Quadrupole Crystalline Electric Field Shielding and Antishielding Factors at Some Rare-Earth and Heavy Ions

We report the results of calculations of Sternheimer crystalline electric field shielding and antishielding factors for ${\mathrm{Pr}}^{3+}$, ${\mathrm{Tm}}^{3+}$, ${\mathrm{W}}^{+}$, and ${\mathrm{Au}}^{+}$ ions at all the core electronic sites, in addition to the unfilled valence electron site and the nuclear site of each ion. The calculations take into account the effect of polarization of all the closed shells within the ions, including the exchange interaction terms. Mann's relativistically corrected Hartree-Fock (HF) wave functions were used in the computations. Our calculations thus extend and improve upon the previous calculations by Sternheimer and others who did the computations for rare-earth ions at the location of the $4f$ electron and at the nuclear site only. Our values of shielding and antishielding factors $\lambda \mathrm{s}$ at the location of the $4f$ electron and at the nuclear site for ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Tm}}^{3+}$ ions agree well with previous calculations and measurements. The possibility of experimentally determining the quadrupole splittings of the atomic-core level by the recently developed technique of electron spectroscopy for chemical analysis (ESCA), which underlines the great significance of these calculations, is discussed.