Transport properties of asymmetric nuclear matter in the spinodal region

We have studied the shear and bulk viscosities of asymmetric nuclear matter in the mechanical and chemical instability region based on isospin-dependent Boltzmann-Uehling-Uhlenbeck transport simulations in a box system. The Green-Kubo method is used to calculate these viscosities with a prepared dynamically equilibrated nuclear system with hot clusters. While the behavior of the shear viscosity is largely affected by energy-dependent nucleon-nucleon cross sections, the bulk viscosity increases significantly in the presence of nuclear clusters compared to that in uniform nuclear matter. Increasing isospin asymmetry generally increases both viscosities, while their behaviors are qualitatively modified once the isospin asymmetry is large enough to affect significantly the spinodal region. Our calculation shows that the bulk viscosity is more sensitive to the nuclear clustering than the shear viscosity and is thus a robust quantity related to the phase diagram of asymmetric nuclear matter.

Figure 1

Left: Total neutron-proton (np) and proton-proton (pp) cross sections as functions of the kinetic energy $E_k^{\mathrm{in}}$ of incident nucleon; Right: Polar angular dependence of differential cross sections for neutron-proton (np) and proton-proton (pp) collisions at $E_k^{\mathrm{in}}=20$ and 40 MeV.

Figure 2

Boundaries of isothermal spinodal (ITS), diffusive spinodal (DS), and liquid-gas phase coexistence (CE) in the $(\rho ,\delta )$ plane at the temperatures $T=5$ (a), 10 (b), and 15 (c) MeV.

Figure 3

Contours of the reduced density $\rho /{\rho }_0$ (first row), the isospin asymmetry $\delta$ (second row), and the temperature $T$ (third row) at time $t=0$, 100, 300, 500, 1000, and 1250 fm/$c$ from IBUU simulations, starting from a uniform box system with initial density $\rho =0.3{\rho }_0$, isospin asymmetry $\delta =0.2$, and temperature $T=10$ MeV, and with a reset of the temperature at $t=500$ fm/$c$.

Figure 4

Time evolution of physics quantities from IBUU simulations in a box system at an average density $\langle \rho \rangle =0.3{\rho }_0$, average isospin asymmetry $\langle \delta \rangle =0.2$, and initial temperature $T=10$ MeV but with a reset of the temperature at $t=500$ fm/$c$. Top: Average kinetic energy density $\langle {\epsilon }_k\rangle$, potential energy density $\langle {\epsilon }_p\rangle$, and total energy density $\langle {\epsilon }_k\rangle +\langle {\epsilon }_p\rangle$; middle: average entropy density $\langle s\rangle$; bottom: average temperature $\langle T\rangle$.

Figure 5

Time dependence of correlations of the shear (left) and bulk (right) components of the energy-momentum tensor, for a nuclear system with an average density $\rho =0.3{\rho }_0$, average isospin asymmetry $\delta =0.2$, and average temperature of about 10 MeV. Results for a uniform system without mean-field potential (MF) are shown in upper panels, and those for a nonuniform system with mean-field potential are shown in lower panels.

Figure 6

Left: Temperature dependence of the entropy density ($s$), the shear viscosity ($\eta$), the specific shear viscosity ($\eta /s$), the bulk viscosity ($\zeta$), and the specific bulk viscosity ($\zeta /s$) in isospin symmetric nuclear matter at fixed average densities $\rho =0.1$, 0.3, and $0.6{\rho }_0$; right: density dependence of these quantities at fixed average temperatures $T=5$, 10, 15 MeV. Results with and without mean-field potential (MF) are compared.

Figure 7

Left: Temperature dependence of the entropy density ($s$), the shear viscosity ($\eta$), the specific shear viscosity ($\eta /s$), the bulk viscosity ($\zeta$), and the specific bulk viscosity ($\zeta /s$) at a fixed average density $\rho =0.6{\rho }_0$ in isospin symmetric ($\delta =0$) and asymmetric ($\delta =0.2$ and 0.6) nuclear matter with and without mean-field potential (MF); right: temperature dependence of these quantities at a fixed average density $\rho =0.3{\rho }_0$ and isospin asymmetry $\delta =0.2$ with and without Coulomb potential (cou) in the presence of mean-field potential.