We calculate the one- and two-loop corrections of order α(Zα)⁶ and α²(Zα)⁶, respectively, to the Lamb shift in hydrogenlike systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order α²(Zα)⁶ includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.
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Jentschura et al. (2005) studied this question.
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