Abstract
We investigate potential scattering of relativistic electrons in the presence of an intense laser field. Neglecting spin effects, the electron is described as a Klein-Gordon particle embedded in the laser field. The interaction with the scattering potential is treated in the lowest order of perturbation theory. The differential scattering cross sections for induced and inverse bremsstrahlung are derived. In the limit of low laser frequencies the sum rule for the cross sections is evaluated and its intensity dependent relativistic corrections are discussed. The same sum rule is rederived using a relativistic generalization of the approximation of instantaneous interactions. The classical origin of this sum rule is indicated.
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