Resonant two-photon annihilation of an E−-E+ pair in the laser field

Resonant two photon annihilation of an electron-positron pair in the field of a moderately strong circularly polarized wave is investigated theoretically. There are two pairs of diagrams different by the type of intermediate particle. The kinematics and resonance conditions are found in the case of electron (positron) birth. For moderately strong light wave we derive the expression for the resonant differential cross section of the process. The resonant singularities in the expressions for the amplitude can be eliminated with the use of the Breit-Wigner procedure.