The photon spectrum in orthopositronium decay at \omega_\gamma << 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 $\omega_\gamma \ll m_e$. In the region $\omega_\gamma \gg m_e \alpha^2$ the Coulomb interaction term gives the leading at low energy one-loop correction, proportional to $\alpha \sqrt{m_e/\omega_\gamma}$, to the decay spectrum. The constant in $\omega_\gamma$ radiative term in the one-loop correction to the spectrum is also presented here in an analytic form.