After 20 years of research plans and experiments, an expansive collaboration of physicists has directly measured the thickness of the layer of neutrons in a lead atom's nucleus, an unprecedented direct observation that informs how atomic nuclei and neutron stars alike remain stable.

By measuring the scattering of electrons fired at lead-208 atoms, the scientists behind the second Lead Radius Experiment learned that the "neutron skin" surrounding the protons in the lead atomic nucleus was thicker than expected. The finding was published April 27 in Physical Review Letters.

Neutrons are small subatomic particles with no electric charge, and they are present in the atomic nucleus of nearly all elements on the periodic table, alongside positively charged protons. Nuclear physicists are interested in how neutrons and protons are distributed within the nuclei of atoms, but neutrons are difficult to measure because they don't interact with electric fields due to a lack of charge. 

The concept behind the Lead Radius Experiment, or PREX, first emerged more than 20 years ago, when physicists decided to drill down into neutrons by harnessing another fundamental force for its unique property: the weak nuclear force. Responsible for radioactive decay in atoms, the weak force interacts with neutrons but also treats particles with left-handed or right-handed spins differently, something not seen in electromagnetism, gravity and the strong nuclear force.

Spin is an inherent quantum property of subatomic particles that has the same units as angular momentum, but the particles do not physically "spin" about an axis. Kent Paschke, a professor of physics at the University of Virginia and a spokesperson for the Lead Radius Experiment II collaboration, likened the weak force's treatment of spin to a football player who catches balls in a fundamentally different way, depending on whether they are thrown by left-handed or right-handed quarterbacks.

"We're looking at this broken-mirror symmetry and finding out analogously that the physics is different for the right-handed thrown footfall versus the left-handed thrown football," Paschke said. "That's already known, but that's now an effect that we're using; we're using that broken-mirror symmetry to tag the neutrons to figure out where they are."

PREX's target has been lead-208, a highly stable isotope of lead with 82 protons and 126 neutrons. In a heavy nucleus like the one in lead-208, many of the neutrons form a shell around a core of protons and neutrons. This "neutron skin" was first observed in a model-independent fashion by PREX, which published the results in a 2012 paper.

Its successor, PREX-II, was conducted in 2019 at the U.S. Department of Energy's Thomas Jefferson National Accelerator Facility. Substituting footballs for electrons, physicists fired a beam of electrons of both spins at samples of lead-208 and measured the electrons as they scattered.

Measures were taken to minimize noise in the results: The device generating the beam was held still so it didn't deviate by any more than the width of 10 atoms, and the beam itself reversed the direction of the electrons' spins 240 times per second to eliminate interference from the electronics used in the experiment.

In the first direct measurement of the neutron skin, the scientists measured that the radius of the neutron shell was about 5.8 femtometers, or 5.8 quadrillionths of a meter. Subtracting the 5.5-femtometer radius of the sphere of protons leaves a layer of neutrons 0.28 femtometers thick.

The result is thicker than earlier estimates of 0.15 or 0.18 femtometers, and it relies much less on theoretical assumptions than other estimates, according to Paschke.

"There have been lots of other measurements dominantly sensitive to this, but they're sensitive to other dynamics that confuse the issue, and this is now the first time that has been measured in such a clean way to such precision," he said.

The finding brings new clarity to the equation of state of nuclear matter, which ties to the structure and stability of atomic nuclei. Specifically, it puts the strongest experimental constraints yet on the equation-of-state parameter known as the "density dependence of the symmetry energy," which helps explain how the density of particles such as the neutrons in lead-208 is tied to energy costs.

The result has implications not only for atomic nuclei but also for one of the most extreme objects in the universe: neutron stars, the collapsed core of massive stars following supernova stellar explosions. Among the densest things in existence, neutron stars contain, almost exclusively, neutrons that are nearly maximally packed.

The new information about neutrons' equations of state changes how the properties of neutron stars are calculated, according to Paul Souder, a professor of physics at Syracuse University and another spokesperson for PREX. Scientists behind a companion paper also published in Physical Review Letters used the neutron-skin result to calculate a radius and "stiffness" of a specific neutron star and found that it agreed with observations from NASA's NICER telescope.

"What our experiment does is limit, by quite a bit, the range of allowed parameters in this density functional theory, which in turn limits the calculated properties of neutron stars," Souder said.

The findings can also be compared with results from the Laser Interferometer Gravitational-Wave Observatory, or LIGO, which in 2015 provided the first observations of gravitational waves, which were generated by colliding neutron stars.

Under the P2 collaboration at the MESA particle accelerator in Germany, follow-up research is expected to cut the uncertainty of the neutron-skin measurement in half, the spokespeople said. Paschke said he does not expect a result for at least five years, but that such a measurement would be a "real eye-opener" that confirms the gap between theoretical and experimental findings for the neutron skin.

The study, "An accurate determination of the neutron skin thickness of 208Pb through parity-violation in electron scattering," published April 27 in Physical Review Letters, was authored by Devi Adhikari and Dustin McNulty, Idaho State University; H. Albataineh, Texas A&M University; D. Androic, University of Zagreb; K. Aniol, California State University; D.S. Armstrong, T. Averett, C. Ayerbe Gayoso, Q. Campagna, C. Metts, V. Owen, E.W. Wertz and B. Yale, College of William & Mary; S. Barcus, J.F. Benesch, A. Camsonne, S. Covrig Dusa, D. Gaskell, J.-O. Hansen, C. Keppel, S. Malace, M. McCaughan, D. Meekins, R. Michaels, Y. Roblin and B. Wojtsekhowski, Thomas Jefferson National Accelerator Facility; V. Bellini, National Institute for Nuclear Physics, Catania; R.S. Beminiwattha, D. Bhatta Pathak and Y. Chen, Louisiana Tech University; H. Bhatt, D. Bhetuwal and D. Dutta, Mississippi State University; B. Blaikie, M. Gericke, I. Halilovic, G. Leverick, J. Mammei, J. Pan and S. Rahman, University of Manitoba; C. Clarke, C. Feldman, T. Kutz, S. Park, M. Petrusky, R. Richards, T. Ye and W. Zhang, The State University of New York at Stony Brook; J.C. Cornejo and B. Quinn, Carnegie Mellon University; P. Datta, E. Fuchey, A.J.R. Puckett and S. Seeds, University of Connecticut; A. Deshpande and M.M. Mondal, The State University of New York at Stony Brook and Center for Frontiers in Nuclear Science; C. Gal, The State University of New York at Stony Brook, University of Virginia and Center for Frontiers in Nuclear Science; T. Gautam, N. Lashley-Colthirst and B. Pandey, Hampton University; C. Ghosh, University of Massachusetts Amherst and The State University of New York at Stony Brook; F. Hauenstein and M.N.H. Rashad, Old Dominican University; W. Henry, D.C. Jones, J. Napolitano and D. Nikolaev, Temple University; C.J. Horowitz and B.T. Reed, Indiana University; C. Jantzi, S. Jian, S. Katugampola, N. Liyange, S. Premathilake, A. Rathnayake, A. Zec and X. Zheng, University of Virginia; S. Johnston, K.S. Kumar and H. Liu, University of Massachusetts Amherst; B. Karki, P.M. King and R. Radloff, Ohio University; D.E. King, P. Souder and Y. Tian, Syracuse University; M. Knauss, Duquesne University; R. Mammei, University of Winnipeg; A. Narayan, Veer Kunwar Singh University; C. Palatchi, University of Virginia and Center for Frontiers in Nuclear Science; M.L. Pitt, Virginia Polytechnic Institute and State University; P.E. Reimer and S. Riordan, Argonne National Laboratory; A. Shahinyan, A.I. Alikhanyan National Science Laboratory; L. Tang, Thomas Jefferson National Accelerator Facility and Hampton University; M. Thiel, Max Planck Institute for Nuclear Physics; G.M. Urciuoli, National Institute for Nuclear Physics, Rome; A. Yoon, Christopher Newport University; and J. Zhang, The State University of New York at Stony Brook, Center for Frontiers in Nuclear Science and Shangdong University.

Clarification: This story has been updated to remove a quote in order to clarify the kinds of calculations used in the experiment.