The Uehling correction in muonic atoms exactly in Z\alpha

TL;DR

This paper derives an exact expression for the Uehling correction in muonic atoms using hypergeometric functions, enabling new asymptotic and approximation methods for atomic energy calculations.

Contribution

It introduces a novel hypergeometric function-based formulation of the Uehling correction, facilitating precise asymptotic analysis and broader applications in atomic physics.

Findings

Exact hypergeometric function representation of the Uehling correction

Derivation of various asymptotic forms and approximations

Potential applications to other atomic characteristics

Abstract

The Uehling correction to the energy levels is presented in terms of the hypergeometric functions 2F1. This presentation allows to derived various asymptotics and approximations. Further applications of this method to other atomic characteristics are also considered.