A non-relativistic Dirac equation: An application to photo ionization of highly charged hydrogen-like ions

Abstract: We investigate the role of relativity in photo ionization of hydrogen-like ions by a laser pulse. For hydrogen, the wavelengths of the laser resides in the weakly ultra violet region. For higher nuclear charges, the laser parameters are scaled in a manner which renders the time-dependent Schr{\"o}dinger equation in the dipole approximation independent of nuclear charge. The ionization potentials of these highly charged ions are strongly modified by relativistic effects. In an earlier work, Ivanova et al., Phys. Rev. A {\bf 98}, 063402 (2018), it is demonstrated how this explains most of the relativistic correction to the ionization probability. Here we investigate to what extent remaining discrepancies can be attributed to relativistic effects stemming from the strong external field. To this end, we solve semi-relativistic formulations of both the Schr{\"o}dinger and the Dirac equations; the former accounts for increased inertia due to the external laser field, while the latter features a non-relativistic interaction term.