Two-loop Bethe logarithms for non-S levels
- Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany) and National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8401 (United States)
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}{sup 8}m{sub e}c{sup 2}, where m{sub e} is the electron mass and c is the speed of light, and scale as Z{sup 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}){sup 2}(Z{alpha}){sup 6} ln[(Z{alpha}){sup -2}]m{sub e}c{sup 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}){sup 2}(Z{alpha}){sup 6}m{sub e}c{sup 2} for states with large angular momenta, and provide an estimate of the entire B{sub 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.
- OSTI ID:
- 20976471
- Journal Information:
- Physical Review. A, Vol. 74, Issue 6; Other Information: DOI: 10.1103/PhysRevA.74.062517; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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