Two-loop Bethe-logarithm correction in hydrogenlike atoms
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Updated: Aug 30, 2026

Neutron Crystallography Data Collection and Processing for Modelling Hydrogen Atoms in Protein Structures
Published on: December 1, 2020
Krzysztof Pachucki1, Ulrich D Jentschura
1Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland.
Abstract:
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 1S-2S transition: It contributes -8.19 and -0.84 kHz for the 1S and the 2S 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 experimental accuracy for the Lamb shift in atomic hydrogen to the level of 10(-7).
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