Calculation of hydrogenic Bethe logarithms for Rydberg states
- Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany)
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8401 (United States)
We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n{<=}200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.
- OSTI ID:
- 20718301
- Journal Information:
- Physical Review. A, Vol. 72, Issue 1; Other Information: DOI: 10.1103/PhysRevA.72.012110; (c) 2005 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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