Photodetachment of negative helium ions below and above the $1s$ ionization threshold: A complex scaled configuration-interaction approach

The photodetachment of the metastable ${\mathrm{He}}^{-}1s2s2p{}^4{P}^o$ state has been calculated in two photon energy regions of interest: the first, named here as energy region I, below the double photoionization threshold ${\mathrm{He}}^{+}\mathrm{}(n=1\mathrm{}),$ involving outer-shell ionization and doubly excited states of ${\mathrm{He}}^{-},$ and the second, named here as region II, above the ${\mathrm{He}}^{-}$ $1s$ ionization threshold and below the ${\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold, involving K-shell detachment and triply excited states of a ${\mathrm{He}}^{-}$ “hollow ion.” We have implemented an ab initio three-electron configuration-interaction method in the LS-coupling scheme combined with complex scaling to obtain resonance positions and widths and the photodetachment cross sections. We have revisited region I, although widely studied before, as a test of our method. Notwithstanding some small discrepancies, our complex scaling results compare well with the previously published results and also add new understanding to some features in the cross section. Our emphasis is given to K-shell photodetachment in photon energy region II, where comparison is made with two other recent theoretical calculations that use completely different methods, and that were in dispute. We also compare with a very recent experiment for the ${\mathrm{He}}^{-}$ K-shell photodetachment, which displays three major features; a broad nonresonant hump after the $\mathrm{He}2s2p{}^3{P}^o$ threshold and two other peaks. A complex scaling analysis of prominent structures in the photodetachment spectra in region II, previously claimed to be nonresonant structures, leads to a different conclusion; i.e., they are all true triply excited-state resonances, and two of them correspond to the peaks observed experimentally.