Finite size corrections to the equation of state for nuclear matter near the phase transition hadron gas to quark gluon plasma

It is widely accepted that the finite size of the hadrons must be taken into account in a thermodynamic description of the hadron gas near the phase transition to quark gluon plasma. Existing thermodynamic models introducing a correction due to the finite size of the particles are reviewed and discussed. A new model to describe dense nuclear matter is developed. The model takes into account the different quantum statistical distributions of the hadrons. The grand canonical pressure partition function is used to obtain the thermodynamic limit. The grand canonical partition function is restricted so that only those states where the extended particles fit into the volume of the system, are counted. The hadrons are described as MIT bags. The pressure in the system compresses the hadrons which leads to an increase of the mass of the hadrons according to the MIT bag equation. The size of the particles is determined by the minimum of the grand canonical potential. A consistent thermodynamc theory is obtained. The equation of state for hadronic matter is discussed before the case of finite temperature and finite chemical potential is used to construct a first order phase transition from hadron gas to quark gluon plasma. It is found that the phase transition is strongly dependent on the value chosen for the bag constant and the application of αs corrections. Therefore a reliable value of the bag constant and a generally accepted theory for αs corrections are essential to obtain a good thermodynamic description of the phase transition from hadron gas to quark gluon plasma. 100 refs., 32 figs., 2 tabs