Bremsstrahlung of a relativistic electron scattered by a nucleus in a strong electromagnetic field

In the Born approximation in the interaction of an electron with a Coulomb field, we consider relativistic bremsstrahlung of an electron scattered by a nucleus in the presence of a plane electromagnetic wave. We analyze resonances due to mass-shell effects in the Green's function of the intermediate electron in the wave field. We obtain full relativistic expressions for the resonance and nonresonance cross sections for moderately strong external fields. It is shown that for electron energies E<<10 MeV and bremsstrahlung frequencies ..omega..'< or =..omega.. (..omega.. is the external field frequency) the magnitude of the resonance cross section with the simultaneous measurement of the emission angles of the bremsstrahlung quantum and the electron (scattered at large angles) exceeds by several orders of magnitude the usual cross section for bremsstrahlung of an electron scattered by a nucleus in the absence of the external field. The effect is most pronounced for nonrelativistic electrons.