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Updated: Apr 13, 2026

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Precision Spectroscopy of 2S-nS Transitions in Atomic Hydrogen: A Determination of the Proton Charge Radius
R G Bullis1, W L Tavis1, M R Weiss1
1Colorado State University, Department of Physics, Fort Collins, Colorado 80523, USA.
Abstract:
We present absolute frequency measurements of 2S_{1/2}-nS_{1/2} two-photon transitions with n=8, 9, and 10 in a cryogenic beam of atomic hydrogen. Each transition has been measured with a fractional uncertainty of ≈2.6×10^{-12}. Combining the results from this Letter and the 1S_{1/2}-2S_{1/2} transition frequency, we extract a root-mean-square proton radius of r_{p}=0.8433(31) fm and a Rydberg frequency of cR_{∞}=3 289 841 960 252.9(9.7) kHz. These are in good agreement with the CODATA 2022 recommended values.
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