Exploring the Nuclear-Shape Phase Transition in Ultrarelativistic ^{129}Xe+^{129}Xe 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 ^{128-130}Xe. In this Letter, we focus on investigating the γ-soft deformation of ^{129}Xe associated with the second-order shape phase transition by constructing novel correlators for ultrarelativistic ^{129}Xe+^{129}Xe collisions. In particular, our iEBE-VISHNU model calculations show that the correlation between elliptic flow v_{2} and mean transverse momentum [p_{T}], denoted as ρ_{2}, as well as the [p_{T}] fluctuation Γ_{p_{T}}, which were previously used to claim the evidence of the rigid triaxial deformation of ^{129}Xe, can also be well explained by the γ-soft deformation of ^{129}Xe. We further propose two novel correlators ρ_{4,2} and ρ_{2,4}, which carry nontrivial higher-order correlations and show unique capabilities to distinguish between the γ-soft and the rigid triaxial deformation of ^{129}Xe in ^{129}Xe+^{129}Xe collisions at the LHC. The present study provides a novel way to explore the second-order shape phase transition of finite nuclei with ultrarelativistic heavy ion collisions.