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.



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

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Document Type

Article - Journal

Document Version

Final Version

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© 2011 American Physical Society (APS), All rights reserved.

Publication Date

01 May 2011

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Physics Commons