Mean free path and shear viscosity in central $^{129}$Xe+$^{119}$Sn collisions below 100 MeV/nucleon

Thermal and transport properties of hot nuclear matter formed in central $^{129}$Xe + $^{119}$Sn collisions at the Fermi energy are investigated using the isospin-dependent quantum molecular dynamical (IQMD) model. Temperature ($T$), average density ($\rho$), chemical potential ($\mu$), mean momentum ($P$), shear viscosity ($\eta$) and entropy density ($s$) are obtained from the phase-space information. The mean free path ($\lambda_{nn}$) and the in-medium nucleon-nucleon cross section ($\sigma_{nn}$) in the highest compressible stage at different incident energies are deduced and compared with the experimental results from Phys. Rev. C $\bf{90}$ (2014) 064602. The result shows that $\lambda_{nn}$ and $\sigma_{nn}$ have the same trend and similar values as the experimental results when the beam energy is greater than 40 MeV/u at maximum compressed state. Furthermore, the derived shear viscosity over entropy density ($\eta/s$) shows a decreasing behaviour to a saturated value around $\frac{3}{4\pi}$ as a function of incident energy.