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Our paper concerns the scattering of intense laser radiation on free electrons and it is focused on the relation between nonlinear Compton and nonlinear Thomson scattering. The analysis is performed for a laser field modeled by an ideal pulse with a finite duration, a fixed direction of propagation and indefinitely extended in the plane perpendicular to it. We derive the classical limit of the quantum spectral and angular distribution of the emitted radiation, for an arbitrary polarization of the laser pulse. We also rederive our result directly, in the framework of classical electrodynamics, obtaining, at the same time, the distribution for the emitted radiation with a well defined polarization. The results reduce to those established by Krafft et al. [G. A. Krafft, A. Doyuran and J. B. Rosenzweig, Phys. Rev. E 72, 056502 (2005)] in the particular case of linear polarization of the pulse, orthogonal to the initial electron momentum. Conditions in which the differences between classical and quantum results are visible are discussed and illustrated by graphs.

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We extend previous nonrelativistic dipole-approximation theoretical studies of two-photon electron bremsstrahlung in the Coulomb field by calculations exploring the cross section that describes the emitted photons, irrespective of the direction of the scattered electron, and its dependence on the charge Z of the target, for different detection geometries. A Born-approximation equation, valid for any emittedphoton configuration, is derived. Comparisons with the most recent experimental data are presented. PACS number(s): 34.80.i 32.80.Wr