Accurate Numerical Hartree-Fock Self-Consistent-Field Wave Functions for Rare-Earth Ions

Abstract

Accurate numerical Hartree-Fock (HF) self-consistent-field (SCF) wave functions have been calculated for ${\mathrm{Pr}}^{+++}$, ${\mathrm{Ce}}^{++}$, ${\mathrm{Nd}}^{+++}$, ${\mathrm{Pr}}^{++}$, ${\mathrm{Pm}}^{+++}$, ${\mathrm{Nd}}^{++}$, ${\mathrm{Sm}}^{+++}$, ${\mathrm{Pm}}^{++}$, ${\mathrm{Eu}}^{+++}$, ${\mathrm{Sm}}^{++}$, ${\mathrm{Gd}}^{+++}$, ${\mathrm{Eu}}^{++}$, ${\mathrm{Tb}}^{+++}$, ${\mathrm{Gd}}^{++}$, ${\mathrm{Dy}}^{+++}$, ${\mathrm{Tb}}^{++}$, ${\mathrm{Ho}}^{+++}$, ${\mathrm{Dy}}^{++}$, ${\mathrm{Er}}^{+++}$, ${\mathrm{Ho}}^{++}$, ${\mathrm{Tm}}^{+++}$, and ${\mathrm{Er}}^{++}$ rare-earth ions having an $f^N$ electron configuration in their ground-state manifolds. Calculations, in general, have an accuracy of seven significant digits in the total energy. Values of several Hartree-Fock parameters have also been obtained from these wave functions.