Accurate Analytical Self-Consistent-Field Wave Functions forNd3+

The need for an accurate description of the electronic structure of the important laseractive ion ${\mathrm{Nd}}^{3+}$ stimulated this work. We calculated self-consistent-field wave functions by the analytical-expansion method for the ground state of the laser-active ion ${\mathrm{Nd}}^{3+}\mathrm{}(Z=60\mathrm{})\mathrm{}$, $4f^3$, ${}_{}{}^4{}_{}{}^{}I$. The results represent the most accurate wave functions for ${\mathrm{Nd}}^{3+}$ published. All the exponents of the basis functions in the analytical expansion were exhaustively optimized. The virial theorem was satisfied to seven significant figures. Values of $〈{\mathcal{r}}^n〉$ for the $4f$ orbital are included.