Ionization of atomic hydrogen by an intense x-ray laser pulse: An ab initio study of the breakdown of the dipole approximation

Abstract

Solving the time-dependent Schr\odinger equation numerically within the framework of an ab initio model, the breakdown of the dipole approximation in modeling the ionization and excitation dynamics of a hydrogen atom exposed to an intense 1.36-keV x-ray laser pulse is investigated in some detail. The relative importance of the ${\mathbit{A}}^{2}$ diamagnetic term in comparison with the $\mathbit{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ contribution to the resulting beyond-dipole (nondipole) light-matter interaction is studied for laser pulse intensities ranging from the weak perturbative to the strong-field regime. It is found that the diamagnetic interaction represents by far the most important correction to the dipole approximation at higher field strengths, while nondipole corrections induced by the $\mathbit{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ operator are generally small and largely independent of the laser intensity. The most profound finding of the present study was the discovery of a forward-backward asymmetry in the underlying electron ejection dynamics: Depending on the electron's kinetic energy in the final state, the photoelectron tends to be emitted in the laser propagation (forward) and/or counterpropagation (backward) directions, for energies corresponding to the low-energy and/or high-energy side of the multiphoton resonances, respectively.