Supported by the National Science Foundation and Indiana Universit

Bent, R.D.

Green, M.C.

Pile, P.H.

Pollock, R.E.

Sjoreen, T.P.

Soga, F.

English

IUScholarWorks

s t a t e  is t h e  ( l p  B 1P312-1 1plI2) c o n f i g u r a t i o n .  The 
c (p,r+) "c* d i f f e r e n t  s l o p e  of t h e  e x c i t a t i o n  f u n c t i o n s  f o r  t h e  3.68 
and 6.86 MeV 2p-lh s t a t e s  compared t o  t h a t  f o r  t h e  3.85 
MeV s i n g l e - p a r t i c l e  s t a t e  i n d i c a t e s  a  d i f f e r e n c e  i n  t h e  
r e a c t i o n  mechanism f o r  p roduc t ion  of 2p-lh and s i n g l e -  
p a r t i c l e  f i n a l  s t a t e s .  The s t e e p e r  s l o p e  f o r  t h e  2p-lh 
f i n a l  s t a t e s  s u g g e s t s  a  m u l t i s t e p  mechanism involv ing  
c o r e  e x c i t a t i o n  by t h e  outgoing pion.  On t h e  o t h e r  hand, 
t h e  s l o p e  of t h e  e x c i t a t i o n  f u n c t i o n  f o r  t h e  9.50 M e V  
s t a t e ,  which i s  supposed t o  b e  a  ( I d  -1 512 @ '312 '~112) 
0 3.68 MeV (3/2') s t r e t c h e d  c o n f i g u r a t i o n ,  appears  t o  b e  s i m i l a r  t o  t h a t  
3.85 MeV (5/2+) 
6.86 MeV (5/2+) f o r  t h e  3.85 MeV s i n g l e - p a r t i c l e  s t a t e .  The enhancement 
0 9.50 MeV (9/2+) of t r a n s i t i o n s  t o  t h e  9.50 MeV s t a t e  is probably due 
t o  i t s  h igh  s p i n ,  which is  favored  because of t h e  l a r g e  
t + 1 angular  momentum mismatch i n  t h e  (p ,n  ) r e a c t i o n .  
F i  ure 3 Excitation Function for t o t a l  cross sections 
M 2 C l p ,  n  ) l 3 ~ *  reactions. 
POSITIVE-PION PRODUCTION BY 149-166 MeV PROTONS ON 160 AND 2 8 ~ i  
T.P. S joreen ,  P.H. P i l e ,  R.D. Bent, M.C.  Green, R.E. Po l lock ,  and F. Soga 
Indiana University Cyc2otro.r~ Faci l i ty ,  Bloomington, Indiana 47405 
Extens ive  d a t a  on t h e  energy dependence of t h e  p ion  and pro toq  o p t i c a l  p o t e n t i a l s  i n  DWBA c a l c u l a -  
(P,n+) r e a c t i o n  e x i s t s  on ly  f o r  t r a n s i t i o n s  l e a d i n g  t i o n s .  
t o  t h e  IB and 4 1 ~ a  ground s t a t e s , '  which involve  Motivated by t h e  above c o n s i d e r a t i o n s ,  a d d i t i o n a l  
t h e  1pjI2 and n e u t r o n  o r b i t a l s ,  r e s p e c t i v e l y .  energy dependence s t u d i e s  of t h e  (p,n+) r e a c t i o n  n e a r  
S i m i l a r  d a t a  f o r  o t h e r  c a s e s  i n v o l v i n g  d i f f e r e n t  t h r e s h o l d  have been c a r r i e d  o u t  w i t h  160 and 2 8 ~ i  
o r b i t a l s  would be  u s e f u l  i n  de te rmin ing  whether t h e  t a r g e t s .  Angular d i s t r i b u t i o n s  have been ob ta ined  
main f e a t u r e s  of t h e  (p  ,T+) a n g u l a r  d i s t r i b u t i o n s  f o r  t r a n s i t i o n s  t o  t h e  170 ground s t a t e  (5/2+) a t  
a r e  due t o  n u c l e a r  s t r u c t u r e  o r  t h e  r e a c t i o n  mecha- 154,  157 and 165 MeV bombarding energy and t h e  0.87 
nism. It would a l s o  be u s e f u l  t o  s t u d y  the energy MeV (1/2+) s t a t e  a t  157 MeV; t h e s e  two s t a t e s  a r e  
dependence of t r a n s i t i o n s  t o  s e v e r a l  d i f f e r e n t  f i n a l  known t o  be  good s i n g l e  p a r t i c l e  s t a t e s  i n v o l v i n g  
s t a t e s  o f  t h e  same nuc leus ,  s i n c e  t h e  p ion  and pro- t h e  ldgI2  and 2slI2 neu t ron  o r b i t a l s ,  r e s p e c t i v e l y .  
t o n  d i s t o r t i o n s  would be  about  t h e  same i n  t h i s  c a s e ,  For t h e  2 8 ~ i ( p , . r r + ) 2 9 ~ i  r e a c t i o n ,  149 and 160 MeV 
and such measurements would s t r o n g l y  c o n s t r a i n  t h e  pro tons  were used t o  o b t a i n  angula r  d i s t r i b u t i o n s  
for the 0.0, 1.27, 2.03 and 3.62 MeV states, for 
which J" = 1/2+, 3/2+, 5/2+ and 712-, respectively. 
These states are generally more complicated in struc- 
ture and typically have small single particle strengths, 
except for the 1.27 MeV state, which has a large 
ldjI2 single particle component. The 0.0, 2.03 and 
3.62 MeV states have some single particle strengths 
involving the 2s ldgI2 and orbitals, 
respectively. The measurements at 149, 154 and 157 MeV 
were made with the DE spectrometer,2 which was designed 
(MeV) (MeV) 
o Uppsala Xl.3 185 3 6  
0 IUCF 165 19 
V IUCF 157 10 
A IUCF 154 7.4 
Figure I .  m e  60 (p, IT') 70 (0.0 MeV 5/2+) di f f eren t ia l  
cross sections a t  four energies plotted as a function 
of momentum transfer .  The Uppsala resu l t s  i n  t h i s  
figure and a l l  the succeeding figures are taken from 
Ref. 4 .  The curves are the resu l t s  o f  DWBA caZcuZa- 
t ions  using the model of Ref. 5 .  
lob 
TP (MeV) 
3 185 
- 
- 
cm. - 
Tn 
(MeV) 
35 -- 
L 
- 0 IUCF 157 9 
I 1 I t I 1 I I I ,  
Fi-qure 2. The 160(p,~f)170(0.87 MeV 1/2+) di f f eren t ia l  
cross sections a t  tuo energies. 
to measure pions over an energy range of 5-13 MeV. For 
the 160-165 MeV measurements, the QDDM spectrometer was 
employed. 3 
The results of the 160(p,~+) 170 and 28~i(p,~+)29~i 
measurements are shown in Figs. 1-6, where the differ- 
ential cross sections are plotted as a function of the 
center-of-mass momentum transfer q in units of MeV/c 
(typical range of pion angles is 20' 2 8iab 2 150'). 
The error bars are statistical only; errors in the 
absolute cross sections are estimated to be 2 15%. 
Also included at the top of each figure are the Uppsnla 4 
differential cross sections obtained at a bombarding 
energy of 185 MeV. The 160 and 2 8 ~ i  Uppsala cross 
sections have been multiplied by factors of 1.3 and 
1.6, respectively, for normalization to the IUCF re- 
sults. The combined IUCF-Uppsala measurements cover 
a range of pion energies from 7 to 36 MeV in 170 and 
7-45 MeV in 29~i. 
Figs .  1-6 and 4 1 ~ a  r e  a s  fol lows:  
(MeV) (MeV) 
o Uppsala x1.6 185 45 
0 IUCF 160 21 
V IUCF 149 1 1  
Figure 3. The 8 ~ i  (p, IT+) 2 9 ~ i  (0.0 MeV 1/2+ ) di f feren-  
t i a l  cross sections a t  three energies. The curves i n  
t h i s  figure and figures 4, 5 and 6 are the resu l t s  o f  
DWBA calculations using the model of Ref. 5. For t h i s  
figure, the curves have been multiplied by a factor of 
0.33. 
The most prominent energy dependent f e a t u r e  of 
t he  170 and 2 9 ~ i  angular  d i s t r i b u t i o n s  is  t h e  s h i f t  
of t h e  minimum t o  l a r g e r  va lues  of momentum t r a n s f e r  
wi th  i nc r ea s ing  p ion  momentum pn. This  f e a t u r e  was 
a l s o  observed f o r  t h e  (p ,IT+) t r a n s i t i o n  t o  t h e  4 1 ~ a  
ground s t a t e  ,' where i t  was observed t h a t  t h e  momentum 
t r a n s f e r  a t t h e m i n i m u m q  v a r i e d l i n e a r l y w i t h  
min 
p according t o  dq /dpT = 0.82 + 0.09. Assuming a 
min 
l i n e a r  dependence f o r  t h e  f i n a l  s t a t e s  i n  170 and 2 9 ~ i ,  
l e a s t  squares  f i t s  t o  t h e  d a t a  y i e l d  va lues  which a r e  
c o n s i s t e n t  w i th  t h e  l ~ a  r e s u l t s .  
Severa l  o t h e r  f e a t u r e s  of t he  combined d a t a  i n  
1 )  For f i n a l  s t a t e s  involv ing  t h e  same neut ron  
o r b i t a l  i n  d i f f e r e n t  n u c l e i ,  qmin is  l a r g e s t  f o r  t h e  
nuc leus  of  s m a l l e s t  mass. 
2)  qmin depends e x p l i c i t l y  on t h e  f i n a l  s t a t e  
produced i n  t h e  r e s i d u a l  nuc leus .  
3) The shapes of angular  d i s t r i b u t i o n s  f o r  t ran-  
s i t i o n s  t o  s t a t e s  which have t h e  same s p i n  and p a r i t y  
a r e  s i m i l a r .  
4) The 2 8 ~ i ( p , m + )  c ro s s  s e c t i o n s  a r e  sma l l e r  than 
those  f o r  160 and 4 0 ~ a .  This  i s  n o t  s u r p r i s i n g  i f  
t he  s t r i p p i n g  mechanism is impor tan t ,  because t h e  
s i n g l e  p a r t i c l e  s t r e n g t h s  i n  t h e  170 and 4 1 ~ a  f i n a l  
s t a t e s  a r e  much l a r g e r  than  those  i n  2 9 ~ i .  An excep- 
t i o n  is t h e  1.27 MeV s t a t e  i n  2 9 ~ i ,  which has  a  l a r g e  
28 
'*F Si (p,n+)29~i (1.27 MeV 3 1 2 ~ )  . 4 
0 Uppsabxl.6 185 4 4  1 
0 IUCF 160 20 
- 
- 
(MeV) (MeV) - 
Figure 4 .  The 2 8 ~ i  (p, n + ) 2 9 ~ i  (1.27 MeV 3/2+) differen- 
t i a l  cross sections a t  three energies. The Tp=185 MeV 
curve has been multiplied by a factor of 0.7. 
l d 3 / 2  s i n g l e  p a r t i c l e  component, b u t  does n o t  appear  
, . V . I . l '  
2 8 ~ i  (p,7 +) 29~i(3. 62 MeV 7/2 -)  
t o  have an  enhanced c r o s s  s e c t i o n .  
Also inc luded  i n  F igs .  1-6 a r e  DWBA ( p i o n i c  
s t r i p p i n g )   calculation^.^ I n  t h e  DWBA model, t h e  
p ro ton  i s  assumed t o  emit  a p ion  and t h e  r e s u l t i n g  
neu t ron  is cap tured  d i r e c t l y  i n t o  a n  a v a i l a b l e  s i n g l e  
nucleon s t a t e .  The c a l c u l a t i o n s  i n c l u d e  bo th  pro ton  
and pion d i s t o r t i o n s ,  a  Laplac ian- l ike  p ion  nucleus 
p o t e n t i a l  w i t h  o f f - s h e l l  damping, and a  neu t ron  bound 
s t a t e  c a l c u l a t e d  from a Woods-Saxon p o t e n t i a l .  I n  
a l l  t h e  c a l c u l a t i o n s ,  a  s p e c t r o s c o p i c  f a c t o r  of 1 .0  
was used. This  should be  a  reasonable  assumption f o r  
t h e  170 ground and 0.87 MeV s t a t e s ,  a s  w e l l  a s  t h e  
2 9 ~ i  1.27 MeV s t a t e .  However, t r a n s f e r  r e a c t i o n  
T:, 
(MeV) (MeV) 
185 4 2  
160 18 
149 7.2 
0 Uppsola 
IUCF 
v IUCF 
Figure 6. The 8 ~ i  ( p ,  n+) 2 9 ~ i  (3.62 MeV 7/2') dif feren- 
t i a l  cross sections a t  three energies. The c w v e s  i n  
t h i s  figure have been muZtipZied by a factor of 0.33. 
measurements sugges t  t h e  0.0,  2.93 and 3.62 MeV s t a t e s  
i n  2 9 ~ i  have s m a l l  s p e c t r o s c o p i c  f a c t o r s ;  us ing  t h e s e  
s p e c t r o s c o p i c  f a c t o r s  would g i v e  c a l c u l a t e d  t o t a l  
c r o s s  s e c t i o n s  f o r  t h e s e  s t a t e s  t h a t  d i f f e r  from 
experiment approximately by f a c t o r s  of 3.0, 0.2 and 
2.0, r e s p e c t i v e l y .  The c a l c u l a t i o n s  a r e  very  s e n s i -  
t i v e  t o  t h e  p ion  d i s t o r t i o n s  and t h e  parameters  of 
t h e  neu t ron  p o t e n t i a l .  5 
o Uppsala x 1.3 185 4 3  
IUCF 160 19 
9 v IUCF 149 8 . 8  
1 )  P.H. P i l e ,  R.D. Bent, R.E. Po l lock ,  P.T. Debevec, 
R.E. Marrs, M . C .  Green, T.P. S joreen ,  and F. Soga, 
Phys. Rev. L e t t .  42, 1461 (1979). 
2) P.H. P i l e  and R.E. Po l lock ,  Nucl. Instrum. Methods 
165, 209 (1979). 
-
Figure 5 .  l'he 2 8 ~ i ( p , n + ) 2 9 ~ i ( 2 . 0 3  MeV 5/2+) dif feren- 
t i a l  cross sections a t  three energies. 3)  R.D.  Bent, P.T. Debevec, P.H. P i l e ,  R.E. Po l lock ,  
R.E. Marrs, and M.C. Green, Phys. Rev. Lett. 40, 5) M.C. Tsangarides, thesis, Indiana University, 1979. 
495 (1978). IUCF Internal Report #79-4; M.C. Tsangarides, J.G. 
Wills, and R.D. Bent, Second International Conf. on 
4) S. Dahlgren, P. Grafstrgm, B. Hzistad, and i. Asberg, Meson-Nuclear Physics, Houston (1979), AIP Conf. 
Nucl. Phys. A227, 245 (1974). Proc. No. 54, ed. E.V. Hungerford 111, p. 192. 
W.W. Jacobs, P.H. Pile, P.P. Singh, T.P. Sjoreen, and S.E. Vigdor 
Indiana University Cyc Zotron Faci Zity, BZoom<ngton, Indiana 4 7405 
A.G.  Drentje 
Kermfysisch VersneZZer Inst i tuut ,  Groningen, The Netherlands 
With a view to compare and contrast the (d,p) 
stripping reaction with the (p,n+) reaction, angular 
+ distribution measurements of 2 8 ~ i  (p, .rr ) 2 9 ~ i  cross 
sections (E el91 MeV) to several low-lying excited 
P 
states in 29Si were made. In addition, existing (d,p) 
angular distribution measurements at Ed=76 MeV were 
extended to larger angles in order to overlap the 
momentum transfer (up to q~600 ~eV/c) inherent to the 
+ (p,n ) reaction. Of particular interest is a compar- 
+ ison of the (d,p) and (p,n ) results for the relative 
population of states of the same J', but different 
single-particle spectroscopic strengths, in 29~i: two 
+ + 312 states (Ex=1.27 and 2.43 MeV) and two 512 states 
(E =2.03 and 3.07 MeV). Such a comparison should be 
X 
sensitive primarily to differences in residual-state 
wave function components sampled by the two reactions. 
Other differences between the two reactions, e.g., in 
angular momentum coupling and matching, and in distor- 
tions of the incident and outgoing waves, should 
effectively cancel in the population ratios. 
Spectra for the two reactions are shown, for nom- 
inal momentum transfer q~550 M~V/C, in Fig. 1. The low- 
+ yield (p,n ) and large-angle (d,p) data were obtained 
with a detectionlidentification system in the QDDM 
spectrograph focal plane similar to that used pre- 
viously at IUCF for other charged pion production 
1 
measurements . The (d,p) data (5°20L5900) were ob- 
tained with a natural Si target ~6 mg/cm2 thtck. At 
+ 
angles larger than 65O, the 3.07 MeV 312 state was 
contaminated by a contribution from the 5.28 MeV 
3- state of 3 0 ~ i  (seen in Fig. la as a high-Ex shoulder). 
The 3.62 MeV 712- state angular distribution, scaled to 
t t 1 '  t 
7/2- 5/2+ 1 1 1 rl'[ 2 8 ~ i ~ p r + 1 2 g s i  
US. 00 Ep=191 MeV 
5.0 4.0 3.0 2.0 1.0 0.0 
EXCITATION ENERGY (MeV) 
+ F?:gure 1. Comparison of fd,p) and ( p ,  n ) spectra from 
S i  a t  a mminaZ mom$ntwn trar$sfer q%550 MeV/c. The 
Zocation of the 3/2 and 5/2 s tates  of in teres t  i n  
2 9 ~ i  are indicated by the arrows. 


Positive-Pion Production by 149-166 MeV Protons on 16-O and 28-Si

https://scholarworks.iu.edu/dspace/bitstream/2022/2879/1/iucf_1979_70-74.pdf

Positive-Pion Production by 149-166 MeV Protons on 16-O and 28-Si

Abstract

Similar works

Full text

Available Versions

IUScholarWorks