Considering that the proton is a basic subatomic component of all ordinary matter — as well as being ubiquitous in its solo role as the hydrogen ion H+ — there are some surprising gaps in our knowledge of its structure and behaviour. A collaborative project to determine the root-mean-square charge radius of the proton to better than the 1% accuracy of the current 'best' value suggests that those knowledge gaps may be greater than was thought. The new determination comes from a technically challenging spectroscopic experiment — the measurement of the Lamb shift (the energy difference between a specific pair of energy states) in 'muonic hydrogen', an exotic atom in which the electron is replaced by its heavier twin, the muon. The result is unexpected: a charge radius about 4% smaller than the previous value. The discrepancy remains unexplained. Possible implications are that the value of the most accurately determined fundamental constant, the Rydberg constant, will need to be revised — or that the validity of quantum electrodynamics theory is called into question. Here, a technically challenging spectroscopic experiment is described: the measurement of the muonic Lamb shift. The results lead to a new determination of the charge radius of the proton. The new value is 5.0 standard deviations smaller than the previous world average, a large discrepancy that remains unexplained. Possible implications of the new finding are that the value of the Rydberg constant will need to be revised, or that the validity of quantum electrodynamics theory is called into question. The proton is the primary building block of the visible Universe, but many of its properties—such as its charge radius and its anomalous magnetic moment—are not well understood. The root-mean-square charge radius, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments1,2. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants3. This value is based mainly on precision spectroscopy of atomic hydrogen4,5,6,7 and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of rp as deduced from electron–proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant3). An attractive means to improve the accuracy in the measurement of rp is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift10 (the energy difference between the 2S1/2 and 2P1/2 states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations11,12,13,14,15 of fine and hyperfine splittings and QED terms, we find rp = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value3 of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by −110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

Proton Still Too Small: Despite a proton's tiny size, it is possible to measure its radius based on its charge or magnetization distributions. Traditional measurements of proton radius were based on the scattering between protons and electrons. Recently, a precision measurement of a line in the spectrum of muonium—an atom consisting of a proton and a muon, instead of an electron—revealed a radius inconsistent with that deduced from scattering studies. Antognini et al. (p. 417 ; see the Perspective by Margolis ) examined a different spectral line of muonium, with results less dependent on theoretical analyses, yet still inconsistent with the scattering result; in fact, the discrepancy increased.

The authors combine modern theoretical calculations with evaluated selected experimental data to produce a comprehensive data resource of K- and L-x-ray transition and absorption edge energies for all of the elements from neon to fermium. The theoretical and experimental components of this work are the result of programs of parallel development extending over more than 20 years. At each of several progressively more refined comparisons, it was possible to identify theoretical components whose systematic improvement then led to the next level of refinement in comparisons with an increasingly robust experimental reference data set. We have now reached a certain practical limit in what can be undertaken with reasonable levels of theoretical effort. This limit is not very different from the practical level of accuracy that can be meaningfully associated with the experimental data. For the more prominent diagram lines, experiment and theory are concordant with a zero-centered distribution of residuals whose statistical metrics allow the uncertainties to be estimated. For the light elements $\mathrm{}(Z<\mathrm{}20\mathrm{})\mathrm{}$ and the very heavy elements $\mathrm{}(Z>\mathrm{}90\mathrm{})\mathrm{}$ there are significant difficulties, as is also the case for a few isolated elements and transitions for $20<Z<\mathrm{}90.\mathrm{}$ Overall, the results reported here represent improvements over previously available data compilations not only because of their scope but also because of their attempt to offer internal metrics of the database accuracy. The identified regions of difficulty are areas where further experimental work may be directed to see if there may remain theoretical issues that are still unresolved.

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. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science , this issue p. 669

We present accurate calculations of the 1${\mathit{s}}^2$2s and 1${\mathit{s}}^2$2p energy levels of lithiumlike ions for 15≤2Z≤92. The multiconfiguration Dirac-Fock method has been used to calculate relativistic effects. One-electron radiative corrections and estimated screening corrections have been calculated. These results are in good agreement with relativistic many-body calculations. General agreement with experimental transition energies (available up to Z=92) is very good.