Nonlinear Nuclear Equation of State and Thermodynamical Instabilities in Warm and Dense Nuclear Matter

We investigate the possible thermodynamic instability in a warm and dense nuclear medium where a phase transition from nucleonic matter to resonance-dominated Δ-matter can take place. Such a phase transition is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the isospin concentration) in asymmetric nuclear matter. Similarly to the liquid-gas phase transition, the nucleonic and the Δ-matter phase have a different isospin density in the mixed phase. In the liquid-gas phase transition, the process of producing a larger neutron excess in the gas phase is referred to as isospin fractionation. A similar effects can occur in the nucleon-Δ matter phase transition due essentially to a Δ excess in the Δ-matter phase in asymmetric nuclear matter. The relevance of such thermodynamic instabilities may be more evident on heavy-ion collisions induced by neutron-rich nuclei, obtainable, in principle, with radioactive ion beam (RIB) facilities where a rather exotic nuclear matter can be formed. In this context we also discuss the relevance of Δ-isobar degrees of freedom in the bulk properties and in the maximum mass of neutron stars.