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

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 γ-soft rotor to a spherical vibrator, with the second-order shape phase transition occurring in the vicinity of ^128-130Xe. In this letter, we focus on investigating the γ-soft deformation of ^129Xe associated with the second-order shape phase transition by constructing novel correlators for ultra-relativistic ^129Xe+^129Xe collisions. In particular, our iEBE-VISHNU model calculations show that the v_2^2-[p_T] correlation ρ_2 and the mean transverse momentum fluctuation Γ_p_T, which were previously interpreted as the evidence for the rigid triaxial deformation of ^129Xe, can also be well explained by the γ-soft deformation of ^129Xe. We also propose two novel correlators ρ_4,2 and ρ_2,4, which carry non-trivial higher-order correlations and show unique capabilities to distinguish between the γ-soft and the rigid triaxial deformation of ^129Xe in ^129Xe+^129Xe 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.