This review contains theoretical study of resonant quantum electrodynamics processes in a pulsed laser field. The approximation is examined when the pulse width is considerably greater than the character istic time of wave oscillations. The lepton's interaction with the Coulomb potential of a nucleus and each other is considered in the Born approximation. It is demonstrated that the resonant differential cross section of a process in a pulsed light fields may considerably exceed the corresponding cross section in an absence of a laser field. Results obtained may be experimentally verified by the scientific facilities at the SLAC National Accelerator Laboratory and FAIR (Facility for Antiproton and Ion Research, Darmstadt, Germany) project.

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Abstract:The nonresonant scattering of an electron by a muon in the pulsed light field in the frame of the Born approximation in general relativistic case is investigated theoretically. The approximation when a pulsewidth is considerably greater than the characteristic time of the wave oscillation is considered. The analytical expressions for the amplitude and cross-section of electron-muon nonresonant scattering process are derived in case of moderately strong elliptically polarized pulsed laser wave. It is demonstrated, that the process partial cross-section in the pulsed laser field differs essentially from the corresponding one in the field of plane monochromatic wave. The dependence of the emission (absorption) probability W l on the quantum parameter γ0eμ at l = 5