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Journal Article

Two-loop Bethe logarithms for non-S levels


Jentschura,  Ulrich David
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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Jentschura, U. D. (2006). Two-loop Bethe logarithms for non-S levels. Physical Review A, 74(6): 062517, pp. 1-13. doi:10.1103/PhysRevA.74.062517.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-7ECF-C
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 α⁸mec₂, 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 (α/π)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 (α/π)²(Zα)⁶mec² 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.