Initial spin fluctuations as a probe of cluster spin structure in $^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}$ nuclei

TL;DR

This work investigates how ground-state spin structures in light, $\alpha$-clustered nuclei influence initial spin fluctuations in ultra-relativistic nucleus–nucleus collisions. By combining NLEFT ab initio configurations with phenomenological $\alpha$-cluster geometries in a Monte-Carlo Glauber/TRENTo framework, the authors compute the event-by-event polarization variance $\langle \mathcal{P}_{\text{ini}}^2 \rangle$ and a scaled fluctuation $ (\sqrt{\langle \mathcal{P}^2 \rangle})_{\text{scaled}} $ that removes trivial finite-size effects, linking to final-state observables via $v_\Lambda^2 = \langle \mathcal{P}^2 \rangle_{\text{final}}$. They find that short-range spin–isospin correlations from clustering suppress initial spin fluctuations relative to a spherical $3$-parameter Woods–Saxon baseline, with a characteristic non-monotonic centrality pattern and a system-size ratio $R_{^{20}\mathrm{Ne}/^{16}\mathrm{O}}$ that serves as a robust probe of cluster geometry. Percent-level deviations in $R_{^{20}\mathrm{Ne}/^{16}\mathrm{O}}$ between clustered and baseline cases suggest that measurements of final-state $\Lambda$-pair spin correlations could constrain ground-state spin structures of light nuclei. The results indicate that a combined program of high-statistics LHC runs and relativistic spin-hydrodynamics modeling could open a new window into imaging nuclear clustering at high temperature. $\langle \mathcal{P}_{\text{ini}}^2 \rangle$, $v_\Lambda^2$, and the scaled fluctuations thus provide a direct, spin-based probe of $\alpha$ clustering in light nuclei.

Abstract

We investigate the imprint of $α$ clustering on initial spin fluctuations in relativistic $^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36$~TeV. Utilizing \textit{ab initio} configurations from Nuclear Lattice Effective Field Theory (NLEFT) and phenomenological $α$-cluster models within a Monte-Carlo Glauber framework, we compute the event-by-event variance of the initial net spin polarization. We find that the strong short-range spin--isospin correlations characteristic of $α$ clusters lead to a significant suppression of spin fluctuations compared to a spherical Woods--Saxon baseline with uncorrelated spins. By constructing a scaled fluctuation observable that accounts for trivial finite-size effects, we demonstrate that this suppression exhibits a non-monotonic centrality dependence sensitive to the detailed cluster geometry. Furthermore, we propose the ratio of scaled spin fluctuations between $^{20}\mathrm{Ne}$ and $^{16}\mathrm{O}$ systems as a robust probe. Our results predict distinct percent-level deviations from the baseline for clustered nuclei, suggesting that measurements of final-state $Λ$-hyperon spin correlations can provide novel constraints on the ground-state spin structure of light nuclei.

Figures (7)

• Figure 1: (Color online) Two-nucleon spin correlation $\langle s_i s_j \rangle$ as a function of the relative distance $\delta r$ in $^{20}\mathrm{Ne}$ from ab initio NLEFT calculations. The blue circles, yellow squares, red triangles, and gray diamonds represent $\langle s_i s_j \rangle(\delta r)$ for proton--proton, proton--neutron, neutron--neutron, and all nucleon pairs, respectively.
• Figure 2: Schematic illustration of the $\alpha$-cluster geometries implemented in the model. (Left) The Tetrahedron configuration of $^{16}\mathrm{O}$ is characterized by the $\alpha$-cluster edge length $\ell_c$. (Middle) The Bowling-pin configuration of $^{20}\mathrm{Ne}$ is characterized by the core parameter $\ell_c$ and the distance $\ell_h$ between the fifth cluster and the core. (Right) A schematic of the $\alpha$ cluster, which contains two protons (orange spheres) and two neutrons (blue spheres). The directions of the black arrows ($\uparrow\downarrow$) in the right panel indicate the spin orientations of the individual nucleons. The spins of the two protons cancel each other out, as do the spins of the two neutrons, resulting in a net-zero spin for the cluster. Each red sphere in the geometry plots (Left and Middle) represents an $\alpha$ cluster.
• Figure 3: (Color online) Standard deviation of the polarization parameter $\sqrt{\langle \mathcal{P}^{2} \rangle}$ as a function of centrality in $^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36~\mathrm{TeV}$ for different nuclear-structure configurations. The green circles, blue triangles, orange squares, and black diamonds correspond to the NLEFT, $^{16}\mathrm{O}+\alpha$, BP, and spherical 3pf Woods--Saxon configurations, respectively.
• Figure 4: (Color online) Centrality dependence of the scaled standard deviation of the polarization parameter $\left(\sqrt{\langle \mathcal{P}^{2}\rangle}\right)_{\mathrm{scaled}}$ in $^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36~\mathrm{TeV}$. The teal circles, blue triangles, orange squares, and black diamonds correspond to the NLEFT, $^{16}\mathrm{O}+\alpha$, BP, and spherical 3pf Woods--Saxon configurations, respectively. The horizontal dashed line indicates the reference value of unity.
• Figure 5: (Color online) Standard deviation of the polarization parameter $\sqrt{\langle \mathcal{P}^{2}\rangle}$ as a function of centrality in $^{16}\mathrm{O}+{}^{16}\mathrm{O}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36~\mathrm{TeV}$. Teal triangles show the ab initio NLEFT result. "tetra (PGCM)", "tetra (VMC)", and "tetra (NLEFT)" (blue circles, green downward triangles, and orange squares) are tetrahedral $4\alpha$ configurations fitted to PGCM, VMC, and NLEFT ab initio data, respectively, while "3pf" (black diamonds) denotes a spherical 3pf Woods--Saxon distribution.