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

Abstract

The influence of electron-electron interaction effects on nuclear quadrupole antishielding factors ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ is studied for the negative halide ions ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, and ${\mathrm{Br}}^{\ensuremath{-}}$. 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 ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{0}$, we have computed the consistency contributions ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}$ to be +2.28, -1.50, and -7.16 in ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, and ${\mathrm{Br}}^{\ensuremath{-}}$, respectively. The resulting values of ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ correct to first order in electron-electron interaction are then -19.29, -56.58, and -140.83. The appearance of negative signs for ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}$ in ${\mathrm{Cl}}^{\ensuremath{-}}$ and ${\mathrm{Br}}^{\ensuremath{-}}$ is seen to be due to large negative interactions between $p$ electrons belonging to different shells. This intershell effect is not present in ${\mathrm{F}}^{\ensuremath{-}}$ ($1{s}^{2}2{s}^{2}2{p}^{6}$). The contributions to ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}$ for all three ions are analyzed in detail, and a comparison is made of ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}$ for ${\mathrm{F}}^{\ensuremath{-}}$ and the isoelectronic positive ion ${\mathrm{Na}}^{+}$. An explanation is proposed for the comparable values of the ratio $\frac{{({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}}{{({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{0}}$ found for these two ions, even though the ${\mathrm{F}}^{\ensuremath{-}}$ ion is substantially more deformable with a larger value of ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{0}$. From the results of the present investigations, as well as earlier ones in related positive ions, it is felt that the consistency contribution ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{1}$ should, in general, be less than 15% of ${({\ensuremath{\gamma}}_{\ensuremath{\infty}})}_{0}$ for most ions.