Positronium hydride decay into proton, electron, and one or zero photons

Abstract

Decay rates of the positronium hydride PsH, a bound state of a proton, a positron, and two electrons, are determined for two rare channels, $\text{PsH}\ensuremath{\rightarrow}{p}^{+}{e}^{\ensuremath{-}}\ensuremath{\gamma}$ and $\text{PsH}\ensuremath{\rightarrow}{p}^{+}{e}^{\ensuremath{-}}$. Previous studies overestimated these rates by factors of about 2 and 700, respectively. We explain the physics underlying these wrong predictions. We confirm a range of static PsH properties, including the nonrelativistic ground-state energy, expectation values of interparticle distances and their powers, and the three- and four-particle coalescence probabilities, using a variational method in the Gaussian basis.