Exploring the Nuclear Shape Phase Transition in Ultra-Relativistic $^{129}$Xe+$^{129}$Xe Collisions at the LHC

TL;DR

This study investigates the shape phase transition in $^{129}$Xe nuclei using ultra-relativistic collision data, introducing new correlators to distinguish between $ ext{γ}$-soft and rigid triaxial deformations, revealing insights into nuclear structure.

Contribution

The paper introduces novel correlators in heavy ion collisions to differentiate $ ext{γ}$-soft and rigid triaxial nuclear deformations, providing a new method to explore nuclear shape phase transitions.

Findings

Correlators $ ho_{2}$ and $ ext{Γ}_{p_T}$ can be explained by $ ext{γ}$-soft deformation.

New correlators $ ho_{4,2}$ and $ ho_{2,4}$ distinguish deformation types.

Heavy ion collisions can probe second-order nuclear shape phase transitions.

Abstract

The shape phase transition for certain isotope or isotone chains, associated with the quantum phase transition of finite nuclei, is an intriguing phenomenon in nuclear physics. A notable case is the Xe isotope chain, where the structure transits from a $\gamma$-soft rotor to a spherical vibrator, with the second-order shape phase transition occurring in the vicinity of $^{128-130}$Xe. In this letter, we focus on investigating the $\gamma$-soft deformation of $^{129}$Xe associated with the second-order shape phase transition by constructing novel correlators for ultra-relativistic $^{129}$Xe+$^{129}$Xe collisions. In particular, our iEBE-VISHNU model calculations show that the $v_2^2-[p_T]$ correlation $\rho_{2}$ and the mean transverse momentum fluctuation $\Gamma_{p_T}$, which were previously interpreted as the evidence for the rigid triaxial deformation of $^{129}$Xe, can also be well explained by the $\gamma$-soft deformation of $^{129}$Xe. We also propose two novel correlators $\rho_{4,2}$ and $\rho_{2,4}$, which carry non-trivial higher-order correlations and show unique capabilities to distinguish between the $\gamma$-soft and the rigid triaxial deformation of $^{129}$Xe in $^{129}$Xe+$^{129}$Xe collisions at the LHC. The present study also provides a novel way to explore the second-order shape phase transition of finite nuclei with ultra-relativistic heavy ion collisions.