Nuclear structure calculations point to proton expansion

Protons and neutrons are composite particles, each comprising three quarks held together by the strong force. The potential confining those quarks is also affected by the nucleon’s surroundings—that is, protons and neutrons in free space are different from those in a nucleus. The details of those differences, however, are still unresolved. Now, using a novel set of calculations, Gerald Miller at the University of Washington in Seattle has amassed strong evidence for one distinction: A proton must be larger when it is in a nucleus.

The first experimental evidence that free and bound nucleons are different came from the European Muon Collaboration (EMC) experiment, shown in the picture, at CERN in 1983 (see the article by Gordon Baym, Physics Today, March 1985, page 40 ). The EMC data showed that nucleons scatter muons differently depending on whether the nucleons are bound, which suggests that their internal structures are modified by their local environments. Subsequent experimental and theoretical work has confirmed that small distinctions in properties such as the quark momentum distribution do exist between bound and free nucleons. Although the radius of a free proton was recently nailed down, the effects of nuclear forces on the proton’s size remain in question.

Miller is not the first to posit that nucleons expand in a confining potential, but he approached the problem in a new way: He determined the proton’s form factor, a function that describes an object’s electromagnetic properties. He also analyzed five proton models rather than just one; each was incomplete but captured important aspects of the proton structure. Each model yielded a different form factor, but they all predicted an increase in the proton charge radius as a result of nuclear binding with the same functional form. Because the result, unlike previous ones, was largely model-independent, it is likely general.

Experimental data can’t yet rule out or confirm Miller’s prediction. For example, his predicted 2% increase in the charge radius of helium-3 is comparable to present measurement uncertainties. Experiments have been proposed to measure the radius of ³He with better than 1% accuracy, which would test his calculations. If the result is confirmed, Miller’s form factor approach to understanding nuclear medium effects could be used to explore other proton properties. (G. A. Miller, Phys. Rev. Lett. 123, 232003, 2019 .)