Calculation of theP1(2s2p)Autoionization State of He with a Pseudostate Nonresonant Continuum

Abstract

Previous Hylleraas calculations of $\mathcal{E}=<\mathrm{QHQ}>\mathrm{}$ for the lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization state of helium are here supplemented by calculations of the shift ($\Delta$), width ($\Gamma$), and shape parameter ($q$) using a ($ls,2\mathrm{}\tilde{p}$) pseudostate nonresonant continuum function. The function is constructed to eliminate the dominant ($2s,2p$) configuration of the autoionization state, while at the same time containing three variationally determined radial functions. Both $\Delta$ and $q$ are also shown to contain contributions from the discrete part of the nonresonant spectrum, although quantitatively that contribution is found to be small. Final results change previous polarized-orbital results minimally, which means that the resonance position, $\mathcal{E}=\mathrm{E}+\Delta$, continues to be on the edge of the experimental error, and $q$ remains somewhat outside the experimental result. Further relativistic corrections are briefly discussed, but a simple argument indicates that they are not likely to explain the differences with experiment. It is concluded that more-accurate experiments should be carried out.