Isospin splitting of nucleon effective mass and shear viscosity of nuclear matter

Based on an improved isospin- and momentum-dependent interaction, I have studied the qualitative effect of isospin splitting of nucleon effective mass on the specific shear viscosity of neutron-rich nuclear matter from a relaxation time approach. It is seen that for $m_n^{☆}>m_p^{☆}$, the relaxation time of neutrons is smaller, and the neutron flux between flow layers is weaker, leading to a smaller specific shear viscosity of neutron-rich matter compared to the case for $m_n^{☆}<m_p^{☆}$. The effect is larger in nuclear matter at higher densities, lower temperatures, and larger isospin asymmetries, but it does not affect the behavior of the specific shear viscosity much near nuclear liquid-gas phase transition.

Figure 1

Binding energy in symmetric nuclear matter (a), symmetry energy (b), symmetry potential at saturation density (c), and relative neutron-proton effective mass splitting (d) in nuclear matter at saturation density and isospin asymmetry $\delta =0.5$ from the two parameter sets based on the ImMDI interaction.

Figure 2

Momentum dependence of the total relaxation time and that for a nucleon to collide with other ones of same or different isospin in nuclear matter at saturation density and isospin asymmetry of $\delta =0.5$ using free-space or in-medium nucleon-nucleon scattering cross sections.

Figure 3

Specific shear viscosity with free-space [(a), (b)] and in-medium [(c), (d)] cross sections in nuclear matter of isospin asymmetry $\delta =0.5$ at different densities and temperatures for $m_n^{☆}>m_p^{☆}$ and $m_n^{☆}<m_p^{☆}$.

Figure 4

Isospin asymmetry dependence of the specific shear viscosity in nuclear matter at different temperatures and densities for $m_n^{☆}>m_p^{☆}$ and $m_n^{☆}<m_p^{☆}$.

Figure 5

Temperature evolution of the entropy (upper panels) and specific shear viscosity (lower panels) in the presence of nuclear liquid-gas phase transition (LGPT) at fixed external pressure $P=0.05$ [(a), (d)], $0.10$ [(b), (e)], and $0.15$ ${\mathrm{MeV}/\mathrm{fm}}^3$ [(c), (f)] and isospin asymmetry $\delta =0.5$ for $m_n^{☆}>m_p^{☆}$ and $m_n^{☆}<m_p^{☆}$.