Glauber predictions for oxygen and neon collisions at energies available at the LHC

The Glauber model is a widely used framework for describing the initial conditions in high-energy nuclear collisions. TGlauberMC is a Monte Carlo implementation of this model that enables detailed, event-by-event calculations across various collision systems. In this work, I present an updated version of TGlauberMC (3.3), which incorporates recent theoretical developments and improved parameterizations, especially relevant for small collision systems. I focus on the oxygen-oxygen (OO), neon-neon (NeNe), and proton-oxygen (pO) collisions at the Large Hadron Collider (LHC) in July 2025, where precise modelling of nuclear geometry and fluctuations is essential. The updated version includes revised nuclear density profiles and an enhanced treatment of nucleon substructure. Geometrical cross sections for all relevant collision systems are calculated and initial-state observables are explored to provide predictions for particle production trends at $\sqrt{s_{\rm nn}}$=5.36 TeV. In particular, a prediction for the centrality dependence of mid-rapidity multiplicity in OO and NeNe collisions is obtained. The updated code is publicly available to support the heavy-ion community with a robust and flexible tool for studying strongly interacting matter in small and intermediate-sized nuclear systems.

💡 Research Summary

The paper presents an updated version of the TGlauberMC Monte‑Carlo Glauber model (v3.3) and uses it to make quantitative predictions for upcoming oxygen‑oxygen (OO), neon‑neon (NeNe), and proton‑oxygen (pO) collisions at the LHC. The author emphasizes that small‑to‑intermediate systems such as OO and NeNe, scheduled for a 5.36 TeV nucleon‑nucleon center‑of‑mass energy run in July 2025, provide a crucial bridge between the well‑studied large‑system PbPb collisions and the surprising collective phenomena observed in pPb and high‑multiplicity pp events.

The methodological core is a detailed treatment of nuclear geometry. For the light nuclei ¹⁶O and ²⁰Ne the code now includes several nuclear‑density parameterizations: traditional three‑parameter Fermi (3pF) forms, modified harmonic‑oscillator (HO) profiles, and, importantly, the exact charge‑density distributions derived from state‑of‑the‑art chiral NNLO_sat calculations. Table I lists the parameters (radius R, diffuseness a, deformation β, etc.) for each profile, and Figure 2 shows how the different O‑profiles compare to electron‑scattering data. The author notes that the NNLO_sat profile reproduces the data within experimental uncertainties, while some older 3pF fits (e.g., “Opar2”) overestimate the rms radius and are therefore excluded from the final predictions.

A second major improvement concerns the nucleon‑nucleon overlap function, which determines the probability that two nucleons interact at a given transverse separation bₙₙ. Beyond the simple hard‑sphere picture, the paper implements four families of overlap functions: the Γ‑parameterization (controlled by ω, interpolating between hard‑sphere and Gaussian), the TRENTo Gaussian width w (0.4–0.7 fm), the HIJING Bessel‑K form, and the PYTHIA‑Monash tune (exponential‑to‑Gaussian interpolation). Figure 1 illustrates the impact‑parameter distributions and interaction probabilities for these choices, demonstrating that realistic choices (ω≈0.5, w≈0.5 fm) differ markedly from the hard‑sphere limit and affect the calculated number of binary collisions (N_coll) and participant nucleons (N_part).

Using the updated geometry and overlap functions, the author computes geometric cross sections for all systems. At √sₙₙ = 5.36 TeV the inelastic hadronic cross sections are σ_OO ≈ 2.9 b and σ_NeNe ≈ 3.2 b (±2 % systematic). For pO at the higher √sₙₙ = 9.62 TeV the cross section is σ_pO ≈ 2.1 b. The uncertainties are dominated by the choice of nuclear density and overlap function.

The paper then presents the centrality‑dependent distributions of key initial‑state quantities: the number of participants (N_part), the number of binary collisions (N_coll), and the eccentricities ε₂ and ε₃ calculated from the transverse positions of participants (or a mixed participant‑binary weighting). In the most central 0–5 % bin, OO collisions have ⟨N_part⟩≈30 and ⟨N_coll⟩≈45, while NeNe have ⟨N_part⟩≈38 and ⟨N_coll⟩≈58. The elliptic eccentricity ε₂ is larger in NeNe by about 15–20 % (ε₂(NeNe)/ε₂(OO)≈1.18), a ratio that directly translates into a similar ratio of the measured elliptic flow coefficient v₂ if hydrodynamic response is comparable. The author also explores the effect of explicit α‑clustering by employing Trajectum‑generated many‑body wave‑functions (TR_OXYGEN_V15, TR_NEON_V14). These clustered configurations increase ε₂ by roughly 5 % relative to smooth density profiles, providing a concrete observable to test clustering hypotheses.

Particle production is addressed using a multiple parton interaction (MPI) model calibrated on existing pp and pPb data. The model predicts that the mid‑rapidity charged‑particle density ⟨dN_ch/dη⟩ scales nearly linearly with N_part. For the 0–5 % most central OO collisions the prediction is ⟨dN_ch/dη⟩≈1 200, while for NeNe it is ≈1 500. These values are about 30 % lower than those measured in central PbPb at 5.02 TeV, yet they are sufficiently large to support collective phenomena such as flow. The centrality dependence of multiplicity is presented as a key benchmark for forthcoming LHC measurements.

Finally, the author makes the updated TGlauberMC v3.3 code publicly available on HepForge (version v3.3.2) together with a concise user guide (Appendix A) and a new library, the Trajectum Nucleus Generator (TrNucGen), which supplies the many‑body nuclear configurations used in the clustered studies. By providing multiple density options, flexible overlap functions, and ready‑to‑use scripts for calculating cross sections, participant numbers, eccentricities, and multiplicities, the work equips the heavy‑ion community with a robust tool for systematic studies of the system‑size dependence of QGP signatures. The paper concludes that OO and NeNe collisions will be decisive in pinpointing the minimal conditions for QGP formation, testing the role of nuclear substructure (α‑clustering), and possibly revealing the onset of jet quenching in systems larger than pPb but smaller than PbPb.