Core-Polarization Effects in Single-Nucleon-Transfer Reactions

An attempt has been made to understand the effects of the core polarization, when a particle (proton, in the present case) is added to an inequivalent orbit of a core having a closed neutron shell. These effects show up in the spectrum of the residual nucleus in the form of the fragmentation of the strength of the lower isobaric-spin single-particle state, as has been confirmed by the measurements of Armstrong et al. and Erskine et al. via (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reactions. Particular cases involving the addition of an inequivalent proton to ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{36}{}_{}{}^{}\mathrm{S}$ have been discussed. The inequivalent two-body interaction is determined, using the constraints given by the linear energy-weighted partial sum rules, and the hole-particle and particle-particle spectra of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$ and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$, respectively. Following the technique given in this article, the calculations can be extended to other cases of interest.