Core polarization in inelastic scattering and effective charges

A perturbation theory treatment is made of core-polarization effects in electromagnetic and inelastic scattering transitions due to high-lying collective excitations. Formulas are presented which make the connection between core-polarization parameters in inelastic scattering and effective charges from electromagnetic transitions. These relationships show that there is a natural disparity in neutron and proton polarizations, which arises from the departure (due to the neutron excess) of these high-lying collective excitations from pure isoscalar or isovector character. The resulting isospin-polarization matrix is calculated both from a schematic model and by making a connection with Bohr-Mottelson parametrization of isoscalar and isovector effective charges. The effects of spreading of the isoscalar giant resonance are taken into account in an approximate way which results in a formulation with one parameter free to be determined from empirical electromagnetic effective charges. Numerical results which show the effects of core polarization in electromagnetic transitions, ($\alpha , {\alpha }^{\prime }$), ($p, p^{\prime }$), and ($n, n^{\prime }$) are presented for ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$.