Energies of metastable ${}^4{S}^o$ states in the alkaline-earth sequence

Theoretical binding energies have been obtained for the metastable ${\mathrm{np}}^3{}^4{S}^o$ states in the alkaline-earth sequence using a B-spline configuration-interaction approach. The results agree with available experimental and theoretical data within 5 meV for ${\mathrm{Be}}^{-}$ and within 10 meV for ${\mathrm{Mg}}^{-}.$ The binding energies of the $p^3{}^4{S}^o$ state in ${\mathrm{Mg}}^{-},$ ${\mathrm{Ca}}^{-},$ and ${\mathrm{Sr}}^{-}$ are larger than the one in ${\mathrm{Be}}^{-}$ by roughly 250 meV due to the stronger interactions with the $d^{2}p$ configurations. For ${\mathrm{Ca}}^{-},$ the ${}^4{S}^o$ binding energy is determined to be 555.5 meV, including a contribution of $-70$ meV due to dielectronic core polarization. For ${\mathrm{Sr}}^{-}$ the ${}^4{S}^o$ binding energy is 557.9 meV, including a decrease of only 6 meV due to dielectronic core polarization. This behavior for the ${}^4{S}^o$ states in ${\mathrm{Ca}}^{-}$ and ${\mathrm{Sr}}^{-}$ is ascribed to the different neutral-atom states to which the ${}^4{S}^o$ states are bound.