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.Comment: 7 pages; RevTe
