The Rydberg constant and proton size from atomic hydrogen

  title={The Rydberg constant and proton size from atomic hydrogen},
  author={Axel Beyer and Lothar Maisenbacher and Arthur Matveev and Randolf Pohl and Ksenia Yu Khabarova and Alexey Grinin and Tobias P. Lamour and Dylan C. Yost and Theodor W. H{\"a}nsch and Nikolai Kolachevsky and Thomas Udem},
  pages={79 - 85}
How big is the proton? The discrepancy between the size of the proton extracted from the spectroscopy of muonic hydrogen and the value obtained by averaging previous results for “regular” hydrogen has puzzled physicists for the past 7 years. Now, Beyer et al. shed light on this puzzle (see the Perspective by Vassen). The authors obtained the size of the proton using very accurate spectroscopic measurements of regular hydrogen. Unexpectedly, this value was inconsistent with the average value of… 

The proton size

The proton charge radius has been measured since the 1950s using elastic electron–proton scattering and ordinary hydrogen atomic spectroscopy. In 2010, a highly precise measurement of the proton

The proton size puzzle: experiment vs theory.

Current status of the proton size puzzle from experimental and theoretical points of view is briefly discussed. The interest to these studies is primarily related to experiments conducted by the

The proton radius revisited

The value of the proton size they deduce from their spectra agrees with the value from muonic hydrogen spectroscopy and disagrees with most previous measurements in regular hydrogen—and there were many; the Rydberg constant disagrees with the literature value by more than three standard deviations.

Nonresonant Effects in the Two-Photon Spectroscopy of a Hydrogen Atom: Application to the Calculation of the Charge Radius of the Proton

A discrepancy of 4σ (σ is the standard deviation) between the proton radii obtained by measuring transition frequencies in electron (H) and muonic (µH) hydrogen atoms has been actively discussed in

A small proton charge radius from an electron–proton scattering experiment

The smaller r p the authors have now measured supports the value found by two previous muonic hydrogen experiments, and agrees with the revised value for the Rydberg constant, one of the most accurately evaluated fundamental constants in physics.


A slight anomaly in optical spectra of the hydrogen atom led Willis E. Lamb to the search for the proton size. As a result, he found the shift of the 2S1/2 level, the first experimental demonstration

2S-4S spectroscopy in hydrogen atom: The new value for the Rydberg constant and the proton charge radius

The core of the “proton radius puzzle” is the discrepancy of four standard deviations between the proton root mean square charge radii (rp) determined from regular hydrogen (H), and the muonic

The MUon Scattering Experiment (MUSE) at the Paul Scherrer Institute

  • S. Strauch
  • Physics
    Proceedings of The 20th International Workshop on Neutrinos — PoS(NuFACT2018)
  • 2019
While consistent results for the charge radius of the proton have been extracted from elastic electron-scattering data and through the spectroscopy of atomic hydrogen, high-precision studies of

The proton charge radius

Nucleons (protons and neutrons) are the building blocks of atomic nuclei, and are responsible for more than 99% of the visible matter in the universe. Despite decades of efforts in studying its



Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen

Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen.

Laser spectroscopy of muonic deuterium

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value.

Muonic Hydrogen and the Proton Radius Puzzle

The extremely precise extraction of the proton radius obtained by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that

The size of the proton

The root-mean-square charge radius, rp, has been determined with an accuracy of 2 per cent by electron–proton scattering experiments, and the present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants.

Precision spectroscopy of 2S–nP transitions in atomic hydrogen for a new determination of the Rydberg constant and the proton charge radius

Precision measurements of transition frequencies in atomic hydrogen provide important input for a number of fundamental applications, such as stringent tests of QED and the extraction of fundamental

Tabulation of the bound-state energies of atomic hydrogen

We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure, and thus this work extends the work of Rev. Mod. Phys. {\bf 84}, 1527

Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA

High-precision measurement of the atomic mass of the electron

A very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics, and the precision of the resulting value for the atomic mass of the electron surpasses the current literature value of the Committee on Data for Science and Technology (CODATA).

Evaluation of the Proton Charge Radius from Electron–Proton Scattering

In light of the proton radius puzzle, the discrepancy between measurements of the proton charge radius from muonic hydrogen and those from electronic hydrogen and electron–proton (e–p) scattering