Confirm the O(Z α) E_F contribution to hyperfine splitting

Establish and confirm the order (Z α) times the Fermi energy (E_F) recoil contribution to the hyperfine splitting in hydrogen-like ions by deriving it rigorously within quantum electrodynamics and validating the coefficient originally reported by Bodwin and Yennie (Phys. Rev. D 37, 498 (1988)).

Background

The paper develops a general quantum electrodynamic framework for nuclear recoil corrections in hydrogenic systems that is exact in Z α, and applies it to derive nonperturbative formulas for the leading recoil correction to hyperfine splitting. These formulas can be used both for direct numerical evaluation and for analytic extraction of Z α expansion coefficients.

In the Summary, the authors explicitly highlight an unresolved issue concerning the O(Z α) E_F term (with E_F denoting the Fermi energy scale for hyperfine splitting): although Bodwin and Yennie previously derived this contribution, it remains without independent confirmation. The authors suggest their framework could be used to address this gap by enabling a rigorous derivation and verification of the coefficient.