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Updated: Aug 19, 2026

Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
Published on: September 17, 2017
Constraints on proton structure from precision atomic-physics measurements
Stanley J Brodsky1, Carl E Carlson, John R Hiller
1Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309, USA.
Abstract:
Ground-state hyperfine splittings in hydrogen and muonium are very well measured. Their difference, after correcting for magnetic moment and reduced mass effects, is due solely to proton structure-the large QED contributions for a pointlike nucleus essentially cancel. The rescaled hyperfine difference depends on the Zemach radius, a fundamental measure of the proton, computed as an integral over a product of electric and magnetic proton form factors. The determination of the Zemach radius, (1.019+/-0.016) fm, from atomic physics tightly constrains fits to accelerator measurements of proton form factors. Conversely, we can use muonium data to extract an experimental value for QED corrections to hydrogenic hyperfine data. There is a significant discrepancy between measurement and theory, in the same direction as a corresponding discrepancy in positronium.
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