Differential equation for the Uehling potential

2024/01/29 by Alexei M. Frolov, Frolov, Alexei M. · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.2402.03360

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 K₀(b r) and K₁(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.

Cited by

• Antiprotonic atoms with nonperturbative inclusion of vacuum polarization and finite nuclear mass
• Influence of a Perfectly Conducting Plate on the Uehling Potential of QED

Related

• On the properties of the Uehling potential
• Computation of the leading order contributions to the Lamb shift for the H atom using spectral regularization
• Vacuum polarization in molecules I: Uehling interaction
• On the interaction between two point electric charges
• QED vacuum polarization in the Coulomb field of a nucleus: a method of high-order calculation