Thermodynamic properties and shear viscosity over entropy density ratio of nuclear fireball in a quantum-molecular dynamics model

Thermodynamic and transport properties of nuclear fireball created in the central region of heavy-ion collisions below 400 MeV/nucleon are investigated within the isospin-dependent quantum molecular dynamic (IQMD) model. These properties including the density, temperature, chemical potential, entropy density ($s$) and shear viscosity ($\eta$), are calculated by a generalized hot Thomas Fermi formulism and a parameterized function, which was developed by Danielewicz. As the collision goes on, a transient minimal $\eta/s=5/4\pi-10/4\pi$ occurs in the largest compression stage. Besides, the relationship of $\eta/s$ to temperature ($T$) in the freeze-out stage displays a local minimum which is about 9-20 times $1/4\pi$ around $T$ = 8-12 MeV, which can be argued as indicative of a liquid gas phase transition. In addition, the influences of nucleon-nucleon (NN) cross section ($\sigma_{NN}$) and symmetry energy coefficient ($C_{s}$) are also discussed, and it is found that the results are sensitive to $\sigma_{NN}$ but not to $C_{s}$.