This work was supported by National Science Foundation Grants PHY 76-84033A01, PHY 78-22774, and Indiana Universit

Bacher, A.D.

Donoghue, T.R.

Jacobs, W.W.

Kaitchuck, M.D.

Meek, J.T.

Meyer, H.O.

Schwandt, P.

Vigdor, S.E.

English

IUScholarWorks

POLARIZATION I N  MEDIUM-ENERGY PROTON-NUCLEUS ELASTIC SCATTERING 
P. Schwandt, A.D. Bacher, T.R. Donoghue,* W.W. Jacobs, M.D. 
Kaitchuck, J.T. Meek, H.-0. Meyer, S.E. Vigdor. 
The optical-model (OM) ana lys i s  of e l a s t i c  sca t -  
t e r i n g  d i f f e r e n t i a l  c ros s  s ec t ion  measurements a t  IUCF 
f o r  p  + 4 0 ~ a ,  9 0 ~ r ,  and 2 0 8 ~ b  a t  proton energies  from 
80 t o  180 MeV exhib i ted  considerable s e n s i t i v i t y  t o  t he  
parametrizat ion of t he  complex spin-orbit  t e n t i a l l )  . 
Nevertheless, s i g n i f i c a n t  parameter ambiguit ies remained 
i n  both c e n t r a l  and sp in-orbi t  terms of t h e  OM p o t e n t i a l  
a s  determined by the  above c ros s  s ec t ion  da ta .  Suffi-  
c i e n t l y  p rec i se  and extens ive  po la r i za t ion  da ta ,  when 
combined w i t h  t h e  e x i s t i n g  high-quali ty c ross  s e c t i o n  
d a t a  i n  t he  ana lys i s ,  should impose more severe  con- 
s t r a i n t s  on the  parametr iza t ion  of t he  proton-nucleus 
o p t i c a l  p o t e n t i a l .  I n  p a r t i c u l a r ,  t he  empir ica l  va lues  
of t he  r e a l  and imaginary sp in-orbi t  s t r eng ths  (or 
volume i n t e g r a l s )  should become more f i rmly  e s t ab l i shed  
f o r  medium-energy proton s c a t t e r i n g  and permit defin-  
i t i v e  comparison wi th  impulse approximation ca l cu l a t i ons  
of t he  f i r s t -o rde r  o p t i c a l  p o t e n t i a l  i n  terms of r ea l -  
i s t i c  2-nucleon t r a n s i t i o n  matr ices2) .  
Although some o lde r  p o l a r i z a t i o n  da t a  e x i s t  f o r  
t he  above nuc l e i  around 155 and 185 MeV proton energy3), 
those d a t a  a r e  i n  most cases  l imi t ed  i n  both quan t i t y  
Csmal l  angular  range, 0  S 40'; few da t a  po in t s ,  S 20) 
and q u a l i t y  ( r e l a t i v e  e r r o r s  AP ;G .02 - . l o ) .  Inclu- 
s i o n  of these  da t a  i n  t he  OM analysis1) e i t h e r  has  
l i t t l e  inf luence  on the  p o t e n t i a l  parameters o r ,  i n  
some cases,  y i e l d s  r e s u l t s  i n  c o n f l i c t  wi th  t he  c ros s  
s ec t ion  da t a  i n  the  sense  t h a t  no common p o t e n t i a l  can 
be found which produces a  good q u a l i t a t i v e  desc r ip t ion  
of both  types of  da t a .  
With t he  r ecen t  a v a i l a b i l i t y  of t h e  polar ized  
proton beam a t  IUCF we i n i t i a t e d  a  modest program of 
measuring d e t a i l e d  angular  d i s t r i b u t i o n s  of t he  
analyzing power $(0) f o r  polar ized  proton s c a t t e r i n g  
from a  few nuc le i  (e.g. 9 0 ~ r ,  2 0 8 ~ b )  a t  a  few proton 
energies  (e.g. 135, 180 MeV). While we may eventua l ly  
propose a  more sys temat ic  and comprehensive program of 
analyzing power measurements, t h e  i n t e n t  of t he  i n i t i a l  
measurements i s  t o  supplement t he  corresponding d e t a i l e d  
c ros s  s ec t ion  measurements wi th  high-quali ty Ay da t a  i n  
those  cases  where no previous d a t a  e x i s t ,  o r  where exis -  
t i n g  d a t a  y i e l d s  cont radic tory  p o t e n t i a l  s e t s .  
The f i r s t  measurements of $(0) were c a r r i e d  ou t  
f o r  ' O Z ~  a t  135 MeV using t h e  QDDM magnetic spectrograph 
over t he  angular  range 10' 1 0 5 60' i n  0.5' t o  1.5' 
s t eps .  Data were taken a t  a  few angles  f o r  a  given s ign  
of  t h e  i nc iden t  beam po la r i za t ion ,  then the  beam polar-  
i z a t i o n  was changed i n  s ign  by revers ing  t h e  d i r e c t i o n  
of t h e  magnetic guide f i e l d  i n  t he  i o n i z e r  of t he  polar-  
ized  ion  source (P .I .S .)+), and the  measurements repeat-  
ed. This procedure proved convenient and acceptable  
because of t he  good s t a b i l i t y  of t he  beam p o l a r i z a t i o n  
P  (changes i n  pB of l e s s  than 5 O.Ol/hr and f 0.02/day B 
were observed). The beam i n t e n s i t y  on t a r g e t  ranged 
from 10 t o  80 nA; t h e  average beam p o l a r i z a t i o n  was P  
B 
= 0.70. The p o l a r i z a t i o n  of t h e  beam p r i o r  t o  i n j e c t i o n  
i n t o  t he  main cyclo t ron  s t a g e  was monitored before  and 
a f t e r  every s p i n  f l i p  wi th  a  low-energy 4 ~ e  polar imeter4) .  
Twice i n  t h e  course of t he  experiment, t he  beam po la r i -  
za t i on  on t a r g e t  was determined from t h e  asymmetry pro- 
duced i n  135 MeV proton s c a t t e r i n g  from 12c a t  0  = 9' L 
and BL = 12.5' where previous double-scattering measure- 
ments5) had e s t ab l i shed  the  abso lu t e  analyzing power a s  
Ay(gO) = 0.405 and %(12.5') = 0.48. These measurements 
of t h e  po la r i za t ion  of t he  135 MeV proton beam yie lded  
PB = 0.70 and P  = 0.73 a t  widely separa ted  times. As 
B 
10' 
p + g O ~ r .  135 MeV 
"\. 
'. 
L., 
the  corresponding r e s u l t s  from the  low-energy polar i -  
meter were PB = 0.695 and PB = 0.715, r e spec t ive ly ,  we 
conclude the re  is no d i sce rn ib l e  depolar iza t ion  r e s u l t -  
i ng  from passage of t h e  beam through the  main cyclo t ron  
a t  t h i s  energy. The low-energy polarimeter  r e s u l t s  were 
thus used f o r  ca l cu l a t i on  of t he  analyzing power da t a  
reported here .  
Charge in t eg ra t ion  f o r  each sp in  d i r e c t i o n  of t h e  
i nc iden t  beam (required f o r  a  one-arm po la r i za t ion  
measurement i n  t h e  absence of a  r e l i a b l e  polar iza t ion-  
i n s e n s i t i v e  monitor of t he  s ca t t e r ed  y i e l d )  was accom- 
p l i shed  using a s o l i d  carbon beam s top  i n s i d e  t he  
spectrograph t a r g e t  chambers. To e l iminate  f a l s e  asym- 
metr ies  a r i s i n g  from d i f f e r ences  i n  average beam posi- 
t i o n  on t a r g e t  f o r  the  two counting i n t e r v a l s  ( sp in  "up" 
and "down"), the  beam s top  was s p l i t  i n  h a l f  along t h e  
beam a x i s  t o  allow automatic l e f t - r i g h t  center ing  of t he  
beam. 
The angular  d i s t r i b u t i o n  of +(8) obtained f o r  6 + 
9 0 ~ r  a t 135 MeV is displayed i n  f i g .  1, together  wi th  a 
\ 
--- - 
A %\ 
-- A;- 
ROOK 
El 
----- IMPULSE APPROX. 
0 
h 
Ep (MeV) 
F i g m  2. 
p a r t i a l  d i s t r i b u t i o n  of t he  d i f f e r e n t i a l  c ross  s ec t ion  
u(8) ( t he  f u l l  s e t  of  c ross  s ec t ion  da t a  extends t o  
126O). The e r r o r s  indica ted ,  A% = f 0.02 t o  f 0.04, 
a r e  mainly s t a t i s t i c a l ;  t he  absolu te  normalizat ion is 
est imated t o  be uncer ta in  by a s imi l a r  amount. The 
curves shown represent  simultaneous OM f i t s  t o  both 
o(8) and +(0) obtained by varying the  r e a l  c e n t r a l ,  
imaginary c e n t r a l ,  and complex sp in-orbi t  p o t e n t i a l  
parameters. The r e s u l t i n g  parameters indica ted  i n  
f i g .  1') do no t  d i f f e r  d r a s t i c a l l y  from those  parameters 
which provided a b e s t  f i t  t o  a (8)  only; t he  d i f f e r ences  
a r e  never the less  s i g n i f i c a n t  s i n c e  t he  p red i c t i on  of 
%(8)  by the  parameter s e t  based on o(0) d i f f e r s  sub- 
s t a n t i a l l y  from t h e  a c t u a l  Py(8) measurements. 
The f i t  t o  Ay(0) i s  q u a l i t a t i v e l y  good o v e r a l l  but  
does n o t  agree  wi th  t h e  measurements i n  d e t a i l ,  par t icu-  
l a r l y  forward of 20'. For 0(8) t he  agreement between a (8 )  d a t a  and which we in tend t o  remeasure). Also 
ca l cu l a t i on  and measurement is only s l i g h t l y  worse than indica ted  on t h i s  graph a r e  p red i c t i ons  of two micro- 
f o r  t he  b e s t  f i t  t o  t he  a (8 )  d a t a  only.  These d iscre-  scopic  models of t h e  proton-nucleus o p t i c a l  p o t e n t i a l  
pancies may r e f l e c t  some i n t r i n s i c  inadequacy i n  t h e  which appear t o  b e  a t  var iance  wi th  the  t rend  of t he  
p a r t i c u l a r  form of the  OM used here ,  e. g., i n  the  form phenomenological OM r e s u l t s .  
f a c t o r s  used (Woods-Saxon and de r iva t ives )  o r  i n  t h e  
a r b i t r a r y  choice of a common geometry f o r  r e a l  and *Ohio S t a t e  Univers i ty ,  Columbus, OH 43210 
imaginary sp in-orbi t  formfactors.  More de t a i l ed  analyses +A f a s t  sp in - f l i p  method employing rapid  switching 
between two d i f f e r e n t  RF t r a n s i t i o n  c a v i t i e s  i n  t he  
t o  i n v e s t i g a t e  var ious  refinements of t he  model a r e  i n  P.I.S. i s  p re sen t ly  being implemented. 
progress.  The main premise underlying the  motivation tThe f a c t o r  y r ep re sen t s  a renormal iza t ion  of t h e  
p o t e n t i a l  i n  a r e l a t i v i s t i c  modificat ion of t he  
f o r  these  A measurements, namely t h a t  they would be a Y SchrGdinger equation.  l )  
necessary,  i f  not  s u f f i c i e n t ,  ingredient  i n  t h e  unambi- 1 )  P.  Schwandt e t  a l . ,  IUCF Techn. and Scient .  
Report 1977, p. 79. 
guous d e f i n i t i o n  of t he  main f e a t u r e s  of t h e  proton OM, 
2) P. Schwandt e t  a l . ,  con t r ibu t ion  t o  t h i s  IUCF 1978 
c e r t a i n l y  appear t o  be born out  by the  new data .  Report, p. 27. 
Afurtherillustrationofthisisgiveninfig.2 3) C , R o l l a n d e t a l . , N u c l . P h y s . ~ , 6 2 5  (1966); 
A. W i l l i s  e t  a l . ,  J .  Physique 30, 1 3  (1969). 
where the  volume i n t e g r a l s  of t h e  r e a l  and imaginary A. Ingemarsson and G. T ibe l l ,  Physica S c r i p t a  5, 
235 (1971). 
spin-orbi  t p o t e n t i a l ,  W.T.H. van Oers e t  a l . ,  Phys. Rev. e, 307 (1974). 
4) Contribution t o  t h i s  IUCF 1978 Report, pp, 133, 140, 
5) O.N. J a r v i s ,  B. Rose and J .P.  Scanlon, Nucl. Phys. 
( r )  d r  , ICs0 - 
- 77, 161 (1966). 
6) M. Nakamura e t  a l . ,  RCNP Ann. Report 1977 (Osaka 
Univ.), p. 129. 
a r e  presented a s  funct ion  of pro ton  energy. The small- 
s i z e  symbols i n d i c a t e  va lues  obtained from f i t s  t o  a(0) 
da ta  only and show s u b s t a n t i a l  s c a t t e r .  The la rge-s ize  
symbols represent  va lues  obtained from f i t t i n g  u(8) and 
Ay(8) da t a  ( t he  shaded symbols correspond t o  t h e  o lde r ,  
lower-quality Ay da t a  r e f e r r ed  t o  above; t he  s o l i d  l a r g e  
symbols f o r  9 0 ~ r  a e  based on the  present  135 MeV Ay 
d a t a  and the  r ecen t ,  high-quali ty 65 MeV Ay measurements 
of Nakamura e t  a 1  . 6) )  . Incorporat ing the  newer % da ta  
( f o r  9 0 ~ r )  along wi th  the  b e s t  of t h e  o lde r  Ay d a t a  
( f o r  4 0 ~ a )  i n  the  ana lys i s  c l e a r l y  he lps  t o  e s t a b l i s h  
t h e  proper t rend  wi th  energy ( s o l i d  l i n e  i n  f i g .  2) and 
a l s o  emphasizes t he  poss ib l e  exceptions t o  such a t rend  
provided by the  o lde r  Ay d a t a  f o r  2 0 8 ~ b  near  160 and 180 
MeV (which we found t o  be i ncons i s t en t  wi th  t he  IUCF 


Polarization in Medium-Energy Proton-Nucleus Elastic Scattering

https://scholarworks.iu.edu/dspace/bitstream/2022/2921/1/iucf_1978_24-26.pdf

Polarization in Medium-Energy Proton-Nucleus Elastic Scattering

Abstract

Similar works

Full text

Available Versions

IUScholarWorks