Exploring above-threshold ionization of hydrogen in an intense x-ray laser field through nonperturbative calculations

Abstract

This paper addresses the problem of above-threshold ionization (ATI) of hydrogen interacting with a short and intense x-ray electromagnetic field. We consider the weakly relativistic regime where the speed of the photoelectron stays well below the velocity of the light $c$. We solve the time-dependent Schr\"odinger equation (TDSE) using a spectral approach with a basis of one-electron orbitals, calculated with ${L}^{2}$-integrable $B$-spline functions for the radial coordinate and bipolar spherical harmonics ${Y}_{lm}$ for the angular part. Retardation effects are included up to $O(1/c)$; they induce two extra terms leading to electric quadrupole and magnetic dipole transitions. These latter terms depend on the polarization and photon momentum directions, forcing the resolution of the TDSE in a three-dimensional space. Relativistic effects [of $O(1/{c}^{2})$] are fully neglected. Photoelectron energy and angular distributions are obtained for photon energies ranging from 200 eV to 3 keV. We study the lower energy region of the ATI spectrum and we analyze nondipole effects, through their $(l,m)$ components, in particular, for the lower two peaks. Although these effects are small, we show that, increasing the photon energy, the photoelectron angular distributions begin to differ significantly from the ones obtained in dipole approximation.