Viscosity in the excluded volume hadron gas model

The shear viscosity η in the van der Waals excluded volume hadron-resonance gas model is considered. For the shear viscosity the result of a nonrelativistic gas of hard-core particles is extended to a mixture of particles with different masses but equal values of hard-core radius r. The relativistic corrections to hadron average momenta in thermal equilibrium are also taken into account. The ratio of the viscosity η to the entropy density s is studied. It monotonically decreases along the chemical freeze-out line in nucleus-nucleus collisions with increasing collision energy. As a function of hard-core radius r, a broad minimum of the ratio η/s≅0.3 near r≅0.5 fm is found at high collision energies. For the charge-neutral system at T=Tc=180 MeV, a minimum of the ratio η/s congruent with 0.24 is reached for r congruent with 0.53 fm. To justify a hydrodynamic approach to nucleus-nucleus collisions within the hadron phase the restriction from below, r≥0.2 fm, on the hard-core hadron radius should be fulfilled in the excluded volume hadron-resonance gas