A metamodeling for the nucleonic equation of state (EOS), inspired from a Taylor expansion around the saturation density of symmetric nuclear matter, is proposed and parameterized in terms of the empirical parameters. The present knowledge of nuclear empirical parameters is first reviewed in order to estimate their average values and associated uncertainties, and thus defining the parameter space of the metamodeling. They are divided into isoscalar and isovector type, and ordered according to their power in the density expansion. The goodness of the metamodeling is analyzed against the predictions of the original models. In addition, since no correlation among the empirical parameters is assumed a priori, all arbitrary density dependences can be explored, which might not be accessible in existing functionals. Spurious correlations due to the assumed functional form are also removed. This meta-EOS allows direct relations between the uncertainties on the empirical parameters and the density dependence of the nuclear equation of state and its derivatives, and the mapping between the two can be done with standard Bayesian techniques. A sensitivity analysis shows that the more influential empirical parameters are the isovector parameters L sym and K sym , and that laboratory constraints at super-saturation densities are essential to reduce the present uncertainties. The present metamodeling for the EOS for nuclear matter is proposed for further applications in neutron stars and supernova matter. arXiv:1708.06894v3 [nucl-th]

The correlation of the tidal polarizabilities Λ1-Λ2 for GW170817 is predicted by combining densematter equations of state (EOSs) that satisfy nuclear physics constraints with the chirp mass and mass asymmetry for this event. Our models are constrained by calculations of the neutron-matter EOS using chiral effective field theory Hamiltonians with reliable error estimates up to once or twice the nuclear saturation density. In the latter case, we find that GW170817 does not improve our understanding of the EOS. We contrast two distinct extrapolations to higher density: a minimal model (MM) which assumes that the EOS is a smooth function of density described by a Taylor expansion and a more general model parametrized by the speed of sound that admits phase transitions. This allows us to identify regions in the Λ1-Λ2 plots that could favor the existence of new phases of matter in neutron stars. We predict the combined tidal polarizability of the two neutron stars in GW170817 to be 80 ≤Λ ≤ 580 (280 ≤Λ ≤ 480 for the MM), which is smaller than the range suggested by the LIGO-Virgo data analysis. Our analysis also shows that GW170817 requires a NS with M = 1.4M to have a radius 9.0 < R1.4 < 13.6 km (11.3 < R1.4 < 13.6 km for the MM). *

The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis, we show that (a) the transition density ρt is mainly correlated with the symmetry energy slope L, (b) the proton fraction Yp,t with the symmetry energy and symmetry energy slope (J, L) defined at saturation density, or, even better, with the same quantities defined at ρ = 0.1 fm −3 , and (c) the transition pressure Pt with the symmetry energy slope and curvature (L, Ksym) defined at ρ = 0.1 fm −3 .

Only one-third of the nucleons in 208Pb occupy the saturation density area. Consequently, nuclear observables related to the average properties of nuclei, such as masses or radii, constrain the equation of state not at the saturation density but rather around the so-called crossing density, localized close to the mean value of the density of nuclei: ρ is approximately equal to 0.11 fm(-3). This provides an explanation for the empirical fact that several equation of state quantities calculated with various functionals cross at a density significantly lower than the saturation one. The third derivative M of the energy per unit of volume at the crossing density is constrained by the giant monopole resonance measurements in an isotopic chain rather than the incompressibility at saturation density. The giant monopole resonance measurements provide M=1100±70 MeV (6% uncertainty), whose extrapolation gives K(∞)=230±40 MeV (17% uncertainty).

20 pages, incl. 12 figuresWe explore the ground-state properties of nuclear clusters embedded in a gas of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations. Two alternative representations of clusters are introduced, namely coordinate-space and energy-space clusters. We parameterize their density profiles in spherical symmetry in terms of basic properties of the energy density functionals used and propose an analytical, Woods-Saxon density profile whose parameters depend, not only on the composition of the cluster, but also of the nucleon gas. We study the clusters' energies with the help of the local-density approximation, validated through our microscopic results. We find that the volume energies of coordinate-space clusters are determined by the saturation properties of matter, while the surface energies are strongly affected by the presence of the gas. We conclude that both the density profiles and the cluster energies are strongly affected by the gas and discuss implications for the nuclear EoS and related perspectives. Our study provides a simple, but microscopically motivated modeling of the energetics of clusterized matter at subsaturation densities, for direct use in consequential applications of astrophysical interest

We propose new types of density dependent contact pairing interaction which reproduce the pairing gaps in symmetric and neutron matter obtained by a microscopic treatment based on the nucleon-nucleon interaction. These interactions are able to simulate the pairing gaps of either the bare interaction or the interaction screened by the medium polarization effects. It is shown that the medium polarization effects cannot be cast into the density power law function usually introduced together with the contact interaction and require the introduction of another isoscalar term. The BCS-BEC crossover of neutrons pairs in symmetric and symmetric nuclear matter is studied by using these contact interactions. It is shown that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter. For the screened pairing interaction, a two-neutron BEC state is formed in symmetric matter at $k_{Fn}\sim 0.2$~fm$^{-1}$ (neutron density $\rho_n/\rho_0\sim 10^{-3}$). Contrary the bare interaction does not form the BEC state at any neutron density

Asymmetric 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.Comment: Version2, Paper + figures included, PT

The stability of the equation of state predicted by Skyrme-type interactions is examined. We consider simultaneously symmetric nuclear matter and pure neutron matter. The stability is defined by the inequalities that the Landau parameters must satisfy simultaneously. A systematic study is carried out to define interaction parameter domains where the inequalities are fulfilled. It is found that there is always a critical density $\rho_{cr}$ beyond which the system becomes unstable. The results indicate in which parameter regions one can find effective forces to describe correctly finite nuclei and give at the same time a stable equation of state up to densities of 3-4 times the saturation density of symmetric nuclear matter.Comment: 20 pages, 5 figures, submitted to Phys.Rev.