On the properties of the Uehling potential

TL;DR

This paper investigates the properties of the Uehling potential, including its Fourier resolution, relation to electron density, and implications for perturbation theory in Coulomb systems, enhancing understanding of vacuum polarization effects.

Contribution

It provides a detailed analysis of the Uehling potential's properties and develops approximations for its application in Coulomb few-body systems, addressing the cusp problem.

Findings

Fourier spatial resolution of the Uehling potential determined

Reformulation of vacuum polarization correction in terms of electron density

Development of perturbation theory approximations for short-range Uehling potential

Abstract

A number of properties of the Uehling potential are investigated. In particular, we determine the Fourier spatial resolution of the Uehling potential. The lowest-order correction on vacuum polarisation is re-written in terms of the electron density distribution function. We also discuss the consecutive approximations of the perturbation theory developed for the short-range Uehling potential in the Coulomb few-body systems (atoms). The cusp problem is formulated for few-body systems in which particles interact with each other by the mixed (Coulomb + Uehling) potential.