The photon spectrum in orthopositronium decay at ω_γ<< m_e

Abstract

A closed analytic expression is given for the spectrum of low energy photons in the annihilation of orthopositronium, which expression sums all the effects of the Coulomb interaction between the electron and the positron. The applicability of the formula is limited only by the condition $ω_γ\ll m_e$. In the region $ω_γ\gg m_e α^2$ the Coulomb interaction term gives the leading at low energy one-loop correction, proportional to $α\sqrt{m_e/ω_γ}$, to the decay spectrum. The constant in $ω_γ$ radiative term in the one-loop correction to the spectrum is also presented here in an analytic form.