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Journal Article

Two-Loop Bethe logarithms for higher excited S levels


Jentschura,  Ulrich David
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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Jentschura, U. D. (2004). Two-Loop Bethe logarithms for higher excited S levels. Physical Review A, 70(5): 052108. doi:10.1103/PhysRevA.70.052108.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0011-8AE5-8
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 mec2 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. 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.