Analytical formula for the Uehling potential

TL;DR

This paper derives a closed-form analytical expression for the Uehling potential, which models vacuum polarization effects in atomic systems, providing a new tool for studying these quantum corrections.

Contribution

The paper presents a novel three-term analytical formula for the Uehling potential, improving the modeling of vacuum polarization effects in atomic physics.

Findings

Derived a closed analytical expression for the Uehling potential.

Formulated an analytical interaction potential including vacuum polarization corrections.

The new formula accurately describes the potential at various distances.

Abstract

The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the interaction potential between two electrically charged point particles which includes correction to the vacuum polarisation, but has correct asymptotic behaviour at larger $r$. Our three-term analytical formula for the Uehling potential opens a new avenue in the study of the vacuum polarisation in light atomic systems.