Multiphoton decays of positronium

Abstract

We compute the branching ratios for parapositronium and orthopositronium into four and five photons, respectively. We find $\frac{\ensuremath{\Gamma}(p\ensuremath{-}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}4\ensuremath{\gamma})}{\ensuremath{\Gamma}(p\ensuremath{-}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}2\ensuremath{\gamma})}=0.274{(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{2}\ensuremath{\simeq}1.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\frac{\ensuremath{\Gamma}(o\ensuremath{-}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}5\ensuremath{\gamma})}{\ensuremath{\Gamma}(o\ensuremath{-}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}3\ensuremath{\gamma})}=0.177{(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{2}\ensuremath{\simeq}0.96\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We also describe the energy spectra of photons from these decays.