Position-dependent antishielding factors for the trivalent gallium ion

We report here the results of our calculation for the position-dependent antishielding factors, $\gamma \mathrm{}\left(r\right)\mathrm{}$ and $\beta \mathrm{}\left(r\right)\mathrm{}$, for the trivalent gallium ion. The dominant part of the contribution which results from the radial mode of excitation of the ion core is calculated in the nonorthogonal Hartree-Fock perturbation theory (NHFPT) of Dalgarno. The less important contribution from the angular mode is evaluated in the Thomas-Fermi (TF) model. The net results of $\gamma \mathrm{}\left(r\right)\mathrm{}$ and $\beta \mathrm{}\left(r\right)\mathrm{}$ show that not only these have the expected variation with respect to distance, but also they correctly reduce to the limiting values at $r=0\mathrm{}$ and $r=\infty$. It is hoped that the use of these antishielding factors in the calculation of electric field gradient in Ga metal will provide a better quantitative understanding of quadrupole interaction in this metal than obtained here-tofore.