Fine structure of negative ions of alkaline-earth-metal atoms

Fine-structure intervals ${\mathit{np}}_{1/2}$-${\mathit{np}}_{3/2}$ (${\mathit{np}}_{1/2}$ is the ground state) are calculated for negative ions using relativistic many-body perturbation theory: ${\mathrm{Ca}}^{\mathrm{-}}$ 4p, 56 ${\mathrm{cm}}^{\mathrm{-}1}$; ${\mathrm{Sr}}^{\mathrm{-}}$ 5p, 178 ${\mathrm{cm}}^{\mathrm{-}1}$; ${\mathrm{Ba}}^{\mathrm{-}}$ 6p, about 460 ${\mathrm{cm}}^{\mathrm{-}1}$; and ${\mathrm{Ra}}^{\mathrm{-}}$ 7p, 1341 ${\mathrm{cm}}^{\mathrm{-}1}$. Comparison of the fine-structure interval with affinity: ${\mathrm{Ca}}^{\mathrm{-}}$ 10%, ${\mathrm{Sr}}^{\mathrm{-}}$ 22%, ${\mathrm{Ba}}^{\mathrm{-}}$ 30%; for ${\mathrm{Ra}}^{\mathrm{-}}$ the fine-structure interval is larger than the affinity. Thus the ${\mathrm{Ra}}^{\mathrm{-}}$ 7${\mathit{p}}_{3/2}$ state is a resonance in the continuous spectrum with energy 0.018 eV. This means that the relativistic spin-orbit interaction plays a determining role in slow electron-radium scattering.