Proton Radius, Darwin-Foldy Term and Radiative Corrections

TL;DR

This paper examines the impact of the Darwin-Foldy term and radiative corrections on the determination of proton and deuteron charge radii, clarifying conventions and addressing discrepancies in recent measurements from atomic and scattering data.

Contribution

It provides a detailed analysis of the conventions regarding the Darwin-Foldy term and proposes a consistent definition of nuclear self energy for scattering experiments.

Findings

Clarified the role of the Darwin-Foldy term in radius evaluations

Highlighted the importance of conventions in interpreting experimental data

Proposed a consistent approach to radiative corrections in scattering measurements

Abstract

We discuss the role of the so-called Darwin-Foldy term in the evaluation of the proton and deuteron charge radii from atomic hydrogen spectroscopy and nuclear scattering data. The question of whether this term should be included or excluded from the nuclear radius has been controversially discussed in the literature. We attempt to clarify which literature values correspond to which conventions. A detailed discussion of the conventions appears useful because a recent experiment [R. Pohl et al., Nature vol. 466, p. 213 (2010)] has indicated that there is a discrepancy between the proton charge radii inferred from ordinary ("electronic") atomic hydrogen and muonic hydrogen. We also investigate the role of quantum electrodynamic radiative corrections in the determination of nuclear radii from scattering data, and propose a definition of the nuclear self energy which is compatible with the subtraction of the radiative corrections in scattering experiments.