Identifying $α$-cluster configurations in $^{20}$Ne via ultracentral Ne+Ne Collisions

TL;DR

The work addresses identifying $\alpha$-cluster configurations in $^{20}$Ne by linking the cluster wave function to the initial geometry in ultracentral heavy-ion collisions. It combines analytical Brink-model calculations with hydrodynamic event-by-event simulations to map cluster structure onto observables $NSC(3,2)$ and $\rho_2(v_2^{2}, \delta[p_{\mathrm{T}}])$, demonstrating sensitivity to the configurations $5\alpha$ vs $\alpha+^{16}$O. A key result is the sign inversion of $NSC(3,2)$ between configurations, with $\rho_2$ providing robust discrimination after hydrodynamic evolution, while $\rho_3$ is less reliable due to fluctuations; fixed-target Pb+Ne tests corroborate the approach. The work establishes a new framework for probing emergent many-body quantum correlations in light nuclei through heavy-ion collisions, offering testable predictions for Ne+Ne at the LHC and fixed-target runs and suggesting broader applicability to other cluster-physics problems.

Abstract

The initial-state geometry in relativistic heavy-ion collisions provides a novel probe to nuclear cluster structure. For $^{20}$Ne, a novel approach is proposed to distinguish between the cluster configurations (5$α$ versus $α+ ^{16}$O) in order to gain insight into nuclear structure transitions governed by many-body quantum correlations. Through analytical calculations with the microscopic Brink model and event-by-event simulations using the hydrodynamic framework, we establish the normalized symmetric cumulant NSC (3, 2) and the Pearson coefficient $ρ_2 (v_{2}^{2},\ δ[p_{\mathrm{T}}])$ as quantitative discriminators to reveal enhanced cluster degrees of freedom in the ground state of $^{20}$Ne. The ultracentral Ne+Ne collisions at the LHC can experimentally identify these two competing configurations via these flow correlation observables, opening a new paradigm for probing clustering in light nuclei.

Figures (9)

• Figure 1: (Color online) (a) The 5$\alpha$ cluster structure diagram of $^{20}$Ne, where the four $\alpha$-particles $\alpha_{1\sim4}$ form a regular tetrahedral structure, and the parameter $D_1$ is the distance from each cluster to the center of the regular tetrahedron, while the parameter $D_2$ is the distance from the cluster $\alpha_{5}$ to the center of the regular tetrahedron. (b) The $D_1-D_2$ schematic diagram of several special structures of $^{20}$Ne with the ratio parameters $k=D_2/D_1$. (c) The schematic diagram for the selection range of the $D_1$, $D_2$ and $b$ for $^{20}\text{Ne}$. Each grey band represents the range of the rms radius within $\pm 10\%$ of the experimental value after fixing $b$ value. The orange band is the overlap region (OR) of all grey regions, which indicates the range of $D_1$ and $D_2$ that satisfies the constraint that the rms radius is within the range $2.7 < \sqrt{\langle r^2\rangle} < 3.3 \text{ fm}$ under the condition $1.46 < b < 1.76\text{ fm}$. The orange dashed line is the average configuration using $b = 1.61\text{ fm}$. The black dashed lines in (b) and (c) present the region of symmetric bi-pyramid 5$\alpha$ configuration satisfying $k = 5/3$.
• Figure 2: (Color online) The analytical results on the dependence of the correlation observables on the parameters $D_1$ and $D_2$ with $b=1.76$ fm, (a): NSC$(3,\ 2)$, (b): $\rho_2$, (c): $\rho_3$. The blue and red dashed lines correspond to $\beta_{2}^{*}=0$ and $\beta_{3}^{*}=0$, respectively. The gray thick dashed lines are the structure phase boundaries separating the $\alpha$+$^{16}$O and $5\alpha$ configurations. (d): The analytical results on the dependences of NSC$(m,\ n)$ and $\rho_n$ on the ratio $k=D_2/D_1$ satisfying the rms radius requirements in Fig. \ref{['Fig:config']}(c), the uncertainty is given by the systematic uncertainty of the analytical model. The initial-state results (e) and final-state results (f) with fluctuation effect using the TRENTo+VISHNU+UrQMD hydrodynamic framework are shown, where the shaded region represents the systematic uncertainty and the error bar indicates the statistical uncertainty.
• Figure 3: (Color online) The single nucleon radial density distribution with $b=1.76$ fm for different settings of $D_1$ and $D_2$. (a): only dependent on $D_2$ for $\alpha$+$^{16}$O configuration, (b): only dependent on $D_1$. The red dashed line represents the W-S density distribution and satisfies the experimental rms value.
• Figure 4: (Color online) The analytical results on the dependence of the deformation parameters (a) $\beta_{2}^{*}$, (b) $\beta_{3}^{*}$, (c) $\beta_{4}^{*}$, and different orders of eccentricities (d) $\varepsilon_{2}$, (e) $\varepsilon_{3}$, (f) $\varepsilon_{4}$ on the parameters $D_1$ and $D_2$. The blue dashed lines in (a) and (d) indicate that $\beta_{2}^{*}=0$. The red dashed lines in (b) and (e) indicate that $\beta_{3}^{*}=0$. The black dashed lines in (b) and (e) present the region satisfying $k=D_{2}/D_{1}=5/3$.
• Figure 5: (Color online) The analytical results on the dependence of the fluctuation of the inverse transverse size $\langle(\delta d_{\perp}/\langle d_{\perp} \rangle)^2\rangle$ with new definition (left) and old definition (right) on the parameters $D_1$ and $D_2$. The blue dashed lines indicate that $\beta_{2}^{*}=0$.