Neutron skins, collision debris and the internal distributions of quarks and gluons reveal different aspects of matter. Connecting those measurements requires a more precise idea of what an image of a nucleus actually means.
An image of a nucleus is rarely a picture in the everyday sense. Researchers scatter particles, measure energy shifts or analyse thousands of fragments, then reconstruct the physical properties compatible with those observations. Change the probe and a different feature becomes visible: electric charge, neutron distribution, collective shape or the motion of quarks and gluons.
The distinction begins with scale. A nucleus is a bound system of protons and neutrons, collectively called nucleons. Each nucleon is itself a strongly interacting system of quarks and gluons. Measuring the neutron-rich outer region of lead does not map the inside of a neutron. Determining a proton’s charge radius does not provide the overall shape of a lead nucleus. Recent experiments are making both kinds of structure more accessible, while showing why they must first be described separately.
Finding the neutron distribution
Electron scattering is dominated by the electromagnetic interaction with nuclear charge, but the weak interaction also offers sensitivity to neutrons. PREX and CREX exploit a tiny difference in scattering rates when the direction of electron spin relative to motion is reversed. A September 2026 collaboration preprint gives the full experimental account of these parity-violating measurements in lead-208 and calcium-48.
The combined PREX measurements give a neutron-skin thickness of 0.283 ± 0.071 femtometres for lead-208. A femtometre is one millionth of one billionth of a metre. The skin is the difference between neutron and proton root-mean-square radii, rather than a sharp shell composed exclusively of neutrons. Extracting it requires corrections and nuclear model information after the scattering asymmetry has been measured.
Calcium-48 gives another point of comparison. The original CREX publication reported a skin of 0.121 femtometres, with separate experimental and model uncertainties of 0.026 and 0.024 femtometres. Comparing a relatively light nucleus with lead challenges nuclear calculations across different systems.
A successful description should account for both measurements and their uncertainties. The scientific opportunity is not simply to announce that one nucleus has a thicker skin. It is to identify which features of the interactions among nucleons allow a theory to explain the pattern across nuclei.
Reconstructing shape from a collision
The STAR collaboration has demonstrated a strikingly different approach to nuclear shape. Its 2024 study compared high-energy uranium–uranium and gold–gold collisions. The colliding nuclei create a quark–gluon plasma whose initial geometry influences how the outgoing particles move. By analysing collective flow and momentum correlations, and comparing them with hydrodynamic calculations, the team constrained the shape of uranium-238.
The analysis supported an elongated uranium shape with triaxiality: its three principal dimensions are not all related by simple axial symmetry. This is reconstructed information about a nuclear distribution, not an optical photograph of a stationary nucleus. The inference passes through the physics of the collision and the expanding plasma.
Its value lies in bringing a different timescale and different observables to nuclear structure. The paper notes that shape information inferred from very energetic collisions need not reproduce every feature accessed by slower, lower-energy probes. Testing how those descriptions connect can reveal where a simplified picture of the nucleus ceases to be sufficient.
The proton has more than one useful radius
Inside a nucleon, even the word radius needs a qualifier. The proton’s charge radius characterises its electric charge distribution. PRad used electron–proton scattering at very small momentum transfer to extract a radius of 0.831 femtometres, with statistical and systematic uncertainties of 0.007 and 0.012 femtometres respectively. Its 2019 result provided an independent electron-scattering comparison with smaller radii inferred from muonic hydrogen.
This radius is a parameter derived from how the proton responds to the probe, not the location of a hard surface. A quantum particle made from interacting constituents does not have the boundary of a solid sphere. Nor must the spatial distributions associated with its charge, energy and internal stresses have identical characteristic sizes.
That is a useful distinction for researchers beyond nuclear physics. A material can respond differently to electrical, magnetic and mechanical measurements without those experiments contradicting one another. At the nucleon scale the mathematics is quantum and relativistic, but the need to specify the measured property is just as fundamental.
Why the mass picture remains contested
A 2023 Jefferson Lab study used near-threshold production of the J/psi particle to investigate the proton’s gluonic gravitational form factors. These quantities describe aspects of how energy and momentum are distributed. The researchers extracted them using several theoretical models and, in each, inferred a mass radius smaller than the electric charge radius.
Despite the name, this was not a measurement of the proton’s gravitational pull. The experiment measured a particle-production process; theoretical relations connected it to the proton’s internal energy structure. The choice and validity of those relations are central to interpreting the derived radius.
A 2025 theoretical study illustrates the live debate. Using a data-driven dispersive approach, Xiong-Hui Cao and colleagues obtained a root-mean-square radius of 0.97 ± 0.03 femtometres for the nucleon’s scalar trace density. They also discussed continuing debate over connecting near-threshold charmonium production to this quantity.
These results should not be compressed into a contest over the proton’s one true size. The definitions, gluon-only or total contributions, theoretical inputs and extraction procedures must be matched before making that comparison. A more detailed map requires resolving those connections, not selecting whichever radius offers the most striking illustration.
Where nucleon and nuclear structure meet
Although the scales must be distinguished, they are connected physically. The EMC effect describes changes in the quark momentum distributions inferred for nucleons bound inside nuclei compared with simpler reference systems. In 2019, the CLAS collaboration measured this effect alongside the abundance of short-range correlated nucleon pairs. It showed that the data could be explained through a common modification associated with neutron–proton pairs.
That result supports a particular explanation of how close neighbours affect nucleon structure. It does not turn every nucleon into a rigid object that swells by a fixed amount. The relevant observables concern scattering and momentum distributions, and establishing a unique microscopic mechanism requires further discriminating measurements.
A June 2026 study sharpened the nuclear side of the problem. By scattering high-energy electrons from calcium-40, calcium-48 and iron-54, researchers found that short-range pairing depended strongly on the quantum orbitals occupied by the nucleons. The dependence exceeded predictions from the models examined and pointed towards additional angular-momentum selection rules.
The lesson is specific: counting neutrons and protons is insufficient to describe all of their close-range behaviour. How they occupy the available quantum states also matters. That gives theorists a concrete relationship to reproduce, rather than merely another overall nuclear size to fit.
Building maps that can be compared
For Europe’s nuclear research community, these measurements create opportunities in theory, detector development and international experiments. They also define a practical requirement for collaboration: preserving the connection between the measured scattering rates and the structural quantities inferred from them. A result becomes more reusable when other groups can revisit that connection with improved calculations.
Consider two proposed descriptions of a neutron-rich nucleus. Both might reproduce its charge radius while predicting different neutron skins or high-momentum nucleon populations. A charge measurement alone cannot choose between them. Adding weak scattering and correlated-pair observations can. Conversely, a theory that fits one experiment but fails another identifies a missing ingredient more clearly than a visually persuasive reconstruction does.
The same principle applies inside the proton. Measurements sensitive to charge, quark motion and gluonic energy distributions should eventually constrain a common description of the strong interaction. They need not yield matching radii. They need to yield predictions that remain consistent when the experimental probe changes.
A nuclear image is therefore best understood as a specified answer to a specified physical question. The emerging advance is the ability to connect several such answers, from neutron distributions across an entire nucleus to the internal dynamics of a single nucleon. The unresolved connections are precisely where new experiments can make the greatest difference.
