ar X iv : h ep - p h / 02 05 01 9 v 2 1 0 Ju l 2 00 2 Double – Logarithmic Two – Loop Self – Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zα can often be derived within a simplified approach , avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by α the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy " potentials " that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B 62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B 62 based on nonrela-tivistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach. Keywords quantum electrodynamics-specific calculations; calculations and mathematical techniques in atomic and molecular physics; Relativistic and quantum electrodynamic effects in atoms and molecules.