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.
Categories: nucl-th hep-ph nucl-ex