Self-Energy Correction to the Hyperfine Splitting for Excited States

TL;DR

This paper calculates the self-energy corrections to hyperfine splitting in excited hydrogenlike ions, providing analytic formulas and numerical results for various states, advancing precision in atomic physics calculations.

Contribution

It introduces new analytic expressions and evaluations for self-energy corrections in excited states, extending previous work to higher principal quantum numbers and angular momenta.

Findings

Analytic formulas for high-energy photon contributions applicable to many states.

Numerical evaluations of low-energy contributions using generalized Bethe logarithms.

Results for states with principal quantum numbers 13 to 16 and specific angular momenta.

Abstract

The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions, using an expansion in the binding parameter Zalpha, where Z is the nuclear charge number, and alpha 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 l = n-2 and l = n-1. A closed-form, analytic expression is derived for the contribution of high-energy photons, valid for any state with l <= 2$ and arbitrary n, l and total angular momentum j. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.