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 mec2, 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] mec2 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 mec2 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.
U. D. Jentschura, "Two-Loop Bethe Logarithms for Non- S Levels," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 74, no. 6, pp. 062517-1-062517-13, American Physical Society (APS), Dec 2006.
The definitive version is available at https://doi.org/10.1103/PhysRevA.74.062517
Keywords and Phrases
Electrodynamics; Electron Energy Levels; Electrons; Hydrogen; Numerical Methods; Quantum Theory; Angular Momentum; Excited States; Hydrogenlike Systems; Two-loop Bethe Logarithms; Molecular Dynamics
International Standard Serial Number (ISSN)
Article - Journal
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