Imprint of $α$-Clustering on Ab Initio Correlations in Relativistic Light Ion Collisions

This study investigates the influence of $α$-cluster structures in relativistic light nuclear collisions. Using a cluster framework, I extract the characteristics of the nucleonic configurations of $^{16}$O and $^{20}$Ne as predicted by various \textit{ab-initio} models, including Nuclear Lattice Effective Field Theory (NLEFT), Variational Monte Carlo (VMC), and the Projected Generator Coordinate Method (PGCM). Additionally, I analyze configurations derived from a three-parameter Fermi (3pF) density function. The investigation focuses on the effects of cluster parameters on two-point correlators using a rotor model for symmetric collisions ($^{16}$O+$^{16}$O and $^{20}$Ne+$^{20}$Ne) and asymmetric collisions ($^{208}$Pb+$^{16}$O and $^{208}$Pb+$^{20}$Ne). The cluster parameters are determined by minimizing the \textit{chi-square} statistic to align the nucleon distributions with those predicted by the aforementioned theories. The results reveal that perturbative calculations effectively capture the structural features of these nuclei, while comparisons with Monte Carlo simulations validate these findings. Furthermore, the analysis reveals distinct cluster geometries: VMC suggests tetrahedral shapes, while NLEFT, PGCM, and 3pF indicate irregular triangular pyramids. Notably, NLEFT shows a bowling pin-like $α$ cluster structure for $^{20}$Ne. The study also identifies constraints on cluster parameters in the different oxygen structures, with a gradual increase in $\varepsilon_2{2}$ for the states of $α$+$^{12}$C. Accurate modeling of asymmetric collisions necessitates a range of nucleons from heavy spherical nuclei, leading to weighted correlators in perturbative calculations. I demonstrate consistency between perturbative calculations and Monte Carlo models, with analytical calculations providing more insights into asymmetric than symmetric collisions.

💡 Research Summary

This paper investigates how α‑cluster structures in the light nuclei ¹⁶O and ²⁰Ne manifest themselves in relativistic heavy‑ion collisions. The author adopts a cluster framework in which the nucleon configurations predicted by several state‑of‑the‑art ab‑initio approaches—Nuclear Lattice Effective Field Theory (NLEFT), Variational Monte Carlo (VMC), and the Projected Generator Coordinate Method (PGCM)—are mapped onto a simple geometric model characterized by two parameters: the inter‑cluster distance ℓ_c and the size of each α particle r_L (or the ratio r_L/ℓ_c). In addition, a three‑parameter Fermi (3pF) density distribution is used as a phenomenological benchmark. By minimizing a χ² statistic the cluster parameters are tuned so that the model reproduces the nucleon density profiles generated by each theory.

The author then studies how these parameters affect the initial‑state two‑point correlators that drive final‑state observables such as anisotropic flow coefficients v_n and the average transverse momentum ⟨p_T⟩. The analysis is performed within a rigid‑rotor model for both symmetric collisions (¹⁶O+¹⁶O, ²⁰Ne+²⁰Ne) and asymmetric collisions (²⁰⁸Pb+¹⁶O, ²⁰⁸Pb+²⁰Ne). The transverse one‑body and two‑body densities are obtained analytically by averaging over Euler angles, separating intra‑α (nucleons inside the same α cluster) and inter‑α (nucleons belonging to different clusters) contributions. These densities are then folded with a Gaussian gluonic profile to construct the transverse energy density ε(r). From ε(r) the author derives the mean energy ⟨E⟩, its variance Var(E), and the mixed correlator ⟨E₂E₂*⟩, which are directly proportional to the experimentally measured flow observables.

Key findings include:

1. Geometric signatures of different ab‑initio models – VMC predicts a regular tetrahedral arrangement of the four α clusters in ¹⁶O, whereas NLEFT, PGCM, and the 3pF fit favor an irregular triangular‑pyramid geometry. For ²⁰Ne, NLEFT uniquely yields a “bowling‑pin” shape where three α clusters form a base and the fourth sits above the centroid, a configuration not seen in the other approaches.

2. Impact on flow observables – The ε₂{2} (second‑order flow cumulant) shows a gradual increase when moving from the ground state of ¹⁶O to the α+¹²C excited configuration, reflecting a shrinking ℓ_c and enhanced spatial anisotropy. The asymmetric collisions amplify this effect because the large spherical ²⁰⁸Pb nucleus provides a broad “weighting” of the light‑ion geometry, making the cluster‑induced fluctuations more visible in the final‑state particle distributions.

3. Perturbative vs. Monte‑Carlo consistency – Analytical perturbative calculations of the correlators agree quantitatively with Monte‑Carlo simulations based on the same cluster configurations (Ref.