The effect of inelastic electron scattering on the elastic, total, and discrete inelastic differential scattering cross sections is investigated in the second Born approximation. It is shown that in this approximation the polarization corrections can be written as a function of the Coulomb phase shift and other auxiliary functions to within an additive constant in the Coulomb phase. This constant is chosen by imposing the physically reasonable condition that the polarization correction must tend to zero with increasing scattering angle. The results of the calculation of polarization effects on the elastic scattering amplitudes for Ar and U are given for an incident electron energy of 40 kV.
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