Second-Order Radiative Corrections to Hyperfine Structure

In this paper the effect of second-order radiative displacements of the energy levels of a bound electron on hyperfine structure separation is examined, and a correction to the Fermi formula for s levels is obtained. The treatment is based on an approximate evaluation of a finite, completely renormalized, and exact expression for the second order energy. The correction, which is restricted to atoms of small αZ, is found to be [α2π-α²Z(5/2-ln2)]EH, where EH is the Fermi energy. The effect of this and other corrections to the Fermi formula on the presently accepted value of the fine structure constant is discussed.