Shear viscosity of nuclear matter

TL;DR

This paper calculates the shear viscosity of nuclear matter modeled with a van der Waals equation, revealing how it varies with density and temperature, and identifying regimes where hydrodynamics is applicable.

Contribution

It introduces a kinetic approach to compute shear viscosity in nuclear matter using the VDW model, highlighting the density and temperature dependence of the viscosity-to-entropy ratio.

Findings

The shear viscosity to entropy density ratio drops below 1 near the critical point.

The ratio exhibits a minimum close to the VDW critical point.

High viscosity values at low and high densities limit hydrodynamic applicability.

Abstract

Shear viscosity $\eta$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 - 1.5)\,n^{}_0$, where $n^{}_0=0.16\,$fm$^{-3}$ is the particle density of equilibrium nuclear matter at zero temperature. A minimum of the $\eta/s$ ratio takes place somewhere in a vicinity of the critical point of the VDW system. Large values of $\eta/s\gg 1$ are, however, found in both the low-density, $n\ll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal hydrodynamic approach inapplicable for these densities.