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

Ahmad, M.

Alford, W.P.

Anderson, B.D.

Baldwin, A.R.

Celler, A.

Elaasar, M.

Foster, C.C.

Helmer, R.

Häusser, O.

Jackson, K.P.

Madey, R.

Miller, C.A.

Mostajabodda'vati, M.

Pourang, R.

Tamimi, N.

Watson, J.W.

Yen, S.

English

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CHARGE EXCHANGE REACTIONS 
THE ENERGY DEPENDENCE OF STRETCHED STATES 
EXCITED IN (p,n) REACTIONS 
R. Pourang, J.W. Watson, B.D. Anderson, A.R. Baldwin, M. Elaasar 
R. Madev, M. Mostajabodda'vati, and N. Tamimi 
Kent State University, Kent, Ohio 44242 
C.C. Foster 
Indiana University Cyclotron Fac ilit y, Bloomington, Indiana 4 74 05 
M. Ahmad, A. Celler, 0. Hausser, K.P. Jackson, C.A. Miller and S. Yen 
TRIUMF, Vancouver, British Columbia, Canada V6T 2AA9 
W.P. Alford and R. Helmer 
University of Western Ontario, London, Ontario, Canada 
We studied excitation of "stretchedn particle-hole states in (p ,n) reactions at 100, 200, 
300, and 400 MeV. This project utilized the beam-swinger (p,n) facility1 at the IUCF for 
measurements at 100 and 200 MeV and the new "Chargex" (p,n) facility2 at TRIUMF for 
measurements at 200, 300, and 400 MeV. 
In stretched state, the particle and the hole are both in "stretched" orbits (j, = 
lp + i ; j h  = lh + i) and their angular momenta are coupled to the maximum possible 
J = l, + eh + 1. Such states have quite large spins and are unique within 2 hw of exci- 
tation so that there is relatively little mixing with other particle-hole configurations. For 
isovector nucleon inelastic scattering processes such as the (p,n) reaction at large momen- 
tum transfers (1 to 2 fm-l) where high-spin stretched states are excited, the dominant 
term in the effective nucleon-nucleon interaction driving the reaction is the isovector-tensor 
term tT,. Because isovector stretched states have a single dominant lp-lh configuration 
and are excited primarily by a single term in the nucleon effective interaction, they should 
in principle provide a powerful tool for studying both the reaction mechanism and nuclear 
structure. 
For the present project, we have chosen to study the energy dependence of the exci- 
tation of the J" = 6- (T f7/2, vd~;~) state excited in the 2 8 ~ i ( p , n ) 2 8 ~  (4.95 MeV) reaction 
and the J" = 9f (rg912,vg&) state excited in the 88~r(p ,n)88~(1 .48 MeV) reaction. The 
former is a ''1 hw" excitation with the (proton) particle and the (neutron) hole in different 
orbits; analogs of this reaction were seen in (p,pf)3, (e,ef)4 and (T, a')' reactions, as well as 
in the (n,p) reaction. the latter reaction is a "0 hw" excitation with the particle and hole 
in the same orbit; because of the Pauli principle, the only inelastic scattering process that 
can excite such states is an isospin-lowering, charge-exchange, reaction on a nucleus with a 
neutron excess. Such 0 hw stretched states are seen quite commonly6s7 in medium-energy 
(p,n) reactions on medium-mass and heavy nuclei, but they have no analogs in (p,pf) and 
(e,el) reactions. As noted by Anderson, et al. in Ref. 7, 0 hw stretched states have normal- 
izations for Distorted Wave Impulse Approximation (DWIA) calculations that are always 
2 112, whereas 1 hw stretched states have DWIA normalizations that are always 5 112; 
presumably, this result is a nuclear structure effect and we chose to study one transition 
of each type to investigate this point. In Fig. 1 we present differential cross sections as 
a function of momentum transfer for the 28 Si(p,n) 2 8 ~  (6- , 4.95 MeV) reaction. the data 
at 133 MeV are from Fazely, et a1.8 In comparing the cross section for this reaction with 
the analog 28~i(p,pf)  28Si(6-,16.4 MeV) reaction, charge symmetry requires that a(p,n) 
= 2 a(p,pf); indeed, the (p,n) data at 100 and 133 MeV agree with (p,pf) data in Ref. 
3. Our data (from TRIUMF) was normalized so that our 300 MeV cross sections agree 
with (p,pf) data (multiplied by 2) at 333 MeV in Ref. 9. In fig. 2 we present data for the 
88Sr(p,n)88Y(9+, 1.48 MeV) state. At TRIUMF, a single point at the two sets of mea- 
surements together, and to establish the overall reliability and consistency of the complete 
set of data. 
28Si(p,n)28P ( 6 ,  4.95 MeV) 
100 MeV 133 MeV 200 MeV 300 MeV 400 MeV 
lo0 
MOMENTUM TRANSFER q( fm-' ) 
Firrure 1. Momentum-transfer dependence of the cross sections for excitation of the 6- 
state at 4.95 MeV in the 28~i(p,n)28P reaction at 100, 133, 200, 300, and 400 MeV. The 
solid curves are D WIA calculations with the effective interaction of Franey and ~ o v e l  l,
and harmonic oscillator bound-state wave functions with a parameter b = 1.743 fm. Cal- 
culations for the individual tensor (- - -), spin-orbit (- - m -) and central (- m - m -) parts of 
the effective interaction are shown also. D WIA normalizations ( "N") are shown for each 
energy. 
In Figs. 1 and 2 also we present DWIA calculations performed with the code ~ ~ 8 1 ' ~  
with the nucleon-nucleon t-matrix of Franey and Love1 l. Optical potentials for 2 8 ~ i  were 
taken from Refs. 3 and 12. Optical potentials for 88Sr were calculated from the global 
parameters of Schwandt, et al.13 for the calculations at 100, 135, and 200 MeV. For 300 
MeV, the 319 MeV 'OZr potentials of ~ a n d a l *  were used. To obtain 400 MeV optical 
potential parameters for "sr, we made a volume integral/nucleon (J/A) extrapolation of 
the energy dependence of the 100, 135, 200, and 319 MeV potentials. We assumed the 
simple shell model for the initial and the final states for both reactions, with harmonic- 
oscillator wave functions with oscillator length parameters of 1.3743 fm and 2.0 fm for 
2 8 ~ i  and 8 8 ~ r ,  respectively. For each calculation the cross sections for the individual 
tensor (- - -), spin-orbit (- - -) and central (- - -) components for the Franey-Love 
t-matrix are shown; we note that the excitation of these stretched states is dominated 
indeed by the isovector-tensor term at all five energies. 
We normalized the DWIA calculations for each transition at each energy to provide 
an optimum fit near the peak of the momentum-transfer distribution. The indicated 
8 8 ~ r ( p , n ) 8 y  (9+, 1.48 MeV) 
100 MeV 135 MeV 200 MeV 300 MeV 400 MeV 
loo 
10" 
0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 3  
MOMENTUM TRANSFER q( fm-' ) 
Figure 2. Momentum-transfer dependence of the cross sections for excitation of the 9+ 
state at 1.48 MeV in the 88Sr(p,n)88Y reaction at 100, 135, 200, 300, and 400 MeV. The 
solid curves are D WIA calculations with the effective interaction of Franey and ~ o v e , l  
and harmonic oscillator bound-state wave functions with a parameter b = 1.743 fm. Cal- 
culations for the individual tensor (- - -) , spin-orbit (- m - m -) and central (- - - -) parts of 
the effective interaction are shown also. D WIA normalizations ("N") are shown for each 
energy. 
normalizations include an ((A-1) /A) J-l  center-of-mass correction factor. We draw two 
important conclusions from these results. Firstly, the ratio of the 88Sr to 2 8 ~ i  DWIA 
normalizations is independent of energy, indicating that the systematic difference in DWIA 
normalizations between 0 fiw and 1 fiw stretched states is indeed a nuclear structure effect. 
Secondly, and equally important, with the Franey-Love t-matrix the normalization for each 
reaction is constant to within a few percent. Olmer, et al. noted in Ref. 3 that over the 
energy range from 80 to 180 MeV the DWIA normalization for the 28Si(p,p')28Si (6-, 16.4 
MeV) reaction (to the analog of the state we observe in 28P) varies with any of several 
different nucleon-nucleon t-matrices they tried. In contrast, with the Franey-Love t-matrix 
(developed since the publication of Ref. 3), we obtain a consistent and coherent picture of 
the excitation of stretched states over a broader energy range. Perhaps as important may 
be the fact that the energy-independent D WIA normalization obtained for the 28 ~ i ( ~ , n )  28 P 
(6-) reaction (- 0.31 k 0.01) now agrees with the value obtained for the excitation of the 
analog 6- state at 16.4 MeV in 2 8 ~ i  by inelastic electron scattering4. 
1. C.D. Goodman, C.C. Foster, M.B. Greenfield, C.A. Goulding, D.A. Lind, and Rapa- 
port, IEEE Trans. Sci. NS-26, 2248 (1979). 
2. W.P. Alford, R.L. Helmer, R. Abegg, A. Celler, 0. Hausser, K. Hicks, K.P. Jackson, 
C.A. Miller, S. Yen, R.E. Azuma, D. Frekers, R.S. Henderson, H. Baer, and C.D. 
Zafiratos, Phys. Lett. B179, 20 (1986). 
3. C. Olmer, A.D. Bacher, G.T. Emery, W.P. Jones, D.W. Miller, H. Nann, P. Schwandt, 
S. Yen, T.E. Drake, and R.J. Sobie, Phys. Rev. Lett. 29, 361 (1984). 
4. R. Lindgren and F. Petrovich, in "Spin Excitations in Nuclei", ed. by F. Petrovich, et 
al. (Plenum, New York, 1984) p. 323 and references therein. 
5. C. Olmer, B. Zeidman, D.F. Gessaman, T.-S.H. Lee, R.E. Segel, L. W. Swenson, R.L. 
Boudrie, G.S. Blanpied, H.A. Thiessen, C.L. Morris, and R.E. Anderson, Phys. Rev. 
Lett. 43, 612 (1979). 
6. B.D. Anderson, C. Lebo, A.R. Baldwin, T. Chittrakarn, R. Madey, J.W. Watson, and 
C.C. Foster, Phys. Rev. Lett. 52, 1872 (1984). 
7. B.D. Anderson, J.W. Watson, and R. Madey, in "Nuclear Structure at High Spin 
Excitation, and Momentum Transfer," ed. by H. Nann, et al. (American Institute of 
Physics, New York, 1986) p. 155 and references therein. 
8. A. Fazely, R. Madey, B.D. Anderson, A.R. Baldwin, C .  Lebo, P.C. Tandy, J.W. Wat- 
son, W. Bertozzi, T. Buti, M. Finn, C. Hyde-Wright, J. Kelly, M.A. Kovash, B. 
Murdock, and B. Pugh, Nucl. Phys. A443, 29 (1985). 
9. N.M. Hintz, M.A. Franey, M.M. Gazzaly, D. Cook, G.S. Kyle, D. Dehahard, S.J. 
Seestrom-Morris, G.W. Hoffmann, M. Bartlett, G.S. Blanpied, J.A. McGill, J.B. Mc- 
Clelland, R.L. Boudrie, F. Irom, and G. Pauletta, Phys. Rev. C30, 1976 (1984). 
10. Computer code D W81, a version of D WBA7O modified by J.R. Comfort, unpublished; 
Computer code DWBA70, J. Raynal and R. Schaeffer, unpublished. 
11. M.A. Franey and W.G. Love, Phys. Rev. C31, 488 (1985). 
12. K. Lin, M. Sci. thesis (Simon Frazer University, 1986), unpublished. 
13. P. Schwandt, H.O. Meyer, W.W. Jacobs, A.D. Bacher, S.E. Vigdor, M.D. Kaitchuck, 
and T.R. Donoghue, Phys. Rev. 26, 55 (1982). 
14. S.K. Nanda, thesis (Rutgers State University of New Jersey, 1984), unpublished. 


The Energy Dependence of Stretched States Excited in (p,n) Reactions

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The Energy Dependence of Stretched States Excited in (p,n) Reactions

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