Eur. Phys. J. B (2012) 85: 348
https://doi.org/10.1140/epjb/e2012-30408-4

Regular Article

Analytical formula for the Uehling potential

Department of Chemistry University of Western Ontario, London, N6H 5B7 Ontario, Canada

^a e-mail: afrolov@uwo.ca
^b Permanent address: Department of Chemistry, Memorial University of Newfoundland, St. John’s, A1C5S7 Newfoundland and Labrador, Canada.

Received: 21 May 2012
Received in final form: 4 August 2012
Published online: 18 October 2012

Abstract

The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the interaction potential between two electrically charged point particles which includes correction to the vacuum polarisation, but has correct asymptotic behaviour at larger r. Our three-term analytical formula for the Uehling potential opens a new avenue in the study of the vacuum polarisation in light atomic systems.