Projection-Operator Approximation for Autoionization States in the Inelastic Scattering Region

A projection-operator technique is used to investigate the resonance states of two-electron systems in the inelastic scattering energy region. Computations are carried out for the $P$ autoionization states for He and the ${\mathrm{H}}^{-}$ ion in the $n=2\mathrm{}$ to $n=3\mathrm{}$ energy region. The results are compared with previous calculations and experiments. For the ${}_{}{}^1{}_{}{}^{}P$ resonance of He, very good agreement is obtained as compared with the accurate measurement of Madden and Codling.