Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge*

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 has not been revealed.This work is proposed to extract the critical temperatures of liquid-gas phase transition in nuclear reactions and study their uncertainties. The isospin-dependent quantum molecular dynamics model coupling with statistical model GEMINI enables us to describe the dynamical path from initial to final state.The isotope thermometer and quantum fluctuation thermometer are applied to extract nuclear temperature. The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in $^{124}$Sn + $^{120}$Sn collisions from 400 to 1000 MeV/nucleon, and $^{124}$Sn + $^{A}$Z collisions at 600 MeV/nucleon. It is observed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge. The critical temperatures extracted by isotope thermometer are relatively uniform with 15% uncertainty, while those by quantum fluctuation thermometer strongly depend on the incident energy and mass number of target nuclei.The excitation energy $E^{*}$ and bound charge $Z_{bound}$ are used for event-sorting. These two ensembles represent the statistical properties of initial and final states of system, respectively. The initial-final correlations of the statistical properties might cause two phenomena. First the size distribution of the largest fragment at pseudo-critical point based on $Z_{bound}$ ensemble is wide, while that based on $E^{*}$ ensemble exhibits the bimodality which is the typical characteristic in the liquid-gas coexistence of finite system. Second the temperature at pseudo-critical point based on $Z_{bound}$ ensemble is higher than that based on $E^{*}$ ensemble. Furthermore the projectile-like system exhibits significant dynamical effect in the evolution path from initial to final state, which is closely related to the fluctuation of critical temperature.