Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2 V cm−1, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 S1/22(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)−1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011); A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)stat(1.8)syst kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)−2P1/2(1) interval [N. Bezginov et al., Science 365, 1007 (2019)], we determine the Rydberg frequency to be cR∞=3 289 841 960 204(15)stat(7)syst(13)2S−2P kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.Received 27 October 2023Revised 18 January 2024Accepted 25 January 2024DOI:https://doi.org/10.1103/PhysRevLett.132.113001© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtomic spectraDetermination of fundamental constantsElectronic transitionsFine & hyperfine structureStark effectPhysical SystemsAtomic & molecular beamsAtomsRydberg atoms & moleculesTechniquesOptical spectroscopyAtomic, Molecular & Optical