Resonant scattering of a lepton by a lepton in the pulsed light field

The process of resonant scattering of a lepton by a lepton in the field of pulsed light wave in general relativistic case is studied theoretically. The approximation when a pulsewidth is considerably greater than the characteristic time of wave oscillation is considered. The analytical expression for the resonant differential cross-section of concerned process is derived within the framework of the first order of the perturbation theory with respect to external laser field; it contains the resonant peak, the altitude and the width of which are defined by the external pulsed wave characteristics. It is demonstrated, that the resonant differential cross-section of scattering of an electron by an electron (an electron by a positron, an electron by a muon) in the pulsed light field may be several orders of magnitude greater than the corresponding one in the external field absence. The derived results may be verified experimentally for example by scientific facility at SLAC National Accelerator Laboratory.