Two-Loop Bethe Logarithms for Higher Excited S Levels

Details Two-Loop Bethe Logarithms for Higher Excited S Levels Two-Loop Bethe Logarithms for Higher Excited S Levels

2004-09-23

arxiv.org/abs/hep-ph/0409271v2

Phys.Rev. A70 (2004) 052108

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, RevTeX, to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.70.052108

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic S states. The corresponding level shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher excited S states, which in contrast to the 1S and 2S states can decay to P states via the electric-dipole (E1) channel. The more complex structure of the excited-state wave functions and the necessity to subtract P-state poles lead to additional calculational problems. In addition to the calculation of the excited-state two-loop energy shift, we investigate the ambiguity in the energy level definition due to squared decay rates.

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