Two-Loop Bethe Logarithms for non-S Levels
arXiv:physics/0612251 · doi:10.1103/PhysRevA.74.062517
Abstract
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 alpha^8 m_e c^2, where m_e is the electron mass and c is the speed of light, and scale as Z^6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z alpha)^(-2)] m_e c^2 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 (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with large angular momenta, and provide an estimate of the entire B_60-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.
14 pages, RevTeX
References in corpus (6)
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- Non-uniform convergence of two-photon decay rates for excited atomic states
- Two-loop QED corrections in few-electron ions
- Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states
- Two-loop electron self-energy with accelerated partial-wave expansion
- Two-Loop Effects and Current Status of the 4He+ Lamb Shift