Accurate Analytical Self-Consistent-Field Wave Functions forPr3+

Ab initio calculations by the analytical-expansion self-consistent-field method were carried out for the ground state of the laser-active ion ${\mathrm{Pr}}^{3+}$ ($Z=59\mathrm{}$), $4f{}_{}{}^{2,3}{}_{}{}^{}H$. The results represent the most accurate wave functions for ${\mathrm{Pr}}^{3+}$ available at this time. The knowledge of these wave functions is shifting the frontier of accurate analytical calculations into the group of rare earths. The numbers of basis functions in the analytical expansions were 10, 8, 5, and 6 for the symmetries $s$, $p$, $d$, and $f$, respectively. All the basis-function exponents were subjected to careful and exhaustive optimizations.