Effective interactions and nuclear structure using 180 MeV protons. II.Si28(p,p’)

Differential cross sections and analyzing powers for the scattering of 180 MeV protons have been measured for 14 states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ for momentum transfers between about 0.4 and 2.1 ${\mathrm{fm}}^{\mathrm{-}1}$. Medium modifications to the effective interaction for normal-parity isoscalar transitions were studied using transition densities fitted to electroexcitation data to minimize uncertainties due to nuclear structure. An empirical effective interaction, guided by nuclear matter theory, was fitted to inelastic scattering data for five states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ using self-consistent distorted waves. A good fit to the inelastic scattering data was achieved with an interaction similar to previous results for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The elastic data, which were not fitted, are also described well. In addition, we tested for mass dependence in the empirical effective interaction by repeating the analysis using data for both ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ simultaneously. This global analysis produced an interaction intermediate between the two independent results without compromising the fit to either data set. Therefore, the effective interaction in finite nuclei appears to depend strongly upon local density but only weakly upon target.