Core polarization in inelastic scattering and effective charges

Abstract

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, ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$), ($p, {p}^{\ensuremath{'}}$), and ($n, {n}^{\ensuremath{'}}$) are presented for $^{118}\mathrm{Sn}$ and $^{207}\mathrm{Pb}$.NUCLEAR REACTIONS Inelastic scattering of $\ensuremath{\alpha}$, $p$, $n$ on $^{207}\mathrm{Pb}$, $^{118}\mathrm{Sn}$, core polarization effect calculated from electromagnetic effective charges as examples of method developed.