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Compression, Expansion and the Equation of State

In central collisions of heavy nuclei with kinetic energies per nucleon of a few hundred MeV up to 1-2 GeV temperatures and densities are reached that clearly obliterate the concept of a hot nucleus. In this energy regime one rather studies the properties of hot and dense hadronic matter. On a macroscopic level, this state is probably realised in nature in the interior of neutron stars and the cores of supernovae where the density, pressure and temperature of such a system are related by an equation of state. It emerges as a consequence of the interactions among the constituents in the limit that there is enough time and space in order to achieve an equilibrated state. The study of the equation of state in small and rapidly developing systems is a new and challenging field. Heavy ion reactions provide the possibility to address the question of the properties of extended strongly interacting hot hadronic matter in the laboratory. In the energy regime discussed here the properties of the system arise chiefly from the interaction among the nucleons and their excitations; hadron production is just starting to become relevant and the pion to nucleon ratio reaches the 10 % level at the 1 GeV/nucleon energy range. The hot hadron gas cools and expands until particles again freeze out, i.e. stop to interact strongly. In contrast to the situation discussed in the previous chapter this happens at conditions well removed from the critical liquid-gas phase transition region. Now the freeze-out is dominated by collective phenomena and this may, similarly as is the case for the macroscopic astronomical systems, again make the concept of an equation of state a useful approach. How collective features form in hot and dense hadronic matter is a complicated process since many interesting and new effects can happen simultaneously: the NN-interaction might change in a surrounding medium, the effective masses of the constituents might change as a consequence of e.g. partial chiral symmetry restoration, and the constituents get excited into hadronic resonances. To separate the various contributions is a demanding task that is however aided by systematically varying the incident energy and the system size since the different processes show different dependences on incident momentum, density and temperature. It also requires a close collaboration between theory and experiment. It should also be emphasised that properties of hadronic matter at densities of a few times normal nuclear matter density need to be known accurately in order to quantitatively describe a possible phase transition into the QGP. This is the link to the physics described in the next subchapter. At the intermediate energies discussed here similar concepts and methods are used as for the highest energies, but the available information is already rather complete and thus can put constraints on the dynamical evolution of the reaction also relevant for the highest energies. 
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