Using a Spline-Garlekin and inverse iteration method, we studied in detail the photodetachment cross section of the ${\mathrm{He}}^{-}$ $\left(1s2s2p{}^4{P}^o\right)$ state in the region of the $1s$ detachment threshold. Details of the cross section from threshold to 44 eV are presented. The effects of core excitation and continuum channel coupling are studied. A very narrow $2s3s4s{}^{4}S$ resonance was found at 42.866 00 eV with a width of 0.103 meV. Other resonance structures are also found and analyzed. We studied the ${2s2p}^2{}^{4}P$ resonance state that lies immediately below the $1s$ threshold. The width and position of this state, obtained from this calculation, are 37.669 eV and 9.850 meV, respectively. This result is in good agreement with other theoretical calculations.

• Received 16 March 1998

DOI:https://doi.org/10.1103/PhysRevA.59.307