Triply excited autodissociating resonant states in the positron-helium system

Abstract

In this paper, we present a complex-coordinate rotation calculation for high-lying S-wave resonances in positron-helium scattering. Highly correlated Hylleraas wave functions containing all six interparticle coordinates are used. A total of seven resonances, including their positions and widths, are reported, where the lowest one, denoted as ${e}^{+}\mathrm{He}(2{s}^{2})$, is formed by a positron attaching to the doubly excited $2{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S^{e}$ state of helium, and the other six resonances, denoted as $\mathrm{P}{\mathrm{s}}^{\ensuremath{-}}\mathrm{H}{\mathrm{e}}^{2+}$ (nS) with $n$ from 2 to 7, are located in the Rydberg series converging to the $\mathrm{P}{\mathrm{s}}^{\ensuremath{-}}+\mathrm{H}{\mathrm{e}}^{2+}$ threshold. Our results are compared with those available in the literature. The calculated energies for $\mathrm{P}{\mathrm{s}}^{\ensuremath{-}}\mathrm{H}{\mathrm{e}}^{2+}$ (nS) with $n$ from 2 to 7 show a good fit to a quantum defect formula that describes the interaction between the positively charged $\mathrm{H}{\mathrm{e}}^{2+}$ ion and the negatively charged $\mathrm{P}{\mathrm{s}}^{\ensuremath{-}}$ ion. The 3S state in this Rydberg series provides an alternative designation for the previously identified ${e}^{+}\mathrm{He}(3{s}^{2})$ state in the literature.