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In this work, we compute the structure and composition of the inner crust of a neutron star in the presence of a strong magnetic field, such as it can be found in magnetars. To determine the geometry and characteristics of the crust inhomogeneities, we consider the compressible liquid drop model, where surface and Coulomb terms are included in the variational equations, and we compare our results with previous calculations based on more approximate treatments. For the equation of state (EoS), we consider two non-linear relativistic mean-field models with different slopes of the symmetry energy, and we show that the extension of the inhomogeneous region inside the star core due to the magnetic field strongly depends on the behavior of the symmetry energy in the crustal EoS. Finally, we argue that the extended spinodal instability observed in previous calculations can be related to the presence of small amplitude density fluctuations in the magnetar outer core, rather than to a thicker solid crust. The compressible liquid drop model formalism, while in overall agreement with the previous calculations, leads to a systematic suppression of the metastable solutions, thus allowing a more precise estimation of the crust-core transition density and pressure, and therefore a better estimation of the crustal radius., Comment: 11 pages, 5 figures, 3 tables. Version published on Phys. Rev. C

International audience; L’immensité de notre Univers ne cesse d’intriguer et de stimuler les imaginations.Pour mieux appréhender l’infiniment grand et l’histoire de l’Univers depuis ses tout premiers instants, il faut se tourner vers un autre infini, l’infiniment petit, et ses quarks, leptons et bosons, à la base du modèle standard de la physique des particules. En les étudiant, on cherche à percer le secret de l’organisation de la matière à la plus petite échelle. Sans l’infiniment petit, on ne peut décrire ni le Big Bang, ni le comportement des grandes structures stellaires, ni la naissance de la matière. Et sans ces deux infinis ensemble, on ne peut bâtir les modèles théoriques expliquant la matière noire, l’énergie noire ou fonder la gravitation quantique.Les physiques des infinis sont des physiques hors normes qui se racontent à grand renfort de superlatifs. Elles nécessitent des installations internationales de très grande envergure, et nous entraînent dans des voyages aux confins de la perception où l’on flirte avec la vitesse de la lumière et jongle avec les limites des propriétés de la matière.En trente courts chapitres abondamment illustrés, cet ouvrage rend compte de ce que l’on sait déjà comme de ce que l’on cherche encore.

The isospin diffusion of the quasi-projectile formed in the $^{64,58}Ni$ on $^{64,58}Ni$ reactions in the Fermi energy domain is investigated in the framework of the Boltzmann-Uehling-Uhlenbeck transport model. The well known isospin transport ratio observable is revisited, with the aim of insuring an optimal comparison between experimental data and theoretical calculations and reducing the present uncertainties in the extraction of empirical equation of state parameters. We show that isospin transport ratios are sensitive to all the low order isovector parameters ($E_{sym}$, $L_{sym}$ and $K_{sym}$). We demonstrate that realistic models of the equation of state, covering the uncertainty that presently affects the theoretical description of neutron stars static observables, can be effectively discriminated by isospin diffusion experiments, provided the neutron to proton ratio of the projectile remnant is precisely measured as a function of centrality., 5 pages, 5 figures

The presence of nuclear pasta is expected to modify the transport properties in the mantle of neutron stars. The non-spherical geometry of the pasta nuclear clusters leads to anisotropies in the collision frequencies, impacting the thermal and electrical conductivity. We derive analytical expressions for the anisotropic collision frequencies using the Boltzmann equation in the relaxation time approximation. The average parallel, perpendicular and Hall electrical conductivities are computed in the high-temperature regime above crustal melting, considering incoherent elastic electron-pasta scattering and randomly oriented pasta structures. Numerical values are obtained at different densities and temperatures by using the IUFSU parametrization of the non-linear Walecka model to determine the crustal structure. We find that the anisotropy of the collision frequencies grows with the length of the pasta structures and, independently of the magnetic field, the presence of rod and slab phases decreases the conductivity by more than one order of magnitude. Our numerical results indicate that, even if the pasta structures might survive above the crustal melting point, no strong anisotropies are to be expected in the conduction properties in this temperature regime, even in the presence of a very high magnetic field., Comment: 15 pages, 12 figures

The evaluation of the sub-saturation nuclear equation of state at finite temperature requires a proper state counting of the internal partition sum of nuclei which are immersed in the background of their continuum states. This classical statistical problem is addressed within the self-consistent mean-field approximation, which naturally accounts for isospin and effective mass effects in the nuclear density of states. The nuclear free energy is decomposed into bulk and surface terms, allowing a simple analytical prescription for the subtraction of gas states from the nuclear partition sum, that avoids double counting of unbound single particle states. We show that this correction leads to a sizeable effect in the composition of matter at high temperature and low proton fractions, such as it is formed in supernova collapse, early proto-neutron star evolution, as well as laboratory experiments. Specifically, the energy stored in the internal nuclear degrees of freedom is reduced, as well as the mass fraction of heavy clusters in the statistical equilibrium. The gas subtraction prescription is compared to different phenomenological methods proposed in the literature, based on a high energy truncation of the partition sum. We show that none of these methods satisfactorily reproduces the gas subtracted level density, if the temperature overcomes ~4 MeV., 18 pages, 6 figures

International audience; No abstract available

Neutron stars are unique laboratories to probe matter in extreme conditions, not accessible in terrestrial laboratories. Here, we discuss the modelling of the neutron-star equation of state, particularly in connection with recent constraints coming from both nuclear physics (experiments and ab-initio calculations) and astrophysical observations., Comment: 8 pages, 3 figures

Chemical constants extracted from $^{124}$Xe+ $^{124}$Sn collisions at 32 AMeV are compared to the predictions of an extended Nuclear Statistical Equilibrium model including mean-field interactions and in-medium binding energy shifts for the light ($Z\leq 2$) clusters. The ion species and density dependence of the in-medium modification is directly extracted from the experimental data. We show that the shift increases with the mass of the cluster and the density of the medium, and we provide a simple linear fit for future use in astrophysical simulations in the framework of the CompOSE data base. The resulting mass fractions are computed in representative thermodynamic conditions relevant for supernova and neutron star mergers. A comparison to the results of a similar analysis of the same data performed in the framework of a relativistic mean-field model shows a good agreement at low density, but significant discrepancies close to the Mott dissolution of clusters in the dense medium., Comment: 7 pages, 4 figures

The interior of a neutron star is expected to exhibit different states of matter. In particular, complex non-spherical configurations known as `pasta' phases may exist at the highest densities in the inner crust, potentially having an impact on different neutron-star phenomena. We study the properties of the pasta phase and the uncertainties in the pasta observables which are due to our incomplete knowledge of the nuclear energy functional. To this aim, we employed a compressible liquid-drop model approach with surface parameters optimised either on experimental nuclear masses or theoretical calculations. To assess the model uncertainties, we performed a Bayesian analysis by largely varying the model parameters using uniform priors, and generating posterior distributions with filters accounting for both our present low-density nuclear physics knowledge and high-density neutron-star physics constraints. Our results show that the nuclear physics constraints, such as the neutron-matter equation of state at very low density and the experimental mass measurements, are crucial in determining the crustal and pasta observables. Accounting for all constraints, we demonstrate that the presence of pasta phases is robustly predicted in an important fraction of the inner crust. We estimate the relative crustal thickness associated with pasta phases as $R_{\rm pasta}/R_{\rm crust}=0.128\pm 0.047$ and the relative moment of inertia as $I_{\rm pasta}/I_{\rm crust}=0.480\pm 0.137$. Our findings indicate that the surface and curvature parameters are more influential than the bulk parameters for the description of pasta observables. We also show that using a surface tension that is inconsistent with the bulk functional leads to an underestimation of both the average values and the uncertainties in the pasta properties, thus highlighting the importance of a consistent calculation of the nuclear functional., Comment: 12 pages, 8 figures, accepted for publication in Astronomy and Astrophysics. Typos corrected

Nuclear pasta, that is an inhomogeneous distribution of nuclear matter characterised by non-spherical clustered structures, is expected to occur in a narrow spatial region at the bottom of the inner crust of neutron stars, but the width of the pasta layer is strongly model dependent. In the framework of a compressible liquid-drop model, we use Bayesian inference to analyse the constraints on the sub-saturation energy functional and surface tension imposed by both ab-initio chiral perturbation theory calculations and experimental measurements of nuclear masses. The posterior models are used to obtain general predictions for the crust-pasta and pasta-core transition with controlled uncertainties. A correlation study allows extracting the most influential parameters for the calculation of the pasta phases. The important role of high-order empirical parameters and the surface tension is underlined., Comment: 15 pages, 11 figures. Contribution to the EPJ A topical issue "CompOSE: a repository for Neutron Star Equations of State and Transport Properties"

International audience; Baryonic matter close to the saturation density is very likely to present complex inhomogeneous structures collectively known under the name of nuclear pasta phase. At finite temperature, the different geometric structures are expected to coexist with potential consequences on the neutron star crust conductivity and neutrino transport in supernova matter. In the framework of a statistical multicomponent approach, we calculate the composition of matter in the pasta phase considering density, proton fraction, and geometry fluctuations. Using a realistic energy functional from relativistic mean-field theory and a temperature- and isospin-dependent surface tension fitted from Thomas-Fermi calculations, we show that different geometries can coexist in a large fraction of the pasta phase, down to temperatures of the order of the crystallization temperature of the neutron star crust. Quantitative estimates of the charge fluctuations are given.

The abundances of light clusters within a formalism that considers in-medium effects are calculated using several relativistic mean-field models, with both density-dependent and density-independent couplings. Clusters are introduced as new quasiparticles, with a modified coupling to the scalar meson field. A comparison with experimental data from heavy ion collisions allows settling the model dependence of the results and the determination of the couplings of the light clusters to the meson fields. We find that extra experimental constraints at higher density are needed to convincingly pin down the density associated to the melting of clusters in the dense nuclear medium. The role of neutron rich clusters, such as $^6$He, in asymmetric matter is discussed., 10 pages, 8 figures, and 1 table; accepted for publication in the EPJA Topical Issue "Light Clusters in Nuclei and Nuclear Matter: Nuclear Structure and Decay, Heavy Ion Collisions, and Astrophysics"

Context. The possible presence of amorphous and heterogeneous phases in the inner crust of a neutron star is expected to reduce the electrical conductivity of the crust, potentially with significant consequences on the magneto-thermal evolution of the star. In cooling simulations, the disorder is quantified by an impurity parameter, which is often taken as a free parameter. Aims. We aim to give a quantitative prediction of the impurity parameter as a function of the density in the crust, performing microscopic calculations including up-to-date microphysics of the crust. Methods. A multicomponent approach was developed at a finite temperature using a compressible liquid-drop description of the ions with an improved energy functional based on recent microscopic nuclear models and optimized on extended Thomas-Fermi calculations. Thermodynamic consistency was ensured by adding a rearrangement term, and deviations from the linear mixing rule were included in the liquid phase. Results. The impurity parameter is consistently calculated at the crystallization temperature as determined in the one-component plasma approximation for the different functionals. Our calculations show that at the crystallization temperature, the composition of the inner crust is dominated by nuclei with charge number around Z ≈ 40, while the range of the Z distribution varies from about 20 near the neutron drip to about 40 closer to the crust-core transition. This reflects on the behavior of the impurity parameter that monotonically increases with density reaching up to around 40 in the deeper regions of the inner crust. Conclusions. Our study shows that the contribution of impurities is non-negligible, thus potentially having an impact on the transport properties in the neutron-star crust. The obtained values of the impurity parameter represent a lower limit; larger values are expected in the presence of nonspherical geometries and/or fast cooling dynamics.

Context. In the cooling process of a non-accreting neutron star, the composition and properties of the crust are thought to be fixed at the finite temperature where nuclear reactions fall out of equilibrium. A lower estimation for this temperature is given by the crystallization temperature, which can be as high as $\approx 7\times 10^9$ K in the inner crust, potentially leading to sizeable differences with respect to the simplifying cold-catalyzed matter hypothesis. Aims. We extend the recent work by Fantina et al. (2019) on the outer crust, to the study of the crystallization of the inner crust and the associated composition in the one-component plasma approximation. Methods. The finite temperature variational equations for non-uniform matter in both the liquid and the solid phases are solved using a compressible liquid-drop approach with parameters optimized on four different microscopic models which cover the present uncertainties in nuclear modeling. Results. We consider separately the effect of the different nuclear ingredients with their associated uncertainties, namely the nuclear equation of state, the surface properties in the presence of a uniform gas of dripped neutrons, and the proton shell effects arising from the ion single-particle structure. Our results suggest that the highest source of model dependence comes from the smooth part of the nuclear functional. Conclusions. We show that shell effects play an important role at the lowest densities close to the outer crust, but the most important physical ingredient to be settled for a quantitative prediction of the inner crust properties is the surface tension at extreme isospin values., 9 pages, 9 figures

We perform extended Thomas-Fermi calculations in the Wigner-Seitz cell below and above neutron drip with realistic functionals. The resulting energy density is decomposed as a sum of bulk terms and a surface term, and a compressible liquid drop analytical formula is used to fit the surface tension. The effect of curvature terms and neutron skin is studied in detail. A very good reproduction of the microscopic data is obtained using an expression that depends only on the mass and charge of the cluster, showing that the in-medium modifications of the nuclear energy in the presence of an external neutron gas can be effectively accounted for in the isospin dependence of the surface tension. In this first application, aimed at establishing the fitting protocol, we concentrate on the Sly4 energy functional, but the study can be easily generalized to different functionals, and the resulting parametrizations can be used for direct applications in pasta calculations in neutron star crusts and supernova matter., Comment: 44 pages, 17 figures, 5 tables

International audience; The equilibrium distributions of the different pasta geometries and their linear sizes are calculated from the mean field Gibbs energy functional in symmetric nuclear matter at finite temperature. The average sizes and shapes coincide approximately with the ones predicted by a standard pasta calculation in the coexisting phase approximation, but fluctuations are additionally calculated and seen to increase with temperature and baryonic density. The different pasta shapes are shown to coexist in a wide domain of density and temperature, in qualitative agreement with the findings of large scale molecular dynamics simulations, but with a much less expensive computational cost.

Context. The interior of a neutron star is usually assumed to be made of cold catalyzed matter. However, the outer layers are unlikely to remain in full thermodynamic equilibrium during the formation of the star and its subsequent cooling, especially after crystallization occurs.Aims. We study the cooling and the equilibrium composition of the outer layers of a non-accreting neutron star down to crystallization. Here the impurity parameter, generally taken as a free parameter in cooling simulations, is calculated self-consistently using a microscopic nuclear model for which a unified equation of state has recently been determined.Methods. We follow the evolution of the nuclear distributions of the multi-component Coulomb liquid plasma fully self-consistently, adapting a general formalism originally developed for the description of supernova cores. We calculate the impurity parameter at the crystallization temperature as determined in the one-component plasma approximation.Results. Our analysis shows that the sharp changes in composition obtained in the one-component plasma approximation are smoothed out when a full nuclear distribution is allowed. The Coulomb coupling parameter at melting is found to be reasonably close to the canonical value of 175, except for specific values of the pressure for which supercooling occurs in the one-component plasma approximation. Our multi-component treatment leads to non-monotonic variations of the impurity parameter with pressure. Its values can change by several orders of magnitude reaching about 50, suggesting that the crust may be composed of an alternation of pure (highly conductive) and impure (highly resistive) layers. The results presented here complement the recent unified equation of state obtained within the same nuclear model.Conclusions. Our self-consistent approach to hot dense multi-component plasma shows that the presence of impurities in the outer crust of a neutron star is non-negligible and may have a sizeable impact on transport properties. In turn, this may have important implications not only for the cooling of neutron stars, but also for their magneto-rotational evolution., info:eu-repo/semantics/published

Four α-particles as a final state of 16O* quasi-projectile decayproduced in peripheral 16O+12C reactions at 130 MeV is thoroughly studied. The differentdecay channels leading to the four α-particles final state are reconstructed by carrying out an event-by-event analysis of α correlations in the population of intermediate 8Be and 12C. Although small, a non negligible contribution due to 8Begs evaporation is found.A comparison between predictions of an accurate Hauser-Feshbach decay code and branching ratios of the different decay channels is performed. Significant deviations are observed, among these the Hoyle state population which is considerably lower than the one predicted according to the statistical model, thus suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

The bimodal behavior of the order parameter is studied in the framework of Boltzmann-Uehling-Uhlenbeck (BUU) transport model. In order to do that, simplified yet accurate method of BUU model is used which allow calculation of fluctuations in systems much larger than what was considered feasible in a well-known and already existing model. It is observed that depending on the projectile energy and centrality of the reaction, both entrance channel and exit channel effects can be at the origin of the experimentally observed bimodal behavior. Both dynamical and statistical bimodality mechanisms are associated in the theoretical model to different time scales of the reaction, and to different energy regimes., arXiv admin note: substantial text overlap with arXiv:1802.05047

The influence of the uncertainties of the equation of state empirical parameters on the neutron stars crust-core phase transition is explored within a meta-modeling approach, in which the energy per particle is expanded as a Taylor series in density and asymmetry around the saturation point. The phase transition point is estimated from the intersection of the spinodal instability region for dynamical fluctuations with the chemical equilibrium curve. Special attention is paid to the inclusion of high-order parameters of the Taylor series and their influence on the transition point. An uncorrelated prior distribution is considered for the empirical parameters, with bulk properties constrained through effective field theory predictions, while the surface parameters are controlled from a fit of nuclear masses using the extended Thomas Fermi approximation. The results show that the isovector compressibility $K_{sym}$ and skewness $Q_{sym}$ have the most significant correlations with the transition point, along with the previously observed influence of the $L_{sym}$ parameter. The estimated density and pressure of the crust-core transition are $n_t = (0.071 \pm 0.011) fm^{-3}$ and $P_t = (0.294 \pm 0.102) MeV fm^{-3}$., 11 pages, 7 figures

The crust-core phase transition of neutron stars is quantitatively studied within a unified meta-modelling of the nuclear Equation of State (EoS). The variational equations in the crust are solved within a Compressible Liquid Drop (CLD) approach, with surface parameters consistently optimized for each EoS set on experimental nuclear mass data. When EoS parameters are taken from known Skyrme or RMF functionals, the transition point of those models is nicely reproduced. A model-independent probability distribution of EoS parameters and of the transition density and pressure is determined with a Bayesian analysis, where the prior is given by an uncorrelated distribution of parameters within the present empirical uncertainties, and constraints are applied both from neutron star physics and ab-initio modelling. We show that the characteristics of the transition point are largely independent of the high density properties of the EoS, while ab-initio EoS calculations of neutron and symmetric matter are far more constraining. The most influential parameter for the determination of the transition point governs the surface properties of extremely neutron rich matter, and it is strongly unconstrained. This explains the large dispersion of existing predictions of the transition point. Only if the surface tension is fixed to a reasonable but somewhat arbitrary value, strong correlations with isovector parameters ($L_{sym},K_{sym}$ and $Q_{sym}$) are recovered. Within the present experimental and theoretical uncertainties on those parameters, we estimate the transition density as $n_t= 0.072\pm 0.011$ fm$^{-3}$ and the transition pressure as $P_t=0.339\pm0.115$ MeV fm$^{-3}$., Comment: 14 pages, 12 figures

Light and heavy clusters are calculated for asymmetric warm nuclear matter in a relativistic mean-field approach. In-medium effects, introduced via a universal cluster-meson coupling, and a binding energy shift contribution, calculated in a Thomas-Fermi approximation, were taken into account. This work considers, besides the standard lightest bound clusters $^4$He, $^3$He, $^3$H, and $^2$H, also stable and unstable clusters with higher number of nucleons, in the range $5\leq A \leq 12$, as it is natural that heavier clusters also form in core-collapse supernova matter, before the pasta phases set in. We show that these extra degrees of freedom contribute with non-negligible mass fractions to the composition of nuclear matter, and may prevail over deuterons and $\alpha$ particles at high density in strongly asymmetric matter, and not too high temperatures. The presence of the light clusters reduces the contribution of heavy clusters to a much smaller density range, and to a smaller mass fraction., Comment: 17 pages, 14 figures, accepted for publication in PRC

The neutron star crustal EoS and transition point properties are computed within a unified meta-modeling approach. A Bayesian approach is employed including two types of filters: bulk nuclear properties are controlled from low density effective field theory (EFT) predictions as well as the present knowledge from nuclear experiments, while the surface energy is adjusted on experimental nuclear masses. Considering these constraints, a quantitative prediction of crustal properties can be reached with controlled confidence intervals and increased precision with respect to previous calculations: {$\approx 11\%$} dispersion on the crustal width and {$\approx 27\%$} dispersion on the fractional moment of inertia. The crust moment of inertia is also evaluated as a function of the neutron star mass, and predictions for mass and radii are given for different pulsars. The possible crustal origin of Vela pulsar glitches is discussed within the present estimations of crustal entrainment, disfavoring a large entrainment phenomenon if the Vela mass is above $1.4M_\odot$. Further refinement of the present predictions requires a better estimation of the high order isovector empirical parameters, e.g. $K_{sym}$ and $Q_{sym}$, and a better control of the surface properties of extremely neutron rich nuclei., Comment: 5 pages, 4 figures

International audience; The four α-particle decay of the excited 16O* quasi-projectile (QP) produced in peripheral 16O + 12C reactions at 130 MeV is studied in detail. The different decay channels leading to the four α-particle final state are reconstructed from an event-by-event analysis of α correlations through the population of intermediate 8Be and 12C resonant states. A small but non-negligible contribution of 8Be gs evaporation is observed. The branching ratios of the different evaporation channels are compared to the prediction of an Hauser-Feshbach code (once characteristics of the QP source are extracted from the experimental data), which very accurately reproduces all the inclusive observables of the reaction. However, significative deviations are observed. In particular, the experimental population of the Hoyle state is significantly lower than the predictions of the statistical model, suggesting possible structure effects in the Coulomb barrier and/or in the transmission coefficients.

The static properties of the heaviest residue and unbound particles produced in central $^{64,58}\mathrm{Ni}$ on $^{64,58}\mathrm{Ni}$ collisions at 50 MeV/nucleon are predicted within the Boltzmann-Uehling-Uhlenbeck transport model, in order to explore the sensitivity of those observables to the density dependence of the symmetry energy. We include fluctuations in the collision integral and use a metamodelling for the mean-field which allows an independent variation of the different empirical parameters of the equation of state. We find that the isospin ratio of pre-equilibrium particles is a good estimator of the stiffness of the symmetry energy, in agreement with previous works. In addition to that, whatever be the functional form of the equation of state, we show that a higher symmetry energy at subsaturation densities leads to an increased size and isotopic ratio for the heaviest residue. This is understood in terms of energy sharing between the pre-equilibrium particles and the (quasi)fused system. The combination of the two observables might be an interesting tool to constrain the different density dependence below and above saturation, which is linked to the relatively poorly known parameter ${K}_{\mathrm{sym}}$.

The modification of the ground state properties of light atomic nuclei in the nuclear and stellar medium is addressed, using chemical equilibrium constants evaluated from a new analysis of the intermediate energy heavy-ion (Xe$+$Sn) collision data measured by the INDRA collaboration. Three different reactions are considered, mainly differing by the isotopic content of the emission source. The thermodynamic conditions of the data samples are extracted from the measured multiplicities allowing for a parametrization of the in-medium modification, determined with the single hypothesis that the different nuclear species in a given sample correspond to a unique common value for the density of the expanding source. We show that this correction, which was not considered in previous analyses of chemical constants from heavy ion collisions, is necessary, since the observables of the analyzed systems show strong deviations from the expected results for an ideal gas of free clusters. This data set is further compared to a relativistic mean-field model, and seen to be reasonably compatible with a universal correction of the attractive $\sigma$-meson coupling., Comment: 5 pages, 2 figures, 1 table, accepted for publication in Phys. Rev. Lett

A quantitative knowledge of the nuclear equation of state (EoS) requires an accurate estimation of the uncertainties on the EoS parameters and their mutual correlations. Such correlations are empirically observed in a large set of EoS models by different authors, but they are not always fully understood. We show that some of these correlations can be interpreted from basic physical constraints imposed on a simple Taylor expansion of the binding energy around saturation density. In particular, we investigate the correlations among the following empirical parameters: the symmetry energy ${E}_{\mathrm{sym}}$, the slope and curvature of the symmetry energy ${L}_{\mathrm{sym}}$ and ${K}_{\mathrm{sym}}$, and the curvature and skewness of the binding energy in symmetric matter ${K}_{\mathrm{sat}}$ and ${Q}_{\mathrm{sat}}$. The uncertainties on these correlations is estimated through analytical modeling as well as a metamodeling analysis of the EoS subject to physical constraints. We show that a huge dispersion of the correlations among low-order empirical parameters is induced by the unknown higher-order empirical parameters, such as ${K}_{\mathrm{sym}}$ (second order) and ${Q}_{\mathrm{sat}}$ and ${Q}_{\mathrm{sym}}$ (third order). We also propose an explanation of the reason why ${Q}_{\mathrm{sat}}$ is weakly constrained by present experimental data. We conclude that selective observables on high-order parameters, such as ${K}_{\mathrm{sym}}$ and ${Q}_{\mathrm{sat}}$, should be better determined before the present uncertainties on the EoS can be further reduced.

International audience; The impact of electron-capture (EC) cross sections on neutron-rich nuclei on the dynamics of core-collapse during infall and early post-bounce is studied performing spherically symmetric simulations in general relativity using a multigroup scheme for neutrino transport and full nuclear distributions in extended nuclear statistical equilibrium models. We thereby vary the prescription for EC rates on individual nuclei, the nuclear interaction for the EoS, the mass model for the nuclear statistical equilibrium distribution and the progenitor model. In agreement with previous works, we show that the individual EC rates are the most important source of uncertainty in the simulations, while the other inputs only marginally influence the results. A recently proposed analytic formula to extrapolate microscopic results on stable nuclei for EC rates to the neutron rich region, with a functional form motivated by nuclear-structure data and parameters fitted from large scale shell model calculations, is shown to lead to a sizable (16%) reduction of the electron fraction at bounce compared to more primitive prescriptions for the rates, leading to smaller inner core masses and slower shock propagation. We show that the EC process involves ≈ 130 different nuclear species around 86 Kr mainly in the N = 50 shell closure region, and establish a list of the most important nuclei to be studied in order to constrain the global rates.

The equation of state with light clusters for nuclear and stellar matter is determined using chemical equilibrium constants evaluated from the analysis of the recently published (Xe$+$Sn) heavy ion data, corresponding to three reactions with different isotopic contents of the emission source. The measured multiplicities are used to extract the thermodynamic properties, and an in-medium correction to the ideal gas internal partition function of the clusters is included in the analysis. This in-medium correction and its respective uncertainty are calculated via a Bayesian analysis, with the unique hypothesis that the different nuclear species in a given sample must correspond to a unique common value for the density of the expanding source. Different parameter sets for the correction are tested, and the effect of the radius of the clusters on the thermodynamics and on the chemical equilibrium constants is also addressed. It is shown that the equilibrium constants obtained are almost independent of the isospin content of the analysed systems. Finally, a comparison with a relativistic mean field model proves that data are consistent with a universal in-medium correction of the scalar $\sigma$-meson coupling for nucleons bound in clusters. The obtained value, $g_s/g_s^0 = 0.92 \pm 0.02$, is larger than that obtained in a previous study not including in-medium effects in the data analysis. This result implies a smaller effect on the binding energy of the clusters and, as a consequence, larger melting densities, and an increased cluster contribution in supernova matter., Comment: 29 pages, 16 figures, accepted for publication in J. Phys. G

International audience; Evaporation chains in the fusion reaction 13C+12C at 95 MeV have been measured. Events complete in charge have been detected with the large acceptance GARFIELD+RCo apparatus at INFN-LNL and the features of the decay of the excited 25Mg compound nuclei have been compared with predictions of statistical models. Some deviations from these predictions have been found, especially for the chains mainly containing α particles

In-medium modifications of light cluster properties in warm stellar matter are studied within the relativistic mean-field approximation. In-medium effects are included by introducing an explicit binding energy shift analytically calculated in the Thomas-Fermi approximation, supplemented with a phenomenological modification of the cluster couplings to the $\sigma$ meson. A linear dependence on the $\sigma$ meson is assumed for the cluster mass, and the associated coupling constant is fixed imposing that the virial limit at low density is recovered. The resulting cluster abundances come out to be in reasonable agreement with constraints at higher density coming from heavy ion collision data. Some comparisons with microscopic calculations are also shown., Comment: 13 pages, 7 figures, 3 tables, accepted for publication in Phys. Rev. C

The origin of bimodal behavior in the residue distribution experimentally measured in heavy ion reactions is reexamined using Boltzmann-Uehling-Uhlenbeck simulations. We suggest that, depending on the incident energy and impact parameter of the reaction, both entrance channel and exit channel effects can be at the origin of the observed behavior. Specifically, fluctuations in the reaction mechanism induced by fluctuations in the collision rate, as well as thermal bimodality directly linked to the nuclear liquid-gas phase transition are observed in our simulations. Both phenomenologies were previously proposed in the literature, but presented as incompatible and contradictory interpretations of the experimental measurements. These results indicate that heavy ion collisions at intermediate energies can be viewed as a powerful tool to study both bifurcations induced by out-of-equilibrium critical phenomena, as well as finite size precursors of thermal phase transitions., 19 pages, 8 figures

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 types, 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 ${L}_{\mathrm{sym}}$ and ${K}_{\mathrm{sym}}$, and that laboratory constraints at supersaturation 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.

International audience; The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

The effect of correlations between the slope and the curvature of the symmetry energy on ground state nuclear observables is studied within the extended Thomas-Fermi approximation. We consider different isovector probes of the symmetry energy, with a special focus on the skin of $^{208}{\rm Pb}$. We use a recently proposed meta-modelling technique to generate a large number of equation of state models, where the empirical parameters are independently varied. The results are compared to a set of calculations using 17 different Skyrme interactions. We show that the curvature parameter plays a non-negligible role on the neutron skin, while the effect is reduced in Skyrme functionals because of the correlation with the slope parameter., 10 pages, 6 figures

Employing recently proposed metamodeling for the nucleonic matter equation of state, we analyze neutron star global properties such as masses, radii, momentum of inertia, and others. The impact of the uncertainty on empirical parameters on these global properties is analyzed in a Bayesian statistical approach. Physical constraints, such as causality and stability, are imposed on the equation of state and different hypotheses for the direct Urca (dUrca) process are investigated. In addition, only metamodels with maximum masses above $2{M}_{\ensuremath{\bigodot}}$ are selected. Our main results are the following: the equation of state exhibits a universal behavior against the dUrca hypothesis under the condition of charge neutrality and $\ensuremath{\beta}$ equilibrium; neutron stars, if composed exclusively of nucleons and leptons, have a radius of $12.7\ifmmode\pm\else\textpm\fi{}0.4$ km for masses ranging from 1 up to $2{M}_{\ensuremath{\bigodot}}$; a small radius lower than 11 km is very marginally compatible with our present knowledge of the nuclear empirical parameters; and finally, the most important empirical parameters which are still affected by large uncertainties and play an important role in determining the radius of neutrons stars are the slope and curvature of the symmetry energy (${L}_{\mathrm{sym}}$ and ${K}_{\mathrm{sym}}$) and, to a lower extent, the skewness parameters (${Q}_{\mathrm{sat}/\mathrm{sym}}$).

The reaction $^{12}\mathrm{C}+^{13}\mathrm{C}$ at $95\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ bombarding energy is studied using the Garfield + Ring Counter apparatus located at the INFN Laboratori Nazionali di Legnaro. In this paper we want to investigate the de-excitation of $^{25}\mathrm{Mg}$ aiming both at a new stringent test of the statistical description of nuclear decay and a direct comparison with the decay of the system $^{24}\mathrm{Mg}$ formed through $^{12}\mathrm{C}+^{12}\mathrm{C}$ reactions previously studied. Thanks to the large acceptance of the detector and to its good fragment identification capabilities, we could apply stringent selections on fusion-evaporation events, requiring their completeness in charge. The main decay features of the evaporation residues and of the emitted light particles are overall well described by a pure statistical model; however, as for the case of the previously studied $^{24}\mathrm{Mg}$, we observed some deviations in the branching ratios, in particular for those chains involving only the evaporation of $\ensuremath{\alpha}$ particles. From this point of view the behavior of the $^{24}\mathrm{Mg}$ and $^{25}\mathrm{Mg}$ decay cases appear to be rather similar. An attempt to obtain a full mass balance even without neutron detection is also discussed.

International audience; Light and heavy clusters are calculated for warm stellar matter in the framework of relativistic mean-field models, in the single-nucleus approximation. The cluster abundances are determined from the minimization of the free energy. In-medium effects of light cluster properties are included by introducing an explicit binding energy shift analytically calculated in the Thomas–Fermi approximation, and the coupling constants are fixed by imposing that the virial limit at low density is recovered. The resulting light cluster abundances come out to be in reasonable agreement with constraints at higher density coming from heavy-ion collision data. Some comparisons with microscopic calculations are also shown.

The question of the competition between $\mathrm{\ensuremath{\Lambda}}$ and ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ in the ground state of multistrange hypernuclei is addressed within a nonrelativistic density functional approach, partially constrained by ab initio calculations and experimental data. The exploration of the nuclear chart for $10lZl120$ as a function of the strangeness number is performed by adding hyperons to a nuclear core, imposing either conserved total charge $Q$ or conserved proton number $Z$. We find that almost all $\mathrm{\ensuremath{\Lambda}}$ hypernuclei present an instability with respect to the strong interaction decay of $\mathrm{\ensuremath{\Lambda}}$ towards ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ and that most of the instabilities generates ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$ (${\mathrm{\ensuremath{\Xi}}}^{0}$) in the case of conserved total charge $Q$ (proton number $Z$). The strangeness number at which the first ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$ appear is generally lower for configurations explored in the case of conserved $Q$ compared to the case of conserved $Z$, and corresponds to the crossing between the $\mathrm{\ensuremath{\Lambda}}$ and the neutron or proton chemical potentials. About two to three hundred thousand pure $\mathrm{\ensuremath{\Lambda}}$ hypernuclei may exist before the onset of ${\mathrm{\ensuremath{\Xi}}}^{0,\ensuremath{-}}$. The largest uncertainty comes from the unknown $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ interaction, since the $N\mathrm{\ensuremath{\Lambda}}$ and the $N\mathrm{\ensuremath{\Xi}}$ ones can be constrained by a few experimental data. The uncertainty on the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ interaction can still modify the previous estimation by 30--40%, while the impact of the unknown $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ interaction is very weak.

Background : The emergence of hyperon degrees of freedom in neutron star matter has been associated to first order phase transitions in some phenomenological models, but conclusions on the possible physical existence of an instability in the strangeness sector are strongly model dependent. Purpose : The purpose of the present study is to assess whether strangeness instabilities are related to specific values of the largely unconstrained hyperon interactions, and to study the effect of the strange meson couplings on phenomenological properties of neutron stars and supernova matter, once these latter are fixed to fulfill the constraints imposed by hypernuclear data. Method : We consider a phenomenological RMF model sufficiently simple to allow a complete exploration of the parameter space. Results : We show that no instability at supersaturation density exists for the RMF model, as long as the parameter space is constrained by basic physical requirements. This is at variance with a non-relativistic functional, with a functional behavior fitted through ab-initio calculations. Once the study is extended to include the full octet, we show that the parameter space allows reasonable radii for canonical neutron stars as well as massive stars above two-solar mass, together with an important strangeness content of the order of 30\%, slightly decreasing with increasing entropy, even in the absence of a strangeness driven phase transition. Conclusions : We conclude that the hyperon content of neutron stars and supernova matter cannot be established with present constraints, and is essentially governed by the unconstrained coupling to the strange isoscalar meson., 13 pages, 8 figures

International audience; The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a Thomas-Fermi meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. An analytical approximation to the full Thomas-Fermi integrals is further proposed giving a fully analytical meta-model for nuclear masses. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction with Bayesian statistical tools. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full Hartree-Fock or extended Thomas-Fermi calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

During the late stages of gravitational core-collapse of massive stars, extreme isospin asymmetries are reached within the core. Due to the lack of microscopic calculations of electron capture (EC) rates for all relevant nuclei, in general simple analytic parameterizations are employed. We study here several extensions of these parameterizations, allowing for a temperature, electron density and isospin dependence as well as for odd-even effects. The latter extra degrees of freedom considerably improve the agreement with large scale microscopic rate calculations. We find, in particular, that the isospin dependence leads to a significant reduction of the global EC rates during core collapse with respect to fiducial results, where rates optimized on calculations of stable $fp$-shell nuclei are used. Our results indicate that systematic microscopic calculations and experimental measurements in the $N\approx 50$ neutron rich region are desirable for realistic simulations of the core-collapse., 14 pages, 8 figures, accepted for publication in Phys. Rev. C

Understanding the properties of the crust and the core as well as its interface is essential for accurate astrophysical modeling of phenomena such as glitches, X-ray bursts or oscillations in neutron stars. To study the crust-core properties, it is crucial to develop a unified and consistent scheme to describe both the clusterized matter in the crust and homogeneous matter in the core. The low density regime in the neutron star crust is accessible to terrestrial nuclear experiments. In order to develop a consistent description of the crust and the core of neutron stars within the same formalism, we use a density functional scheme, with the model coefficients in homogeneous matter related directly to empirical nuclear observables. In this work, we extend this scheme to non-homogeneous matter to describe nuclei in the crust. We then test this scheme against nuclear observables., Comment: 11 pages, 11 figures, accepted for publication in PASA

The presence of strong magnetic fields in neutron stars, such as in magnetars, may significantly affect their crust-core transition properties and the crust size. This knowledge is crucial in the correct interpretation of astrophysical phenomena involving magnetars, such as glitches in observed rotation frequencies, cooling, bursts and possibly tidal polarizabilities. A recently developed meta-modelling technique allows exploring the model dependence of density functional theory equation of state calculations. In this work, we extend this meta-model to investigate the effect of strong magnetic fields on spinodal instabilities of neutron star matter and the associated crust-core properties. Both Tolman-Oppenheimer-Volkov and a full self-consistent numerical calculations are performed for the neutron star structure, the results being quantitatively different for strong magnetic fields., Comment: 24 pages, 10 figures, 9 tables, regular journal article

The uncertainties in neutron star (NS) radii and crust properties due to our limited knowledge of the equation of state (EOS) are quantitatively analysed. 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 EOS based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\sim 30\%$ 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 EOS for purely nucleonic matter is obtained based on 24 Skyrme interactions and 9 relativistic mean-field nuclear parametrizations. In addition, for relativistic models 17 EOS including a transition to hyperonic matter at high density are presented. All these EOS have in common the property of describing a $2\;M_\odot$ star and of being causal within stable NS. A span of $\sim 3$ km and $\sim 4$ km is obtained for the radius of, respectively, $1.0\;M_\odot$ and $2.0\;M_\odot$ star. Applying a set of nine further constraints from experiment and ab-initio calculations the uncertainty is reduced to $\sim 1$ km and $2$ km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the EOS near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope $L$ which exhibits a linear correlation with the stellar radius, particularly for masses $\sim 1.0\;M_\odot$. Potential constraints on $L$, the NS radius and the EOS from observations of thermal states of NS are also discussed. [Abriged], Comment: Submitted to Phys. Rev. C. Supplemental material not included