Two-photon above-threshold ionization of hydrogen over the photon energy range from 15 eV to 50 keV

We investigate the absorption of two identical photons from the ground state of hydrogen-like atoms over an energy range that extends beyond that explored up to now. Our approach is based on a hybrid formula, valid in second-order perturbation theory, in which the A² contribution from the nonrelativistic Hamiltonian is treated exactly, while the A·P contribution is calculated in dipole approximation. We find that, at least up to 50 keV, the nonrelativistic dipole approximation, based only on the A·P contribution, determines the values of the total cross section. Our numerical results, covering photon energies from 90 nm (13.7 eV) to 0.0248 nm (50 keV) are in very good agreement with most previous theoretical works. Differences with recent results are discussed.