Relativistic and nondipole effects in multiphoton ionization of hydrogen by a high-intensity x-ray laser pulse

Abstract

In the theory of multiphoton ionization, the effects of relativity and spatial dependence in the laser field are typically neglected for the sake of computational feasibility, as well as being too small to measure. As advances in high-intensity, short-wavelength lasers are developed, ultimately it becomes necessary to investigate the impact of relativistic and/or beyond-dipole (nondipole) corrections, as they are no longer small enough to neglect. Using an ab initio approach and the time-dependent Dirac equation to simulating the ionization process in an exact nondipole treatment, we study the high-intensity multiphoton ionization of hydrogen by a short x-ray laser pulse in the relativistic regime, yielding the kinetic-energy spectrum of the photoelectron, and observe a shift in the energy of the emitted electron as induced by relativistic and nondipole effects. Overall, relativistic effects are seen to give rise to a positive energy shift (blueshift), while nondipole effects cause a corresponding negative shift (redshift), and in aggregate the relativistic and nondipole ionization result in a tiny redshift. Considering only photoelectrons that are emitted along the laser polarization direction, the blueshift is recovered, and the shift may be explained in terms of the relativistic mass shift of the electron in the oscillating field.