Resonant scattering of ultrarelativistic electrons in the strong field of a pulsed laser wave

Electron-electron scattering in a strong field of a pulsed laser wave is studied theoretically. Resonant scattering kinematics at the small polar angles for electron ultrarelativistic energy is studied in detail. Compact analytical expressions for the amplitude and the differential cross section for wave elliptical polarization are obtained under resonant conditions. The resonant cross section of electron-electron scattering is shown to decrease sharply with increasing the electron ultrarelativistic energies for weak and moderately strong fields. It was demonstrated that the resonant cross section of electron-electron scattering at wave circular polarization is four times greater than the corresponding cross section at linear polarization. The resonant cross section may exceed the corresponding cross section of a field-free process: by 5-6 orders of magnitude for electron MeV-energy and petawatt optical lasers (PHELIX, Vulcan); and 8-9 orders for multipetawatt laser fields within the femtosecond range (Vulcan10, ELI).