Exploring the Nuclear-Shape Phase Transition in Ultrarelativistic129Xe+129XeCollisions 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 ultrarelativistic 129Xe+129Xe collisions. In particular, our iEBE-VISHNU model calculations show that the correlation between elliptic flow 𝑣2 and mean transverse momentum [𝑝𝑇], denoted as 𝜌2, as well as the [𝑝𝑇] fluctuation Γ𝑝𝑇, which were previously used to claim the evidence of the rigid triaxial deformation of 129Xe, can also be well explained by the 𝛾-soft deformation of 129Xe. We further propose two novel correlators 𝜌4,2 and 𝜌2,4, which carry nontrivial 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 provides a novel way to explore the second-order shape phase transition of finite nuclei with ultrarelativistic heavy ion collisions.