Resonant annihilation and production of high-energy electron-positron pairs in an external electromagnetic field

A resonant process of annihilation and production of high-energy electron-positron pairs in an external electromagnetic field is studied theoretically. This process is the annihilation channel of an electron-positron scattering. It is shown that the resonance in an external electromagnetic field is possible only when the certain combination of electron and positron initial energies is more than threshold energy. Also, the angle between initial electron and initial positron momenta directions must be small and satisfy the resonant conditions. This angle is determined by the high-energy of the initial pair and the threshold energy. An emerging electron-positron pair also flies out in a narrow cone along the direction of the initial pair and must be ultrarelativistic. For each fixed angle, energies of the final electron and positron can take from one to two values. It is shown that the resonant differential cross section can significantly exceed the corresponding Bhabha cross section without an external field.