Theory of electron-electron interaction effects on antishielding factors of negative ions

The influence of electron-electron interaction effects on nuclear quadrupole antishielding factors ${\gamma }_{\infty }$ is studied for the negative halide ions ${\mathrm{F}}^{-}$, ${\mathrm{Cl}}^{-}$, and ${\mathrm{Br}}^{-}$. Using a procedure developed earlier which utilizes the nuclear-quadrupole-moment-perturbed and external-point-charge-perturbed wave functions for the ions, obtained by the differential equation procedure for the zero-order antishielding factor ${\left({\gamma }_{\infty }\right)}_0$, we have computed the consistency contributions ${\left({\gamma }_{\infty }\right)}_1$ to be +2.28, -1.50, and -7.16 in ${\mathrm{F}}^{-}$, ${\mathrm{Cl}}^{-}$, and ${\mathrm{Br}}^{-}$, respectively. The resulting values of ${\gamma }_{\infty }$ correct to first order in electron-electron interaction are then -19.29, -56.58, and -140.83. The appearance of negative signs for ${\left({\gamma }_{\infty }\right)}_1$ in ${\mathrm{Cl}}^{-}$ and ${\mathrm{Br}}^{-}$ is seen to be due to large negative interactions between $p$ electrons belonging to different shells. This intershell effect is not present in ${\mathrm{F}}^{-}$ ($1s^{2}2s^{2}2p^6$). The contributions to ${\left({\gamma }_{\infty }\right)}_1$ for all three ions are analyzed in detail, and a comparison is made of ${\left({\gamma }_{\infty }\right)}_1$ for ${\mathrm{F}}^{-}$ and the isoelectronic positive ion ${\mathrm{Na}}^{+}$. An explanation is proposed for the comparable values of the ratio $\frac{{\left({\gamma }_{\infty }\right)}_1}{{\left({\gamma }_{\infty }\right)}_0}$ found for these two ions, even though the ${\mathrm{F}}^{-}$ ion is substantially more deformable with a larger value of ${\left({\gamma }_{\infty }\right)}_0$. From the results of the present investigations, as well as earlier ones in related positive ions, it is felt that the consistency contribution ${\left({\gamma }_{\infty }\right)}_1$ should, in general, be less than 15% of ${\left({\gamma }_{\infty }\right)}_0$ for most ions.