We investigate a (3+1)-dimensional hydrodynamic expansion of the hot and dense system created in head-on collisions of Pb+Pb/Au+Au at beam energies from 5 to 200 GeV/nucleon. An equation of state is used that incorporates a critical end point (CEP) in line with the lattice data. The necessary initial conditions for the hydrodynamic evolution are taken from a microscopic transport approach, the ultrarelativistic quantum molecular dynamics (UrQMD) model. We compare the properties of the initial state and the full hydrodynamic calculation with an isentropic expansion employing an initial state from a simple overlap model. We find that the specific entropies ($S/A$) from both initial conditions are very similar and only depend on the underlying equation of state. Using the chiral (hadronic) equation of state, we investigate the expansion paths for both initial conditions. Defining a critical area around the critical point, we show at what beam energies one can expect to have a sizable fraction of the system close to the critical point. Finally, we emphasize the importance of the equation of state of strongly interacting matter in the (experimental) search for the CEP.

• Received 15 October 2007

DOI:https://doi.org/10.1103/PhysRevC.77.034901