Self-Energy Correction to the Hyperfine Splitting for Excited States
  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. 
B. J. Wundt, U. D. Jentschura
physics.atom-ph hep-ph