Lowest inelasticHe−autodetachment state (P∘2) in a Feshbach resonance

Abstract

The lowest inelastic (${}_{}{}^2{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$) resonance in the scattering of electrons from helium is recalculated using the quasiprojection formalism. An eigenvalue has been found at 20.52 eV using a closed-shell target ground-state quasiprojector, and is confirmed by using an open-shell target projector (yielding $\mathcal{E}=20.56\mathrm{}$ eV). The width is also calculated and is very large: $\Gamma =0.44\mathrm{}$ eV, thus unambiguously showing that the well-known experimental structure at ∼20.3 eV is a Feshbach and not a shape resonance. The associated nonresonant continuum phase shift reveals a pronounced enhancement beyond the $2{}_{}{}^1{}_{}{}^{}S$ threshold. This finding supports the observational inference of a second ${}_{}{}^2{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$ (shape) resonance at 20.8 eV by Phillips and Wong.