We determine the third Zemach moment of hydrogen (⟨r³⟩₍₂₎) using only the world data on elastic electron-proton scattering. This moment dominates the O(Zα)⁵ hadronic correction to the Lamb shift in muonic atoms. The resulting moment, ⟨r³⟩₍₂₎=2.71(13)0.3em0exfm³, is larger than some previously inferred values based on simple models. The contribution of that moment to the muonic hydrogen 2S level is -0.0247(12)0.3em0exmeV.
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Friar et al. (2005) studied this question.
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