Precision Spectroscopy of 2S-nS Transitions in Atomic Hydrogen: A Determination of the Proton Charge Radius

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 approximately 2.6*10^(-12). Combining the results from this work 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_{\infty} = 3,289,841,960,252.9(9.7) kHz. These are in good agreement with the CODATA 2022 recommended values.