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: ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ 4p, 56 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$; ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$ 5p, 178 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$; ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$ 6p, about 460 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$; and ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ 7p, 1341 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Comparison of the fine-structure interval with affinity: ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ 10%, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$ 22%, ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$ 30%; for ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ the fine-structure interval is larger than the affinity. Thus the ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ 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.

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