Solution of the time-dependent Dirac equation for describing multiphoton ionization of highly-charged hydrogenlike ions

TL;DR

This paper solves the time-dependent Dirac equation to study multiphoton ionization in hydrogenlike ions, revealing gauge dependence and relativistic effects like ionization potential shifts, with a proposed scaling method.

Contribution

It introduces a method for solving the time-dependent Dirac equation for multiphoton ionization and analyzes gauge dependence and relativistic effects in the process.

Findings

Velocity-gauge results match length gauge only with negative-energy states included.

No significant difference in length gauge results with or without negative-energy states.

Relativistic effect mainly causes a shift in ionization potential, which can be scaled.

Abstract

A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A simple scaling procedure is proposed to account for this effect.