This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

Anantaraman, N.

Banks, S.M.

Crawley, G.M.

Devins, D.W.

Friesel, D.L.

Officer, V.C.

Ronningen, R.M.

Shute, G.G.

Spicer, B.M.

English

IUScholarWorks

POLARIZED PROTON SCATTERING AT 134 M e V  FROM lS4sm and 1 6 6 ~ r  
R. M. Ronningen, N. Anantaraman, and G.M. Crawley 
Michigan S t a t e  Univers i ty ,  East Lansing, M I  48824 
B.M. Spicer ,  G.G. Shute, V.C. Of f i ce r ,  and S.M. Banks 
Melbourne Univers i ty ,  Pa rkv i l l e ,  V ic to r i a  3052, A u s t r a l i a  
D.W. Devins and D.L. F r i e s e l  
Indiana Univers i ty  Cyclotron F a c i l i t y ,  Bloomington, Indiana 47405 
The coupled-channels a n a l y s i s  of t he  d a t a  from the  r ap id ly  wi th  angle. While the  angular  d i s t r i b u t i o n s  
54~m(p ,  p1  ) and 6 6 ~ r ( p , p  ') r eac t ions  a t  134 MeV a r e  f o r  t he  2+ s t a t e s  f o r  t hese  two nuc le i  a r e  very  s i m i l a r  
nea r ly  complete. The angular  d i s t r i b u t i o n s  of c ross  and the  4+ angular  d i s t r i b u t i o n s  a r e  f a i r l y  s i m i l a r  
s e c t i o n s  and asymmetries f o r  the  0+, 2+, 4+, and 6+ e s p e c i a l l y  beyond 30°, t he  6+ c r o s s  s e c t i o n s  a r e  q u i t e  
ground band s t a t e s  a r e  shown i n  Figs. 1 t o  4. These d i s s imi l a r .  Not only a r e  the  6+ c r o s s  s e c t i o n  
angular  d i s t r i b u t i o n s  a r e  s t rong ly  o s c i l l a t o r y ,  even d i s t r i b u t i o n s  out of phase but t he  magnitude i n  the  
f o r  the  6+ s t a t e s ,  and the  c ross  s e c t i o n s  decrease  case of lS4sm is  twice t h a t  f o r  166~r .  The asymmetries 
l e.L- ----*-... , @; , . , , . , 1 
?@ r u  uu 60 60 90 BO Od 20 90 40 BB 66 0u 80 BB 
8,.,. (degrees) 
r " 
; 1) ' 5 4 ~ r n  (F, p') . ' - 1 1 133.9 MeV 1 E 
Qc,m, (degrees) 
Figure  1, Angular d i s t r i b u t i o n s  of c ross  s e c t i o n s  f o r  Figure  2. Angular d i s t r i b u t i o n s  of asymmetries f o r  
elasticandinelasticexcitationsof P = 0 + ,  2+, 4' e las t i cand ine las t i cexc i ta t ionso f  P = o + ,  2+, 4' 
and 6+ ground band s t a t e s  i n  lS4sm from (p,p')  and 6+ ground band s t a t e s  i n  1 5 4 ~ m  from (p ,pl )  
r e a c t i o n s  a t  134 MeV. The curves a r e  coupled-channels r e a c t i o n s  a t  134 MeV. The curves a r e  coupled-channels 
c a l c u l a t i o n s  a s  descr ibed i n  the  t e x t ,  c a l c u l a t i o n s  a s  descr ibed i n  the  t ex t .  
I**--- . ----. - .-- - - .  
n w .o u rr *a  *a  : ! o g 4  
@,.,. (degrees) 
:;I 4+ 
- 3 r  
- ! 4 1  
- 5 
- 6 1  
- 7 
- 8 L  
- 00 1 20 00 40 , 00 , 60 , 00 , 80 , ,  00 00 20 00 r e  , ee , so 6 + , i  00 80 ee 
8,.,. (degrees) 
Figure 3. Angular distributions of cross sections for Figure 4. Angular distributions of analyzing power for 
elastic and inelastic excitations of J1F = 0+, 2+, 4+ elastic and inelastic excitations of .P = 0+, 2+, 4'
and 6+ ground band states in 166~r from (p,p') and 6+ ground band states in 166~r from (p,pl) 
reactions at 134 MeV. The curves are coupled-channels reactions at 134 MeV. The curves are coupled-channels 
calculations as described in the text. calculations as described in the text. 
are positive in the angular range measured, and are final calculations. Extensive multivariable searches 
especially large when compared to proton scattering on well depth, diffuseness, and deformation parameters 
from lead near this energy. l were made. In all calculations we constrained the 
The data were analyzed using a deformed optical deformations of the real and imaginary potential terms 
model with the coupled-channels code ECIS~ which to be equal. We find somewhat better fits when the 
included a deformed full-Thomas spin-orbit term and spin-orbit deformations are allowed to vary 
employed relativistic kinematics. The nuclear independently. These in general are larger than those 
potential was assumed to have the standard Woods-Saxon of the central term. As shown in Figs. 1-4 the cross 
shape with the deformation parameters introduced in sections are well fitted but the asymmetries are not. 
the usual way by replacing real, imaginary, and These show a steady slip of phase between data and 
spin-orbit radii by calculations with increasing scattering angle and 
increasing spin. 
The values of the central term deformation 
All nonzero couplings between the 0+ through 8t states 
parameters $2 and $4 we find are consistent with those 
involving $2, p4, $6 deformations were included in the 
obtained by o the r  methods: f o r  lS4sm, $2 ~ 0 . 2 8  and $4 
= 0.06, and f o r  1 6 6 ~ r ,  $2  = 0.28 and $4 = 0.01. 
However, t he  values  of $6 we f i n d  a r e  f o r  1 5 4 ~ m ,  
86 = 0.008, and f o r  1 6 6 ~ r ,  86 = -0.007. Although these  
values  a r e  c o n s i s t e n t  with the  p red ic t ions  of Nilsson 
e t  a1. ,3  t h e  1 5 4 ~ m  r e s u l t  d i sag rees  with e a r l i e r  a lpha 
s c a t t e r i n g  r e s u l t s 4  which ind ica t ed  a value  wi th  the  
same magnitude but opposi te  sign. 
We plan more meaningful comparisons between our 
r e s u l t s  and those  from d i f f e r e n t  experiments i n  terms 
of a mul t ipole  moment a n a l y s i s O 5  Also we a r e  comparing 
the  c ross  s e c t i o n  angular  d i s t r i b u t i o n s  wi th  those  from 
the  a n a l y t i c  e ikonal  model of Amado and co-workers.6 
1)  P. Schwandt e t  a l . ,  Phys. Rev. C 26, 55 (1982). 
2) J. Raynal, unpublished. 
3)  S.G. Nilsson e t  a l . ,  Nucl. Phys. A131, 1 (1969). 
4) D.L. Hendrie e t  a l . ,  Phys. Let t .  z, 127 (1968). 
5) R.S. Mackintosh, Nucl. Phys. A266, 379 (1976). 
6) R.D. Amado, J.A. McNeil and D.A. Sparrow, Phys. 
Rev. C 25, 13 (1982). 
+ 
THE PRELIMINARY OPTICAL MODEL ANALYSIS OF 200 MeV p + 9 ~ e  ELASTIC SCATTERING 
C.W. Glover, P. Schwandt, H.O. Meyer, W.W. Jacobs,  J.R. Hal l ,  M.D. Kaitchuck, and R.P. DeVito 
Indiana Univers i ty  Cyclotron F a c i l i t y ,  Bloomington, Indiana 47405 
The c ross  s e c t i o n  and analyzing power angular  where 
f i ( r )  = { l  + exp[ ( r  - r i~1/3) /a i ] ) '1  (2 )  
d i s t r i b u t i o n s  have been measured f o r  200 MeV 
and 
e l a s t i c a l l y  s c a t t e r e d  polar ized< protons from 9 ~ e .  The 
r = l r d d r l  + e x r  - r j ~ ~ ~ ) / a ~ I - ~  ( 3 )  
angular  d i s t r i b u t i o n s  were measured t o  8cm=1300 which 
corresponds t o  a momentum t r a n s f e r  of q - 5.3 fm'l. The c a l c u l a t i o n s  us ing the  s i n g l e  Woods-Saxon 
The da ta  a r e  d isplayed i n  Fig. 1, a long wi th  the  parameter iza t ion f o r  t he  c e n t r a l  p o t e n t i a l s  (Eq. 2) and 
pre l iminary  r e s u l t s  of o p t i c a l  model c a l c u l a t i o n s  t h e  Thomas form (Eq. 3) f o r  t he  s p i n - o r b i t  w i l l  be 
employing two d i f f e r e n t  parameter iza t ions  f o r  t he  r e a l  l abe led  a s  'SWS' throughout t h i s  d iscuss ion.  
p a r t  of the  c e n t r a l  p o t e n t i a l .  A d i scuss ion  of the  A second parameter iza t ion used i n  the  o p t i c a l  model 
d a t a  and how the  measurements were made a r e  descr ibed a n a l y s i s  c o n s i s t s  of s u b s t i t u t i n g  f o r  t he  term VRfR(r) 
elsewhere1 and w i l l  not be repeated here. Only the  i n  Eq. 1 the  express ion 
r e s u l t s  of t he  o p t i c a l  model a n a l y s i s  of t he  d a t a  w i l l  
VRfR(r) = VRlfRl(r) + V R ~ [ ~ R ~ ( ' ) I " ,  n = 192 
be repor ted  here. 
The o p t i c a l  model c a l c u l a t i o n s  were performed and the  c e n t r a l  imaginary p o t e n t i a l  remains unchanged. 
us ing the  computer code SNOOPY~. The s tandard o p t i c a l  Ca lcu la t ions  us ing t h i s  double Woods-Saxon form with 
model a n a l y s i s  employs the  fo l lowing parameter iza t ion n-2 w i l l  be denoted by 'DWS'. This shape modif ica t ion 
t o  desc r ibe  the  l o c a l  nucleon-nucleus p o t e n t i a l  U(r): i n t roduces  t h r e e  new parameters. The mot ivat ion f o r  
t h e  DWS parameter iza t ion is given elsewhere3 and w i l l  
no t  be repeated here. 
+ + 
h2 [Vso g ~ ~ o ( r )  + i W s o  g ~ s ~ ( r ) l  (LOU) (1) I n  t h i s  pre l iminary  o p t i c a l  model a n a l y s i s  of t he  
R 
p + 9 ~ e  e l a s t i c  s c a t t e r i n g  da ta ,  t he  o p t i c a l  model 


Polarized Proton Scattering at 134 MeV from 154-Sm and 166-Er

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Polarized Proton Scattering at 134 MeV from 154-Sm and 166-Er

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