A determination of the Rydberg constant and proton radius through hydrogen 2S-nS spectroscopy.

We will discuss measurements of three 2S-nS two-photon transitions in atomic hydrogen [1].  These results relied on a recently developed method to obtain narrow experimental linewidths by mitigating the AC Stark shift [2].  Our measurements can be used in conjunction with the hydrogen 1S-2S transition [3], and bound-state quantum electrodynamics corrections, to extract a value for the Rydberg constant with a relative uncertainty of 3 x 10^-12.  Our value for the mean charge radius of the proton is  0.8433(31) fm, which is in excellent agreement with the muonic hydrogen value [4].

[1] Bullis et al, PRL 136, 123001 (2026)

[2] Bullis et al, PRA 110, 052807 (2024)

[3] Parthey et al, PRL 107, 203001 (2011)

[4] Antognini et al, Science 339, 417 (2013)