (see t a b l e 5-1) from t h e p r e v i o u s l y c a l c u l a t e d p o l a r i z a t i o n by more than t h e e r r o r on t h e e x p e r i m e n t a l result.  50 The normalization of  P ( 9 ) , 0°  results of  <0<9O°,  of t h i s t  o  over  study  ± 2 % , and  f i x the  absolute  hence n o r m a l i z e  the energy  range  o f 200  a l l values t o 500  since  the a n g u l a r dependence o f P i s w e l l determined  shift  analyses.  by  MeV, phase  51  BIBLIOGRAPHY 1. L. W o l f e n s t e i n ,  P h y s . Rev.  96.(1954)  1654  2. L. W o l f e n s t e i n , Ann.  Rev, Nuc.  S c i . 6.(1956)  3. M.H.  Rev. Nuc.  S c i . 10(1960)  M a c G r e g o r , Ann.  4. M. M o r a v c s i k ,  "The Two  43 291  Nucleon I n t e r a c t i o n " ,  Oxford  Press  (1963) 5. A. B e r e t v a s , P h y s . Rev.  171  (1968)  1392  6. P. Limon e t a l , P h y s . Rev.  169  (1968)  1026  7. D. Cheng  163  (1967)  1470  8. H.G.  e t a l , P h y s . Rev.  d e C a r v a l h o e t a l , P h y s . Rev.  9. J.H. T i n l o t  e t a l , P h y s . Rev.  124  9±  (1954)  (1961)  890  10. A . E . T a y l o r e t a l , N U c . P h y s . 16. (1960)  320  11. J . M a r s h a l l e t a l , P h y s . Rev.  1020  12. G. C o z z i k a e t a l , P h y s . Rev. 13. M.  Albrow e t a l , N c . u  95_ (1954) 164  P h y s . B23  14. F. B e t z e t a l , P h y s . Rev.  148  (1967) (1970)  (1966)  1796  1672 445  1289  15. O. C h a m b e r l a i n e t a l , P h y s . Rev. 105 (1957) 28 8 16. R. R o t h e t a l , P h y s . Rev. 140 (1965) B1533 17. P. Hansen S u r k o , T h e s i s , UCRL-19451, J a n . 15,  1970  18. J . B y s t r i c k y , " E l a s t i c N u c l e o n - N u c l e o n S c a t t e r i n g 270 - 3000 MeV", CEA-N-1547(E) 19. G. L u d g a t e , T h e s i s , R u t h e r f o r d HEP/T/62, O c t . 1976. 20. C. Oram, T h e s i s , R u t h e r f o r d HEP/T/65, May 1977. 21. T. Hodges,  22. G.M.  Triumf  Stinson,  23. E. S e g r e ,  Internal  Triumf  "Nuclei  H i g h E n e r g y Lab  H i g h E n e r g y Lab  Publication,  Publication,  R e p o r t , TRI-I-73-2  Internal  (1973)  R e p o r t , TRI-NA-76-1  and P a r t i c l e s " ,  W.A.  Data  (1976)  Benjamin Inc.  (1965)  52 24.  " S t u d i e s i n P e n e t r a t i o n o f Charge P a r t i c l e s i n M a t t e r , " N a t i o n a l Academy o f S c i e n c e s , NRC P u b l i c a t i o n 1133, (1964)  25.  "Reviews o f P a r t i c l e P r o p e r t i e s , " 48(2)  (1976)  26.  P. K i t c h i n g ,  27.  A. B a n f o r d , E  Rev. Mod.  Phys.  S50  Triumf  Internal  R e p o r t , TRI-71-2  (1971)  " T r a n s p o r t o f C h a r g e d P a r t i c l e Beams,"  & F.N.  Spon L t d . (1966)"  28.  D.V.  Bugg, P r i v a t e  Communication  29.  G. Cox e t a l , Nuc. P h y s . B4  (1967)  353  

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