Two-loop Bethe logarithms for non- S levels

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Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of α8 me c2, where me is the electron mass and c is the speed of light, and scale as Z6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (απ)2 (Zα)6 ln [(Zα)-2] me c2 for D states and all states with higher angular momenta. For higher excited P and D states, a number of poles from lower-lying levels have to subtracted in the numerical evaluation. We find that, surprisingly, the corrections of the "squared decay-rate type" are the numerically dominant contributions in the order (απ)2 (Zα)6 me c2 for states with large angular momenta, and provide an estimate of the entire B60 coefficient for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.

Original languageEnglish
Article number062517
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number6
Publication statusPublished - Dec 1 2006


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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