We propose a model to explain how a gamma-ray burst can take place days or years after a supernova explosion. Our model is based on the conversion of a pure hadronic star (neutron star) into a star made at least in part of deconfined quark matter. The conversion process can be delayed if the surface tension at the interface between hadronic and deconfined quark matter phases is taken into account. The nucleation time (i.e., the time to form a critical-size drop of quark matter) can be extremely long if the mass of the star is small. Via mass accretion the nucleation time can be dramatically reduced and the star is finally converted into the stable configuration. A huge amount of energy, on the order of 10 52 -10 53 ergs, is released during the conversion process and can produce a powerful gamma-ray burst. The delay between the supernova explosion generating the metastable neutron star and the new collapse can explain the delay inferred in GRB 990705 and in GRB 011211.

We discuss the formation of isobars in neutron star matter. We show that their threshold density strictly correlates with the density derivative of the symmetry energy of nuclear matter: the L parameter. By restricting L to the range of values indicated by recent experimental and theoretical analysis, i.e., 40 MeV L 62 MeV, we find that isobars appear at a density of the order of 2 to 3 times the nuclear matter saturation density, i.e., the same range as for the appearance of hyperons. The range of values of the couplings of the s with the mesons is restricted by the analysis of the data obtained from photoabsorption, electron and pion scattering on nuclei. If the potential of the in nuclear matter is close to the one indicated by the experimental data then the equation of state becomes soft enough that a " puzzle" exists, similar to the "hyperon puzzle" widely discussed in the literature. Possible solutions to this puzzle are also discussed.

Starting from the experimental evidence that high-energy nucleus-nucleus collisions cannot be described in terms of superpositions of elementary nucleon-nucleon interactions, we analyze the possibility that memory effects and long-range forces imply a nonextensive statistical regime during high energy heavy ion collisions. The relevance of these statistical effects and their compatibility with the available experimental data are discussed. In particular we show that theoretical estimates, obtained in the framework of the generalized nonextensive thermostatistics, can reproduce the shape of the pion transverse mass spectrum and explain the different physical origin of the transverse momentum correlation function of the pions emitted during the central Pb+Pb and during the p+p collisions at 158 A GeV.

We show that a natural realization of the thermostatistics of q bosons can be built on the formalism of q calculus, and that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative in place of the ordinary thermodynamics derivative. This framework allows us to obtain a generalized q boson entropy which depends on the q basic number. We study the ideal q boson gas in the thermodynamic limit which is shown to exhibit Bose-Einstein condensation with a higher critical temperature and a discontinuous specific heat.

We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric (q<-->q(-1)) algebra and show that it can be built on the formalism of q calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semiclassical limit and the low-temperature regime and demonstrate that the nature of the q deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.

We study the transition from hadronic matter to a mixed phase of quarks and hadrons at high baryon and isospin densities reached in heavy ion collisions. We focus our attention on the role played by the nucleon symmetry energy at high density.In this respect the inclusion of a scalar isovector meson, the \delta-coupling, in the Hadron Lagrangian appears rather important. We study in detail the formation of a drop of quark matter in the mixed phase, and we discuss the effects on the quark drop nucleation probability of the finite size and finite time duration of the high density region. We find that, if the parameters of quark models are fixed so that the existence of quark stars is allowed, then the density at which a mixed phase starts forming drops dramatically in the range Z/A \sim 0.3--0.4. This opens the possibility to verify the Witten-Bodmer hypothesis on absolute stability of quark matter using ground-based experiments in which neutron-rich nuclei are employed. These experiments can also provide rather stringent constraints on the Equation of State (EoS) to be used for describing the pre-Supernova gravitational collapse. Consistent simulations of neutron rich heavy ion collisions are performed in order to show that even at relatively low energies, in the few AGeV range, the system can enter such unstable mixed phase. Some precursor observables are suggested, in particular a ``neutron trapping'' effect

The existence of neutron stars with masses of 2M⊙ requires a stiff equation of state at high densities. On the other hand, the necessary appearance also at high densities of new degrees of freedom, such as hyperons and Δ resonances, can lead to a strong softening of the equation of state with resulting maximum masses of ∼1.5M⊙ and radii smaller than ∼10  km. Hints for the existence of compact stellar objects with very small radii have been found in recent statistical analyses of quiescent low-mass X-ray binaries in globular clusters. We propose an interpretation of these two apparently contradicting measurements, large masses and small radii, in terms of two separate families of compact stars: hadronic stars, whose equation of state is soft, can be very compact, while quark stars, whose equation of state is stiff, can be very massive. In this respect an early appearance of Δ resonances is crucial to guarantee the stability of the branch of hadronic stars. Our proposal could be tested by measurements of radii with an error of ∼1  km, which is within reach of the planned Large Observatory for X-ray Timing satellite, and it would be further strengthened by the discovery of compact stars heavier than 2M⊙

In this paper we will show that, because of the long-range microscopic memory of the random force, acting in the solar core, mainly on the electrons and the protons than on the light and heavy ions (or, equally, because of anomalous diffusion of solar core constituents of light mass and of normal diffusion of heavy ions), the equilibrium statistical distribution that these particles must obey, is that of generalized Boltzmann-Gibbs statistics (or the Tsallis non-extensive statistics), the distribution differing very slightly from the usual Maxwellian distribution. Due to the high-energy depleted tail of the distribution, the nuclear rates are reduced and, using earlier results on the standard solar model neutrino fluxes, calculated by Clayton and collaborators, we can evaluate fluxes in good agreement with the experimental data. While proton distribution is only very slightly different from Maxwellian there is a little more difference with electron distribution. We can define one central electron temperature as a few percent higher than the ion central temperature nearly equal to the standard solar model temperature. The difference is related to the different reductions with respect to the standard solar model values needed for B and CN O neutrinos and for Be neutrinos.PACS number(s): 73.40.Hm, 71.30.+h, 96.60.K