Internal structure of the positronium ion Ps−

Abstract

The positronium ion ${\mathrm{Ps}}^{--}$ is often qualitative described as a positronium Ps with a loosely bound second electron, since the value of the annihilation rate for ${\mathrm{Ps}}^{--}$ is nearly equal to that of the spin-averaged neutral positronium. This similarity however has never been fully explained. To study its internal structure, we decompose the electron-positron distribution function of ${\mathrm{Ps}}^{--}$ into the sum of two terms: one for the electron closest to the positron and the other for the farthest. We show that the inner electron behaves almost as if the outer electron were not present, forming a Ps substructure inside ${\mathrm{Ps}}^{--}$ and that the effect of electron correlation is such that the outer electron tries to stay as close as possible to the positron but without interfering too much with the distribution of the inner electron. We show that this phenomenon is closely related to the problem of the critical stability of the system $({Z}^{+},\phantom{\rule{0.28em}{0ex}}{e}^{--},\phantom{\rule{0.28em}{0ex}}{e}^{--})$ with varying $Z$ charge.