Comparison between the nonrelativistic dipole approximation and the exact relativistic theory for radiative recombination

The nonrelativistic dipole approximation (Stobbe theory) for the atomic photoelectric effect and its inverse reaction, radiative recombination, is contrasted with an exact relativistic formulation taking into account relativistic electron motion and all multipole orders for the interaction with the photon. A comparison is performed for total cross sections as a function of energy and nuclear charge as well as for angular distributions. It is found that even for small velocities of the continuum electron, discrepancies between both approaches persist for high nuclear charges.