Rare decays of the positronium ion and molecule, $\text{Ps}^{-}\to e^{-}\gamma$ and $\text{Ps}_{2}\to e^{+}e^{-}\gamma,~\gamma\gamma,~e^{+}e^{-}$

TL;DR

This paper recalculates the decay rates of the positronium molecule into different channels, correcting previous overestimations and underestimations, and provides a more accurate ratio of decay widths.

Contribution

The authors introduce a simple calculational method tested on known decays and apply it to improve predictions for $ ext{Ps}_2$ decay rates, resolving discrepancies in prior estimates.

Findings

Corrected decay rate ratios for $ ext{Ps}_2$ decays.

Found previous estimates overestimated $e^{+}e^{-}$ decay by factor 5.44.

Found previous estimates underestimated $ ext{Ps}_2 o ext{γγ}$ decay by factor 3.93.

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, \[ \Gamma\left(\text{Ps}_{2}\to e^{+}e^{-}\right)/\Gamma\left(\text{Ps}_{2}\to\gamma\gamma\right)\simeq250\text{ (previous studies)}. \] 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 $e^{+}e^{-}$ and underestimated the $\gamma\gamma$ channel by factors of about 5.44 and 3.93 respectively. Our results give $\Gamma\left(\text{Ps}_2\to e^+e^-\right)/\Gamma\left(\text{Ps}_2 \to \gamma\gamma\right) \simeq 11.7$.