Study finds diameter of proton at 0.83 femtometers

Journal Science -The Rydberg constant and proton size from atomic hydrogen

How big is the proton?

This study and one of the prior studies have the diameter of the proton was about 0.83 femtometers (m). A femtometer is 10^-15 meters.

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. 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 previous measurements of the same type. Also unexpectedly, it was consistent with the size extracted from the muonic hydrogen experiments. Resolving the puzzle must now include trying to understand how the old results relate to the new, as well as reexamining the sources of systematic errors in all experiments.

Abstract

At the core of the “proton radius puzzle” is a four–standard deviation discrepancy between the proton root-mean-square charge radii (rp) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant R∞ = 10973731.568076(96) per meter and rp = 0.8335(95) femtometer. Our rp value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.

“Our measurement is almost as precise as all previous measurements on regular hydrogen combined,” summarizes Prof. Thomas Udem, the project leader. “We are in good agreement with the values from muonic hydrogen, but disagree by 3.3 standard deviations with the hydrogen world data, for both the Rydberg constant and the proton radius. To find the causes of these discrepancies, additional measurements with perhaps even higher precision are needed. After all, one should keep in mind that many new discoveries first showed up as discrepancies.”

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