Autoionization states of the positronium negative ion

Abstract

The complex-rotation method has been applied to investigate autoionization states of the positronium negative ion (${e}^{\ensuremath{-}}{e}^{+}{e}^{+}$). Only the singlet $S$ states are considered, but both the lowest resonance below the $n=2$ and $n=3$ positronium thresholds are calculated. Using the Hylleraas-type wave function with 161 terms, the resonance parameters (position and width) are determined by the complex-rotation method. The higher members of the resonances are estimated by the stabilization method but no width and shift are provided. In addition, by varying the mass of the positron from $1{m}_{e}$ (electron mass) to $\ensuremath{\infty}$, we are able to investigate the lowest resonance for systems ranging from ${\mathrm{Ps}}^{\ensuremath{-}}$ to ${\mathrm{H}}^{\ensuremath{-}}$. From this analysis, the lowest resonance for other three-body systems (${e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{\ensuremath{-}}p{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{\ensuremath{-}}d{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{\ensuremath{-}}t{\ensuremath{\mu}}^{\ensuremath{-}}$) are deduced.