Using the first new method in half a century for measuring the size of the proton via electron scattering, nuclear physicists have produced a new value for the proton’s radius.
Using the first new method in half a century for measuring the size of the proton via electron scattering, nuclear physicists have produced a new value for the proton’s radius.
Image courtesy of Jefferson Lab

The Science

Textbook pictures make atomic nuclei seem tidy, but they are actually fuzzy clouds of subatomic particles. This makes it hard to measure the size of positively charged protons in nuclei. Historically, scientists used two different methods to get an approximate measure of proton size. The “proton radius puzzle” arose in 2010. That’s when a then-new, more sensitive experimental method for measuring the size of the proton by replacing the electron with the heavier muon unexpectedly revealed a value that was 4 percent smaller than obtained from the two previous methods. Nuclear physicists may have now solved the proton radius puzzle with a unique new measurement of the charge radius using a novel electron scattering technique.

The Impact

This new research gives researchers a more precise way of measuring components of the atom. This will help scientists better understand these basic components of our universe. In addition, the results put an end to speculation that the proton radius puzzle suggested the existence of a new force of nature that acted differently between electrons and muons.


Prior to 2010, the most precise measurements of the proton’s charge radius came from two different experimental methods. In electron-scattering experiments, electrons are shot at the protons, and the proton’s charge radius is determined by the change in path of the electrons after they bounce off or scatter from the proton. In atomic spectroscopy measurements, the transitions between energy levels by electrons are observed (in the form of photons that are given off by the electrons) as they orbit a small nucleus, such as hydrogen (with one proton) or deuterium (with one proton and one neutron). When combined, these two methods yielded a radius of 0.8751 ± .0061 femtometers. In 2010, atomic physicists announced results from a new method that measured the transition between energy levels of muons in orbit around lab-made hydrogen atoms that replaced an orbiting electron with a muon, which orbits much closer to the proton and is more sensitive to the proton’s charge radius. This result yielded a value that was 4 percent smaller than before, at 0.84184 ± .00067 femtometers. This discrepancy was dubbed the proton radius puzzle. In 2012, a collaboration of scientists came together to revamp the electron-scattering method for a more precise measurement of the proton’s charge radius. The PRad experiment implemented a new type of windowless target system that allowed scattered electrons to move nearly unimpeded into the detectors; the experiment used a combination of calorimeter and gas electron multiplier devices to detect the electrons' positions and energies within relatively large intervals and with high accuracy. They also managed to place these detectors extremely close in angular distance from the target to test the proton size in a most gentle way. PRad measured the charge radius of the proton to be 0.831 ± .014 femtometers, which is smaller than the previous electron-scattering value and is in agreement with the muonic atomic spectroscopy results.


Ashot Gasparian
North Carolina A&T State University


This research was funded by the Department of Energy Office of Science, Nuclear Physics program.


Xiong, W.. et al. “A small proton charge radius from an electron–proton scattering experiment.” Nature 575, 147–150 (2019). [doi:10.1038/s41586-019-1721-2]

Related Links

Jefferson Lab news release: New Measurement Yields Smaller Proton Radius

Jefferson Lab news story: Physicists Team Up to Tackle Proton Radius Problem