Resonance of the Annihilation Channel of a Laser-assisted Electron-positron Scattering in Super-Strong Fields

The resonance of the annihilation channel of a laser-assisted electron-positron scattering in super-strong fields is investigated theoretically. In the case of the resonance intermediate virtual photon becomes real and the second order in fine structure constant process transforms into two consistent processes of the first order in the fine structure constant. Resonant conditions and kinematics of the process is studied in detail. The final positron (electron) energy as a function of its output angle is found. The resonant differential cross-section as a function of the final particle energy is obtained analytically. It is shown that the resonant cross-section significantly exceeds the corresponding cross-section without an external field for super-strong fields with intensities up to $10^{\wedge}27\mathrm{W}/\text{cm}^{\wedge}2$. The paper calculations can be experimentally tested at the facilities of pulsed laser radiation.