Viscosity and the equation of state in high energy heavy-ion reactions

Viscous hydrodynamic calculations of high energy heavy-ion collisions (Nb-Nb and Au-Au) from 200 to 800 MeV/nucleon are presented. The resulting baryon rapidity distributions, the in-plane transverse momentum transfer (bounce-off), and the azimuthal dependence of the midrapidity particles (off-plane squeeze out) compare well with Plastic Ball data. We find that the considered observables are sensitive both to the nuclear equation of state and to the nuclear shear viscosity {η}. Transverse momentum distributions indicate a high shear viscosity ({η}{}60 MeV/fm² c) in the compression zone, in agreement with nuclear matter estimates. The bulk viscosity {ζ} influences only the entropy production during the expansion stage; collective observables like flow and dN/dY do not depend strongly on {ζ}. The recently observed off-plane ({φ}=90^∘{}) squeeze-out, which is found in the triple-differential rapidity distribution, exhibits the strongest sensitivity to the nuclear equation of state. It is demonstrated that for very central collisions, b=1 fm, the squeeze-out is visible even in the double-differential cross section. This is experimentally accessible by studying azimuthally symmetric events, as confirmed recently by data of the European 4{π} detector collaboration at Gesellchaft f\"ur Schwerionforschung Darmstadt.