The percolation phase transition and statistical multifragmentation in finite systems

TL;DR

This study investigates the phase transition signatures in nuclear fragmentation using cumulant ratios, linking experimental data with percolation theory and statistical models to understand the nature of the transition.

Contribution

It demonstrates that cumulant ratios reveal second-order phase transition signatures in nuclear fragmentation, supported by experimental data and statistical model simulations.

Findings

Cumulant ratios indicate second-order phase transition signatures.

Pseudocritical points are weakly dependent on A/Z ratio.

Experimental results are well reproduced by the Statistical Multifragmentation Model.

Abstract

The cumulant ratios up to fourth order of the $Z$ distributions of the largest fragment in spectator fragmentation following $^{107,124}$Sn+Sn and $^{124}$La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of $^{197}$Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the $A/Z$ ratio of the fragmenting spectator source. The same holds for the corresponding chemical freeze-out temperatures of close to 6 MeV. The experimental cumulant distributions are quantitatively reproduced with the Statistical Multifragmentation Model and parameters used to describe the experimental fragment multiplicities, isotope distributions and their correlations with impact-parameter related observables in these reactions. The characteristic coincidence of the zero transition of the skewness with the minimum of the kurtosis excess appears to be a generic property of statistical models and is found to coincide with the maximum of the heat capacity in the canonical thermodynamic fragmentation model.