Relativistic theory of electron scattering from hydrogenic systems

The electron-hydrogen scattering problem is formulated using the Dirac equation. A set of coupled equations is obtained for the radial wavefunctions for the various states of the incident electron, analogous to the coupled equations in the non-relativistic theory. A set of scattering amplitudes is obtained from which excitation cross sections, elastic and inelastic differential cross sections, and data on final electron and target polarizations can be obtained for any initial electron beam or target polarizations. Explicit formulae for the differential cross section and final electron polarization are given for certain special cases. Inclusion of magnetic and retardation effects in the interaction between the two electrons is discussed.