Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge* *Supported by the National Natural Science Foundation of China (11875328, 12075327), the Key Laboratory of Nuclear Data foundation (JCKY2022201C157), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (22lgqb39)

Abstract

The new signature of liquid-gas phase transition has been well indicated by the higher-order fluctuations of the largest fragment charge, but the uncertainties of critical temperatures based on this signature have not been revealed. This study extracts the critical temperatures of liquid-gas phase transition in nuclear reactions and investigates their uncertainties. Utilizing the isospin-dependent quantum molecular dynamics model in conjunction with the statistical model GEMINI enables us to describe the dynamical path from the initial to the final state. An isotope thermometer and a quantum fluctuation thermometer are employed to extract the nuclear temperature. The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in 124Sn + 120Sn collisions ranging from 400 to 1000 MeV/nucleon and 124Sn + AZ collisions at 600 MeV/nucleon. Observations revealed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge. The critical temperatures extracted by the isotope thermometer are relatively consistent, with an uncertainty of 15%, while those obtained by the quantum fluctuation thermometer are heavily influenced by the incident energy and mass number of target nuclei. The excitation energy and bound charge are used for event-sorting. These two ensembles represent the statistical properties of the initial and final states of the system, respectively. The initial-final correlations of statistical properties might lead to two phenomena. First, the size distribution of the largest fragment at the pseudo-critical point based on the ensemble is wide, while that based on ensemble exhibits bimodality, which is a typical characteristic in the liquid-gas coexistence of a finite system. Second, the temperature at the pseudo-critical point based on the ensemble is higher than that based on the ensemble. Furthermore, the projectile-like system exhibits a significant dynamical effect in its evolution path from the initial to final state, closely associated with the fluctuation of critical temperature.