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.



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

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Document Type

Article - Journal

Document Version

Final Version

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© 2002 American Physical Society (APS), All rights reserved.

Publication Date

01 Aug 2002

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Physics Commons