Probing the density dependence of the symmetry potential at low and high densities

We have investigated the influence of different forms of symmetry energies on various observables proposed to be sensitive to the symmetry energy at subnormal and supranormal densities for reactions ²⁰⁸Pb +²⁰⁸Pb, ¹³²Sn +¹²⁴Sn, and ⁹⁶Zr +⁹⁶zR at E_b=0.4A GeV within the microscopic transport model—ultrarelativistic quantum molecular dynamics model. The same systems are adopted for testing the probes of the symmetry potential at both subnormal and supranormal densities. It is shown that the differences between the predicted values of investigated quantities by different symmetry potentials have a close correspondence with the different behavior of the density dependence of the interaction part of the different symmetry energies. We also find that the comprehensive study with multiple probes provides a possibility for gaining the density dependence of the symmetry potential in a broad density region, which allows us to extract the information of the isospin-dependent part of the effective interaction.