Extended Skyrme interaction (I): spin fluctuations in dense matter

Most of the Skyrme interactions are known to predict spin or isospin instabilities beyond the saturation density of nuclear matter which contradict predictions based on realistic interactions. A modification of the standard Skyrme interaction is proposed so that the ferromagnetic instability is removed. The new terms are density dependent and modify only the spin p-h interaction in the case of spin-saturated system. Consequences for the nuclear response function and neutrino mean free path are shown. The overall effect of the RPA correlations makes dense matter more transparent for neutrino propagation by a factor of 2 to 10 depending of the density.Comment: 6 pages, 5 Figs., 2 Tab

Nuclear symmetry energy and core-crust transition in neutron stars: a critical study

The slope of the nuclear symmetry energy at saturation density $L$ is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between $L$ and the core-crust transition. We confirm that the transition density is soundly correlated with $L$ despite differences between models, and we propose a clear understanding of this correlation based on a generalised liquid drop model. Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure $P_t$ and $L$. From a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. The correlation between the isovector coefficients $K_{\rm sym}$ and $L$ plays a crucial role in this discussion

Nuclear Superfluidity and Cooling Time of Neutron-Star Crust

We analyse the effect of neutron superfluidity on the cooling time of inner crust matter in neutron stars, in the case of a rapid cooling of the core. The specific heat of the inner crust, which determines the thermal response of the crust, is calculated in the framework of HFB approach at finite temperature. The calculations are performed with two paring forces chosen to simulate the pairing properties of uniform neutron matter corresponding respectively to Gogny-BCS approximation and to many-body techniques including polarisation effects. Using a simple model for the heat transport across the inner crust, it is shown that the two pairing forces give very different values for the cooling time

Low densities in asymmetric nuclear matter

Version2, Paper + figures included, PTHAsymmetric nuclear matter is investigated in the low density region below the nuclear saturation density. Microscopic calculations based on the Dirac Brueckner Hartree-Fock (DBHF) approach with realistic nucleon-nucleon potentials are used to adjust a low density functional. This functional is constructed on a density expansion of the relativistic mean field theory which allows a clear interpretation of the role of the mesons to the equation of state. It is shown that a correction term should be added to the functional in order to take into account the effects beyond the mean field. Two functionals with different corrections are obtained. Those functionals converge to predict a reduction of the spinodal zone in asymmetric nuclear matter by about 15-20\% and an isoscalar unstable mode closer to the constant Z/A direction than the functional without correction

Microscopic calculation of neutrino mean free path inside hot neutron matter

We calculate the neutrino mean free path and the Equation of State of pure neutron matter at finite temperature within a selfconsistent scheme based on the Brueckner--Hartree--Fock approximation. We employ the nucleon-nucleon part of the recent realistic baryon-baryon interaction (model NSC97e) constructed by the Nijmegen group. The temperatures considered range from 10 to 80 MeV. We report on the calculation of the mean field, the residual interaction and the neutrino mean free path including short and long range correlations given by the Brueckner--Hartree--Fock plus Random Phase Approximation (BHF+RPA) framework. This is the first fully consistent calculation in hot neutron matter dedicated to neutrino mean free path. We compare systematically our results to those obtain with the D1P Gogny effective interaction, which is independent of the temperature. The main differences between the present calculation and those with nuclear effective interactions come from the RPA corrections to BHF (a factor of about 8) while the temperature lack of consistency accounts for a factor of about 2

A full quantal theory of one-neutron halo breakup reactions

We present a theory of one-neutron halo breakup reactions within the framework of post-form distorted wave Born approximation wherein pure Coulomb, pure nuclear and their interference terms are treated consistently in a single setup. This formalism is used to study the breakup of one-neutron halo nucleus 11Be on several targets of different masses. We investigate the role played by the pure Coulomb, pure nuclear and the Coulomb-nuclear interference terms by calculating several reaction observables. The Coulomb-nuclear interference terms are found to be important for more exclusive observables.Comment: 22 pages latex, 9 figures, submitted to Phy. Rev.

Cluster formation in asymmetric nuclear matter: semi-classical and quantal approaches

The nuclear-matter liquid-gas phase transition induces instabilities against finite-size density fluctuations. This has implications for both heavy-ion-collision and compact-star physics. In this paper, we study the clusterization properties of nuclear matter in a scenario of spinodal decomposition, comparing three different approaches: the quantal RPA, its semi-classical limit (Vlasov method), and a hydrodynamical framework. The predictions related to clusterization are qualitatively in good agreement varying the approach and the nuclear interaction. Nevertheless, it is shown that i) the quantum effects reduce the instability zone, and disfavor short-wavelength fluctuations; ii) large differences appear bewteen the two semi-classical approaches, which correspond respectively to a collisionless (Vlasov) and local equilibrium description (hydrodynamics); iii) the isospin-distillation effect is stronger in the local equilibrium framework; iv) important variations between the predicted time-scales of cluster formation appear near the borders of the instability region.Comment: 27 pages, 11 figures, Submitted to Nuclear Physics A, Nuclear Physics A In press (2008

Nuclear response functions in homogeneous matter with finite range effective interactions

The question of nuclear response functions in a homogeneous medium is examined. A general method for calculating response functions in the random phase approximation (RPA) with exchange is presented. The method is applicable for finite-range nuclear interactions. Examples are shown in the case of symmetric nuclear matter described by a Gogny interaction. It is found that the convergence of the results with respect to the multipole truncation is quite fast. Various approximation schemes such as the Landau approximation, or the Landau approximation for the exchange terms only, are discussed in comparison with the exact results.Comment: 9 pages, 9 figure

On the validity of the Wigner-Seitz approximation in neutron star crust

The inner crust of neutron stars formed of nuclear clusters immersed in a neutron sea has been widely studied in the framework of the Wigner-Seitz approximation since the seminal work of Negele and Vautherin. In this article, the validity of this approximation is discussed in the framework of the band theory of solids. For a typical cell of $^{200}$Zr, present in the external layers of the inner crust, it is shown that the ground state properties of the neutron gas are rather well reproduced by the Wigner-Seitz approximation, while its dynamical properties depend on the energy scale of the process of interest or on the temperature. It is concluded that the Wigner-Seitz approximation is well suited for describing the inner crust of young neutron stars and the collapsing core of massive stars during supernovae explosions. However the band theory is required for low temperature fluid dynamics.Comment: 7 pages, with figures - PTH, version

Phase diagram of neutron-rich nuclear matter and its impact on astrophysics

Dense matter as it can be found in core-collapse supernovae and neutron stars is expected to exhibit different phase transitions which impact the matter composition and equation of state, with important consequences on the dynamics of core-collapse supernova explosion and on the structure of neutron stars. In this paper we will address the specific phenomenology of two of such transitions, namely the crust-core solid-liquid transition at sub-saturation density, and the possible strange transition at super-saturation density in the presence of hyperonic degrees of freedom. Concerning the neutron star crust-core phase transition at zero and finite temperature, it will be shown that, as a consequence of the presence of long-range Coulomb interactions, the equivalence of statistical ensembles is violated and a clusterized phase is expected which is not accessible in the grand-canonical ensemble. A specific quasi-particle model will be introduced to illustrate this anomalous thermodynamics and some quantitative results relevant for the supernova dynamics will be shown. The opening of hyperonic degrees of freedom at higher densities corresponding to the neutron stars core modifies the equation of state. The general characteristics and order of phase transitions in this regime will be analyzed in the framework of a self-consistent mean-field approach.Comment: Invited Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS