Effect of self-consistency and crystalline potential in the solid state on nuclear quadrupole Sternheimer antishielding factors in closed-shell ions

The Sternheimer quadrupole antishielding factor ${\gamma }_{\infty }$ including self-consistency effects have been studied for several closed-shell ions isoelectronic with He, Ne, A, Kr, Xi, ${\mathrm{Cu}}^{+}$, and ${\mathrm{Ag}}^{+}$ in both free state as well as in ionic solid-state systems. Solid-state effects have been included using the Watson sphere model for ionic solids. The self-consistency contributions ${\gamma }_{\infty }^{\mathrm{}\left(1\right)\mathrm{}}$ are found to be in general less than 30% of the zero-order antishielding factor ${\gamma }_{\infty }^{\mathrm{}\left(0\right)\mathrm{}}$. The net free ionic ${\gamma }_{\infty }(={\gamma }_{\infty }^{\mathrm{}\left(0\right)\mathrm{}}+{\gamma }_{\infty }^{\mathrm{}\left(1\right)\mathrm{}})$ results agree very well with the results of corresponding coupled Hartree-Fock and polarized orbital calculations wherever available. For negative ions, ${\gamma }_{\infty }^{\mathrm{}\left(0\right)\mathrm{}}$ decreases significantly in going from the free ion to the solid state. For positive ions the opposite holds good. The solid-state effect on ${\gamma }_{\infty }^{\mathrm{}\left(0\right)\mathrm{}}$ is usually more important than the consistency effects ${\gamma }_{\infty }^{\mathrm{}\left(1\right)\mathrm{}}$ for the negative ions. For positive ions, the two effects are comparable except in some cases where the consistency effects are larger in magnitude. These trends in the relative importance of ${\gamma }_{\infty }^{\mathrm{}\left(1\right)\mathrm{}}$ as compared to solid-state effects are discussed in terms of the relative changes in the respective radial charge-density distributions in going from free ions to solid state. The possible influence of many-body correlations effects on ${\gamma }_{\infty }$ is considered. Finally, the utility of the ${\gamma }_{\infty }$ obtained in the present work for the net field gradients in ionic crystals, for which overlap and covalency effects between immediate neighbors have also to be considered, is discussed.