# Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms

## TL;DR

This paper investigates relativistic effects on non-resonant two-photon K-shell ionization in neutral atoms, highlighting significant reductions in cross sections for heavy atoms due to wavefunction contraction and analyzing gauge and approximation impacts.

## Contribution

It provides a comprehensive theoretical comparison of relativistic and non-relativistic calculations, including effects of higher multipoles and negative continuum states in different gauges.

## Key findings

- Relativistic effects significantly decrease ionization cross sections in heavy atoms.
- Negative continuum states influence the cross section mainly in the velocity gauge.
- Higher multipole contributions are weaker but counteract relativistic contraction effects.

## Abstract

Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically within the framework of second-order perturbation theory. The non-relativistic results are compared with the relativistic calculations in the dipole and no-pair approximations as well as with the complete relativistic approach. The calculations are performed in both velocity and length gauges. Our results show a significant decrease of the total cross section for heavy atoms as compared to the non-relativistic treatment, which is mainly due to the relativistic wavefunction contraction. The effects of higher multipoles and negative continuum energy states counteract the relativistic contraction contribution, but are generally much weaker. While the effects beyond the dipole approximation are equally important in both gauges, the inclusion of negative continuum energy states visibly contributes to the total cross section only in the velocity gauge.