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Method of approximate treatment of the relativistic compound free-free matrix elements

We extend the method introduced recently by Korol for the approximate calculation of the compound relativistic free-free matrix elements. The method is based on the accurate treatment of the diagonal singularities in the one-photon relativistic matrix elements, which appear in the compound matrix element. For the case of relativistic projectile scattering in the field of a short-range potential we present the evaluation of the singular parts of the free-free single-photon matrix elements. The result is used to treat approximately the amplitude of the two-photon bremsstrahlung (2BrS) process for the relativistic electron. This is done for the first time.