Approximate Relativistic Coulomb Scattering Wave Function

A relativistic scattering wave function, which is valid to second order in $\ensuremath{\alpha}Z$ for all electron velocities, is developed. The wave function has as its dominant term the Sommerfeld-Maue function. The computational simplicity of the closed form Sommerfeld-Maue wave function is retained in this modified Sommerfeld-Maue function.Applications of the wave function to the calculation of cross sections for the scattering of polarized electrons and bremsstrahlung production at the short wave limit of the spectrum are given. A large first-order correction to the Sauter-Fano formula for the bremsstrahlung cross section is obtained.