Lead nuclei have a thick skin

In studies of nuclear structure, lead-208 is special. It has a whopping 44 more neutrons than protons, but unlike most other neutron-rich isotopes, it’s stable. It’s also doubly magic—both its proton and neutron numbers correspond to full nuclear energy levels—and each nucleon type thus forms a sphere of nearly constant density. With that uniformity, the nuclide is a good approximation of uniform nuclear material and therefore potentially useful for understanding neutron stars.

The proton radius of a nucleus is straightforward to measure using electron scattering. But because neutrons lack electric charge, the neutron radius is much trickier to probe. Now the Lead Radius Experiment (PREX) collaboration at the Thomas Jefferson National Accelerator Facility in Virginia has made the most precise measurement of the neutron radius in ²⁰⁸Pb and found that the particles extend 0.283 ± 0.071 femtometers beyond the protons, as shown in the graph. That length, known as the neutron-skin thickness, is larger than most theoretical predictions and challenges existing models of neutron-rich matter.

PREX measured the neutron radius by isolating the neutrons’ tiny contributions to electron–Pb scattering. Neutrons may not have electric charge, but they have a weak charge nearly 10 times that of protons. So the collaboration set out to separate the neutron-dominated weak scattering from the proton-dominated electromagnetic contribution.

To tease out the effect, the experiment exploits the weak force, which treats electrons differently depending on their spins. Electrons whose spins are aligned with their direction of motion scatter slightly more often than those whose spins are antialigned. The researchers repeatedly flipped the polarization of the electrons directed at a lead target and compared the scattered electron fluxes for each polarization. They then used the size of the flux difference to calculate the neutrons’ radius.

The size of the neutron sphere in ²⁰⁸Pb is set by a balance between surface tension, which favors a compact configuration, and symmetry pressure, an outward push caused by having excess neutrons. Because the surface-tension contribution is well understood, a measurement of the neutron-skin thickness is effectively a measurement of the symmetry pressure. Researchers are particularly interested in that quantity because it also appears in models of neutron stars. (For more about the connection, see the article by Jorge Piekarewicz and Farrukh Fattoyev, Physics Today, July 2019, page 30 .)

Adjusting the strength of the symmetry pressure leads to different predictions of stellar radius and compositions. The PREX result suggests that a neutron star of a given mass should be large and have a high proton fraction. That’s also consistent with masses and radii derived from data collected by NICER (Neutron Star Interior Composition Explorer), a NASA instrument aboard the International Space Station. The PREX and NICER results, however, are in tension with neutron-star properties extracted from gravitational waves that were detected after two neutron stars merged. The discrepancy may be a sign of exotic behavior in the extremely dense stars. (D. Adhikari et al., PREX collaboration, Phys. Rev. Lett. 126, 172502, 2021. )