Antishielding and Polarizabilities in Alkali Halide Gases

Abstract

The ionic model that has been used in an attempt to explain $\frac{\mathrm{eQq}}{h}$ data in ionic gases and solids is examined, extended, and applied to alkali halide gases. It is shown that the antishielding factor, ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$, multiplies the unshielded value of $q$, ($\frac{{\ensuremath{\partial}}^{2}V}{\ensuremath{\partial}{Z}^{2}}$), produced not only by an external charge but by all the external moments, and some of these effects are important in alkali halide gases. In order to estimate the magnitude of the contributions to $q$ of such moments, polarizabilities are calculated that apply to alkali halide internuclear distances. These polarizabilities are often much smaller than those calculated for the free ion. Polarizabilities and ${\ensuremath{\gamma}}_{\ensuremath{\infty}}'\mathrm{s}$ are calculated using both Hartree and Hartree-Fock wave functions and are compared. The values obtained using the Hartree-Fock wave functions are consistently smaller. Some second order calculations of the polarizabilities and antishielding factors are calculated by a direct substitution method. The results indicate that for the alkali halide gas calculations perturbation theory is applicable to the alkali ions but not to the easily deformable halide ions for the situation considered here. This is probably the reason the ionic model has always yielded poor results for the halide ions. When the ionic model is extended, as described in this paper, and applied to the alkali ions, a set of antishielding factors is found for which there is agreement between theory and experiment or would be if Hartree-Fock wave functions were available to calculate ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$. From this model the nuclear quadrupole moment, $Q$, of ${\mathrm{Li}}^{7}$ is found to be -0.016\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$.