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Differential equation for the Uehling potential

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  • Alexei M. Frolov

    (University of Western Ontario)

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

Suggested Citation

  • Alexei M. Frolov, 2024. "Differential equation for the Uehling potential," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-5, June.
  • Handle: RePEc:spr:eurphb:v:97:y:2024:i:6:d:10.1140_epjb_s10051-024-00728-x
    DOI: 10.1140/epjb/s10051-024-00728-x
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