The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions using an expansion in the binding parameter Zα, where Z is the nuclear-charge number and α is the fine-structure constant. We present analytic results for D, F, and G states, and for a number of highly excited Rydberg states, with principal quantum numbers in the range 13≤n≤16, and orbital angular momenta =n-2 and =n-1. A closed-form analytic expression is derived for the contribution of high-energy photons, valid for any state with ≥2 and arbitrary n, , and total angular momentum j. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.
B. J. Wundt and U. D. Jentschura, "Self-Energy Correction to the Hyperfine Splitting for Excited States," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 83, no. 5, pp. 052501-1-052501-6, American Physical Society (APS), May 2011.
The definitive version is available at https://doi.org/10.1103/PhysRevA.83.052501
Keywords and Phrases
Analytic Expressions; Binding Parameter; Closed Form; Fine Structure Constants; High Energy Photons; Hydrogenlike Ion; Hyperfine Splittings; Low Energies; Orbital Angular Momentum; Principal Quantum Numbers; Self-energy Corrections; Algebra; Angular Momentum; Quantum Theory; Excited States
International Standard Serial Number (ISSN)
Article - Journal
© 2011 American Physical Society (APS), All rights reserved.
01 May 2011