PROPRIETA' DELLA MATERIA SUPERFLUIDA IN PRESENZA DEL RETICOLO NUCLEARE NELLA CROSTA INTERNA DELLE STELLE DI NEUTRONI

In this thesis I study three different properties of superfluid nuclear matter in the inner crust of neutron stars, which is formed by nuclear clusters immersed in a superfluid neutron gas and ultrarelativistic electrons. In the first part the cluster structure is calculated in the self-consistent HFB approach at zero temperature. The mean field and the pairing correlations of the inner crust nuclear matter are described, respectively, by a Skyrme-type effective interaction and by a zero range density dependent pairing force. The inner crust matter is treated in the Wigner-Seitz approximation. The properties of the Wigner-Seitz cells, i.e., their neutron to proton ratio and their radius at a given baryonic density, are obtained from the energy minimization at beta equilibrium. We have found that the Wigner-Seitz cells have a much smaller number of protons compared to the previous HF or HF+BCS calculations. In the second part the specific heat of the nuclear matter is calculated with the same HFB formalism used in the first part, but at finite temperature. This study represent a considerable improvement respect to the specific heats that are generally used in the literature on which the superfluid corrections to the specific heat were calculated in the BCS approach and considering the matter as homogeneous neutron gas. Using the HFB approach, in fact, it is possible to calculate directly the specific heat of the nuclear matter considering at the same time the composition, the interaction between particles, the clusters structure and the pairing properties. We have then used this specific heat in the study of the thermalization process in the cooling of a neutron star and we have found that the nuclear clusters have a non-negligible influence on the time evolution of the surface temperature of neutron stars. Finally, in the third part we have used numerical simulations of interaction of vortex with lattice to study the pinning force per unit length that binds a vortex to the nuclear lattice, one of the most important quantities in the vortex model for pulsar glitches, i.e. sudden variation of the rotation velocity of some neutron stars. The forces that we have found are almost two order of magnitude smaller than those reported in the literature and of the same order of those that have been suggested to explain the peculiar behaviour of real pulsar glitches. They can thus be applied in a quantitative model of the vortex dynamics in order to reproduce those phenomena.