Self-energy corrections involving logarithms of the parameter Z α can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic nonlogarithmic 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 B62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B62 based on nonrelativistic quantum electrodynamics. 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 ogarithm is not contained in the effective-potential approach.
U. D. Jentschura and I. Nandori, "Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 66, no. 2, pp. 1-9, American Physical Society (APS), Aug 2002.
The definitive version is available at https://doi.org/10.1103/PhysRevA.66.022114
Keywords and Phrases
Electrodynamics; Electronic Density Of States; Hydrogen; Numerical Methods; Quantum Theory, Double Logarithmic Two Loop Self Energy Corrections; Lamb Shift Measurement; Nuclear Charge Number; Quantum Electrodynamics, Electron Energy Levels
International Standard Serial Number (ISSN)
Article - Journal
© 2002 American Physical Society (APS), All rights reserved.