General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order α(Zα)6] and for the two-loop Lamb shift [of order α2(Zα)6] 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 Δn=n3ΔE(nS)-ΔE(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.
A. Czarnecki et al., "Calculation of the One- and Two-loop Lamb Shift for Arbitrary Excited Hydrogenic States," Physical Review Letters, vol. 95, no. 18, pp. 180404-1-180404-4, American Physical Society (APS), Oct 2005.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.95.180404
Keywords and Phrases
Fermion Loops; Hydrogenic States; Lamb Shifts; Electrodynamics; Electron Energy Levels; Normal Distribution; Numerical Methods; Phase Shift; Quantum Theory
International Standard Serial Number (ISSN)
Article - Journal
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