Uehling potential and lowest-order corrections on vacuum polarization to the cross sections of some QED processes

TL;DR

This paper investigates the Uehling potential's properties and introduces a new analytical method to evaluate the lowest-order vacuum polarization corrections to various QED process cross sections, enhancing computational clarity and physical insight.

Contribution

The paper presents a novel analytical procedure for calculating vacuum polarization corrections in QED processes, based on properties and Fourier transforms of the Uehling potential.

Findings

Developed a new analytical method for vacuum polarization corrections.

Applied the method to processes like Mott scattering, bremsstrahlung, and pair creation.

Provided explicit formulas for corrections in heavy Coulomb fields.

Abstract

Properties and different representations of the Uehling potential are investigated. Based on these properties and by using our formulas for the Fourier transform of the Uehling potential we have developed the new analytical, logically closed and physically transparent procedure which can be used to evaluate the lowest-order vacuum polarization correction to the cross sections of a number of QED processes, including the Mott electron scattering, bremsstrahlung, creation and/or annihilation of the $(e^{-}, e^{+})-$pair in the field of a heavy Coulomb center, e.g., atomic nucleus.