Variational Approach to the Quadrupole Polarizability of Ions

Abstract

A variation method has been developed for treating the problem of polarization of electron shells of ions by external charges. The induced quadrupole moment has been calculated for a number of He-like ions and the two Ne-like ions ${\mathrm{Al}}^{+++}$ and ${\mathrm{Na}}^{+}$. For the former a shielding effect occurs, while for the latter a net antishielding effect is obtained in agreement with Sternheimer's conclusions. It is possible to compare the results of Sternheimer's numerical solution of the first-order Schr\"odinger equation with the variation method used here in the case of ${\mathrm{Na}}^{+}$. Agreement is reasonably good.