Gaussian basis set approach to one-loop self-energy

TL;DR

This paper introduces a Gaussian basis set method for calculating the one-loop self-energy in atomic systems, enabling high-precision QED corrections for heavy molecules, with results matching exact wave functions.

Contribution

The paper presents a novel Gaussian basis set approach for one-loop self-energy calculations applicable to all orders in the external field.

Findings

Excellent agreement with Dirac--Coulomb wave functions for one-electron atoms.

Method is suitable for high-precision QED studies of heavy molecules.

Potential to simplify complex QED calculations in molecular physics.

Abstract

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a one-electron atom, our results show excellent agreement with those obtained using the exact Dirac--Coulomb wave functions. The developed method can be of interest for high-precision studies of heavy few-electron molecular systems, where the rigorous computation of QED corrections is currently a formidable task.