Method for calculating the relativistic Coulomb scattering amplitudes of electrons

The scattering amplitudes for the scattering of electrons by a point charge nucleus can be represented by power series in the variables (sin Θ/2)² or (cos Θ/2)², whereΘ is the scattering angle. A method for calculating the coefficients of these series including all terms up to an arbitrarily high order in (Z/137)², whereZ is the nuclear charge, is described. The method makes extensively use of recurrence relations and does not contain any approximation. Since all power series occurring in the course of the computation converge rapidly, very accurate results can be obtained with the help of a computer. The method is particularly advantageous for small and large scattering angles, where other methods fail to give accurate results.