Pairing effects on spinodal decomposition of asymmetric nuclear matter

Abstract

We investigate the impact of pairing correlations on the behavior of unstable asymmetric nuclear matter at low temperature. We focus on the relative role of the pairing interaction, coupling nucleons of the same type (neutrons or protons), with respect to the symmetry potential, which enhances the neutron-proton attraction, along the clusterization process driven by spinodal instabilities. It is found that, especially at the transition temperature from the normal to the superfluid phase, pairing effects may induce significant variations in the isotopic content of the clusterized matter. This analysis is potentially useful to gather information on the temperature dependence of nuclear pairing and, in general, on the properties of clusterised low-density matter, of interest also in the astrophysical context. Investigations of many-body interacting systems have always been an exciting and attractive field in different domains of physics. Indeed understanding the properties of complex systems in terms of their constituent particles and the interaction among them is a true challenge. The original (and unsolvable) quantal many-body problem, is often approached adopting the mean-field approximation, yielding a so-called effective interaction [1,2]. However, suitable extensions of mean-field models have been introduced to take explicitly into account the effects of relevant interparticle correlations. This is the case, for instance, of pairing correlations which occur, under suitable conditions, in fermionic systems [3].Many efforts are currently focused on the study of the properties of complex nuclei and infinite nuclear matter. It is well known that nucleons can form paired states, analogous to the way electrons pair in metals, yielding a superconducting phase [3]. Pairing effects on nuclear masses are widely investigated nowadays, also in connection with astrophysical applications requiring the knowledge of the mass of very neutron-rich nuclei, which play a crucial role in the r process of nucleosynthesis [4]. Moreover, the presence of neutron superfluidity in the crust and the inner part of neutron stars is considered well established in the physics of these compact stellar objects, and has a significant effect on cooling processes [5] and glitch phenomena [6,7].Complex many-body systems are also characterized by the possible occurence of different kinds of phase transitions. For nuclear matter at sub-saturation density and relatively low temperature (T 15M eV ) liquidgas phase transitions are expected to appear, driven by the unstable mean-field. Such a process is closely linked to the multifragmentation mechanism experimentally observed in nuclear reactions [8] and to the occurrence of clustering phenomena in the inner crust of neutron stars [9,10]. Owing to the two-component structure of nuclear matter, a central role in this mechanism pertains to the density behavior of the isovector part of the effective interaction and the corresponding term in the nuclear Equation of State, the symmetry energy [11,12], on wh...

Pairing effects on neutrino transport in low-density stellar matter

“…It was recently pointed out that large density fluctuations, associated with the first order nuclear liquid-gas phase transition, hugely increase the scattering of neutrinos [18], thus quenching their emissivity processes in low density regions.As a quite general feature, fermionic systems may also exhibit pairing correlations. Their importance is widely discussed in the astrophysical context, as far as cooling processes [19] and glitch phenomena [20,21] are concerned.Since pairing correlations are mostly active at low density and relatively low temperature, below the critical temperature for the transition from superfluid to normal matter, in a certain region of the nuclear matter phase diagram volume instabilities may co-exist with strong pairing effects [22].The aim of this work is to investigate the influence of pair-ing correlations on the neutrino scattering cross section, in conditions of moderate temperature, charge asymmetry and low density (close to the spinodal border), which are encountered in neutron stars, as well as in supernova explosions (prebounce phase). At the onset of spinodal instabilities, the speed of sound vanishes and the nucleonic free energy density exhibits a negative curvature, both in symmetric and asymmetric matter.…”

Impact of pairing on thermodynamical properties of stellar matter

“…The complete formalism that we use can be found in [4]. We detail here our extension of the NSE model, that is the inclusion of pairing in the bulk region of the Wigner-Seitz cell.…”

“…The energy density of a superfluid and spin saturated nuclear gas at finite temperature T, in the mean field approximation, reads [5] (q=n,p):…”

“…The pairing interaction v πq (ρ gq ), as a function of the gas density ρ gq , is given by [7] : 1 S 0 pairing gap as a function of density for homogeneous neutron matter at zero temperature, as obtained from BruecknerHartree Fock calculations (full line from [8]). The figure also shows the energy gap deduced solving the BCS gap equations at finite temperature (symbols from [5]). …”

“…The equilibrium distribution is obtained by minimizing the total free energy corresponding to an arbitrary collection of different Wigner-Seitz cells, subject to the constraint of total baryonic and charge density conservation [4].…”