Effective interactions and pairing correlations: from nuclei to compact stars
The purpose of this dissertation is to study some general properties of nuclear many-body systems, ranging from infinite nuclear matter to finite nuclei. Our investigations is focused in particular on nuclear systems with neutron excess, to get a deeper insight in the open issue which concerns the isospin dependence of the nuclear interaction. The analysis is concentrated on the behavior of nuclear matter at densities which lie below the saturation one, with the aim to address several nuclear phenomena, which involve surface effects in nuclei and clustering processes emerging in nuclear reactions and compact stellar objects. Our study is devoted also to shed light on the impact of some relevant interparticle correlations, mainly active in the low density region of the phase diagram, which occur in fermionic system and are responsible for the superfluid phenomena: the pairing correlations. Our goal is therefore to examine the interplay of these correlations with the other terms of the effective interaction, usually introduced to approach the nuclear many-body problem. Wide attention is dedicated to the role of the pairing interaction in the astrophysical setting of stellar matter, especially when the cooling process of proto-neutron stars is concerned. Our analysis evidences in fact important pairing effects on neutrino emissivity and specific heat, which are two key ingredients in the thermal evolution of a compact star. On the one hand, superfluidity turns out to be responsible for a significant modification of the neutrino emission, for suitable density, asymmetry and temperature conditions, which can be of interest for the evolution of neutron stars and supernovae explosion in the pre-bounce phase. Focusing on neutral current neutrino scattering, we observe an increase of the neutrino differential cross section in a paired and low-density nuclear medium, at least close to the spinodal border, where the matter is characterized by quite large density fluctuations. This behavior leads to an enhancement of neutrino trapping and a reduction in the energy flux carried by neutrinos. On the other hand, we present a calculation of the specific heat in the inner crust of proto-neutron stars, within an approach based on cluster degrees of freedom, that considers the complete distribution of different nuclear species in thermal and beta-equilibrium. The resulting specific heat brings to light a strong influence of resonance population at moderate temperatures and in density regions close to the crust-core transition and the importance of an accurate treatment of beta-equilibrium for a quantitative determination of the specific heat and of the neutron star cooling curve. Since nuclear systems with neutron excess have an essential role also in the context of nuclear structure, we investigate, within a semi-classical as well as in a quantal transport model, the structure and small amplitude dynamics of neutron-rich nuclei, focusing on the mixed isoscalar-isovector character of their collective excitations. In particular, we address some of the open questions concerning the nature of the low-lying isovector dipole strength experimentally observed in neutron-rich nuclei and known in literature as pygmy dipole resonance (PDR). We show that the relative isoscalar-isovector weight of the different modes is determined by their intrinsic structure, as well as by the type of initial perturbation considered so the PDR excitations turns to be essentially isoscalar-like, i.e., neutrons and protons oscillate in phase but with different amplitude. Moreover, we explore the relation between the mixed isoscalar-isovector structure of the dipole collective modes and the density dependence of the symmetry energy, focusing on its importance in shaping the neutron skin thickness. Further developments are moreover enviseged to get a deeper insight on the role of pairing and quantal effects in characterizing the collective excitations of neutron-rich nuclei.
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