Abstract
In the frame of the Born approximation we theoretically investigate resonant scattering of an electron by a muon in the field of elliptically polarized electromagnetic wave in the general relativistic case. It is studied kinematics of a scattering of an electron in resonant region. It is derived the expressions for the amplitude and the cross-section of the resonant scattering of an electron by a muon when the invariant intensity parameter of the laser field is small (ηe ≪1). It is demonstrated that the resonant cross-section of a scattering may be several orders of magnitude higher than the cross-section of a scattering in the absence of the external field.
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