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

TL;DR

This paper explores the impact of relativistic effects on photo ionization of highly charged hydrogen-like ions using semi-relativistic equations, revealing how strong external fields influence ionization probabilities beyond previous non-relativistic models.

Contribution

It introduces a semi-relativistic approach to compare relativistic and non-relativistic effects in laser-induced ionization of highly charged ions, extending prior work on relativistic corrections.

Findings

Relativistic effects significantly modify ionization potentials.

Discrepancies in ionization probabilities are partly due to relativistic external field effects.

Semi-relativistic models help clarify the role of relativity in strong-field ionization.

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.