Heavy-ion reactions especially those induced by radioactive beams provide useful information about the density dependence of the nuclear symmetry energy, thus the Equation of State of neutron-rich nuclear matter, relevant for many astrophysical studies. The latest developments in constraining the symmetry energy at both sub- and supra-saturation densities from analyses of the isopsin diffusion and the $π^-/π^+$ ratio in heavy-ion collisions using the IBUU04 transport model are discussed. Astrophysical ramifications of the partially constrained symmetry energy on properties of neutron star crusts, gravitational waves emitted by deformed pulsars and the w-mode oscillations of neutron stars are presented briefly.
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We fi…
A Gaussian Process framework for constraining the nuclear equation of state from microscopic calculations with correlated uncertainties
Ohio University（俄亥俄大学）；Argonne National Laboratory（阿贡国家实验室）；University of Washington（华盛顿大学）；University of California, Berkeley（加州大学伯克利分校）；Michigan State University（密歇根州立大学）
Using FOPI data on elliptic flow in Au+Au collisions between 0.4 and 1.5A GeV we extract constraints for the equation of state (EOS) of compressed symmetric nuclear matter using the transport code IQMD by introducing an observable describing the evolution of the size of the elliptic flow as a function of rapidity. This observable is sensitive to the nuclear EOS and a robust tool to constrain the compressibility of nuclear matter up to 2 $ρ_0$.
The quest for the nuclear equation of state (EoS) at high densities and/or extreme isospin is one of the longstanding problems of nuclear physics. Ab initio calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the EoS far away from the saturation point of nuclear matter. On the other hand, in recent years substantial progress has been mode to constrain the EoS both, from the astrophysical side and from accelerator based experiments. Heavy ion experiments support a soft EoS at moderate densities while recent neutron star observations require …
Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformati…
Within the Time Dependent Hartree Fock (TDHF) approach, we investigate the impact of several ingredients of the nuclear effective interaction, such as incompressibility, symmetry energy, effective mass, derivative of the Lane potential and surface terms on the exit channel (fusion vs quasifission) observed in the reaction $^{238}$U+$^{40}$Ca, close to the Coulomb barrier. Our results show that all the ingredients listed above contribute to the competition between fusion and quasifission processes, however the leading role in determining the outcome of the reaction is played by incompressibilit…
The LIGO-Virgo collaboration ground-breaking detection of the binary neutron-star merger event, GW170817, has intensified efforts towards the understanding of the equation of state (EoS) of nuclear matter. In this letter, we compare directly the density-pressure constraint on the EoS obtained from a recent analysis of the neutron-star merger event to density-pressure constraints obtained from nuclear physics experiments. To relate constraints from nuclear physics to the radii and the tidal deformabilities of neutron stars, we use a large collection of Skyrme density functionals that describe p…
Cluster formation is a fundamental aspect of the equation of state (EOS) of warm and dense nuclear matter such as can be found in supernovae (SNe). Similar matter can be studied in heavy-ion collisions (HIC). We use the experimental data of Qin et al. [Phys. Rev. Lett. 108, 172701 (2012)] to test calculations of cluster formation and the role of in-medium modifications of cluster properties in SN EOSs. For the comparison between theory and experiment we use chemical equilibrium constants as the main observables. This reduces some of the systematic uncertainties and allows deviations from ideal…
In this article the role of the supersaturation density equation of state (EOS) is explored in simulations of failed core-collapse supernova explosions. Therefore the nuclear EOS is extended via a one-parameter excluded volume description for baryons, taking into account their finite and increasing volume with increasing density in excess of saturation density. Parameters are selected such that the resulting supernova EOS represent extreme cases, with high pressure variations at supersaturation density which feature extreme stiff and soft EOS variants of the reference case, i.e. without exclud…
There is a degeneracy between the equation of state (EOS) of superdense neutron-rich nuclear matter and the strong-field gravity in understanding properties of neutron stars. While the EOS is still poorly known, there are also longstanding ambiguities in choosing General Relativity or alternative gravity theories in the not-so-well tested strong-field regime. Besides possible appearance of hyperons and new phases, the most uncertain part of the nucleonic EOS is currently the density dependence of nuclear symmetry energy. To provide information that may help break the EOS-gravity degeneracy, we…
We construct an equation of state (EOS) for neutron stars by interpolating hadronic EOS at low density and quark EOS at high density. A hadronic model based on the parity doublet structure is used for hadronic matter and a quark model of Nambu--Jona-Lasinio type is for quark matter. We assume crossover between hadronic matter and quark matter in the the color-flavor locked phase. The nucleon mass of the parity doublet model has a mass associated with the chiral symmetry breaking, and a chiral invariant mass $m_0$ which is insensitive to the chiral condensate. The value of $m_0$ affects the nuc…
The NICER collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. (2019) explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars. In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of neutron stars from the gravitational wave signal o…
We show how observations of gravitational waves from binary neutron star (BNS) mergers over the next few years can be combined with insights from nuclear physics to obtain useful constraints on the equation of state (EoS) of dense matter, in particular, constraining the neutron-matter EoS to within 20% between one and two times the nuclear saturation density $n_0\approx 0.16\ {\text{fm}^{-3}}$. Using Fisher information methods, we combine observational constraints from simulated BNS merger events drawn from various population models with independent measurements of the neutron star radii expec…
We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate …
Experiments with rare isotopes are shedding light on the role isospin plays in the equation of state (EoS) of nuclear matter, and isoscaling -an straight-forward comparison of reactions with different isospin- could deliver valuable information about it. In this work we test this assertion pragmatically by comparing molecular dynamics simulations of isoscaling reactions using different equations of state and looking for changes in the isoscaling parameters; to explore the possibility of isoscaling carrying information from the hot-and-dense stage of the reaction, we perform our study in confin…
The $^{22}$Ne($α$,$γ$)$^{26}$Mg and $^{22}$Ne($α$,n)$^{25}$Mg reactions play an important role in astrophysics because they have significant influence on the neutron flux during the weak branch of the s-process. We constrain the astrophysical rates for these reactions by measuring partial $α$-widths of resonances in $^{26}$Mg located in the Gamow window for the $^{22}$Ne+$α$ capture. These resonances were populated using $^{22}$Ne($^6$Li,d)$^{26}$Mg and $^{22}$Ne($^7$Li,t)$^{26}$Mg reactions at energies near the Coulomb barrier. At these low energies $α$-transfer reactions favor population of …
We examine the influence of the density dependence of the symmetry energy on several properties of neutron stars. In particular, we study the constraints set on the nuclear matter equation of state by the values of the tidal deformability and neutron star radius, using a diverse set of relativistic and non-relativistic mean field models consistent with bulk properties of finite nuclei and the observed lower bound on the maximum mass of neutron star. The tidal deformability and radius show a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter param…
In the framework of mean-field based transport approaches, we discuss recent results concerning collective motion and low-energy heavy ion reactions involving neutron-rich systems. We focus on aspects which are particularly sensitive to the isovector terms of the nuclear effective interaction and the corresponding symmetry energy. As far as collective excitations are concerned, we discuss the mixed nature of dipole oscillations in neutron-rich systems. On the other hand, for reactions close to the Coulomb barrier, we investigate the structure of pre-equilibrium collective dipole oscillations, …
We study the star matter properties for Hybrid equation of state (EoS) by varying the bag constant. We use the Effective-Field-Theory motivated Relativistic Mean-Field model (E-RMF) for hadron phase with recently reported FSUGarnet, G3 and IOPB-I parameter sets. The result of NL3 and NL3${ωρ}$ sets are also shown for comparison. The simple MIT Bag model is applied for the quark phase to construct the hybrid EoS. The hybrid neutron star mass and radius are calculated by varying with $B^{1/4}$ to constrain the $B^{1/4}$ values. It is found that $B^{1/4}$=130-160 MeV is suitable for explaining th…
Nuclear reactions induced by high energy radioactive beams create a transient state of nuclear matter with high density and appreciable neutron to proton asymmetry. This will provide a unique opportunity to explore novel properties of dense neutron-rich matter and the isospin-dependence of the nuclear equation of state (EOS). Here we study the $π^-/π^+$ ratio as a probe of the EOS of dense neutron-rich matter.
Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $\sim 2 ~ {\rm M}_\odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest …
Only one third of the nucleons in $^{208}$Pb occupy the saturation density area. Consequently nuclear observables related to average properties of nuclei, such as masses or radii, constrain the equation of state (EOS) not at saturation density but rather around the so-called crossing density, localised close to the mean value of the density of nuclei: $ρ\simeq$0.11 fm$^{-3}$. This provides an explanation for the empirical fact that several EOS quantities calculated with various functionals cross at a density significantly lower than the saturation one. The third derivative M of the energy at t…
The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imp…
The isospin dependence of in-medium nuclear effective interactions is a fundamental issue in nuclear physics and has broad ramifications in astrophysics. Its uncertainties, especially the difference of neutron-proton interactions in the isosinglet and isotriplet channels, affect significantly the density and momentum dependence of the isovector single-nucleon potential and nucleon-nucleon short-range correlation in neutron-rich matter. Consequently, the neutron-proton effective mass splitting and the density dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion reactions …
This article summarizes theoretical predictions for the density and isospin dependence of the nuclear mean field and the corresponding nuclear equation of state. We compare predictions from microscopic and phenomenological approaches. An application to heavy ion reactions requires to incorporate these forces into the framework of dynamical transport models. Constraints on the nuclear equation of state derived from finite nuclei and from heavy ion reactions are discussed.
Based on the distribution of tidal deformabilities and component masses of binary neutron star merger GW170817, the parametric equation of states (EOS) are employed to probe the nuclear symmetry energy and the properties of neutron star. To obtain a proper distribution of the parameters of the EOS that is consistent with the observation, Bayesian analysis is used and the constraints of causality and maximum mass are considered. From this analysis, it is found that the symmetry energy at twice the saturation density of nuclear matter can be constrained within $E_{sym}(2{ρ_{0}})$ = $34.5^{+20.5}…
The $^{23}$Al($p,γ$)$^{24}$Si reaction is among the most important reactions driving the energy generation in Type-I X-ray bursts. However, the present reaction-rate uncertainty limits constraints on neutron star properties that can be achieved with burst model-observation comparisons. Here, we present a novel technique for constraining this important reaction by combining the GRETINA array with the neutron detector LENDA coupled to the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The $^{23}$Al($d,n$) reaction was used to populate the astrophysically important states…
We investigate the contributions of various reaction channels to the interaction, reaction, charge-changing and neutron-changing cross sections. The goal is to investigate the relation between microscopic interactions and the symmetry energy component of the equation of state (EoS) of interest for the structure of neutron stars. We have made a comparison of the neutron skins extracted from diverse experimental techniques with those obtained with Hartree-Fock-Bogoliubov calculations with 23 Skyrme and with 8 density-dependent interactions used in the relativistic mean field method. We have show…
Recently it has been discovered that the elliptic flow, v2, of composite charged particles emitted at midrapidity in Heavy-Ion collisions at intermediate energies shows the strongest sensitivity to the Nuclear Equation of State (EoS) which has been observed up to now within a microscopic model. This dependence on the nuclear EoS is predicted by Quantum Molecular Dynamics (QMD) calculations [1] which show as well that the absorption or rescattering of in-plane emitted particles by the spectator matter is not the main reason for the EoS dependence of the elliptic flow at mid-rapidity but differe…
We perform an extensive study of the influence of nuclear weak interactions on core-collapse supernovae (CCSNe), paying particular attention to consistency between nuclear abundances in the equation of state (EOS) and nuclear weak interactions. We compute properties of uniform matter based on the variational method. For inhomogeneous nuclear matter, we take a full ensemble of nuclei into account with various finite-density and thermal effects and directly use the nuclear abundances to compute nuclear weak interaction rates. To quantify the impact of a consistent treatment of nuclear abundances…
The mechanism of fusion hindrance, an effect preventing the synthesis of superheavy elements in the reactions of cold and hot fusion, is investigated using the Boltzmann-Uehling-Uhlenbeck equation, where Coulomb interaction is introduced. A strong sensitivity is observed both to the modulus of incompressibility of symmetric nuclear matter, controlling the competition of surface tension and Coulomb repulsion, and to the stiffness of the density-dependence of symmetry energy, influencing the formation of the neck prior to scission. The experimental fusion probabilities were for the first time us…
Heavy-ion reactions provide a unique means to investigate the equation of state (EOS) of neutron-rich nuclear matter, especially the density dependence of the nuclear symmetry energy $E_{sym}(ρ)$. The latter plays an important role in understanding many key issues in both nuclear physics and astrophysics. Recent analyses of heavy-ion reactions have already put a stringent constraint on the $E_{sym}(ρ)$ around the saturation density. This subsequently allowed us to constrain significantly the radii and cooling mechanisms of neutron stars as well as the possible changing rate of the gravitationa…
The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore symmetry-energy (SE) parameters such as J (value at saturation density), L (slope), Ksym (curvature) and so on independently of each other and of assumptions about the effective mass. Here we examine the performance of EoSs with different SE parameters in reproducing nuclear properties and astronomical observations in an effort to constrain especially L and Ksym or the droplet-model counterpart Ktau. Assuming a standard EoS for symmetric matter, we explore several po…
The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between …
The equation of state (EOS) of infinite nuclear matter with a small proton/neutron fraction is a crucial input to determine the properties of neutron stars and compare model predictions to astronomical observations. The so-called `symmetry energy' is the part of the EOS accounting for the difference in the number of neutrons and protons. Numerous experiments have been devised to assess the symmetry energy and constrain its functional dependence with the nucleon density. Further constraints follow from a stellar modeling using the EOS to reproduce astronomical observations such as neutron star …
The nuclear matter parameters define the nuclear equation of state (EoS), they appear as coefficients of expansion around the saturation density of symmetric and asymmetric nuclear matter. We review their correlations with several properties of finite nuclei and of neutron stars within mean-field frameworks. The lower order nuclear matter parameters such as the binding energy per nucleon, incompressibility and the symmetry energy coefficients are found to be constrained in narrow limits through their strong ties with selective properties of finite nuclei. From the correlations of nuclear matte…
Understanding the equation of state (EOS) of cold nuclear matter, namely, the relation between the pressure and energy density, is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova, all depend critically on the equation of state of hadronic matter. In this contribution I will concentrate on the special role that nuclear physics plays in constraining the EOS of cold baryonic matter and its impact on the properties of neutron…
Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen {\it a priori} in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au c…
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the $ρ$ pole. Except for S+Au collisions our calculations reproduce the CERES data.
