https://doi.org/10.1140/epjb/s10051-024-00728-x
Regular Article - Computational Methods
Differential equation for the Uehling potential
Department of Applied Mathematics, University of Western Ontario, N6H 5B7, London, ON, Canada
Received:
27
April
2024
Accepted:
10
June
2024
Published online:
22
June
2024
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald’s functions 
and 
. This central potential is of great interest in many QED problems, since it describes the lowest order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
