Light-Speed Nuclear Collisions Reveal Neon-20's 'Bowling Pin' Shape

An atomic nucleus is only a few femtometers across (one femtometer is 10 to the minus 15 meters). The neon-20 nucleus, for instance, measures about 6 femtometers in diameter. Packed into this tiny space are 10 protons and 10 neutrons. Physics textbooks typically depict nucleons as nearly uniform spheres, with electrons orbiting around them—the standard image of an atom that has persisted for generations.

But not all nuclei are spherical. In 1937, the German physicist Wilfried Wefelmeier proposed that even-even nuclei (those with equal numbers of protons and neutrons, such as $^{12} C$ , $^{16} O$ , and $^{20} Ne$ ) might be stabilized by molecule-like arrangements of alpha particles (helium-4 nuclei). John Archibald Wheeler developed a similar cluster model around the same time. For roughly 90 years since, alpha-cluster structure has remained a central theme in nuclear structure physics.

For $^{16} O$ , a structure in which four alpha particles sit at the vertices of a regular tetrahedron was experimentally suggested by D. Robson in 1979 (Phys. Rev. Lett. 42, 876). $^{20} Ne$ is predicted to take this tetrahedral structure and add a fifth alpha particle along the symmetry axis—forming a shape resembling a bowling pin.

The invisible wall imposed by quantum mechanics

The trouble is that directly observing this shape is extraordinarily difficult. An atomic nucleus is a quantum mechanical object, and in a ground state with zero angular momentum, all orientations are superposed with equal probability. Measuring a nucleus at rest in the laboratory frame will always make a non-spherical nucleus appear spherical. This constraint arises from a fundamental principle of quantum mechanics and cannot be overcome simply by improving measurement precision.

Conventional low-energy nuclear spectroscopy experiments have instead inferred deformation indirectly, for example by measuring quadrupole moments through Coulomb excitation. The spectroscopic quadrupole moment of $^{20} Ne$ has been measured as $Q_{s} (2_{1}^{+}) = - 0.22 (2)$ eb, corresponding to a deformation parameter of $β_{2} = 0.96 (11)$ —among the largest deformations found anywhere on the nuclear chart. By comparison, $^{238} U$ has a deformation parameter of only $β_{2} \approx 0.29$ . Neon-20 is roughly three times more deformed than uranium-238.

However, because low-energy experiments proceed through transitions to excited states, they do not directly "image" the geometric shape of the ground state itself. Interpretation always depends on nuclear structure models.

Shape imprinted on how the collision debris scatters

So how can the ground-state shape be probed more directly? In 2020, Giuliano Giacalone of Paris-Saclay University theoretically showed that collective flow in ultrarelativistic heavy-ion collisions is sensitive to nuclear deformation (Phys. Rev. C 102, 024901). The principle behind this method works as follows.

When two atomic nuclei collide head-on at near light speed, the collision zone produces a hot, dense state of matter known as the quark-gluon plasma (QGP). This matter behaves like a fluid, converting initial spatial asymmetries into momentum-space asymmetries. In other words, the shape of the colliding nuclei before impact is "transcribed" onto the angular distribution of particles emitted afterward.

Specifically, the observable quantities are the coefficients obtained by Fourier-expanding the azimuthal distribution of produced particles—the flow harmonics $v_{n}$ . The second-order coefficient $v_{2}$ (elliptic flow) is sensitive to the ellipticity of the initial collision zone, while the third-order coefficient $v_{3}$ (triangular flow) is sensitive to fluctuations in energy density.

The first demonstration of this method came from the STAR collaboration at the RHIC accelerator at Brookhaven National Laboratory (BNL) in the United States, using $^{238} U$ collisions. By comparing $^{238} U$ collisions with those of the nearly spherical $^{197} Au$ , the team extracted $β_{2} = 0.297 \pm 0.015$ and a triaxiality parameter of $γ = 8.5° \pm 4.8°$ . These results agreed with low-energy experiments and, for the first time, directly measured the triaxiality of a ground state.

A natural comparison: oxygen and neon, similar mass, different shapes

In July 2025, the LHC ran oxygen-oxygen (OO) and neon-neon (NeNe) collisions over several days, at a center-of-mass energy per nucleon pair of 5.36 TeV. The CMS detector collected an integrated luminosity of 7 nb $^{- 1}$ for OO collisions and 0.8 nb $^{- 1}$ for NeNe collisions.

There is a clear reason why $^{16} O$ and $^{20} Ne$ were chosen for comparison. Their mass numbers are close (16 and 20), so the fluid-dynamical evolution following collision is similar in both cases. Taking the ratio of their flow observables therefore cancels out much of the final-state physics, allowing the geometric differences in the initial state to stand out. Moreover, the structures of both nuclei are well constrained by ab initio calculations: $^{16} O$ is tetrahedral, while $^{20} Ne$ has the bowling-pin shape. The key question was how this predicted difference would manifest in the flow ratios.

The CMS collaboration extracted $v_{2}$ and $v_{3}$ from two-particle and four-particle correlations of charged particles, measured as a function of collision centrality (how head-on the collisions were).

Elliptic flow speaks to deformation, triangular flow leaves a puzzle

The results were clear. The NeNe/OO ratio of $v_{2}$ was close to 1 in peripheral collisions but rose toward central collisions, reaching about 1.08 in the most head-on events. This is consistent with a picture in which the deformed shape of $^{20} Ne$ adds extra ellipticity to the initial geometry of the collision zone, which the fluid response then translates into enhanced elliptic flow.

Observable	Peripheral collisions (50%)	Central collisions (0–5%)	Physical implication
$v_{2}$ ratio (NeNe/OO)	≈1.0	≈1.08	$^{20} Ne$ 's deformation enhances elliptic flow
$v_{3}$ ratio (NeNe/OO)	≈1.06	drops to ≈1.0	Insufficient description of initial-state fluctuations
$v_{2}$ (PbNe/PbAr, LHCb)	(not measured)	1.40 ± 0.06	Deformation confirmed with an independent method

Meanwhile, the $v_{3}$ ratio started at around 1.06 in peripheral collisions and decreased toward central collisions. While this trend itself was observed, it did not quantitatively match predictions from fluid-dynamical models. In their paper, the CMS collaboration states that "none of the three model calculations quantitatively reproduce the measured $v_{3}$ ratio, indicating a need for an improved treatment of initial-state fluctuations in small collision systems."

This discrepancy suggests that $v_{3}$ , arising primarily from event-by-event statistical fluctuations in nucleon configurations, is sensitive to microscopic structural details beyond just the nucleus's average shape. It has been suggested that the tetrahedral structure of $^{16} O$ may produce a particular fluctuation pattern, but a quantitative understanding has not yet been reached.

LHCb's fixed-target experiment independently confirms the deformation

Around the same time, the LHCb collaboration approached the shape of $^{20} Ne$ using an independent method. Using the SMOG2 gas-target system, LHCb collected fixed-target collision data in November 2024 between a lead beam and neon gas, and separately between the lead beam and argon gas, at $s_{N N}$ = 70.9 GeV. Since argon-40 is expected to be nearly spherical, comparing PbNe with PbAr isolates the deformation of $^{20} Ne$ .

The result: in the most central collisions, $v_{2}$ for PbNe reached 1.40 ± 0.06 times that of PbAr. This large difference is consistent with the strong ellipticity that the bowling-pin shape of $^{20} Ne$ would impose on the initial collision zone. LHCb's results were posted to arXiv (2509.12399) in September 2025.

Experiment	Method	Collision system	Energy	Key result
CMS (this study)	Beam-beam collision	OO / NeNe	5.36 TeV per nucleon pair	$v_{2}$ ratio rises to ≈1.08 in central collisions
LHCb	Fixed target (SMOG2)	PbNe / PbAr	70.9 GeV per nucleon pair	$v_{2}$ 1.40 ± 0.06 times higher for PbNe
ALICE	Beam-beam collision	OO / NeNe	5.36 TeV per nucleon pair	First observation of geometry-driven flow
STAR (prior study)	Beam-beam collision	U+U / Au+Au	193–200 GeV per nucleon pair	Extracted $β_{2} = 0.297 \pm 0.015$

Toward particle accelerators as probes of nuclear structure

What this study demonstrates is that collective flow in high-energy collisions is indeed sensitive to the ground-state geometry of nuclei. A property of $^{20} Ne$ —its deformation, previously inferred only indirectly through low-energy spectroscopy—has now been independently confirmed in an experiment operating at a completely different energy regime.

That said, what has been achieved so far is only qualitative confirmation. Extracting precise values of deformation parameters from flow measurements will require improvements across the board: in modeling event-by-event fluctuations in the initial state, in the fluid-dynamical evolution models, and in the nuclear structure inputs (the precision of ab initio calculations). The authors of the CMS paper write that "these results establish that collective flow in light-ion collisions is sensitive to both the initial geometry and the fluid-dynamical response of the medium," while cautioning that "quantitative determination of the deformation requires further dedicated studies."

Three questions remain open. First, what theoretical description of initial-state fluctuations would resolve the $v_{3}$ discrepancy? Second, how can a model-independent—or at least less model-dependent—method be established for extracting deformation parameters from flow measurements? Third, how will this approach fare when extended to other nuclei, such as the triangular structure of $^{12} C$ or the octupole deformation of $^{96} Zr$ ?

The geometric arrangement of alpha particles that Wefelmeier sketched on paper in 1937 is now, roughly 90 years later, being read out in collisions at teraelectronvolt energies. A new experimental frontier is emerging at the boundary between nuclear physics and particle physics.