Relativistic and retardation effects in the two–photon ionization of hydrogen–like ions

The non–resonant two–photon ionization of hydrogen–like ions is studied in second–order perturbation theory, based on Dirac’s equation. To carry out the summation over the complete Coulomb spectrum, a Green’s function approach has been applied to the computation of the ionization cross sections. Exact second–order relativistic cross sections are compared with data as obtained from a relativistic long– wavelength approximation as well as from the scaling of nonrelativistic results. For high–Z ions, the relativistic wave function contraction may lower the two–photon ionization cross sections by a factor of two or more, while retardation effects appear less pronounced but still give rise to non-negligible contributions.