New calculation of the properties of the positronium ion

Abstract

The positronium negative ion (${\mathrm{Ps}}^{\ensuremath{-}}$), the system composed of two electrons and a positron, has been reinvestigated theoretically. Using a Hylleraas wave function with two nonlinear parameters and more than 200 linear terms, we have obtained excellent values of binding energy and annihilation lifetime of the particle-stable $^{1}S^{e}$ ground state. In addition, we have examined the question of stability of the $^{3}P^{e}$ state discussed by Mills, and we agree with his conclusion that the state is probably not stable against breakup into $\mathrm{Ps}(n=2)+{e}^{\ensuremath{-}}$. Improved limits on the critical "positron" mass for binding the $^{3}P^{e}$ state have also been obtained.