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

TL;DR

This paper explores how $ extalpha$-cluster structures influence correlations in relativistic light ion collisions, comparing ab initio models and analyzing geometric configurations to improve understanding of nuclear structures.

Contribution

It introduces a comprehensive analysis of $ extalpha$-clustering effects on nucleonic correlations using multiple ab initio models and collision scenarios, revealing distinct cluster geometries and validating perturbative approaches.

Findings

Perturbative calculations effectively capture nuclear structural features.

Monte Carlo simulations validate the perturbative results.

Distinct cluster geometries: tetrahedral, triangular pyramids, and bowling pin shapes.

Abstract

This study investigates the influence of $\alpha$-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 $\alpha$ 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 $\alpha$+$^{12}$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.