über die Streuung relativistischer Elektronen im Coulombfeld

Abstract

An approximative method for summing the partial wave series for the scattering amplitude of the relativistic scattering of electrons by an atomic nucleus is investigated in the simplest case of a point charge nucleus for electron energies not less 10 MeV. In the course of the computationΒ=1 is assumed (Β=v/c,v andc denote the velocity of the electron and of light, respectively). The Sommerfeld-Watson-transformation is the starting point. The method consists in setting up an asymptotic expansion in 1/sin² (θ/2) (θ is the scattering angle) of the amount coming from the Regge-poles. Two further amounts, the dependence of which on the scattering angle especially for easy nuclei is little, are computed numerically without simplification, which should be possible. The method is developed from a special way of summing the partial wave series for the non-relativistic Rutherford scattering, which may be done analytically.Mott's scattering formula is verified and finally the applicability of the method is examined for summing the relativistic partial wave series with the exact S-Matrix. The results are as exact as the expension of the cross section to order (Z/137)⁵ (Z is the nuclear charge). The method should in principle be applicable for an extended nucleus, but in this case there remain still several problems.