Covariance Analysis of Symmetry Energy Observables from Heavy Ion Collision

TL;DR

This study uses covariance analysis to explore how different observables in heavy ion collisions relate to the nuclear symmetry energy and effective mass parameters, aiding in constraining these properties.

Contribution

It introduces a covariance analysis approach to quantify correlations between model parameters and observables in heavy ion collision experiments, identifying key observables for constraining nuclear matter properties.

Findings

Neutron and proton yield ratios are strongly correlated with effective mass splitting.

Isospin diffusion is the best observable for determining the slope of symmetry energy, L.

Effective mass splitting and isoscalar effective mass show opposite correlations at 120 MeV/u.

Abstract

Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter in experiments. By simulating $^{124}$Sn+$^{124}$Sn, $^{124}$Sn+$^{112}$Sn and $^{112}$Sn+$^{112}$Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective mass splitting are most strongly correlated to the neutrons and protons yield ratios with high kinetic energy from central collisions especially at high incident energy. The best observable to determine the slope of the symmetry energy, L, at saturation density is the isospin diffusion observable even though the correlation is not very strong ($\sim$0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective mass. At 120 MeV/u, the effective mass splitting and the isoscalar effective mass also have opposite correlation for the double n/p and isoscaling p/p yield ratios. By combining data and simulations at different beam energies, it should be possible to place constraints on the slope of symmetry energy (L) and effective mass splitting with reasonable uncertainties.