Rare decays of the positronium ion and molecule, ${\text{Ps}}^{-}\to e^{-}\gamma$ and ${\text{Ps}}_2\to e^{+}{e}^{-}\gamma ,\gamma \gamma ,e^{+}{e}^{-}$

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, \[ Γ\left(\text{Ps}_{2}\to e^{+}e^{-}\right)/Γ\left(\text{Ps}_{2}\toγγ\right)\simeq250\text{ (previous studies)}. \] 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 $\Gamma \left({\text{Ps}}_2\to e^{+}{e}^{-}\right)/\Gamma \left({\text{Ps}}_2\to \gamma \gamma \right)\simeq 11.7$.

References in corpus (5)

• Discovery of doubly-charmed Xi_{cc} baryon implies a stable (b b ubar dbar) tetraquark
• Stability of tetrons
• Spectroscopy, lifetime and decay modes of the $T_{bb}^{-}$ tetraquark
• Positronium-ion decay
• Two-Photon Total Annihilation of Molecular Positronium