Wichmann-Kroll vacuum polarization correction to lithium-like systems in a Gaussian basis set

TL;DR

This paper extends the application of Gaussian basis sets to compute the Wichmann-Kroll vacuum polarization correction in lithium-like systems, demonstrating good agreement with existing results and showcasing the method's utility for complex atomic potentials.

Contribution

It introduces a Gaussian basis set approach for multi-electron systems to evaluate vacuum polarization corrections, expanding beyond single-electron cases.

Findings

Good agreement with literature for lithium-like systems.

Demonstrates Gaussian basis sets' effectiveness for complex atomic potentials.

Extends vacuum polarization calculations to multi-electron systems.

Abstract

Recent developments have seen the application of finite Gaussian basis sets to the $\alpha(Z\alpha)^{n\geq3}$ vacuum polarization. The energy shift for $s$ and $p$ electron states have been tabulated and their convergence investigated. In this work, we extend this problem to the multi-electron case. Hartee-Fock potentials obtained self-consistently are used to treat the vacuum polarization for lithium-like systems and are found to be in good agreement with comparable results in the literature. The results presented in this work demonstrate the use of Gaussian basis sets for atomic potentials whose Green's functions expressions cannot be simply obtained via analytic or numerical methods.