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

Thermal and transport properties of hot nuclear matter formed in central ${}^{129}\mathrm{Xe}+{}^{119}\mathrm{Sn}$ collisions at the Fermi energy are investigated using the isospin-dependent quantum molecular dynamical 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 90, 064602 (2014). 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/nucleon at maximum compressed state. Furthermore, the derived shear viscosity over entropy density ($\eta /s$) shows a decreasing behavior to a saturated value around $\frac{3}{4\pi }$ as a function of incident energy.

Figure 1

The time evolution of the (a) average density and (b) temperature of central region at different incident energies.

Figure 2

The time evolution of (a) shear viscosity, (b) chemical potential, and (c) mean momentum in central region at different energies.

Figure 3

The time evolution of the (a) mean free path and the (b) nucleon-nucleon cross section of central region at different incident energies.

Figure 4

The time evolution of entropy density in central region at different energies.

Figure 5

The maximum density and the corresponding moment of central region at different energies.

Figure 6

(a) Energy dependence of in-medium nucleon nucleon cross section. ${\sigma }^{*}$ and $\sigma$ are the result of the IQMD model output and the value calculated by formula, respectively. (b) Energy dependence of the mean free path. ${\lambda }^{*}$ and $\lambda$ are the value calculated from the value of ${\sigma }^{*}$ and $\sigma$ shown in Fig. 6, respectively. ${\sigma }^{**}$ and ${\lambda }^{**}$ are the result from Ref. [52].

Figure 7

Energy dependence of (a) shear viscosity ($\eta$) and (b) the shear viscosity over entropy density ($\eta$/s, in units of $1/4\pi$) at the largest compressible state. ${\eta }^{*}$ and $\eta$ are the values calculated from the value of ${\sigma }^{*}$ and Eq. (11), respectively.