&Bullet; physics 14, 58

The researchers have so far measured the neutron distribution in a heavy nucleus most precisely, which has an impact on the structure of neutron stars.

Illustration 1: A cartoon image of a lead-208 core showing the mixed proton-neutron core and the neutron “skin” (left). Measuring the thickness of the neutron skin provides information on how neutron stars are structured (right).

Popular cartoon visualizations show the protons and neutrons in a nucleus as colored marbles that are randomly packed into a sphere. In reality, heavy nuclei – in which neutrons tend to be more protons – are more differentiated, with the neutrons pushed radially outward. At the outer boundaries of such nuclei, the neutrons form a thin “skin” that encloses a nucleus of mixed neutrons and protons (Fig. 1). Now the PREX (Lead Radius Experiment) collaboration at the Thomas Jefferson National Accelerator Facility in Virginia has determined the thickness of this neutron-rich skin in lead-208, a stable isotope with 44 more neutrons than protons [1] . The measurement, which deals with questions about all four fundamental forces of nature, provides insights into the structure of neutron stars and will have far-reaching effects on multimessenger astronomy and particle physics.

The spatial distribution of protons within nuclei is known as the result of decades of scattering experiments with electromagnetic probes. Getting a similar understanding of neutrons is more difficult because these neutral particles are largely invisible to electrically charged probes. Since neutrons interact via the strong force, their nuclear distributions can in principle be discovered with strongly charged hadronic probes. However, strong interactions, which are described by quantum chromodynamics, have great theoretical uncertainties, and precise measurements with such methods are therefore difficult to achieve in practice.

Another approach is to use weak scattering, and techniques based on this interaction are much more effective. The reason for this is twofold: weak scattering is far better understood than scattering through strong interactions, and the weak charge of the nucleus – in contrast to its electromagnetic – is dominated by its neutron content. However, the weak interaction is much weaker than the electromagnetic interaction, which means that its subtle effects on electron nucleus scattering must be carefully worked out.

These subtle effects result from a special characteristic of the weak interaction that gives it the violation of signature parity: the strength of the interaction depends on a spatial direction. When electrons from neutrons scatter in the nucleus, they exchange Z. Bosons, the weak force carrier particles. When the electrons are polarized, the scattering process is asymmetrical, with left-handed electrons (whose spins are not aligned with their momentum) scattering from nuclei a little less often than right-handed ones. The size of the asymmetry is related to the distribution of the neutrons in the nucleus. The effect is tiny – only about a part per two million for the PREX experiment – so measuring it requires heroic control of systematic uncertainties.

It is this tiny, parity-violating asymmetry that the PREX Collaboration has managed to measure on lead-208 with the Jefferson Lab’s high-resolution spectrometers. The experimenters scattered spin-polarized 953 MeV electrons from a lead foil sandwiched between thin layers of diamond. The polarization of the electrons was reversed hundreds of times per second, following a specific sequence the details of which were hidden from the experimenters, to reduce the potential analysis bias. The measured excess in the right-handed electron scattering cross section was


Parts per billion, with most of the uncertainty caused by statistical errors. From this data, the team deduced a “neutron radius” (the radius of the neutron distribution within the nucleus; not that of the individual neutrons) of


fm. Given the proton radius value determined by previous experiments, this measurement resulted in a neutron skin width of


fm – a two-fold improvement in precision over the previous collaboration estimate [2] .

As small as these dimensions are, their effects are astronomical: The measurement of the neutron skin in a single nucleus (0.2 fm scale) can influence our knowledge of the neutron star structure (km scale). The connection between these objects is based on a quantity called symmetry energy – a contribution to the nuclear binding energy that arises in nuclei with unequal numbers of neutrons and protons due to the Pauli principle – and a related phenomenon called symmetry pressure becomes [3] . If the symmetry energy increases rapidly with increasing core density, the symmetry pressure is greater. In a core, greater symmetry pressure means that neutrons will be pushed further out, resulting in a thicker neutron skin. Similarly, in a neutron star, a higher symmetry pressure correlates with a larger radius for a given mass.

These neutron star properties, indicated by the PREX measurements, influence the interpretation of observations of binary neutron star fusions that are now routinely recorded by gravitational wave interferometers. Gravitational wave signals can show how matter deforms in such collisions [4] However, the details depend on how big a neutron star is for a given mass. Findings from the PREX result therefore inform about our understanding of these catastrophic events. A new study already shows that the theoretical expectations of the symmetry pressure are systematically somewhat low compared to the value derived from PREX, although the experimental result still agrees with predictions within uncertainties [5] . This study also finds that PREX is in slight tension with gravitational wave determinations of the deformability of neutron stars. Future gravitational wave and x-ray observations will help clarify the picture [3, 6] .

Precise measurements of neutron skin thickness could also lead to new discoveries in particle physics. Neutrinos rarely interact with nuclei, but when they do, they can coherently disperse an entire nucleus via the exchange of a Z.Boson that gives the core a gentle kick [7] . The distribution of the nuclear recoil energies depends on the arrangement of the neutrons in the nucleus; Anomalies in power distribution can be used to test for new physics. Although the rarity of such neutrino interactions limits the effectiveness of current generation experiments, a thorough understanding of the spatial distributions of neutrons within the nucleus will reduce the ambiguity in highly statistical tests of the next generation of neutrino interactions beyond the Standard Model [8] .

There are several present and future perspectives for nuclear scattering based neutron skin measurements that will complement the recent outcome of the PREX collaboration. A similar measurement of polarized electron scattering on calcium-48, called the Calcium Radius Experiment (CREX), was recently performed at the Jefferson Lab, and the data is currently being analyzed [9] An improved measurement of lead-208 is planned in an accelerator facility in Mainz [10] . High force measurements on rare nuclei are planned for the rare isotope ray facility at Michigan State University [11] . In a different approach, future observations of gravitational waves, X-rays and neutrinos have exciting potential to shed different kinds of “light” on this history of nuclear structure connections on very different scales.


  1. D. Adhikari et al. (PREX Collaboration), “Exact determination of the neutron skin thickness of

    due to parity violation during electron scattering ” Phys. Rev. Lett.126172502 (2021).

  2. S. Abrahamyan et al. (PREX Collaboration), “Measurement of the neutron radius of

    due to parity violation during electron scattering ” Phys. Rev. Lett.108112502 (2012).

  3. J. Piekarewicz and FJ Fattoyev, “Neutron-Rich Matter in Heaven and on Earth” Phys. today7230 (2019).
  4. BP Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GW170817: Observing Gravitational Waves from an Inspirational Binary Neutron Star”. Phys. Rev. Lett.119161101 (2017).
  5. BT Reed et al., “Implications of PREX-II on the equation of state of neutron-rich matter” Phys. Rev. Lett.126172503 (2021).
  6. G. Raaijmakers et al., “Restriction of the equation of state of dense matter by joint analysis of NICER and LIGO / Virgo measurements” Astrophys. J. Lett.893L21 (2020).
  7. D. Akimov et al. (Coherent cooperation), “Observation of the coherent elastic neutrino-nucleus scattering”, science3571123 (2017).
  8. D. Aristizabal Sierra et al., “Influence of form factor uncertainties on the interpretation of coherent elastic neutrino core scatter data” J. High Energy Phys.6th141 (2019).
  9. J. Mammei et al. (CREX Collaboration), proposal to Jefferson Lab PAC 40, CREX: Parity-violating measurement of the weak charge distribution of Ca with an accuracy of 0.02 fm (unpublished).
  10. D. Becker et al., “The P2 experiment” EUR. Phys. YES54208 (2018).
  11. The Nuclear Advisory Committee 2015, “Towards the Horizon: The 2015 Long-Term Plan for Nuclear Science”.

About the author

Image by Kate Scholberg

Kate Scholberg is the distinguished Physics Professor and Bass Fellow at Duke University in North Carolina. She received a Ph.D. She studied physics at the California Institute of Technology in 1997. She is currently a member of the Super-Kamiokande, T2K and Deep Underground Neutrino Experiment collaborations. She is the spokesperson for COHERENT, a neutrino scattering experiment at the Neutron Source Spallation at Oak Ridge National Laboratory in Tennessee. Her research focuses mainly on the physics of neutrinos and has broad interfaces with particle physics, astrophysics and nuclear physics.

Subject areas

Nuclear PhysicsAstrophysics

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