Two-Loop Bethe Logarithms for non-S Levels

Published

October 16, 2008

Author(s)

Ulrich D. Jentschura

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. The obtained results complete our knowledge of the P and D energy levels in hydrogen at the order of a8 mec2, where me is the electron mass and c is the speed of light, and it scales with Z6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms or order (a/p)2 (Za)6 In [(Za)-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 be subtracted in the numerical evaluation, which complicates the evaluation. We find that, surprisingly, the corrections of the squared decay-rate type are the numerically dominant contributions in the order (a/p)2 (Za)6 mec2 for states with high angular momenta, and provide an estimate of the entire B60-coeeficiant for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Pub Type

Journals

Keywords

Bethe logarithms, QED, two-loop

Citation

Jentschura, U. (2008), Two-Loop Bethe Logarithms for non-S Levels, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed October 12, 2025)