Partial-wave expansion of the Uehling potential

Abstract

A coordinate space approach to vacuum polarization using Pauli-Villars regularization is used to calculate the Uehling potential as a partial-wave expansion. This is done to develop a method that can be extended to cases of vacuum polarization where there is no simple analytic form to use to carry out the necessary renormalization. The numerical behavior of the partial-wave expansion is examined for the Uehling potential itself, its contribution to the fine structure of muonic hydrogen, and its contribution to electron scattering.