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 .



Keywords and Phrases

Electrodynamics; Green's Function; Hamiltonians; Quantum Theory; Atomic Energy Levels; Atomic Physics

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

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© 2003 American Physical Society (APS), All rights reserved.

Publication Date

01 Sep 2003

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Physics Commons