On the interaction between two point electric charges

TL;DR

This paper derives a comprehensive analytical formula for the interaction potential between two point electric charges, incorporating lowest order vacuum polarization corrections, and discusses its implications for Coulomb systems and related phenomena.

Contribution

It introduces an original algebraic method to systematically determine vacuum polarization corrections for Coulomb interactions, extending previous models.

Findings

Correct asymptotic behavior at small and large distances

Analytical expression for vacuum polarization corrections

Application to Coulomb scattering and cusp problems

Abstract

The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the closed analytical expression for the Uehling potential obtained earlier. Our analytical formula has the correct asymtotic behaviour at small and large distances between two interacting electric charges. We also discuss a number of problems which are of great interest in applications, e.g., vacuum polarization corrections to the Coulomb scattering and cusp value between two electrically charged particles. An original algebraic procedure developed in this study allows one to determine consequtive corrections for vacuum polarization for Coulomb systems.