We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1 S – 2 S transition: It contributes - 8.19 and - 0.84 k H z for the 1 S and the 2 S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb shift to date. Together with the ongoing measurement of the proton charge radius at the Paul Scherrer Institute, its calculation will bring theoretical and perimental accuracy for the Lamb shift in atomic hydrogen to the level of 10- 7 .
K. Pachucki and U. D. Jentschura, "Two-Loop Bethe-Logarithm Correction in Hydrogenlike Atoms," Physical Review Letters, vol. 91, no. 11, pp. 1130051-1130054, American Physical Society (APS), Sep 2003.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.91.113005
Keywords and Phrases
Electrodynamics; Green's Function; Hamiltonians; Quantum Theory; Atomic Energy Levels; Atomic Physics
International Standard Serial Number (ISSN)
Article - Journal
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