Finite nuclear mass ${\left(Z\alpha \right)}^{2}m/M{E}_F$ corrections to the hyperfine splitting in hydrogenic systems are calculated using a combined relativistic heavy particle and nonrelativistic quantum electrodynamics. The obtained results are in disagreement with previous calculations by Bodwin and Yennie [Phys. Rev. D 37, 498 (1988)]. The comparison of improved theoretical predictions with the corresponding measurements in hydrogen reveals $2\sigma$ discrepancy, which may indicate problems with the proton structure corrections.

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• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions