Bremsstrahlung in the presence of a laser field

For the process of spontaneous one photon emission by an electron scattered on a potential in the presence of a monochromatic laser field, we review the formalism and the approximations on which the existing nonrelativistic calculations are based, in classical and quantum descriptions. In the case of the Coulomb potential, we give new numerical results for the radiation spectrum, using either the Born approximation [Karapetyan, P.V., Fedorov, M.V., 1978. Spontaneous electron bremmstrahlung in the field of an intense electromagnetic wave. Zh. Teor. Fiz. 75, 816–826 [Sov. Phys. JETP 48, 412 (1979)]] or the low laser frequency approximation [Zhou, F., Rosenberg, L., 1993. Bremsstrahlung in laser-assisted scattering. Phys. Rev. A 48, 505–515]. The frequency of the external field is in the eV range and the incident electron energy in the keV range. The need for more theoretical work is emphasized.