Nonlinear relativistic equation of state and phase transitions in nuclear matter at finite temperature and baryon density

The main goal of this Thesis, is the study of the thermodynamic properties of strongly interacting and dense nuclear matter, away from the nuclear ground state. This analysis constitutes one of the most interesting aspect and one of the major tasks in the modern high-energy nuclear physics. The first part of this dissertation, addresses the phenomenological and theoretical study of the nuclear matter equation of state, under the extreme conditions reached in high energy heavy ion collision experiments and in astrophysical object, such as for example neutron stars. Of particular interest is the determination of the microscopic hadronic and quark-gluon plasma equation of state in the framework of a relativistic mean field theory and in regime of high density and temperature. This is realized by means of a theoretical-computational approach and comparing the results with the recent experimental data obtained from the relativistic heavy ion collisions experiments. We adopt and develop a method based on the so-called non-extensive statistical mechanics to derive momentum and energy distribution functions to simply evaluate the physical quantities, taking into account of the correlations among the strongly interacting particles of the medium. Deconfinement phase transition is investigated by applying the Gibbs condition on a system of two (B, C) or three (B, C, S) conserved charges, by requiring the global conservation of each charges in the total phase. A multi-component system, in fact, implies a global and not a local charge conservation. Therefore, the charge densities ρB, ρC and ρS are fixed only as long as the system remains in one of the two pure phases. In the mixed phase, the charge concentration in each of the regions of one phase or the other may be different. We also study the strangeness production at finite temperature and baryon density by means of an effective relativistic mean-field model, with the inclusion of the full baryon octet and the meson degrees of freedom. In this context, lightest pseudo-scalar (π, K, K, η, η′) and vector mesons (ρ, ω, K∗, K∗, ϕ) are introduced in the QHD-Lagrangian density through an effective chemical potential depending on the self-consistent interaction between baryons. Hence, the obtained results are compared with those of minimal coupling scheme. The different meson ratios, strangeness production and possible kaon condensation are deeply investigated. Finally, in the last part of this dissertation, we investigate the possible thermodynamical instabilities in a warm (T ≤ 50 MeV) and dense nuclear medium (ρ0 ≤ ρB≤ 3ρ0), where a phase transition from nucleonic matter to resonance-dominated Δ matter can take place. This analysis is performed by requiring the global conservation of baryon and electric charge numbers in the framework of a relativistic equation of state. Similarly to the liquid-gas phase transition, we show that the nucleon-Δ matter phase transition is characterized by both mechanical instability ( fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the charge concentration) in asymmetric nuclear matter. We then perform an investigation and a comparative study on the different nature of such instabilities and phase transitions. In this context, the liquid-gas phase transition is also investigated in the framework of non-extensive statistical effects and in the last part of this analysis we also investigate the possible onset of strangeness-diffusive instability (fluctuation on the strangeness density) in a hot (70 ≤ T ≤ 140 MeV) and dense nuclear medium (ρ0 ≤ ρB≤ 3ρ0). The goal of this thesis, is therefore a deeper knowledge of the proprieties of nuclear matter at high density and finite temperature, with the study and the implementation of the nuclear equation of state through effective models (non-extensive statistical mechanics and effective relativistic mean-field model), through which overcome some theoretical and experimental difficulties in the determination of the physical parameters of the system. Finally, the study of the thermodynamical proprieties of strongly interacting nuclear matter, away from the nuclear ground state, allow us to deal and respond to one of the major questions of modern high-energy nuclear physics.