Resonant scattering of photon by electron in the presence of the pulsed laser field

The scattering of photon by electron in the presence of the field of the low-intensity circularly-polarized pulsed laser wave is analyzed at a laser pulse duration that is significantly greater than the characteristic oscillation time. The conditions for the resonance process in which the intermediate particle is located in the vicinity of the mass surface are determined. The existence of three resonance ranges is demonstrated. The first one corresponds to the resonance of direct diagram, and two ranges correspond to the resonance of exchange diagram via electron and positron intermediate states. The conditions under which only the resonance of the direct diagram takes place are determined, and the probability of such process is calculated. It is demonstrated that the resonance probability can be significantly greater than the probability of the Compton effect in the absence of the external field.