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 uncertainties in neutron star radii and crust properties due to our limited knowledge of the equation of state are quantitatively analyzed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core equation of state based on models with different properties at nuclear matter saturation, the uncertainties can be as large as ∼30 % for the crust thickness and 4% for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified equations of state for purely nucleonic matter is obtained based on twenty-four Skyrme interactions and nine relativistic mean-field nuclear parametrizations. In addition, for relativistic models fifteen equations of state including a transition to hyperonic matter at high density are presented. All these equations of state have in common the property of describing a 2M star and of being causal within stable neutron stars. Spans of ∼3 and ∼4 km are obtained for the radius of, respectively, 1.0M and 2.0M stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to ∼1 and 2 km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the equation of state near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope L. Indeed, this parameter exhibits a linear correlation with the stellar radius, which is particularly clear for small mass stars around 1.0M . The other equation-of-state parameters do not show clear correlations with the radius, within the present uncertainties. Potential constraints on L, the neutron star radius, and the equation of state from observations of thermal states of neutron stars are also discussed. The unified equations of state are made available in the Supplemental Materials and via the CompOSE database.

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An experimental indication of negative heat capacity in excited nuclear systems is inferred from the event by event study of energy fluctuations in Au quasi-projectile sources formed in Au + Au collisions at 35 A.MeV. The excited source configuration is reconstructed through a calorimetric analysis of its de-excitation products. Fragment partitions show signs of a critical behavior at about 5 A.MeV excitation energy. In the same energy range the heat capacity shows a negative branch providing a direct evidence of a first order liquid gas phase transition.Phase transitions are the prototype of a complex system behavior which goes beyond the simple sum of individual properties [1]. In macroscopic systems the thermostatistical potential presents non analytical behaviors which unambiguously marks a phase transition. Non analytical behaviors of infinite systems originate from anomalies of the thermostatistical potentials in finite systems [2,3]. Specifically in microcanonical finite systems, the entropy is known to present a convex intruder in 1-st order phase transitions associated to a negative heat capacity between two poles. A 2-nd order phase transition is characterized by the merging of the two poles.The experimental study of phase transitions in finite systems has recently attracted a strong interest from various communities. Bose condensates with a small number of particles [4], melting of solid atomic clusters [5], vaporization of atomic nuclei [6] are examples of attempts to study phase transitions in finite systems. The problem usually encountered with these small systems is how to control the equilibrium and how to extract the thermostatistical variables from observable quantities in order to identify the possible phase transition. This is for instance the case in heavy ion reactions in which excited nuclear systems are formed. Comparing the observed decay channels with statistical models [2,7] it seems that a certain degree of equilibration is reached [8,9] but up to now it has not been possible to unambiguously identify the presence of the expected liquid-gas phase transition.It has recently been shown [3] that for a given total energy the average partial energy stored in a part of the system is a good microcanonical thermometer while the associated fluctuations can be used to construct the heat capacity. In the case of a phase transition anomalously large fluctuations are expected as a consequence of the divergence and of the possible negative branch of the heat capacity. Let us consider an equilibrated system which can be decomposed into two independent components so that the energy is simply the sum of the two partial energies E t = E 1 + E 2 and that the total level density W t ≡ exp(S t ) is the folding product of the two partial level densities W i ≡ exp(S i ).An example of such a decomposition is given by the kinetic and the potential energies in the absence of velocity dependent interactions.The probability distribution of the partial energy where: , 2) are the heat capacities calculated for th...

The attribute of rotational profile to the hyperon puzzle in the prediction of heaviest compact star M. Bhuyan et al Since the discovery of neutron stars with masses around M 2 ⊙ the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars with (i) a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of M 1.4 ⊙ , and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.

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

The liquid-gas phase transition in finite systems is studied within a lattice gas model in the canonical ensemble. In the coexistence region, the existence of conservation laws is shown to result in anomalies in the associated equation of state leading, for example, to negative compressibility due to surface effects. The associated partitions exhibit scaling behavior inside the coexistence zone. When the thermodynamical limit is taken this scaling disappears while the anomaly of the equation of state becomes the usual nonanalytical behavior. Therefore, in the fragmentation of small systems such as nuclei the experimentally observed critical behavior is demonstrated to be compatible with a first order phase transition because of finite size effects

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