Radiative Corrections to Pair Annihilation

Abstract

The ${e}^{6}$ corrections to the probability of direct two-photon pair annihilation are obtained by applying the substitution law to the Compton scattering radiative corrections. General results are given, as well as low-and high-energy limits. Divergence of the corrected matrix element for small relative velocity, due to failure of the Born approximation, is removed by a more accurate treatment of Coulomb effects based on the Sommerfeld factor. The results are applied to the singlet ground state of positronium, yielding an increase in the lifetime of 0.59%.