Resonance of the Annihilation Channel of a Laser-Assisted Electron-Positron Scattering

Abstract

A resonance of the annihilation channel of an electron-positron scattering in the laser field with intensity $I\\lesssim 10^{16}\\mathrm{W}/\\mathrm{cm}^{2}$ is investigated theoretically. Intermediate virtual photon in the laser field become real under resonant conditions. As a result, the second order in fine structure constant process in the laser field transforms into two consistent processes of first order in the fine structure constant: Annihilation of initial electron-positron pair into intermediate photon in laser field and production of final electron-positron pair by intermediate photon in the laser field (laser-stimulated Breit-Wheeler process). Resonant kinematics of the process is studied in detail. It is shown that the resonance for the considered laser intensities is possible only when the certain combination of electron and positron initial energies exceed threshold energy. It is important to emphasize that the initial electron-positron momentums directions must lay in narrow cone with apex angle which satisfied certain resonant condition. This resonant apex angle of the initial electron pair is determined by the energies of the electron and positron, as well as the threshold energy. An emerging ultrarelativistic electron-positron pair also flies out in a narrow cone along the direction of the initial pair. In this case, the apex angle of the cone of the final pair can vary from zero to some maximum value. For each fixed apex angle, energies of the final electron and positron can take from one to four values. A resonant differential cross section of the studied process is obtained. It is shown that the resonant differential cross section can significantly exceed the corresponding Bhabha cross section without an external field. The project calculations may be experimentally verified by the scientific facilities of pulsed laser radiation (SLAC, FAIR, XFEL, ELI, XCELS).