On the breakdown of the electric dipole approximation for hard x-ray photoionization cross sections

Abstract

Photoionization of K- and L-shells of H, He, Be, Ne, Ar and Kr atoms by hard x-ray radiation resulting in the emission of photoelectrons with kinetic energy of up to 20 keV is studied beyond the electric dipole approximation. Thereby we investigate the effect of higher-multipole expansion (retardation) of hard x-ray radiation on the angular-averaged ionization cross section. Numerical calculations, performed in the relativistic Pauli–Fock approximation, demonstrate that in this energy range quadrupole transitions introduce dominant contributions beyond the electric dipole approximation. The computed relative contributions of the nondipole interactions to the cross sections grow as a function of the photoelectron kinetic energy almost equally for the 1s and 2s shells of all considered atoms. The same holds for the 2p shells of Ne, Ar and Kr. We, thus, confirm analytical predictions of the Born approximation suggesting that in the considered energy range the relative error introduced to the ionization cross section of low and intermediate Z elements by the electric dipole approximation is almost independent of the spatial extent of the absorbing atomic orbital.