Rare decays of the positronium ion and molecule, Ps− → e−γ and Ps2 → e+e−γ , γγ , e+e−

Abstract

Decay rates of the positronium molecule ${\text{Ps}}_{2}$ into two photons and into an electron-positron pair are determined. Previous studies find that these rates are very different, $\mathrm{\ensuremath{\Gamma}}({\text{Ps}}_{2}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})/\mathrm{\ensuremath{\Gamma}}({\text{Ps}}_{2}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})\ensuremath{\simeq}250$. This is puzzling since both processes have two-body final states and are of the same order in the fine-structure constant. We propose a simple calculational method and test it with the well-established decay of the positronium ion into an electron and a photon. We then employ it to correct predictions for both these ${\text{Ps}}_{2}$ decays. We find that previous studies overestimated the ${e}^{+}{e}^{\ensuremath{-}}$ channel and underestimated the $\ensuremath{\gamma}\ensuremath{\gamma}$ channel by factors of about 5.44 and 3.93, respectively. Our results give $\mathrm{\ensuremath{\Gamma}}({\text{Ps}}_{2}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})/\mathrm{\ensuremath{\Gamma}}({\text{Ps}}_{2}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})\ensuremath{\simeq}11.7$.