Relativistic and magnetic effects in photo ionization of hydrogen-like ions

We investigate the role of relativistic and magnetic corrections in photo ionization of hydrogen-like ions. 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. By comparing with numerical solutions of both the relativistic time-dependent Dirac equation and the non-relativistic Schr{o}dinger equation -- with and without magnetic interactions, the influence of these interactions are revealed. Moreover, we investigate to what extent relativistic effects are induced by the relativistic shift in the structure of the ions or by the strong external field. In agreement with a recent work, Ivanova et al., Phys. Rev. A {\bf 98}, 063402 (2018), we find that the dominant relativistic correction is the former, i.e., the relativistic shift in the binding energy of the ions. However, dynamical relativistic corrections induced by the laser field are also seen -- in addition to a significant influence of the magnetic field for the longer wavelengths.