Binding energies forpelectrons in negative alkaline-earth elements

Multiconfiguration Hartree-Fock (MCHF) calculations recently predicted a positive binding energy for the p electron in the $s^2$ $p^2$P state of ${\mathrm{Ca}}^{\mathrm{-}}$, in good agreement with experiment. The present paper explores the binding of electrons in several alkaline-earth elements. Fixed-core Hartree-Fock potentials demonstrate the angular momentum barrier. From a simple correlation study it is shown that the 3$d^2$4p configuration relative to the 3$s^2$3p configuration in ${\mathrm{Mg}}^{\mathrm{-}}$ lies much higher than the (n-1)$d^2$np configurations relative to ${\mathrm{ns}}^2$np in the heavier alkaline-earth elements. Accurate MCHF correlation studies are reported for two and three electrons outside a core from which binding energies are predicted for ${\mathrm{Ca}}^{\mathrm{-}}$, ${\mathrm{Sr}}^{\mathrm{-}}$, and ${\mathrm{Ba}}^{\mathrm{-}}$. Not included is correlation with the core (core polarization) and correlation within the core. The same procedures were also applied to Sc. Theoretical results with relativistic shift corrections are compared with experiment in the case of ${\mathrm{Ca}}^{\mathrm{-}}$ and Sc.