This work was supported by the National Science Foundation Grants NSF PHY 78-22774 A03, NSF PHY 81-14339, and by Indiana Universit

Bent, R.

Dillig, M.

Soga, F.

English

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STUDY OF THE (p,x) REACTION IN THE TWO-NUCLEON MODEL 
F. Soga 
Institute for Nuclear Study, The University of Tokyo, Tokyo 188, Japan 
and Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
M. Dillig 
Institute for Theoretical Physics University of Erlangen-Nurnberg, Erlangen, W. Germany 
R. Bent 
Indiana University Cyclotron Facility, Bloomingtou, Indiana 47405 
Recently acquired high-quality data on the (p,~) production from nuclei is a two-nucleon process in 
reaction, 1 especially in the near-threshold region, which the essential ingredient is the NN + NNa 
have stimulated new theoretical efforts to understand amplitude. We use non-relativistic time-ordered 
the reaction mechanism and associated nuclear perturbation theory. At the pion production vertex, 
+ + 
structure. It is evident, in some cases, that both the operator form used is a'q, which comes from the 
single-particle states and 2p-lh states in the residual non-relativistic reduction of the covariant form of the 
nucleus are strongly excited in the (p,x+) reaction. pseudo-scalar coupling yg. 
Significant differences are observed, however, in the It is well known that AN scattering is dominated by 
+ - *  - * +  
energy dependence of the reaction leading to final the P-wave interaction, and an operator form (a0q)(S*q) 
states of different structures . 3  is used for the NN + NA transition *otentia14 (G is the 
-* + 
We have carried out preliminary calculations of momentun of the virtual exchanged pion; a and S are the 
the (p,n+) reaction based on the two-nucleon model spin matrices for the nucleori and A respectively). 
taking into account the increasing importance of S-wave Four different diagrams are calculated (see Fig. 1). 
pion rescattering in the near-threshold region. We As we are interested in the near-threshold region, 
assume that the basic mechanism of coherent pion the S-wave pion scattering amplitude is also 
incorporated together with the P-wave term. For the 
S-wave rescattering term, the parametrization of the 
scattering lengths for the a and the p meson exchange 
and the hard core contribution are included in the 
amplitude. 
El E2 El E2 El E2 El E2 potential and Laplacian potential with and without 
(a) (b) (c) (dl local off-shell damping). 
E: E; , , E; E; E: E;, , E: E; The distorted waves for the incident proton and the 
The bound state wave functions are calculated using 
I \ 
/ \ / \ 
7r 
P 
either a harmonic oscillator or a Woods-Saxou potential 
outgoing pion are calculated using the piouic stripping 
model code of ~san~arides.~ Several options for the 
pion optical potential are available (Kisslinger 
N 
Figure 1. Four different diagrams (a) Direct (b) well. Our initial calculations are for a closed-shell 
Operator Exchange (c) Final-State Exchange (d) Operator 
and Final-State Exchange. target nucleus and either single-particle or 2p-lh 
P-wave con t r ibu t ion  overwhelms the  S-uave con t r ibu t ion .  
F i  u r e  2. Angular d i s t r i b u t i o n  of t h e  d i f f e r e n t i a l  
c r t s s  s e c t i o n  f o r  t h e  6.86 MeV s t a t e  i n  13c  a t  Tp=185 
MeV. The c a l c u l a t i o n  uses  the  Laplacian p o t e n t i a l  with 
o f f - s h e l l  damping. The c ross  sec t ions  a r e  decomposed 
i n t o  d i f f e r e n t  components. 
f i n a l  s t a t e s .  
To i l l u s t r a t e  t h e  c a p a b i l i t i e s  o f  t h e  code, we show 
i n  Fig. 2 pre l iminary r e s u l t s  f o r  the  1 2 ~ ( p , n + )  
r e a c t i o n  leading t o  the  6.86 MeV 2p-lh s t a t e  (assumed 
t o  have a ld5/2(1P312-1,p112)2+ conf igurat ion) .  The 
d i f f e r e n t i a l  c ross  s e c t i o n  is decomposed i n t o  seve ra l  
components from the  d i f f e r e n t  diagrams, which a r e  added 
coherent ly  f o r  the  c r o s s  sec t ion .  At Ep = 185 MeV, t h e  
Among the  four  d i f f e r e n t  P-wave diagrams, the  opera to r  
and f i n a l - s t a t e  exchange terms determine the  o v e r a l l  
shape of the  angular d i s t r i b u t i o n ,  whi le  the  d i r e c t  
term tends t o  f i l l  i n  the  deep minimum around 90 
degrees.  
We s t r e s s  t h a t  these  r e s u l t s  a r e  preliminary arid 
r ep resen t  only a f i r s t  s t e p  toward understauding t h e  
complicated i n t e r p l a y  between t h e  (p,n) r e a c t i o n  
mechanism and t h e  a s soc ia ted  nuclear  s t r u c t u r e .  
1 )  H.W. Fearing, Bibliography of (p ,x)  d a t a ,  TRIUMF 
Rep. TRI-80-3 (1980). 
2) F. Soga, R.D. Bent, P.H. P i l e ,  T.P. Sjoreen and 
M.C. Green, Phys. Rev. C 22, 1348 (1980); B. 
Hoistad, P.H. P i l e ,  TIP. Sjoreen, R.D. Bent, M.C. 
Green, and F. Soga, Phys. Le t t .  w, 315 (1980); 
T.P. Sjoreen, M.C. Green, W.W. Jacobs, R.E. 
Pol lock,  F. Soga, R.D. Bent and T.E. Ward, Phys. 
Rev. Le t t .  45, 1769 (1980); F. Soga, P.B. P i l e ,  
R.D. Bent, M.C. Green, W.W. Jacobs, T.P. Sjoreen, 
T.E. Ward and A.G. Drent je ,  Phys. Rev. C 24, 570 
(1981); T.P. Sjoreen, P.H. P i l e ,  R.E. Pollock, W.W. 
Jacobs, H.O. Meyer, R.D. Bent, M.C. Green and F. 
Soga, Phys. Rev. C 24, 1135 (1981); P.H. P i l e ,  R.D. 
Bent, R.E. Pollock, P.T. Debevec, R.E. Marrs, M.C. 
Green, T.P. Sjoreen and F. Soga, Phys. Rev. Le t t .  
42, 1461 (1979); T.P. Sjoreen,  P.H. P i l e ,  R.D. 
-
Bent, M.C. Green, J.J. Kehayias, R.E. Pollock, F. 
Soga, M.C. Tsangarides and J.G. W i l l s ,  Phys. Rev. C 
24, 2569 (1981). 
-
3) J.F. Amann, P.D. Barnes, K.G.R. Doss, S.A. Dytmn, 
R.A. Eisenate in ,  J.D. Sherman and W.R. Wharton, 
Phys. Rev. Lett. 40, 758 (1978); F. Soga, P.H. 
P i l e ,  R.D. Bent, 14.C. Green, W.W. Jacobs, T.P. 
Sjoreen,  T.E. Ward, and A.G. Drent je ,  Phys. Rev C 
24, 570 (1981) 
-
4) H. Sugawara and F. von Hippel, Phys. Rev. 172, 
1764 (1968). 
5) D.S. Koltun and A. Rei tan,  Phys. Rev. 141, 1413 
(1966). 
6) M. Tsangarides,  Ph.D. t h e s i s ,  Indiana Univers i ty ,  
1979 (unpublished). 


Study of the (p,Pi) Reaction in the Two-Nucleon Model

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Study of the (p,Pi) Reaction in the Two-Nucleon Model

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