Slope Of Symmetry Energy Research Articles

Isospin symmetry breaking in the charge radius difference of mirror nuclei

Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of $^{48}\mathrm{Ca}$ and $^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon

Within a transport model, we investigated the effects of the momentum dependence of the nuclear symmetry potential on the pion observables in central Sn + Sn collisions at 270 MeV/nucleon. To this end, the quantity \(U_\text {sym}^{\infty }(\rho _{0})\) (i.e., the value of the nuclear symmetry potential at the saturation density \(\rho _{0}\) and infinitely large nucleon momentum) was used to characterize the momentum dependence of the nuclear symmetry potential. With a certain L (i.e., the slope of the nuclear symmetry energy at \(\rho _{0}\)), the characteristic parameter \(U_\text {sym}^{\infty }(\rho _{0})\) of the symmetry potential significantly affects the production of \(\pi ^{-}\) and \(\pi ^{+}\) and their pion ratios. Moreover, by comparing the charged pion yields, pion ratios, and spectral pion ratios of the theoretical simulations for the reactions \(^{108}\)Sn + \(^{112}\)Sn and \(^{132}\)Sn + \(^{124}\)Sn with the corresponding data in the S\(\pi \)RIT experiments, we found that our results favor a constraint on \(U_\text {sym}^{\infty }(\rho _{0})\) (i.e., \(-160^{+18}_{-9}\) MeV), and L is also suggested within a range of 62.7 MeV\(<L<93.1\) MeV. In addition, the pion observable for \(^{197}\)Au + \(^{197}\)Au collisions at 400 MeV/nucleon also supports the extracted value for \(U_\text {sym}^{\infty }(\rho _{0})\).

Decoding the nuclear symmetry energy event-by-event in heavy-ion collisions with machine learning

Inferences of the nuclear symmetry energy from heavy-ion collisions are currently based on the comparison of measured observables and transport model simulations. Only the expectation values of observables over all considered events are used in these approaches, however, observables can be obtained event-by-event both in experiments and transport model simulations. By using the light gradient boosting machine (LightGBM), a modern machine-learning algorithm, we present a framework for inferring the density-dependent nuclear symmetry energy from observables in heavy-ion collisions on the event-by-event analysis. The ultrarelativistic quantum molecular dynamics (UrQMD) model simulations are used as training data. The symmetry energy slope parameter extracted with LightGBM event-by-event from test data also by UrQMD has an average spread of approximately 30 MeV from the truth, and is found to be robust against variations in model parameters. In addition, LightGBM can identify features that have the greatest effect on the physics of interest, thereby offering valuable insights. Our study suggests that the present framework can be a powerful tool and may offer a new paradigm to study the underlying physics in heavy-ion collisions.

Density dependence of the nuclear symmetry energy and neutron skin thickness in the KIDS framework

The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore systematically the effect of EoS parameters on predictions for a variety of observables. The EoS parameters can be varied independently of each other and independently of assumptions regarding the in-medium nucleon effective mass. Here I present a pilot study of the neutron skin thickness (NST) in nuclei of current interest. The results indicate that variations of the symmetry energy slope parameter L by roughly 10 MeV and variations of the droplet-model counterpart of the curvature parameter Kτ by roughly 20 MeV affect predictions by comparable amounts. However, structural details may also have sizable effects on predictions, notably in the cases of 68Ni and 208Pb. This work is part of a systematic investigation of the NST within the KIDS framework and of a broader effort to constrain the density dependence of the nuclear symmetry energy.

Fast Neutrino Cooling in the Accreting Neutron Star MXB 1659-29

Modeling of crust heating and cooling across multiple accretion outbursts of the low mass X-ray binary MXB 1659-29 indicates that the neutrino luminosity of the neutron star core is consistent with direct Urca (dUrca) reactions occurring in ∼1% of the core volume. We investigate this scenario with neutron star models that include a detailed equation of state parametrized by the slope of the nuclear symmetry energy L, and a range of neutron and proton superfluid gaps. We find that the predicted neutron star mass depends sensitively on L and the assumed gaps. We discuss which combinations of superfluid gaps reproduce the inferred neutrino luminosity. Larger values of L ≳ 80 MeV require superfluidity to suppress dUrca reactions in low mass neutron stars, i.e., the proton or neutron gap is sufficiently strong and extends to high enough density. However, the largest gaps give masses near the maximum mass, making it difficult to accommodate colder neutron stars. The heat capacities of our models span the range from fully paired to fully unpaired nucleons meaning that long-term observations of core cooling could distinguish between models. As a route to solutions with a larger emitting volume, which could provide a more natural explanation for the inferred neutrino luminosity, we discuss the possibility of alternative, less efficient, fast cooling processes in exotic cores. To be consistent with the inferred neutrino luminosity, such processes must be within a factor of ∼1000 of dUrca. We discuss the impact of future constraints on neutron star mass, radius, and the density dependence of the symmetry energy.

Massive relativistic compact stars from SU(3) symmetric quark models

We construct a set of hyperonic equations of state (EoS) by assuming SU(3) symmetry within the baryon octet and by using a covariant density functional (CDF) theory approach. The low-density regions of our EoS are constrained by terrestrial experiments, while the high-density regime is modeled by systematically varying the nuclear matter skewness coefficient Qsat and the symmetry energy slope Lsym. The sensitivity of the EoS predictions is explored in terms of z parameter of the SU(3) symmetric model that modifies the meson-hyperon coupling constants away from their SU(6) symmetric values. Our results show that model EoS based on our approach can support static Tolman-Oppenheimer-Volkof (TOV) masses in the range 2.3-2.5M⊙ in the large-Qsat and small-z regime, however, such stars contain only a trace amount of hyperons compared to SU(6) models. We also construct uniformly rotating Keplerian configurations for our model EoS for which the masses of stellar sequences may reach up to 3.0M⊙. These results are used to explore the systematic dependence of the ratio of maximum masses of rotating and static stars, the lower bound on the rotational frequency of the models that will allow secondary masses in the gravitational waves events to be compact stars with M2≲3.0M⊙ and the strangeness fraction on the model parameters. We conclude that very massive stellar models can be, in principle, constructed within the SU(3) symmetric model, however, they are nucleonic-like as their strangeness fraction drops below 3%.

Hyperon bulk viscosity and r-modes of neutron stars

ABSTRACT We propose and apply a new parametrization of the modified chiral effective model to study rotating neutron stars with hyperon cores in the framework of the relativistic mean-field theory. The inclusion of mesonic cross couplings in the model has improved the density content of the symmetry energy slope parameters, which are in agreement with the findings from recent terrestrial experiments. The bulk viscosity of the hyperonic medium is analyzed to investigate its role in the suppression of gravitationally driven r-modes. The hyperonic bulk viscosity coefficient caused by non-leptonic weak interactions and the corresponding damping time-scales are calculated and the r-mode instability windows are obtained. The present model predicts a significant reduction of the unstable region due to a more effective damping of oscillations. We find that from ∼108 K to ∼109 K, hyperonic bulk viscosity completely suppresses the r-modes leading to a stable region between the instability windows. Our analysis indicates that the instability can reduce the angular velocity of the star up to ∼0.3 ΩK, where ΩK is the Kepler frequency of the star.

Unified neutron star EOSs and neutron star structures in RMF models

In the framework of the Thomas-Fermi approximation, we systematically study the EOSs and microscopic structures of neutron star matter in a vast density range with n b ≈ 10−10-2 fm−3, where various covariant density functionals are adopted, i.e., those with nonlinear self couplings (NL3, PK1, TM1, GM1, MTVTC) and density-dependent couplings (DD-LZ1, DDME-X, PKDD, DD-ME2, DD2, TW99). It is found that the EOSs generally coincide with each other at n b ≲ 10−4 fm−3 and 0.1 fm−3 ≲ n b ≲ 0.3 fm−3, while in other density regions they are sensitive to the effective interactions between nucleons. By adopting functionals with a larger slope of symmetry energy L, the curvature parameter K sym and neutron drip density generally increases, while the droplet size, proton number of nucleus, core-crust transition density, and onset density of non-spherical nuclei, decrease. All functionals predict neutron stars with maximum masses exceeding the two-solar-mass limit, while those of DD2, DD-LZ1, DD-ME2, and DDME-X predict optimum neutron star radii according to the observational constraints. Nevertheless, the corresponding skewness coefficients J are much larger than expected, while only the functionals MTVTC and TW99 meet the start-of-art constraints on J. More accurate measurements on the radius of PSR J0740 + 6620 and the maximum mass of neutron stars are thus essential to identify the functional that satisfies all constraints from nuclear physics and astrophysical observations. Approximate linear correlations between neutron stars’ radii at M = 1.4M ⊙ and 2M ⊙, the slope L and curvature parameter K sym of symmetry energy are observed as well, which are mainly attributed to the curvature-slope correlations in the functionals adopted here. The results presented here are applicable for investigations of the structures and evolutions of compact stars in a unified manner.

The Hadron-quark Crossover in Neutron Star within Gaussian Process Regression Method

The equations of state of the neutron star at the hadron-quark crossover region are interpolated with the Gaussian process regression (GPR) method, which can reduce the randomness of present interpolation schemes. The relativistic mean-field (RMF) model and Nambu–Jona-Lasinio (NJL) model are employed to describe the hadronic phase and quark phase, respectively. In the RMF model, the coupling term between ω and ρ mesons is considered to control the density-dependent behaviors of symmetry energy, i.e., the slope of symmetry energy L. Furthermore, the vector interaction between quarks is included in the NJL model to obtain the additional repulsive contributions. Their coupling strengths and the crossover windows are discussed in the present framework under the constraints on the neutron star from gravitational-wave detections, massive neutron star measurements, mass–radius simultaneous observation of the NICER Collaboration, and the neutron skin thickness of 208Pb from PREX-II. It is found that the slope of symmetry energy, L, should be around 50−90 MeV and the crossover window is (0.3, 0.6) fm−3 with these observables. Furthermore, the uncertainties of neutron star masses and radii in the hadron-quark crossover regions are also predicted by the GPR method.

Low Density Neutron Star Matter with Quantum Molecular Dynamics: The Role of Isovector Interactions

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.

Dark matter component in hadronic models with short-range correlations

A relativistic mean-field hadronic model with a dark matter (DM) particle coupled to nucleons including short-range correlations (SRC) is applied to study neutron stars (NS). The lightest neutralino is chosen as the dark particle candidate, which interacts with nucleons by the exchange of Higgs bosons. A detailed thermodynamical analysis shows that the contribution of the DM fermions to the energy density of the matter composed by these particles and nucleons is completely dominated by the DM kinetic terms. The model reproduces satisfactorily the constraints on the mass-radius diagram obtained from the analysis of the combined data from the NICER mission, LIGO collaboration, and mass measurements from radio observations. We show that the SRC balance the reduction of the neutron star mass due to the DM component, and because of that the model is able to present more massive NS. We also present a study of the effect, in the NS mass-radius profiles, of the uncertainties in some bulk parameters related to the hadronic sector. We find that it is possible to generate parametrizations, with DM content, compatible with the recent astrophysical constraints and with the uncertainty in the symmetry energy slope obtained from the results reported by the updated lead radius experiment (PREX-2).

Influence of the nuclear symmetry energy slope on observables of compact stars with Δ -admixed hypernuclear matter

In this work, we study the effects of the nuclear symmetry energy slope on the neutron star dense matter equation of state and its impact on neutron star observables (mass-radius, tidal response). We construct the equation of state within the framework of covariant density functional theory implementing coupling schemes of nonlinear and density-dependent models with viability of heavier non-nucleonic degrees of freedom. The slope of the symmetry energy parameter $({L}_{\text{sym}})$ is adjusted following the density dependence of isovector meson coupling to baryons. We find that smaller values of ${L}_{\text{sym}}$ at saturation favor early appearance of $\mathrm{\ensuremath{\Delta}}$ resonances in comparison to hyperons, leading to latter's threshold at higher matter densities. We also investigate the dependence of ${L}_{\text{sym}}$ on tidal deformability and the compactness parameter of a $1.4{M}_{\ensuremath{\bigodot}}$ neutron star for different equations of state and observe similar converging behavior for larger ${L}_{\text{sym}}$ values.

Relativistic hybrid stars in light of the NICER PSR J0740+6620 radius measurement

We explore the implications of the recent radius determination of PSR J0740+6620 by the NICER experiment combined with the neutron skin measurement by the PREX-II experiment and the associated inference of the slope of symmetry energy, for the structure of hybrid stars with a strong first-order phase transition from nucleonic to quark matter. We combine a covariant density-functional nucleonic equation of state (EOS) with a constant-speed-of-sound EOS for quark matter. We show that the radius and tidal deformability ranges obtained from GW170817 can be reconciled with the implication of the PREX-II experiment if there is a phase transition to quark matter in the low-mass compact star. In the high-mass segment, the EoS needs to be stiff to comply with the large-radius inference for PSR J0740+6620 and J0030+0451 with masses $M\simeq 2M_{\odot}$ and $M\simeq 1.4M_{\odot}$. We show that twin stars are not excluded, but the mass and radius ranges (with $M \geq M_\odot$) are restricted to narrow domains $\Delta M_{\rm twin} \lesssim 0.05 M_\odot$ and $\Delta R_{\rm twin} \sim 1.0$~km. We also show that the existence of twin configurations is compatible with the light companion in the GW190814 event being a hybrid star in the case of values of the sound-speed square $s=0.6$ and $s=1/3$.

Impact of the nuclear symmetry energy on the post-merger phase of a binary neutron star coalescence

The nuclear symmetry energy plays a key role in determining the equation of state of dense, neutron-rich matter, which governs the properties of both terrestrial nuclear matter as well as astrophysical neutron stars. A recent measurement of the neutron skin thickness from the PREX Collaboration has lead to new constraints on the slope of the nuclear symmetry energy, $L$, which can be directly compared to inferences from gravitational wave observations of the first binary neutron star merger inspiral, GW170817. In this paper, we explore a new regime for potentially constraining the slope, $L$, of the nuclear symmetry energy with future gravitational wave events: the post-merger phase of a binary neutron star coalescence. In particular, we go beyond the inspiral phase, where imprints of the slope parameter $L$ may be inferred from measurements of the tidal deformability, to consider imprints on the post-merger dynamics, gravitational wave emission, and dynamical mass ejection. To this end, we perform a set of targeted neutron star merger simulations in full general relativity using new finite-temperature equations of state, which systematically vary $L$ while keeping the magnitude of the symmetry energy at the saturation density, $S$, fixed. We find that the post-merger dynamics and gravitational wave emission are mostly insensitive to the slope of the nuclear symmetry energy. In contrast, we find that dynamical mass ejection contains a weak imprint of $L$, with large values of $L$ leading to systematically enhanced ejecta.

Information Content of the Parity-Violating Asymmetry in ^{208}Pb.

The parity-violating asymmetry A_{PV} in ^{208}Pb, recently measured by the PREX-2 Collaboration, is studied using modern relativistic (covariant) and nonrelativistic energy density functionals. We first assess the theoretical uncertainty on A_{PV} which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability α_{D} of ^{208}Pb. We then add the quantified value of A_{PV} together with α_{D} to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in ^{208}Pb r_{skin}=0.19±0.02 fm and the symmetry-energy slope L=54±8 MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the A_{PV} value in ^{48}Ca that will be soon available from the CREX measurement.

Influence of the treatment of initialization and mean-field potential on the neutron to proton yield ratios

In this work, we first investigate how to reproduce and how well one can reproduce the Woods-Saxon density distribution of initial nuclei in the framework of the improved quantum molecular dynamics model. Then, we propose a new treatment for the initialization of nuclei which is correlated with the nucleonic mean-field potential by using the same potential energy density functional. In the mean field potential, the three-body force term is accurately calculated. Based on the new version of the model, the influences of precise calculations of the three-body force term, the slope of symmetry energy, the neutron-proton effective mass splitting, and the width of the wave packet on heavy ion collision observables, such as the neutron to proton yield ratios for emitted free nucleons $[R(n/p)]$ and for coalescence invariant nucleons $[{R}_{ci}(n/p)]$ for $^{124}\mathrm{Sn}+^{112}\mathrm{Sn}$ at the beam energy of 200 MeV per nucleon, are discussed. Our calculations show that the spectra of neutron to proton yield ratios $[R(n/p)]$ can be used to probe the slope of symmetry energy ($L$) and the neutron-proton effective mass splitting. In detail, the $R(n/p)$ in the low kinetic energy region can be used to probe the slope of symmetry energy ($L$). With a given $L$, the inclination of $R(n/p)$ to kinetic energy (${E}_{k}$) can be used to probe the effective mass splitting. In the case where the neutron-proton effective mass splitting is fixed, $R(n/p)$ at high kinetic energy can also be used to learn the symmetry energy at suprasaturation density.

Effect of the symmetry energy on the secondary component of GW190814 as a neutron star

The secondary component of GW190814 with a mass of 2.50-2.67 $M_{\odot}$ may be the lightest black hole or the heaviest neutron star ever observed in a binary compact object system. To explore the possible equation of state (EOS), which can support such massive neutron star, we apply the relativistic mean-field model with a density-dependent isovector coupling constant to describe the neutron-star matter. The acceptable EOS should satisfy some constraints: the EOS model can provide a satisfactory description of the nuclei; the maximum mass $M_\textrm{TOV}$ is above 2.6 $M_{\odot}$; the tidal deformability of a canonical 1.4 $M_{\odot}$ neutron star $\Lambda_{1.4}$ should lie in the constrained range from GW170817. In this paper, we find that the nuclear symmetry energy and its density dependence play a crucial role in determining the EOS of neutron-star matter. The constraints from the mass of 2.6 $M_{\odot}$ and the tidal deformability $\Lambda_{1.4}=616_{-158}^{+273}$ (based on the assumption that GW190814 is a neutron star-black hole binary) can be satisfied as the slope of symmetry energy $L \leq 50$ MeV. Even including the constraint of $\Lambda_{1.4}=190_{-120}^{+390}$ from GW170817 which suppresses the EOS stiffness at low density, the possibility that the secondary component of GW190814 is a massive neutron star cannot be excluded in this study.

Crust-core transition and dynamical instabilities in neutron stars for model with point-coupling interactions * *Supported by Changsha Municipal Natural Science Foundation (kq2007004) and the construct program of the key discipline in Hunan province

We explore the effects of the density dependence of symmetry energy on the crust-core phase transition and dynamical instabilities in cold and warm neutron stars in the relativistic mean field (RMF) theory with point-coupling interactions using the Vlasov approach. The role of neutrino trapping is also considered. The crust-core transition density and pressure, distillation effect, and cluster size and growth rates are discussed. The present work shows that the slope of symmetry energy at saturation, temperature, and neutrino trapping have non-negligible effects.

Nuclear pasta structures and symmetry energy

In the framework of the relativistic mean field model with Thomas-Fermi approximation, we study the structures of low density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $\beta$-equilibration. It is found that the properties of droplets/bubbles are similar in body-centered cubic (BCC) and face-centered cubic (FCC) lattices, where the FCC lattice generally becomes more stable than BCC lattice as density increases. For the rod/tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $\omega$-$\rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L = 41.34$ MeV, which predicts larger onset densities for core-crust transition and non-spherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.

Effect of inner crust EoS on neutron star properties

The neutron star maximum mass and the radius are investigated within the framework of the relativistic mean-field (RMF) model. The variation in the radius at the canonical mass, R1.4, using different inner crust equation of state (EoS) with different symmetry energy slope parameter is studied. It is found that although the NS maximum mass and the corresponding radius do not vary much with different inner crust EoSs, the radius and the tidal deformability at 1.4M⊙ vary with the different choice of crust EoS and variation of about 1-2 km is seen in the radius at the canonical mass. For non-unified EoSs, the crust with a low symmetry energy slope parameter produces a low NS radius at the canonical mass. The properties of maximally rotating neutron stars are also studied. The variation in the radius of rotating star at the canonical mass 1.4M⊙ is also seen with the slope parameter. Similar to the static neutron star, the radius at 1.4M⊙ of rotating neutron star is affected by slope parameter of the inner crust. Other important quantities like moment of inertia, frequency, rotational kinetic energy to gravitational energy ratio are also calculated. The variation in these quantities with the crust slope parameter is found to be more proportional to the mass and the radius of NS.