Saturation Properties Of Nuclear Matter Research Articles

Impact of the stiffness of equation of state on saturation properties of asymmetric nuclear matter and Urca cooling in neutron stars

Abstract We consider nuclear equation of state (EOS) based on the semi-realistic M3Y-Paris and M3Y-Reid effective nucleon-nucleon (NN) interactions to assess the influence of the stiffness of the isospinasymmetric nuclear matter (ANM) on its isoscalar and isovector saturation properties, and on the β-stable proton fraction in neutron star (NS) matter. Two parameterizations schemes of the CDM3Y isovector density dependence of the NN interaction are adopted, one is scaled to the isoscalar density dependence and the other (IVF1) is developed independently of it. We found that the stiffer EOS yields larger binding saturation density that decreases with the isospin asymmetry (I), and slightly decreases the maximum asymmetry (Imax) reached for bound ANM. The density-slope (L) of the symmetry energy is found to correlate directly with the stiffness of ANM, meanwhile the symmetryenergy curvature (Ksym) and the quadratic isovector incompressibility coefficient (Kτ ) are found to correlate with it inversely. We found also that the stiffer EOS indicates larger neutron-rich npeμ NS matter under β-equilibrium. Only the CDM3Y-Paris EOSs of isoscalar incompressibility K0 up to 270 MeV and that of CDM3Y-Reid with K0 = 200 MeV indicate allowed direct URCA (DU) cooling process in β-stable NS matter, at densities greater than 3.5 ρ0, based on the IVF1 density dependence. The stiffer EOS proposes a narrower density range for DU process in NS. According to the considered Paris (Reid) forces, muons can emerge in cold β-stable npe matter at ρ ≥ 0.85 ρ0 (0.79 ρ0), which slightly decreases both the neutron richness at NS core and the DU threshold density.

Emulating ab initio computations of infinite nucleonic matter

We construct efficient emulators for the computation of the infinite nuclear matter equation of state. These emulators are based on the subspace-projected coupled-cluster method for which we here develop a new algorithm called small-batch voting to eliminate spurious states that might appear when emulating quantum many-body methods based on a non-Hermitian Hamiltonian. The efficiency and accuracy of these emulators facilitate a rigorous statistical analysis within which we explore nuclear matter predictions for >106 different parametrizations of a chiral interaction model with explicit Δ-isobars at next-to-next-to leading order. Constrained by nucleon-nucleon scattering phase shifts and bound-state observables of light nuclei up to He4, we use history matching to identify nonimplausible domains for the low-energy coupling constants of the chiral interaction. Within these domains we perform a Bayesian analysis using sampling and importance resampling with different likelihood calibrations and study correlations between interaction parameters, calibration observables in light nuclei, and nuclear matter saturation properties. Published by the American Physical Society 2024

Influence of saturation property of cold nuclear matter on the parameterization process of fusion barriers

Influence of saturation property of cold nuclear matter on the parameterization process of fusion barriers

Nuclear Matter Properties and Neutron Star Phenomenology Using the Finite Range Simple Effective Interaction

The saturation properties of symmetric and asymmetric nuclear matter have been computed using the finite range simple effective interaction with Yukawa form factor. The results of higher-order derivatives of the energy per particle and the symmetry energy computed at saturation, namely, Q0, Ksym, Kτ, Qsym, are compared with the corresponding values extracted from studies involving theory, experiment and astrophysical observations. The overall uncertainty in the values of these quantities, which results from a wide spectrum of studies described in earlier literature, lies in the ranges −1200≲Q0≲400 MeV, −400≲Ksym≲100 MeV, −840≲Kτ≲−126 MeV and −200≲Qsym≲800 MeV, respectively. The ability of the equations of state computed with this simple effective interaction in predicting the threshold mass for prompt collapse in binary neutron star merger and gravitational redshift has been examined in terms of the compactness of the neutron star and the incompressibility at the central density of the maximum mass star. The correlations existing between neutron star properties and the nuclear matter saturation properties have been analyzed and compared with the predictions of other model calculations.

Frequencies of f - and p -oscillation modes in cold and hot compact stars

A large collection of equations of state (EOSs) built within the covariant density functional theory of hadronic matter and allowing for density dependent couplings is employed to study polar $f$- and $p$-oscillations of cold and hot compact stars. Correlations between oscillation frequencies of cold purely nucleonic neutron stars (NSs), their global parameters as well as properties of nuclear matter (NM) are investigated by considering a set of models from Beznogov and Raduta, [Phys. Rev. C 107, 045803 (2023)], where a number of constraints on the saturation properties of NM, pure neutron matter and the lower bound of the maximal NS mass were imposed within a Bayesian framework. The roles of finite temperature and exotic particle degrees of freedom, e.g., hyperons, $\mathrm{\ensuremath{\Delta}}$-resonances, antikaon condensates or a hadron to quark phase transition, are addressed by employing a family of models publicly available on compose and assuming idealized profiles of temperature or entropy per baryon and charge fraction. We find that finite temperature effects reduce the oscillation frequencies of nucleonic stars while the opposite effect is obtained for stars with exotic particle degrees of freedom. When the $\mathrm{\ensuremath{\Gamma}}$-law is employed to build finite temperature EOSs, errors in estimating oscillation modes frequencies are of the order of 10% to 30%, depending on the mass. Throughout this work the Cowling approximation is used.

Probing nuclear equation of state with the cdm3y version of B3y-fetal effective interaction

This paper is a study of the nuclear Equation of State (EOS) of cold nuclear matter with the B3Y-Fetal effective interaction in its CDM3Y density-dependent version within the framework of Hartree-Fock approximation. The well-known saturation properties of both symmetric and asymmetric nuclear matter are well-reproduced in this work. Using the CDM3Y-K approach, this study has evolved a new set of user interactions, some of which are CDB3Y1-, CDB3Y2-, CDB3Y3-, CDB3Y4-, CDB3Y5-, CDB3Y6-Fetal interactions with corresponding incompressibilities K0 = 188, 204, 217,228, 241 and 252 MeV respectively, in excellent agreement with those of the M3Y-Paris and M3Y-Reid effective interactions. For asymmetric nuclear matter, the new set of interactions has produced the symmetry energy Esym = 32.00 MeV with an associated slope parameter L = 55 MeV at a saturation density ρ = 0.17fm−3 and asymmetry parameter δ = 1.00 (pure neutron matter) in good agreement with the standard values obtained from coupled channel analysis of charge exchange reactions, statistical multifragmentation model and terrestrial Nuclear Physics experimental analyses. Furthermore, the new set of interactions has been found to have bright prospects in a nuclear reaction as the real folded potential computed with the CDB3Y6-Fetal interaction within the framework of double folding potential has been found to be good and similar to that of CDB3Y6-Paris whose optical potential has a repulsive direct component.

The optimized point-coupling interaction for the relativistic energy density functional of Hartree-Bogoliubov approach quantifying the nuclear bulk properties

We propose a newly optimized nonlinear point-coupling parameterized interaction, PC-L3R, for the relativistic Hartree-Bogoliubov framework with a further optimized separable pairing force by fitting to observables, i.e., the binding energies of 91 spherical nuclei, charge radii of 63 nuclei, and 12 sets of mean pairing gaps consisting of 54 nuclei in total. The separable pairing force strengths of proton and neutron are optimized together with the point-coupling constants, and are justified in satisfactory reproducing the empirical pairing gaps. The comparison of experimental binding energies compiled in AME2020 for 91 nuclei with the ones generated from the present and other commonly used point-coupling interactions indicates that the implementation of PC-L3R in relativistic Hartree-Bogoliubov yields the lowest root-mean-square deviation. The charge radii satisfactory agree with experiment. Meanwhile, PC-L3R is capable of estimating the saturation properties of the symmetric nuclear matter and of appropriately predicting the isospin and mass dependence of binding energy. The experimental odd-even staggering of single nucleon separation energies is well reproduced. The comparison of the estimated binding energies for 7,373 nuclei based on the PC-L3R and other point-coupling interactions is also presented.

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.

Medium modification of the nucleon mechanical properties: Abel tomography case

We investigate how the gravitational form factors of the nucleon undergo changes in nuclear matter, emphasizing the Abel transformation from the three-dimensional (3D) Breit frame to the two-dimensional (2D) light-front frame. Since the gravitational form factors reveal the mechanical structure of the nucleon, we examine also the medium modifications of the energy–momentum, pressure, and shear-force distributions. We scrutinize the stabilities of the nucleon in nuclear matter. For this purpose, we employ the in-medium modified SU(2) Skyrme model to study these mechanical quantities of the nucleon, since it provides a simple but clear framework. In this in-medium modified SU(2) Skyrme model, the modification of pionic properties is performed by using low-energy pion-nucleus scattering data and the saturation properties of nuclear matter near the normal nuclear matter density, rho _0=0.5m_pi ^3. The results reveal how the nucleon swells in nuclear matter as the mass distribution of the nucleon is broadened in medium. We also show that the mean square radii corresponding to the mass and angular momentum distributions increase in nuclear medium. This feature is kept both in 3D and 2D cases. We visualize how the strong force fields inside the nucleon in the 2D plane are distributed and illustrate how these forces undergo change in nuclear matter.

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.

Nuclear Matter and Neutron Stars from Relativistic Brueckner–Hartree–Fock Theory

The momentum and isospin dependence of the single-particle potential for the in-medium nucleon are the key quantities in the Relativistic Brueckner–Hartree–Fock (RBHF) theory. It depends on how to extract the scalar and the vector components of the single-particle potential inside nuclear matter. In contrast to the RBHF calculations in the Dirac space with the positive-energy states (PESs) only, the single-particle potential can be determined in a unique way by the RBHF theory together with the negative-energy states, i.e., the RBHF theory in the full Dirac space. The saturation properties of symmetric and asymmetric nuclear matter in the full Dirac space are systematically investigated based on the realistic Bonn nucleon–nucleon potentials. In order to further specify the importance of the calculations in the full Dirac space, the neutron star properties are investigated. The direct URCA process in neutron star cooling will happen at density ρ DURCA = 0.43, 0.48, 0.52 fm−3 with proton fractions of Y p,DURCA = 0.13. The radii of a 1.4M ⊙ neutron star are predicated as km, and their tidal deformabilities are for potential Bonn A, B, C. Compared with the results obtained in the Dirac space with PESs only, the full-Dirac-space RBHF calculation predicts the softest symmetry energy, which would be more favored by the gravitational wave detection of GW170817. Furthermore, the results from the full-Dirac-space RBHF theory are consistent with the recent astronomical observations of massive neutron stars and simultaneous mass–radius measurement.

A bag model of matter condensed by the strong interaction

Inspired by various astrophysical phenomenons, it is suggested that pulsar-like compact stars are comprised entirely of strangeons (quark-clusters with three-light-flavor symmetry) and a small amount of electrons. In order to better constrain the properties of strangeon stars, we propose a linked bag model to describe the condensed matter by the strong interaction (i.e., strong condensed matter) in both 2-flavored (nucleons) and 3-flavored (hyperons, strangeons, etc.) scenarios. The model parameters are calibrated to reproduce the saturation properties of nuclear matter, which are later applied to hyperon matter and strangeon matter. Compared with baryon matter, the derived energy per baryon of strangeon matter is reduced if the strangeon carries a large number of valence quarks, which stiffens the equation of state and consequently increases the maximum mass of strangeon stars. In a large parameter space, the maximum mass and tidal deformability of strangeon stars predicted by the linked bag model are consistent with the current astrophysical constraints. It is found that the maximum mass of strangeon stars can be as large as [Formula: see text], while the tidal deformability of a [Formula: see text] strangeon star lies in the range of [Formula: see text].

The influence of the nuclear matter incompressibility on heavy-ion fusion reactions at near- and above-barrier energies

Based on simulating the saturation property of cold nuclear matter for complete fusion channel of two approaching nuclei, we systematically investigate the role of nuclear incompressibility in the nucleus-nucleus potential and fusion-evaporation cross section of 69 medium-heavy and heavy mass systems with 208≤Z1Z2≤1520. Our observations based on the uncoupled single-barrier potential model and the M3Y double-folding potential which is corrected with a repulsive core term reveal that the incompressibility of cold nuclear matter can be responsible for the discrepancy between the measured and calculated values of the fusion cross sections at energies around and above the Coulomb barrier. In other words, one can find that the high energy fusion cross sections can not be reproduced using the standard form of the M3Y-DF potential model without considering the repulsive core effects. We show that the strength of the repulsive contact term and also the incompressibility of the compound nuclei exhibit systematic behaviors with respect to the atomic and mass numbers of reacting nuclei. It is shown that the hardness level of nuclear matter reduces when one passes from lighter to heavier systems.

Heavy-ion fusion cross sections in the barrier and high-energy regions: Signature of energy dependence in the repulsive core potential

The effect of incompressibility of cold nuclear matter (CNM) on the high-energy fusion data of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb, 50Ti+209Bi and 40,48Ca+238U colliding systems with 1152≤Z1Z2≤1840 has been analyzed using coupled-channels (CC) calculations. To apply the effect of saturation property of nuclear matter, we use the M3Y double-folding model which is corrected with a repulsive term. The repulsive parameters are adjusted to provide an optimum fit to the available experimental fusion cross sections. For each of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb colliding systems, the best fit to the measured fusion cross sections at high energies is achieved using the CC calculations based on the M3Y+Repulsion potential with a constant value for the strength of the repulsive contact term. While focusing on the heavy-ion fusion reactions existing in the mass range Z1Z2>1800 reveals that it is necessary to consider an energy-dependent behavior for the repulsive parameters. When these conditions are imposed on entrance channel potential, it is possible to obtain an excellent description of the fusion data for 50Ti+209Bi, 40Ca+238U, and 48Ca+238U reactions. Our findings indicate that the extracted values of the strength Vrep of the repulsive contact term increase with increasing incident energy Ec.m.. In addition, we conclude that the repulsive part of the density distribution becomes more diffused with an increase in bombarding energy.

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.

Constraints of observational mass of neutron stars on the saturation parameters of nuclear matter with SU(6) symmetry

Since the massive neutron stars (NSs) were detected, NSs have received more extensive attention and research. The discoveries of pulsars PSR J0348-0432 and MSP J0740 $$+$$ 6620 confirm the existence of massive NS and therefore present a strict limit to the equation of state (EoS) of nuclear matter, but the appearance of hyperons will soften the EoS. In order to get a stiff EoS and solve the hyperon puzzle, in this paper we firstly study the effects of the saturation properties of nuclear matter on the mass of NS and then in turn, constrain the saturation properties of nuclear matter by the observed mass of massive NSs with SU(6) symmetry. The study shows that based on the SU(6) symmetry, it is almost impossible to obtain a stiff enough EoS to support the maximum mass of a NS up to 2.0 $$M_{\odot }$$ within the range of empirical value of saturation properties of nuclear matter.

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.

The holographic paradigm of hadron dynamics for medium modified nuclear matters

We propose a medium-modified holographic-hadron dynamics suitable for the study of symmetric nuclear matter, with a key property of a simple law for the evolution of the five dimensional mass with the scalar background field. We show that the model satisfies symmetric nuclear matter constraints, namely, incompressibility and density dependence of the pressure, with only three free adjustable parameters fitted to the free nucleon mass and the nuclear matter saturation properties. We found that the holographic nucleon swells and the UV behavior of the associated string amplitude is damped, with the scaling property at short distances softened. Both effects can also generate observable consequences reflecting an average leakage of partons to the nuclear medium when density is increased, in the route towards the deconfinement of the internal nucleon degrees of freedom.

The effect of the three-body force on the β-stable matter in RLOCV framework

The symmetry energy of isospin asymmetric nuclear matter (IANM), the density dependence of symmetry energy and also the equation of state (EOS) of the β-stable matter (BSM) are considered within relativistic corrections in the lowest order constrained variation approach (RLOCV) by using AV18 potential, with and without including Urbana (UIX) three-body force (TBF). The relative proton abundance for a wide range of baryon number density is calculated by including TBF in RLOCV approach. It is observed that if the bare two-body force (2BF) interaction AV18 is used, the relative proton abundance (ρp/ρB) increases by increasing baryon number density which tends to be saturated at high densities in both relativistic and non-relativistic treatments, while including TBF to our potential produces the ρp/ρB with higher values at low densities, which is saturated at the moderate densities in both LOCV and RLOCV frameworks. Moreover, adding the relativistic corrections (RC) to the results of β-stable matter decreases the value of proton abundance. In contrast, including TBF increases the value of ρp/ρB at low baryonic densities, which is saturated at the moderate baryon number densities. The opposite behaviors are also found on the saturation properties of nuclear matter by including TBF and RC to our calculations. It is also shown that the effect of TBF is much larger than that of the RC. Our results agree with other interactions and methods.

Are nuclear matter properties correlated to neutron star observables?

We investigate properties of nuclear matter and examine possible correlations with neutron star observables for a set of microscopic nuclear equations of state derived within the Brueckner-Hartree-Fock formalism employing compatible three-body forces. We find good candidates for a realistic nuclear EOS up to high density and confirm strong correlations between neutron star radius, tidal deformability, and the pressure of betastable matter. No correlations are found with the saturation properties of nuclear matter.