This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Brown, J.D.

Jacobs, W.W.

Jones, W.P.

Miller, D.W.

Nann, H.

Puttaswamy, N.G.

Radhakrishna, M.C.

Singh, P.P.

Stephenson, E.J.

English

IUScholarWorks

TEST OF THE DWBA DESCRIPTION OF TRANSFER REACTIONS AT INTERMEDIATE ENERGIES BY MEASURING A CGMPLETE SET 
OF SINGLE NUCLEON AND ELASTIC SCATTERING DATA 
M.C. Radhakrishna,  H. Nann, W.W. Jacobs ,  W.P. Jones ,  D.W. M i l l e r ,  P.P. Singh and E.J. Stephenson 
Indiana  Un ive r s i t y  Cyclo t ron  F a c i l i t y ,  Bloomington, Indiana  47405 
N.G. Puttaswamy 
Department of Phys ics ,  Bangalore Un ive r s i t y ,  Bangalore,  I n d i a  
J . D .  Brown 
P r ince ton  Un ive r s i t y ,  P r ince ton ,  N J  08544 
Mechanisms f o r  t h e  s imp le s t  one-nucleon t r a n s f e r  O p t i c a l  model ana ly se s  u s ing  Woods-Saxon (WS) 
r e a c t i o n s  v i z . ,  ( p ,d )  and ( d , 3 ~ e )  r e a c t i o n s ,  have been forms f o r  t h e  p o t e n t i a l  have been c a r r i e d  ou t  and t h e  
t h e  s u b j e c t  of much exper imenta l  and t h e o r e t i c a l  work. be s t  f i t  o p t i c a l  model parameters f o r  a l l  t h e  e l a s t i c  
The D i s t o r t e d  Wave Born Approximation (DWBA) theory  has s c a t t e r i n g  d a t a  have been obta ined .  Following is  t h e  
been s u c c e s s f u l  i n  d e s c r i b i n g  t he se  r e a c t i o n s  a t  low procedure used t o  e x t r a c t  deuteron  parameters  on 2 0 6 ~ b .  
ene rg i e s .  At i n t e rmed ia t e  ene rg i e s  t he se  r e a c t i o n s  Optical-model c a l c u l a t i o n s  wi th  both r e l a t i v i s t i c  and 
have been thought not  t o  be w e l l  descr ibed  by DWBA n o n - r e l a t i v i s t i c  k inemat ics  were used and i t  was found 
theory  because of t h e  l a r g e  momentum t r a n s f e r  involved.  t h a t  t h e  c a l c u l a t i o n s  wi th  r e l a t i v i s t i c  k inema t i c s  
I n  many cases  DWBA has f a i l e d  t o  reproduce exper imenta l  y i e l d  a  b e t t e r  X2 va lue  by almost a  f a c t o r  of 2. F i r s t  
d a t a ,  e s p e c i a l l y  ana lyz ing  power angu la r  we s t a r t e d  wi th  a  s t anda rd  Woods-Saxon (WS) shape of 
d i s t r i b u t i o n s  .l Bef o r e  a  d e f i n i t e  conclus ion  is t h e  p o t e n t i a l  wi th  t h e  g l o b a l  deuteron  parameters  from 
reached,  whether or  not  DWBA works a t  i n t e rmed ia t e  Ref. 2 and ob t a ined  a  s e t  of be s t  f i t  parameters .  
ene rg i e s ,  a l l  r equ i r ed  i n g r e d i e n t s  which go i n t o  t h e  The shape of t h e  p o t e n t i a l  was then  a l t e r e d  by u s ing  
s t anda rd  DWBA have t o  be v igo rous ly  t e s t e d .  o t h e r  forms of p o t e n t i a l s  l i k e  Woods-Saxon wi th  a n  
This  p r e sen t  exper imenta l  work a t  IUCF is designed imaginary sp in -o rb i t  term (WS + ISO), squared 
t o  t e s t  s e v e r a l  i n g r e d i e n t s  of DWBA a t  i n t e rmed ia t e  Woods-Saxon ( w s ~ ) ,  and squared Woods-Saxon wi th  
ene rg i e s .  A complete s e t  of angular  d i s t r i b u t i o n s  of imaginary sp in -o rb i t  term ( W S ~  + ISO). Each time when 
d i f f e r e n t i a l  c r o s s  s e c t i o n s  and ana lyz ing  powers f o r  t h e  shape of t h e  p o t e n t i a l  i s  changed t h e r e  is an 
t h e  s i n g l e  nucleon t r a n s f e r  r e a c t i o n s  8 7 ~ r ( ; , d ) 8 6 ~ r  and improvement i n  t h e  X 2  v a l u e  a s  can be s een  from 
206Pb( i ,3He)205Tl  a t  ene rg i e s  Ep = 94.2 MeV and Table  1. The number of parameters  i n  a l l  t h e s e  ca se s  
Ed = 79.4 MeV and f o r  e l a s t i c  s c a t t e r i n g  of p  + 8 7 ~ r  a t is very small compared t o  t h e  number of exper imenta l  
Ep = 94.2 MeV, d  + 8 6 ~ r  a t Ed = 88.0 Mev, d  + 2 0 6 ~ b  a t  d a t a  po in t s .  F ig .  1 shows t h e  o p t i c a l  model f i t  
Ed = 79.4 MeV have been obta ined .  D i f f e r e n t i a l  c r o s s  ob t a ined  f o r  t h e  deuteron  e l a s t i c  s c a t t e r i n g  d a t a  on 
s e c t i o n  angu la r  d i s t r i b u t i o n  has  a l s o  been obta ined  f o r  2 0 6 ~ b ,  wi th  t h e  va r ious  types  of p o t e n t i a l s .  The forms 
3 ~ e  + 2 0 5 ~ 1  e l a s t i c  s c a t t e r i n g  a t  78.4 MeV. of t h e  r e a l  and imaginary p a r t s  of be s t  f i t  WS and W S ~  
These two p a r t i c u l a r  r e a c t i o n s  were chosen a s  t h e  a r e  shown i n  Fig.  2.  
r a d i a l  wave f u n c t i o n s  of t he  va lence  nucleons,  I I ( ~ s ~ / ~ )  The d i s t o r t e d  waves gene ra t ed  from t h e s e  d i f f e r e n t  
and v( lgg12)  r e s p e c t i v e l y  a r e  p r e c i s e l y  known from p o t e n t i a l s  have d e f i n i t e l y  an  i n f l u e n c e  on t h e  DWBA 
e l a s t i c  e l e c t r o n  s c a t t e r i n g .  c a l c u l a t i o n s  i n  p r e d i c t i n g  t he  shape  and magnitude of 
TABLE I 
O p t i c a l  model parameters f o r  2 0 6 ~ b  + d a t  79.4 MeV i n c i d e n t  energy 
- - - -  - - - 
P o t e n t i a l  form V 0 a 0 Ws W~ r~ a W v~~ 
g l o b a l  WSa 77.76 1.17 0.812 6.76 7.7 1.29 0.919 4.66 
b e s t  f i t  WS 79.22 1.183 0.811 6.28 9.31 1.281 0.855 4.95 
WS+ISO 79.87 1.178 0.824 7.55 8.31 1.306 0.813 4.593 
ws2 86.9 1.367 0.6 6.51 8.75 1.256 0.959 5.898 
ws2 +IS0 87.72 1.308 0.606 7.05 8.04 1.27 0.956 5.532 
r~~ a~~ WSO r~~ a~~ X2 /po in t  
o Ay t o t a l  
a )  Ref. 2 
l ~ ~ ~ ~ I . l I I I I I I I I 1 , I I l l l l l l l l l j  
0 25 50 75 100 125 
63c.m. (deg) 0 25 50 75 100 125 8c.m. (deg) 
Finure  1. 
t h e  angu la r  d i s t r i b u t i o n s .  F ig .  3 shows t h e  
p r e d i c t i o n s  of t h e  s t anda rd  DWBA f o r  t h e  ground s t a t e  
t r a n s i t i o n  of 2 0 6 ~ b ( d ,  3 ~ e ) 2 0 5 ~ 1  r e a c t i o n .  There is a 
r educ t ion  i n  t h e  magnitude of t h e  c r o s s  s e c t i o n  maximum 
a t  8", between t h e  p r e d i c t i o n s  from g l o b a l  parameters 
and our  be s t  f i t  WS parameters.  There is another  
r educ t ion  i n  t h e  c ro s s  s e c t i o n  when a squared  WS 
p o t e n t i a l  form i s  used. On t h e  o t h e r  hand, t he  
i n c l u s i o n  of an imaginary sp in -o rb i t  term has 
n e g l i g i b l e  e f f e c t  on t h e  c a l c u l a t e d  t r a n s f e r  c ro s s  
s e c t i o n .  
Thus i n  o rde r  t o  remove t h e  amb igu i t i e s  a s s o c i a t e d  
wi th  t he  shape of t h e  o p t i c a l  p o t e n t i a l s  and t o  o b t a i n  
a b e s t  p o s s i b l e  shape of t he  t r u e  p o t e n t i a l ,  ano the r  
method3 is being used f o r  ana lyz ing  phenomenlogically , 
t h e  r e a l  and imaginary p a r t s  of t h e  o p t i c a l  p o t e n t i a l s .  
This  method c o n s i s t s  of adding t o  t h e  convent ional  WS 
p o t e n t i a l  an e x t r a  p o t e n t i a l  g iven  by a Four ier -Besse l  
s e r i e s .  The c o e f f i c i e n t s  of t he se  s e r i e s  w i l l  be 
'5 
a -40- 
9 E 
0 2.5 5 7.5 10 12.5 0 2.5 5 7.5 10 12.5 
Radius (fm) Radius (fm) 
Figu re  2. 
determined by a l e a s t - squa re s  f i t  t o  t h e  da t a .  
Although t h i s  method i n c r e a s e s  t h e  number of 
parameters ,  it w i l l  s t i l l  be a very sma l l  number 
compared t o  t h e  number of exper imenta l  d a t a  po in t s .  
1) J.R. Shepard,  E. Rost  and P.D. Kunz, Phys. Rev. 
C 25, 1127 (1982).  
2 )  W.W. Daehnick, J .D .  Chi lds  and 2. V r c e l j ,  Phys. 
Rev. C 21, 2253 (1980).  
3 )  E. Friedman and C . J .  Ba t t y ,  Phys. Rev. C 17, 34 
(1978).  
2 0 6 ~ b  (d, 3 ~ e )  2 0 5 ~ 1  1 
- . - . - . - . -  Global WS 
------------- Best fit WS+ISO 1 
0 10 2 0 3 0 
8c.m. (deg) 
F i e u r e  3. 


Test of the DWBA Description of Transfer Reactions at Intermediate Energies by Measuring a Complete Set of Single Nucleon and Elastic Scattering Data

https://scholarworks.iu.edu/dspace/bitstream/2022/975/1/iucf_1985_56-58.pdf

Test of the DWBA Description of Transfer Reactions at Intermediate Energies by Measuring a Complete Set of Single Nucleon and Elastic Scattering Data

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