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

Bent, R.D.

Conte, J.S.

Dillig, M.

English

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ORCHID: A TWO-NUCLEON MODEL CODE FOR (p , n) CALCULATIONS 
J.S. ~ o n t e +  and R.D. Bent 
Indiana Univers i ty  Cyclotron F a c i l i t y ,  Bloomington, Indiana 47405 
M. D i l l i g  
I n s t i t u t e  f o r  Theore t i ca l  Physics,  Univers i ty  of Erlangen-Nurnberg Erlangen, West Germany 
Work on the  Indiana-Erlangen two-nucleon model previous two-nucleon model  calculation^^^^ l5 f o r  the  
code f o r  c a l c u l a t i n g  (p,n) c ross  s e c t i o n s  and analyzing r e a c t i o n  I * C ( ~  ,n+)13c. The pion d i s t o r t i o n s ,  on the  
powers was brought t o  a s t a g e  of completion dur ing o t h e r  hand, produce a s u r p r i s i n g l y  l a r g e  e f f e c t ,  i n  
1984. The model includes  a l l  of t he  resonant  p-wave view of the  f a c t  t h a t  most of t he  mosentum sha r ing  is  
p a r t  of t he  i n t e r a c t i o n ,  which is  thought t o  be bel ieved t o  be incorporated microscopical ly  i n  the  
dominant a t  IUCF ene rg ie s  except very c l o s e  to  two-nucleon r e a c t i o n  mechanism. Even with t h i s  l a r g e  
threshold .  The Non-resonant p-wave and s-wave p a r t s  of enhancement, t he  c a l c u l a t e d  c ross  s e c t i o n  is  below the  
t h e  i n t e r a c t i o n  a r e  not included. I n i t i a l  s t a t e  d a t a  by a f a c t o r  of about 10. The c a l c u l a t e d  analyzing 
i n t e r a c t i o n s  and higher order  c o r r e c t i o n s  f o r  powers agree  with the  d a t a  only a t  forward angles .  
r e s c a t t e r i n g  of the  outgoing pion a r e  t r e a t e d  a s  Fig. 2 shows a comparison between c a l c u l a t i o n  and 
d i s t o r t i o n s  v i a  proton-nucleus and pion-nucleus o p t i c a l  data16 f o r  the  r e a c t i o n  1 4 ~ ( p ,  n') 5 ~ *  l ead ing  t o  the  
p o t e n t i a l s .  The ideas  of t h i s  model and previous s t r e t c h e d  2p-lh s t a t e  a t  7.3 MeV. For these  
progress  i n  developing the  computer program have been 10 
r epo r t ed  previously.  
The proton d i s t o r t e d  waves a r e  ca l cu la t ed  using 
- 
L 
t h e  o p t i c a l  model code S N O O P Y . ~  The pion d i s t o r t e d  c lo3 n 
C 
V 
waves a r e  c a l c u l a t e d  us ing the  r e l a t i v i s t i c  o p t i c a l  E 
0 
model code M J P I E S , ~  which is  a modified ve r s ion  of the  C? 
- I  
' 10 
code P I K K . ~  For both protons  and pions,  p lane  wave b 
-0 
expansions of t he  d i s t o r t e d  waves a r e  made using the  
technique of Char l ton , l0  s o  t h a t  t he  distorted-wave 
(p ,n)  c a l c u l a t i o n  is a sum over plane wave s t a t e s .  
1 1 
3 H e ( p , a + )  4 ~ e  
- Tp=201 .7  MeV 
OO 0 0 
- 
O P - 0 
.rr DW 
- 
Figure  1 shows the  r e s u l t s  of c a l c u l a t i o n s  f o r  t he  a DW 
0.5 - 
3 ~ e ( p , n + ) 4 ~ e  r e a c t i o n  and r ecen t  IUCF data .  l1 The )r 
a 
proton o p t i c a l  p o t e n t i a l  parameters were taken from van 
Oers e t  a1.12 The pion o p t i c a l  p o t e n t i a l  parameters 
chosen reproduce q u a l i t a t i v e l y  I T - ~ H ~  e l a s t i c  
data.13 The proton d i s t o r t i o n s  produce the  expected 
e f f e c t  of lowering the  (p,n+) c ross  s e c t i o n  by about a e"," 
f a c t o r  of t h ree ,  without changing the  angular  Figure  1. Calcula ted  and experimental  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 analyzing powers f o r  t he  r e a c t i o n  
d i s t r i b u t i o n  very  much. This is c o n s i s t e n t  with 3 ~ e ( p p n + ) 4 ~ e p . s .  
c a l c u l a t i o n s  t h e  pro ton  d i s t o r t e d  waves were c a l c u l a t e d  
u s i n g  p r o t o n - 1 2 ~  o p t i c a l  p o t e n t i a l  parameters  from 
Meyer e t  a1.17 The pion o p t i c a l  p o t e n t i a l  parameters  
used  reproduce q u a l i t a t i v e l y  p ion  e l a s t i c  da t a .  Here 
t h e  e f f e c t s  of t h e  pro ton  and pion d i s t o r t i o n s  
a r e  reasonable ,  and t h e  agreement between theory  and 
experiment is b e t t e r  than  f o r  3 ~ e ( p , ~ + ) 4 ~ e .  
to3 I I I I I 
14 c ( ~ , T - )  15 0 (7.3 MeV,7/2+) 
Tp = 183 MeV 
F i  u r e  2. Ca l cu l a t ed  and exper imenta l  d i f f e r e n t i a l  
c r t s s  s e c t i o n s  f o r  t h e  r e a c t i o n  14~(p ,n- )150(7 .3  MeV, 
7/2+). 
+Present  Address: Purdue Un ive r s i t y  Computing Center ,  
West La faye t t e ,  I nd i ana  47907. 
1 )  M. D i l l i g ,  F. Soga and T.P. S joreen ,  IUCF 
S c i e n t i f i c  and Technica l  Report  1980, p. 62. 
2) F. Soga, M. D i l l i g  and R. Bent, IUCF S c i e n t i f i c  
and Technica l  Report  1981, p. 47. 
3) M. D i l l i g ,  F. Soga and J. Conte, AIP Conference 
Proceedings  No. 79, P ion  Product ion  and Absorpt ion  
i n  Nucle i  - 1981, ed. R.D. Bent (American I n s t i t u t e  
of Phys ics ,  New York, 1982) p. 275. 
4)  F. Soga and M. D i l l i g ,  i b i d ,  p. 289. 
5 )  J. Conte, R. Bent and M. D i l l i g ,  IUCF S c i e n t i f i c  
and Tech ica l  Report  1982, p. 83. 
6 )  J. Conte, R. Bent and M. D i l l i g ,  IUCF S c i e n t i f i c  
and Tech. Rep. 1983, p. 88. 
7)  P. Schwandt, IUCF Keport No. 84-2 ( Ju ly  15, 1984). 
8 )  M.B. Johnson and E.R. S i c i l i a n o ,  Phys. Rev. C 27, 
730 (1983) and Phys. Rev. C 27, 1647 (1983). 
9 )  R.A. E i s e n s t e i n  and G.A. M i l l e r ,  Computer Phys ics  
Communications 8, 130 (1974). 
10) L.A. Char l ton ,  Phys. Rev. C 8, 146 (1972). 
11) J.J. Kehayias, Ph.D. Thes is ,  Indiana  Un ive r s i t y ,  
1983 (IUCF I n t e r n a l  Report  #83-4). 
12) W.T.H. van Oers e t  a l . ,  Phys. Rev. C 25, 390 
(1982). 
13) G. Fou rn i e r  e t  a l . ,  Nucl. Phys. A426, 542 (1984). 
14) B.D. K e i s t e r  and L.S. K i s s l i n g e r ,  Nucl. Phys. A412, 
301 (1984). 
15) M.J. Iqba l ,  Ph.D. Thes is ,  Indiana  Un ive r s i t y ,  1982. 
16) S.E. Vigdor e t  a l . ,  Nucl. Phys. A396, 61c (1983). 
17) H.O. Meyer e t  a l . ,  Phys. Rev. C 27, 459 (1983). 


Orchid: A Two-nucleon Model Code for (p, pi) Calculations

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Orchid: A Two-nucleon Model Code for (p, pi) Calculations

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