Projection-operator calculations of the loweste−-He resonance

Abstract

Results for the lowest (Schulz) autodetaching state of ${\mathrm{He}}^{\mathrm{-}}$ [1s(2s${)}^2$] are reported. The calculation utilizes the full projection-operator formalism as explicitly developed by Temkin and Bhatia [Phys. Rev. A 31, 1259 (1985)]. Eigenvalues, scrE=〈Φ‖QHQ‖Φ〉, are calculated using projection operators Q depending on increasingly elaborate target wave functions going up to a 10-term Hylleraas-form, and a configuration-interaction total wave function Φ of 40 configurations. Results are well converged, but our best value is ∼0.13 eV above the experimental position at 19.37 eV. We conclude that the shift (Δ) in the Feshbach formalism gives a large contribution (relative to the width) to the position $E_r$ (=scrE+Δ). An appendix is devoted to the evaluation of the most complicated type of three-center integral involved in the calculation.