Core polarization in inelastic scattering

Inelastic scattering is a source of much useful information about core polarization effects in nuclei near closed shells. Although there have been many theoretical treatments of core polarization effects reported in the literature, the results of these calculations have rarely been applied to the interpretation of inelastic scattering data. In the present paper we review the microscopic models for the treatment of inelastic proton and electron scattering and the microscopic models for the treatment of core polarization. Estimates are made of core excited admixtures in the wave functions for low-lying states in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. The resulting wave functions are used to calculate theoretical ($p,p^{\prime }$) cross sections and ($e,e^{\prime }$) form factors for comparison with available experimental data. "Realistic" $G$ matrix interactions are used as the starting point in both the structure and the ($p,p^{\prime }$) calculations. In the structure calculations the interaction is modified by means of a "bootstrap" prescription to account for important long-range core correlations and in the ($p,p^{\prime }$) calculations it is modified by the addition of an imaginary component. It is concluded that the overall features of the experimental data can be understood from these calculations.