Virial Expansion of the Nuclear Equation of State

We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2,3,. . .,N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second order phase transition to the Quark Gluon Plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second order phase transition we calculate the critical exponent ? by using Landau's theory of phase transition. We find ? = 3. Refining the properties of the EOS near the critical point gives ? = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures.