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Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

Andrzej Czarnecki·Ulrich D. Jentschura·Krzysztof Pachucki
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Abstract

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of order alpha^2(Zα)^] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.

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Andrzej Czarnecki, Ulrich D. Jentschura, Krzysztof Pachucki. 2006-03-15. Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States. https://doi.org/10.1103/physrevlett.95.180404

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