This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Bacher, A.D.

Bowyer, S.M.

Chang, S.

Lisantti, J.

Liu, J.

Olmer, C.

Stephenson, E.J.

Wells, S.P.

Wissink, S.W.

English

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TEST OF A DENSITY-DEPENDENT EFFECTIVE INTERACTION 
USING IN-PLANE 28 Si(p',j5')28 Si POLARIZATION TRANSFER MEASUREMENTS 
J. Liu, E.J. Stephenson, A.D. Bacher, S.M. Bowyer, 
S. Chang, C. Olmer, S.P. Wells, and S.W. Wissink 
I nd iana  Univers i ty  Cyc lo t ron  Facili ty,  Bloornington,  I nd iana  4 74 08 
J. Lisantti 
C e n t e n a r y  College of Louis iana,  Shreveport ,  Louis iana  7 1 1  04 
Medium modifications of the effective NN interaction for isoscalar , nat ural-parity tran- 
sitions have been studied by fitting the differential cross section and analyzing power data 
for 160(p',p'1)160 at 135 MeV and 180 MeV, and 28Si(p',p'1)28Si at 180 In this 
work, the transition densities were determined from electron scattering to minimize the 
uncertainties due to the nuclear structure, and the distorted waves were calculated using 
a self-consistent optical potential determined from the effective interaction. In order to 
parametrize the effective interaction inside the nucleus, a simple density-dependent form 
was chosen for the spin-independent isoscalar central and real spin-orbit components. The 
dependence of this form on momentum transfer was modelled to resemble Pauli-blocking 
corrections. The parameters were adjusted to produce the best possible agreement with 
the measured inelastic cross sections and analyzing powers. Even though it was not in- 
cluded in the data used for the fitting, the calculation of the elastic scattering cross section 
and analyzing power was consistent with the elastic scattering measurements as well. In 
addition, the effective interaction for 28Si was shown to be consistent with the 160 results. 
The empirical effective interaction for the isoscalar natural-parity transition was stud- 
ied without the benefit of any polarization transfer data. Thus, it is important to ask 
whether these results are sufficiently general that they may be used to predict other (p', p") 
observables. For isoscalar, natural-parity transitions, DWB A calculations suggest that the 
polarization transfer coefficients follow a pat tern similar to that for elastic scattering from 
a spin-0 target, namely that P = A, DNN1 = I, DLL1 = DSS1, DSL1 = -DLS1, and 
DiLl  + D$Ll + A2 = 1. For elastic scattering these relationships reduce the new informa- 
tion to one additional observable. While various authors often choose the spin rotation 
parameter Q, essentially any in-plane polarization transfer coefficient or combination of 
in-plane polarization transfer coefficients carries the same information. 
The primary objective of Experiment E353 was the measurement of a complete set 
of polarization transfer observables for the two 6- states in 28Si at 11.58 MeV (T=O) 
and 14.36 MeV (T=l). As a part of that experiment, we chose to check the accuracy 
of the effective interaction for isoscalar, natural-parity transitions by measuring a combi- 
nation (D,) of the in-plane polarization transfer observables at low excitation energy for 
laboratory angles of 19" and 23". This combination is defined by 
Excitation Energy (MeV) 
Figure 1. K600 focal plane spectrum for the low-excited states in 28Si(p',p")28Si. The 
states are labelled in a manner similar to that used in Ref. 2. 
where 
D, = DSSl cosa + DSL1 sina 
DX = DLSl cosa + DLL1 sina 
with 0 defined to be the reaction plane angle between the spin direction and the longitudinal 
direction and a defined to be the spin precession angle through the K600 spectrometer 
relative to the proton momentum. The spin precession angle ol depends on the proton 
energy and its path through the magnetic spectrometer. It is averaged over the paths 
allowed by the entrance collimator. For the states considered here, the 0 and a values 
were about 115" and 242". 
The beam line polarization values were monitored continuously with the BL3 and BL5 
p+d polarimeter. Particles were momentum analyzed by the K600 magnetic spectrometer 
with an energy resolution of about 50 keV for a 198.5 MeV proton beam. A spectrum for 
23" scattering is shown in Fig. 1. The labels of these natural parity isoscalar states are the 
same as in Ref. 2. The 2:, 4:, 0;) 2; and 5;  states were used in Kelly's determination 
of the interaction, while 2:) 24+, 2: and 1; states were not chosen for the analysis of the 
effective interaction because of the lack of electron inelastic data to determine the transition 
density. The 2: and 1; cross section data had large discrepancies with the calculated 
results from the fitted effective interaction, probably because of the uncertainties in the 
transition densities of these states. 
Figure 2 shows the calculated D, from Kelly's effective interaction for all of these 
transititions. The optical potential was calculated by folding the effective interaction 
with the three parameter Fermi density determined from elastic electron scattering. The 
Figure 2. The calculated D, value from Kelly's effective interaction, compared with 
data from E353. The experimental data are consistent with the empirical interaction 
calculations (solid) for all the natual-parity isoscalar transitions, but not with the von 
Geramb interaction (dashed). 
transition densities were the same as calcluated in Ref. 2 and used the assumption that 
proton and neutron densities were the same. The match of the calculation with the data 
shows the medium modification of the effective interaction for spin-independent isoscalar 
transitions to be very successful. The accuracy of the calculations for the 2: and 1; states 
does not reveal any serious problem with the spin-dependence of the transition densities 
used in the calculation. The dashed curves shown in Fig. 2 are the free (zero density) von 
Geramb interactioq3 and the difference with the solid curves demonstrates the size of the 
effects due to the nuclear medium. From this result, it is clear that the empirically derived 
interaction is capable of accurately predicting other polarization observables in isoscalar 
(p,p' ) reactions. 
1. J.J. Kelly, et al., Phys. Rev. C 41 (1990) 2504. 
2. Q. Chen, et al., Phys. Rev. C 41 (1990) 2514. 
3. H.V. von Geramb, in The Interaction between Medium Energy Nucleons in Nuclei - 
1982, ed. H.O. Meyer (AIP, New York, 1983), p. 44. 


Test of a Density-Dependent Effective Interaction Using In-Plane 28-Si(p,p')28-Si Polarization Transfer Measurements

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Test of a Density-Dependent Effective Interaction Using In-Plane 28-Si(p,p')28-Si Polarization Transfer Measurements

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