Covariance Analysis of Symmetry Energy Observables from Heavy Ion Collision

Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the experimental observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter. Using the simulations of Sn+Sn, Sn+Sn and Sn+Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective masses splitting are most strongly correlated to the neutrons and protons yield ratios 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 at low incident energy even though the correlation is not very strong (∼0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective masses. 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 the data and simulations at high and low energy, it should be possible to disentangle the effects the slope of symmetry energy (L), isoscalar effective mass (m∗s/m) and effective mass splitting and place the constraints on L, m∗s/m and effective mass splitting with reasonable uncertainties.