Vacuum polarization in molecules II: higher order corrections

TL;DR

This paper develops a formalism for calculating higher-order vacuum polarization effects in molecules, enabling more accurate modeling of quantum electrodynamics phenomena in molecular systems.

Contribution

It introduces a general effective field approach for vacuum polarization, including efficient calculation strategies and applications to heavy molecules with higher-order corrections.

Findings

Successfully applied to E119F molecule with higher-order effects.

Developed fitting potentials for molecular electronic structure calculations.

Analyzed virtual muon and pion field contributions.

Abstract

We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced charge densities and form factors in momentum space. A strategy for the efficient calculation of vacuum polarization potentials is outlined, implemented, and applied towards the construction of fitting potentials that are suitable for molecular electronic structure calculations, which enclose no overall charge by construction. The order $\alpha(Z \alpha)$, $\alpha (Z \alpha)^{3}$ and $\alpha^{2}(Z\alpha)$ effects of a Gaussian nuclear charge on the electron-positron field are applied variationally towards the E119F molecule, as well as the order $\alpha(Z \alpha)$ effects arising from the virtual muon and charged pion fields.