${}^{4}S$ resonances of ${\mathrm{He}}^{-}$ below the ${\mathrm{He}}^{+}\mathrm{}(n=1\mathrm{})\mathrm{}$ threshold

Resonances of ${}^4{S}^e$ symmetry in ${\mathrm{He}}^{-}$ are searched for in the region below the ${\mathrm{He}}^{+}\mathrm{}(n=1\mathrm{})\mathrm{}$ threshold. The energies and widths of the resonances are calculated with an ab initio three-electron description of the ion. The complex rotation method is combined with the use of B splines in a spherical cavity to describe the ion and the decaying channels. Four resonances are found. The first three resonances agree well with experiments. The fourth resonance has not been seen in an experiment yet, due to a small photodetachment cross section and large width.