Nuclear hexadecapole antishielding factors: Tripositive lanthanide and tetrapositive actinide ions

The nuclear hexadecapole antishielding factor ${\eta }_{\infty }$ has been calculated using nonrelativistic Hartree-Fock-Slater wave functions and the Sternheimer uncoupled perturbation-numerical method for the tripositive lanthanide ions of ${\mathrm{Ce}}^{3+}$, ${\mathrm{Pr}}^{3+}$, ${\mathrm{Pm}}^{3+}$, ${\mathrm{Sm}}^{3+}$, ${\mathrm{Eu}}^{3+}$, ${\mathrm{Gd}}^{3+}$, ${\mathrm{Tb}}^{3+}$, ${\mathrm{Dy}}^{3+}$, ${\mathrm{Ho}}^{3+}$, ${\mathrm{Tm}}^{3+}$, ${\mathrm{Yb}}^{3+}$, and ${\mathrm{Lu}}^{3+}$, and the tetrapositive actinide ions of ${\mathrm{Th}}^{4+}$, ${\mathrm{Pa}}^{4+}$, ${\mathrm{U}}^{4+}$, ${\mathrm{Np}}^{4+}$, ${\mathrm{Pu}}^{4+}$, ${\mathrm{Am}}^{4+}$, ${\mathrm{Cm}}^{4+}$, ${\mathrm{Bk}}^{4+}$, ${\mathrm{Cf}}^{4+}$, ${\mathrm{Es}}^{4+}$, ${\mathrm{Md}}^{4+}$, ${\mathrm{No}}^{4+}$, and ${\mathrm{Lw}}^{4+}$. In all ions a more than 80% contribution to ${\eta }_{\infty }$ comes from $d\to d$ radial perturbation corresponding to the outermost $d$ orbital. The nonrelativistic $\left|{\eta }_{\infty }\right|$ values can be taken as 510±50 and 4000±1000 in the cases of tripositive lanthanide ions and tetrapositive actinide ions, respectively.