Quadrupole Antishielding Factors of Ions

Abstract

Values of the quadrupole antishielding factor ${\gamma }_{\infty }$ have been obtained for the following ions: ${\mathrm{Y}}^{3+}$, ${\mathrm{In}}^{3+}$, ${\mathrm{Bi}}^{3+}$, and ${\mathrm{Am}}^{2+}$, using the method of direct solution of the inhomogeneous Schrödinger equation for the perturbed wave functions. The wave functions ${v_1}^{\prime } (nd\to s)$ and the resulting terms ${\gamma }_{\infty }(nd\to s)$ have been calculated for the case of ${\mathrm{Cu}}^{+}3d\to s$, ${\mathrm{Ag}}^{+}4d\to s$, and ${\mathrm{Bi}}^{3+}5d\to s$. We have also obtained the hexadecapole antishielding factor ${\eta }_{\infty }$ for the ${\mathrm{In}}^{3+}$ ion. Values of the lattice sums for $\frac{{\partial }^{4}V}{\partial z^4}$ pertaining to the nuclear hexadecapole interaction ($V=\mathrm{crystal}\mathrm{potential}$) have been determined for the following types of cubic lattice: simple cubic, NaCl structure, body-centered cubic, and face-centered cubic.