Static-field ionization model of He-like ions for diagnostics of light field intensity

TL;DR

This paper develops a static-field ionization model for He-like ions across a range of nuclear charges, comparing approximate methods with detailed multielectron calculations to understand ionization rates and exchange effects.

Contribution

It introduces a comprehensive comparison of ionization rate calculation methods for He-like ions, highlighting the accuracy of PPT-based formulas and the significance of exchange interactions.

Findings

PPT-based fitting formula and third-order perturbation theory agree within 10% of MCTDHF rates.

Exchange interaction effects scale approximately as 1/Z, affecting ionization rate estimates.

Single-active electron approximation overestimates ionization rates by up to 30% for He.

Abstract

We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z \le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10\%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30\% for He and 2\% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as $1/Z$.