Differential equation for the Uehling potential

Alexei M. Frolov ()
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Alexei M. Frolov: University of Western Ontario

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 6, 1-5

Abstract: Abstract 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 $$K_{0}(b r)$$ K 0 ( b r ) and $$K_{1}(b r)$$ K 1 ( b r ) . 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. Graphic Abstract

Date: 2024
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DOI: 10.1140/epjb/s10051-024-00728-x

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