Energy densities, initial conditions and hydrodynamic equations for ultra-relativistic nucleus-nucleus collisions

We discuss ultra-relativistic nucleus-nucleus collisions using an inside-outside cascade model. Our considerations are valid only for Esub(cm)>20 GeV/nucleon for collisions of nuclei of equal baryon number A>>1. The time and space development of the cascade are described, and the maximum energy and quark number densities produced in such collisions are analytically estimated. Assuming thermalization immediately after materialization from the cascade, hydrodynamic equations, with source terms corresponding to the hadronic matter materialization, are determined. These equations are valid globally in the beam and target fragmentation regions, and in the central region, and determine the energy density epsilon, baryon number density, nsub(B), and local flow velocity of the hadronic matter, usup(μ), if an equation of state is given. (orig.)