Properties Of Symmetric Nuclear Matter Research Articles

Neutron Star Matter as a Dilute Solution of Protons in Neutrons.

Neutron stars contain neutron-rich matter with around 5% protons at nuclear saturation density. In this Letter, we consider equilibrium between bulk phases of matter based on asymmetric nuclear matter calculations using chiral effective field theory interactions rather than, as has been done in the past, by interpolation between the properties of symmetric nuclear matter and pure neutron matter. Neutron drip (coexistence of nuclear matter with pure neutrons) is well established, but from earlier work it is unclear whether proton drip (equilibrium between two phases, both of which contain protons and neutrons) is possible. We find that proton drip is a robust prediction of any physically reasonable equation of state, but that it occurs over a limited region of densities and proton fractions. An analytical model based on expanding the energy in powers of the proton density, rather than the neutron excess, is able to account for these features of the phase diagram.

Relativistic Brueckner-Hartree-Fock Theory: an ab initio Approach for Nuclear Matter and for Finite Nuclei

Recent years have seen considerable progress with ab-initio calculations of the nuclear structure by non-relativistic many-body methods. Dirac-Brueckner-Hartree-Fock Theory provides a relativistic ab-intio approach, which is able to reproduce saturation properties of symmetric nuclear matter without three-body forces. However, so far, the corresponding equations have been solved only for positive energy states. Negative energy states have been included for forty years in various approximations, leading to differences in the isospin dependence. This problem has been solved only recently by a complete solution of the self-consistent relativistic Brueckner-Hartree-Fock equations in asymmetric nuclear matter. Due to its numerical complexity, however, it is very difficult to extend the Relativistic Brueckner-Hartree-Fock theory to the study of finite nuclear systems. Recent efforts will be discussed to overcome this problem.

Nuclear Symmetry Energy and Hyperonic Stars in the QMC Model

The nuclear symmetry energy, together with the other saturation properties of symmetric nuclear matter, plays an important role in low energy nuclear structure of terrestrial systems, as well as astrophysical objects. In particular, its density dependence, both in sub- and supra-saturation regions in high density matter in neutron stars, is of utmost significance and has been a subject of active research for decades, usually within a mean-field framework. We report results obtained using the latest version of Quark-Meson-Coupling Model (QMC-A) with just three variable parameters, the baryon-meson coupling constants in free space. It is shown that these parameters can be determined directly using nuclear matter (NM) properties at saturation; two parameters of symmetric nuclear matter (SNM), the baryon number density and the energy per particle, and the symmetry energy coefficient of asymmetric nuclear matter (ANM). The effects of uncertainties in the these parameters and propagation of these uncertainties through the calculation of properties of dense hyperonic matter and cold neutron stars are demonstrated. This approach leads to new limits on both the NM parameters and the QMC coupling constants. The results, which exploit the unique features of the QMC model, are discussed and future prospects are outlined.

Overview of symmetric nuclear matter properties from chiral interactions up to fourth order of the chiral expansion

We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N3LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.

Hyperonic neutron stars: reconciliation between nuclear properties and NICER and LIGO/VIRGO results

Using an extended version of quantum hadrodynamics, I propose a new microscopic equation of state (EoS) that is able to correctly reproduce the main properties of symmetric nuclear matter at the saturation density, as well as produce massive neutron stars and satisfactory results for the radius and the tidal parameter. I show that this EoS can reproduce at least a 2.00 solar mass neutron star, even when hyperons are present. The constraints about the radius of a 2.00 M ⊙ and the minimum mass that enables a direct Urca effect are also checked.

Nuclear matter in relativistic Brueckner-Hartree-Fock theory with Bonn potential in the full Dirac space

Starting from the Bonn potential, relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for nuclear matter in the full Dirac space, which provides a unique way to determine the single-particle potentials and avoids the approximations applied in the RBHF calculations in the Dirac space with positive-energy states (PESs) only. The uncertainties of the RBHF calculations in the Dirac space with PESs only are investigated, and the importance of the RBHF calculations in the full Dirac space is demonstrated. In the RBHF calculations in the full Dirac space, the empirical saturation properties of symmetric nuclear matter are reproduced, and the obtained equation of state agrees with the results based on the relativistic Green's function approach up to the saturation density.

Critical properties of calibrated relativistic mean-field models for the transition to warm, nonhomogeneous nuclear and stellar matter

The critical properties for the transition to warm, asymmetric, non-homogeneous nuclear matter are analysed within a thermodynamical spinodal approach for a set of well calibrated equations of state. It is shown that even though different equations of state are constrained by the same experimental, theoretical and observational data, and the properties of symmetric nuclear matter are similar within the models, the properties of very asymmetric nuclear matter, such as the one found inside of neutron stars, differ a lot for various models. Some models predict larger transition densities to homogeneous matter for beta-equilibrated matter than for symmetric nuclear matter. Since one expects that such properties have a noticeable impact on the the evolution of either a supernova or neutron star merger, this different behavior should be understood in more detail.

Analysis of critical parameters for nonrelativistic models of symmetric nuclear matter

In this work we have analyzed several features of symmetric nuclear matter (SNM) at finite temperature described by different zero- and finite-range nonrelativistic families of models, namely, Skyrme, Gogny, Momentum-dependent interaction (MDI), Michigan three-range Yukawa (M3Y) and Simple Effective Interaction (SEI). We have calculated the critical parameters (CP) associated to the liquid-gas phase coexistence for nuclear matter from these parametrizations and show that they are in agreement with their experimental and theoretical values obtained in the literature. Our study also points out to a strong evidence of universality presented by the hadronic models, namely, model independence in the gaseous phase and distinguishability among different interactions in the liquid phase. We have performed a correlation study among different CP and SNM properties. Such studies involving different finite range interactions are scarce in literature. The analyzed models show an overall increasing trend of the critical temperature as a function of critical pressure.

Critical properties of symmetric nuclear matter in low-density regime using effective-relativistic mean field formalism

The effective field theory motivated relativistic mean-field (E-RMF) formalism is employed to study the equation of state (EoS) for the infinite symmetric nuclear matter (SNM) at finite temperature using the recently developed forces FSUGarnet, IOPB-I, G3, and the well known NL3 force parameter. The EoS is then used to estimate the critical temperature T c, pressure P c and density ρ c of the SNM for the liquid–gas phase transition. As T c is not a constrained parameter in both experiments and theoretical calculations, there is a large uncertainty around its value. Although, the critical parameters are correlated among themselves. It is revealed that vector self-coupling ζ 0 of used forces play determining role in EoS in finite temperature limit. Keeping the incompressibility in acceptable limit i.e. 240 ± 20 MeV, the lower value of ζ 0 gives a better result of T c when compared to the several experimental data. The critical parameters however show weak correlation with the properties at saturation density at zero temperature. The compressibility factors calculated with these parameters are in agreement with the universal value of liquid–gas systems. Stability conditions are examined along with binodal and spinodal regions. Besides this, the thermodynamic properties like specific heat and latent heat are also worked out. We have carried out detailed consistency check of our calculations using critical exponents and standard scaling laws. All the exponents are well within the theoretical mean-field results.

Properties of nuclear matter in relativistic Brueckner–Hartree–Fock model with high-precision charge-dependent potentials

Properties of nuclear matter are investigated in the framework of relativistic Brueckner–Hartree–Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as a pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon–nucleon (NN) interactions, G matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleon are around −10.72 MeV to −16.83 MeV at saturation densities, 0.139 fm−3 to 0.192 fm−3 with these three potentials, respectively. It clearly demonstrates that the pseudovector coupling between pion and nucleon can generate reasonable saturation properties comparing with pseudoscalar coupling. Furthermore, these saturation properties have strong correlations with the tensor components of NN potentials, i.e., the D-state probabilities of deuteron, PD to form a relativistic Coester band. The equations of state of pure neutron matter from pvCD-Bonn potentials are almost identical, since the prominent difference of pvCD Bonn potentials are the components of tensor force, which provides very weak contributions in the case of total isospin T = 1. In addition, the charge symmetry breaking (CSB) and charge independence breaking (CIB) effects are also discussed in nuclear matter from the partial wave contributions with these high-precision charge-dependent potentials. In general, the magnitudes of CSB from the differences between nn and pp potentials are about 0.05 MeV, while those of CIB are around 0.35 MeV from the differences between np and pp potentials.

Neutron and nuclear matter properties with chiral three-nucleon forces

The equation of state of neutron and symmetric matter is calculated within the lowest order constrained variational (LOCV) method using the Argonne V18 (AV18) nucleon–nucleon interaction supplemented by the local, coordinate space versions of the chiral three-nucleon force (TNF) at next-to-next-to-leading order (N2LOL). We present the first results of studying the nuclear equation of state in the LOCV framework by employing a chiral TNF. It is shown that although some calculated values of saturation properties lie well in the empirically determined ranges, all of the saturation quantities can not be predicted simultaneously. We also study other possible parametrizations of the N2LOL TNF by fitting the low-energy constants (LECs) to nuclear saturation point. It is found that by employing the proposed sets of LECs, LOCV method is able to successfully produce the equilibrium properties of symmetric nuclear matter.

Temperature Effects on the Equation of State and Symmetry Energy at Low and High Densities

Thermal properties of symmetric nuclear matter and pure neutron matter are studied in a selfconsistent Green’s function and Brueckner–Hartree–Fock approaches with the inclusion of the contact interaction using CDBONN potential. Also we investigate the temperature dependence of the symmetry energy. The symmetry energy at fixed density is found to generally decrease with temperature. The temperature effects on the nuclear matter symmetry energy are found to be stronger at lower densities while become much weaker at higher densities. The results of several microscopic approaches are compared. Also the results are compared with recent experimental data. There is good agreement between the experimental symmetry energy and those calculated in the Brueckner–Hartree–Fock approach.

Equation of state of asymmetric nuclear matter using re-projected nucleon–nucleon potentials

In this paper, we have calculated the equation of state of asymmetric nuclear matter using the lowest order constrained variational approach and Argonne family potentials with and without three-nucleon interaction (TNI) contribution. In particular, we have used the AV18 potential and the re-projected potentials, AV8′, and AV6′. We have also calculated the saturation properties of symmetric nuclear matter, and the nuclear symmetry energy using AV18+TNI, AV8′+TNI and AV6′+TNI potentials. The inclusion of TNI has modified the agreement with experiment. We have also made a comparison between our results and those of other many-body calculations.

Effective interactions of hyperons and mass-radius relation of neutron stars

We examine the role of hyperons in a neutron star based on the relativistic mean field approach. For nuclear matter below 1.5 times the normal nuclear density we constrain the model parameters by using the symmetric nuclear matter properties and theoretical investigations for neutron matter in the literature. We then extend the model to higher densities by including hyperons and isoscalar vector mesons that contain strangeness degree of freedom. We confirm that the $\phi$ meson induces a $\Lambda$ repulsive force and hardens the equation of state. The hardening arising from the $\phi$ meson compensates the softening from the existence of hyperons. The flavor SU(3) and spin-flavor SU(6) relations are examined as well. We found that the coupling constants fitted by neutron matter properties could yield high enough maximum mass of a neutron star and the obtained results satisfy both the mass and radius constraints. The onset of the hyperon direct Urca process in neutron stars is also investigated using our parametrization.

Quark–meson coupling model based upon the Nambu–Jona Lasinio model

The NJL model for the octet baryons, using proper time regularization to simulate some of the features of confinement, is solved self-consistently in nuclear matter. This provides an alternative framework to the MIT bag model which has been used in the quark-meson coupling model. After fitting the parameters of the model to the saturation properties of symmetric nuclear matter the model is used to explore the equation of state of pure neutron matter as well as nuclear matter at densities relevant to heavy ion collisions. With a view to future studies of high mass neutron stars, the binding of hyperons is also explored.

Global analysis of isospin dependent microscopic nucleon-nucleus optical potentials in a Dirac-Brueckner-Hartree-Fock approach

The Microscopic Otical Model Potential is evaluated within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of the isospin asymmetric nuclei. Therefore, the present work aims to perform a global analysis of the isospin-dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. The DBHF is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schr\"odinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The nucleon-nucleus scattering calculations are carried out for a broad spectrum $n$ and $p$ scattering experiments below 200 MeV with targets ranging from $^{12}$C to $^{208}$Pb.

Thomas-Fermi calculations for determination of critical properties of symmetric nuclear matter on the basis of extended effective mass approach

Thomas-Fermi calculations for determination of critical properties of symmetric nuclear matter on the basis of extended effective mass approach

Effects of angular correlations on particle-particle propagation in infinite nuclear matter

The effect of angular correlations on self-consistent solutions for single-particle (sp) potentials in infinite nuclear matter is investigated. To this end we treat explicitly the angular dependence of the particle-particle (pp) propagator in Brueckner-Hartree-Fock (BHF) equation for the g matrix. It is observed that the exact angular dependence of the pp propagator yields highly fluctuating structures, posing stringent difficulties in the actual search of self-consistent solutions for the sp energy. A perturbative approach is presented to evaluate the effect of the angular correlations in the self-consistent solutions. Solutions at Fermi momenta kF in the range 1.20 - 1.75 fm-1 are reported using Argonne v18 nucleon- nucleon potential. Although the sp potentials are sensitive to the treatment of the angular behaviour of the propagator, such sensitivity appears at momenta well above the Fermi surface. As a result, the saturation properties of symmetric nuclear matter differ marginally from those calculated using angle-averaged energy denominators in pp propagators.

Neutron stars interiors: Theory and reality

There are many fascinating processes in the universe which we observe in more detail thanks to increasingly sophisticated technology. One of the most interesting phenomena is the life cycle of stars, their birth, evolution and death. If the stars are massive enough, they end their lives in a core-collapse supernova explosion, one of the most violent events in the universe. As a result, the densest objects in the universe, neutron stars and/or black holes, are created. The physical basis of these events should be understood in line with observation. Unfortunately, available data do not provide adequate constraints for many theoretical models of dense matter. One of the most open areas of research is the composition of matter in the cores of neutron stars. Unambiguous fingerprints for the appearance and evolution of particular components, such as strange baryons and mesons, with increasing density, have not been identified. In particular, the hadron-quark phase transition remains a subject of intensive research. In this contribution we briefly survey the most promising observational and theoretical directions leading to progress in understanding high density matter in neutron stars. A possible way forward in modeling high-density matter is outlined, exemplified by the quark-meson-coupling model (QMC). This model makes connection between hadronic structure and the underlying quark make-up. It offers a natural explanation for the saturation of nuclear force and treats high-density matter, containing the full baryon octet, in terms of four uniquely defined parameters adjusted to properties of symmetric nuclear matter at saturation.

Equation of State and Symmetry Energy at High Densities for Zero and Finite Temperatures

The equation of state of isospin asymmetric nuclear matter within the framework of the Brueckner theory is used to calculate the energy per particle for nuclear and neutron matter. Pressure and symmetry energy are also presented. Here we extended our work to include Skyrme-like zero-range density-dependent two-body forces, which could mimic three-body forces. A three-body forces are shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter. We also studied the effect of extending the calculation to finite temperatures.