Scaling relations of the time-dependent Dirac equation describing multiphoton ionization of hydrogen-like ions

TL;DR

This paper introduces approximate scaling laws for the time-dependent Dirac equation to describe multiphoton ionization of hydrogen-like ions under laser fields, validated across a range of nuclear charges and laser parameters, highlighting relativistic effects.

Contribution

The paper develops and validates approximate scaling relations for the Dirac equation in multiphoton ionization, extending understanding of relativistic effects in intense laser interactions with highly-charged ions.

Findings

Scaling relations accurately predict ionization across nuclear charges

Good agreement between scaled and actual calculations

Relativistic effects identified and quantified

Abstract

Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogen-like ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogen-like ions with the nuclear charges ranging from $Z=1$ to $92$ by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good agreement is found and thus the approximate scaling relations are shown to capture the dominant effect of the response of highly-charged ions to intense laser fields compared to the one of atomic hydrogen. On the other hand, the remaining differences are shown to allow for the identification and quantification of additional, purely relativistic effects in light-matter interaction.