Investigating isovector properties of finite nuclei through neutron stars

The nuclear symmetry energy plays a crucial role in the structure of finite nuclei and the bulk properties of neutron stars. However, its values at high densities are highly uncertain, and the corresponding experimental data have large errors. One way to determine or at least estimate these high-density values is through neutron star observations. Recently, observations of gravitational waves from binary neutron star mergers have provided useful information on their radius and tidal deformability, which are directly related to the symmetry energy. This work attempts to use recent observations to constrain the structure of finite nuclei. Specifically, we parameterize the equation of state (EoS) describing asymmetric and symmetric nuclear matter using the parameter η = (K0L2)1/3, where K0 is the incompressibility and L is the slope parameter, The parameter η regulates the stiffness of the EoS, and we expect its values to affect both finite nuclei and neutron star properties, especially given the important role of isovector interactions. It is natural to expect that constraints on η for finite nuclei will also imply constraints on neutron star properties and vice versa. In light of the above, we propose a simple yet self-consistent method to simultaneously examine the effects of η on the properties of finite nuclei and neutron stars. We found constraints on these systems by combining recent experimental data (PREX-2) and observational data from the LIGO and Virgo detectors.

The secondary component of the GW190814 event left us with a question, “whether it is a supermassive neutron star or lightest black-hole?” Recently, Fattoyev et al. obtained an energy density functional (EDF) named as BigApple, which reproduces the mass of the neutron star is 2.60 [Formula: see text] which is well consistent with GW190814 data. This study explores the properties of finite nuclei, nuclear matter and neutron stars by using the BigApple EDF along with four well-known relativistic mean-field forces, namely NL3, G3, IOPB-I and FSUGarnet. The finite nuclei properties like binding energy per particle, skin thickness, charge radius, single-particle energy, and two-neutron separation energy are well predicted by the BigApple for a series of nuclei. The calculated nuclear matter quantities, such as incompressibility, symmetry energy and slope parameters at saturation density, are consistent with the empirical or experimental values where ever available. The predicted canonical tidal deformability by the BigApple parameter set is well-matched with the GW190814 data. Also, the dimensionless moment of inertia lies in the range given by the analysis of PSR J0737-3039A.

Re-visiting the role of short-range correlations on neutron-star properties

The effects of \ensuremath{\omega} meson self-coupling (OMSC) on the properties of finite nuclei and neutron stars are investigated within the framework of an effective field theory based relativistic mean-field (ERMF) model that includes the contributions from all possible mixed interactions between the scalar-isoscalar (\ensuremath{\sigma}), vector-isoscalar (\ensuremath{\omega}), and vector-isovector (\ensuremath{\rho}) mesons up to the quartic order. For a realistic investigation, several parameter sets corresponding to different values of OMSC are generated by adjusting the remaining parameters of the ERMF model to fit the properties of the finite nuclei. Though all these parameter sets give equally good fit to the properties of the finite nuclei, only moderate values of OMSC are favored from the ``naturalness'' point of view. The equations of state for the symmetric nuclear and pure neutron matters resulting from the parameter sets, with the moderate values of OMSC are in close agreement with the ones obtained within the Dirac-Brueckner-Hartree-Fock approximation. For such parameter sets, the limiting mass for the neutron stars composed of \ensuremath{\beta}-stable matter is $~1.9\phantom{\rule{0.3em}{0ex}}{M}_{\ensuremath{\bigodot}}$. It is found that the direct Urca process can occur in the neutron stars with ``canonical'' mass of $1.4\phantom{\rule{0.3em}{0ex}}{M}_{\ensuremath{\bigodot}}$ only for the moderate and higher values of OMSC. Some other interesting properties for the neutron stars are also discussed.

In this paper, the properties of the symmetry energy in asymmetric nuclear matter, including the quadratic and quartic symmetry energies as well as their density slopes at the saturation density, are studied by the radioactivity of unstable nuclei. The symmetry energy was initially introduced as a quantum correction energy in the Weizsacker-Bethe liquid-drop model, which was proposed to describe the binding energies of finite nuclei. In order to systematically study the properties of the symmetry energy, the concept of the nuclear matter was introduced, which consists of neutrons and protons with finite neutron and proton densities but infinite neutron and proton numbers. By comparing the properties of the isospin symmetric nuclear matter, in which the neutron density is equal to the proton density, and those of the isospin asymmetric nuclear matter, in which the two densities are unequal, the symmetry energy is found to approximately represent the difference of the energy per nucleon in them. That is to say, the symmetry energy is an evaluation of the energy cost to convert protons in symmetric nuclear matter to neutrons in asymmetric nuclear matter. Since the symmetry energy characterizes the isospin asymmetric effect in nuclear matter, it plays critical roles in not only nuclear physics but also astrophysics. For example, the symmetry energy is closely related to the nuclear masses, the structures and properties of nuclei far away from stability line and near drip lines, the mechanism of heavy-ion reactions, the structures and component of neutron stars, the masses and radii of neutron stars, the cooling process of neutron stars, and so on. Besides of the quadratic symmetry energy, the quartic symmetry energy can have obvious effects on the properties of neutron stars as well. The quartic symmetry energy can significantly affect both the proton fraction in β-stable neutron stars and the critical density for the direct Urca process, which leads to faster cooling of neutron stars. In addition, the quartic symmetry energy is found to be very important for the location of the inner edge of crusts and the core-crust transition density and pressure in neutron stars. So the quartic symmetry energy can also have an influence on the structure of neutron stars. Because of the very important roles of the symmetry energy playing in not only nuclear physics but also astrophysics, it is of great significance to study the properties of both the quadratic and quartic symmetry energies. Based on the fundamental Hugenholtz-Van Hove (HVH) theorem, the properties of the symmetry energy are found to be closely related to the isoscalar and the isovector parts of the nucleon single-particle potentials, where the latter two parts can be extracted from the nuclear radioactivity. So by linking both the symmetry energy and the nuclear radioactivity to the nucleon single-particle potentials, the symmetry energy can be directly studied by nuclear radioactivity. In this paper, both the heavy-cluster radioactivity and the proton radioactivity are employed to constrain the properties of not only the quadratic symmetry energy but also the quartic symmetry energy. Besides, the effect of both the spectroscopic factor of proton radioactivity and the deformation in the daughter nucleus on the extracted results are also discussed, which are subsequently found to be very limited.

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic interaction NL-RS which provides an opportunity to readjust the coupling constants keeping in view the properties of finite nuclei, nuclear matter, PREX-II results for neutron skin thickness in 208Pb and astrophysical observations. The NL-RS model interaction has been proposed by fitting the ground state properties (binding energies and charge radii) of finite nuclei, bulk nuclear matter properties, and PREX-II results for neutron skin thickness of 208Pb. The relativistic interaction has been generated by including nonlinear self-interactions of σ and ω μ -mesons and mixed interactions of ω μ , and ρ μ -meson up to the quartic order. The proposed interaction harmonizes with the finite nuclei, bulk nuclear matter, and neutron star properties. A covariance analysis is performed to assess the statistical uncertainties on the model parameters and nuclear observables of interest along with correlations amongst them. The equation of state (EoS) composed of nucleons and leptons in β-equilibrium is computed with the proposed parameter set and used to study the neutron star structure. The maximum mass of the neutron star by employing the EoS computed with the NL-RS parameter set is 2.04 ± 0.03M ⊙ and the radius of a canonical mass neutron star (R 1.4) comes out to be equal to 13.06 ± 0.16 Km. The value of dimensionless tidal deformability, for canonical mass, is 602.23 ± 33.13 which satisfies the constraints of waveform models analysis of GW170817 within 90% confidence level.

The effects of the isovector-scalar $\delta$-meson field on the properties of finite nuclei, infinite nuclear matter and neutron stars are investigated within the Relativistic Mean Field (RMF) model which includes non-linear couplings. Several parameter sets (SRV's) are generated to asses the influence of $\delta$-meson on the properties of neutron star. These parametrizations correspond to different values of coupling constant of $\delta$-meson to the nucleons with remaining ones calibrated to yield finite nuclei and infinite nuclear matter properties consistent with the available experimental data. It is observed that to fit the properties of finite nuclei and infinite nuclear matter, a stronger coupling between isovector-vector $\rho$ meson and nucleons is required in the presence of $\delta$ field. Furthermore, the $\delta$-meson is found to affect the radius of canonical neutron star significantly. The value of dimensionless tidal deformability, ${\Lambda}$ for the canonical neutron star also satisfies the constraints from the waveform models analysis of GW170817 binary neutron star merger event. A covariance analysis is performed to estimate the statistical uncertainties of the model parameters as well as correlations among the model parameters and different observables of interest.

Extending the relativistic mean field (RMF) models either with higher order couplings or with density-dependent couplings has been proven to be successful in explaining several properties of finite nuclei, infinite matter, and neutron stars (NSs) in a unified way. Here, we compare how these two extensions fare while explaining NSs with and without antikaons. Both these extensions soften the equation of state (EoS), but the higher order couplings are more efficient in doing so. Even for a very soft EoS, we find that there is a strong possibility of antikaons being condensed. We find an exception for correlation between NS radius and density dependence of symmetry energy, which gets restored when we introduce antikaons. The implication of a precisely measured 2${M}_{\ensuremath{\bigodot}}$ NS on our results is discussed with four sets of interactions which cover all four combinations of stiff and soft symmetry energy and equations of state.

The impacts of various symmetry energy parameters on the properties of neutron stars (NSs) have been recently investigated, and the outcomes are at variance, as summarized in Table III of Phys. Rev. D 106, 063005 (2022). We have systematically analyzed the correlations of slope and curvature parameters of symmetry energy at the saturation density ($\rho_0=0.16 \text{fm}^{-3}$) with the tidal deformability and stellar radius of non-spinning neutron stars in the mass range of $1.2 - 1.6 M_\odot$ using a large set of minimally constrained equations of state (EoSs). The EoSs at low densities correspond to the nucleonic matter and are constrained by empirical ranges of a few low-order nuclear matter parameters from the finite nuclei data and the pure neutron matter EoS from chiral effective field theory. The EoSs at high densities ($\rho > 1.5 - 2\rho_0$) are obtained by a parametric form for the speed of sound that satisfies the causality condition. Several factors affecting the correlations between the NS properties and the individual symmetry energy parameters usually encountered in the literature are considered. These correlations are quite sensitive to the choice of the distributions of symmetry energy parameters and their interdependence. But, variations of NS properties with the pressure of $\beta -$ equilibrated matter at twice the saturation density remain quite robust which maybe due to the fact that the pressure depends on the combination of multiple nuclear matter parameters that describe the symmetric nuclear matter as well as the density dependence of the symmetry energy. Our results are practically insensitive to the behavior of EoS at high densities.

Neutron stars are born when massive stars run out of their nuclear fuel and undergo gravitational collapse. Neutron stars belong to the most compact objects in the observable Universe. Macroscopic properties of neutron stars like their masses and radii are sensitive to the microscopic properties of the nuclear equation of state of dense matter. The equation of state is determined by the strong interaction among the constituents. The underlying theory is quantum chromodynamics that is, however, highly non-perturbative in the physics regime relevant for neutron stars. Moreover, neutron stars provide an interplay between nuclear physics and astrophysics. Astrophysical observations like the detection of 2 solar mass neutron stars have a major impact on the equation of state. Radii are, however, inherently difficult to measure due to systematic uncertainties. Other observables like the moment of inertia or the tidal deformability present promising alternatives. The double neutron star system PSR J0737-3039 constitutes an outstanding system as it provides the prospect of a moment of inertia measurement for the first time. A new era stated with the pioneering observation of gravitational waves from a binary neutron star merger. The analysis of the gravitational wave signal of GW170817 provides a range for the tidal deformability of typical neutron stars. Moreover, the current NICER mission will provide simultaneous mass-radius measurements. In this thesis, we use state-of-the-art chiral effective field theory interactions to describe the equation of state at nuclear densities. In the high-density regime beyond nuclear saturation density, we use different extrapolation approaches. First, we utilize the established ansatz of piecewise polytropic equations of state which provides a direct parametrization. However, piecewise polytropic equations of state possess unphysical behavior such as discontinuities in the speed of sound. Second, we use a physically motivated parametrization of the speed of sound inside the neutron star from which we derive the equation of state. Both methods allow us to probe the equation of state over a large range of densities. We further impose general constraints on the equation of state such as the requirement of causality at all densities and the support of at least 2 solar mass neutron stars. From the equations of state compatible with the constraints, we determine diverse neutron star observables. We begin with non-rotating neutron stars and focus on their masses and radii. We study correlations among properties of the equation of state at nuclear densities and observables of typical neutron stars. Moreover, we explore the impact of hypothetical, simultaneous measurements of masses and radii of neutron stars on the equation of state. Applying both simple compatibility cuts and the framework of Bayesian statistics, we investigate the sensitivity of the inference on the chosen parametrization of the equation of state. We extend then our considerations to slowly rotating neutron stars and study the moment of inertia. Assuming hypothetical moment of inertia measurements, we determine constraints for the radius of neutron stars and thus the equation of state. In addition, we extend our considerations of isolated neutron stars to binary neutron star systems. In particular, we treat the tidal field of the companion as a small perturbation. This allows us to determine the tidal deformability. By applying higher orders in the metric perturbation, we calculate the quadrupole moment of neutron stars. Although the structure of neutron stars is sensitive to the equation of state, relations between the moment of inertia, the tidal deformability, and the quadrupole moment are remarkably insensitive. We investigate the properties of neutron stars in binary systems and ultimately confront the results of our models with the gravitational wave constraints from a binary neutron star merger.

We address the question of the role of low-energy nuclear physics data in constraining neutron star global properties, e.g., masses, radii, angular momentum, and tidal deformability, in the absence of a phase transition in dense matter. To do so, we assess the capacity of 415 relativistic mean field and nonrelativistic Skyrme-type interactions to reproduce the ground state binding energies, the charge radii, and the giant monopole resonances of a set of spherical nuclei. The interactions are classified according to their ability to describe these characteristics, and we show that a tight correlation between the symmetry energy and its slope is obtained provided that $N=Z$ and $N\ensuremath{\ne}Z$ nuclei are described with the same accuracy (mainly driven by the charge radius data). By additionally imposing the constraints from isobaric analog states and neutron skin radius in $^{208}\mathrm{Pb}$, we obtain the following estimates: ${E}_{\mathrm{sym},2}=31.8\ifmmode\pm\else\textpm\fi{}0.7$ MeV and ${L}_{\mathrm{sym},2}=58.1\ifmmode\pm\else\textpm\fi{}9.0$ MeV. We then analyze predictions of neutron star properties and we find that the $1.4{M}_{\ensuremath{\bigodot}}$ neutron star (NS) radius lies between 12 and 14 km for the ``better'' nuclear interactions. We show that (i) the better reproduction of low-energy nuclear physics data by the nuclear models only weakly impacts the global properties of canonical mass neutron stars and (ii) the experimental constraint on the symmetry energy is the most effective one for reducing the uncertainties in NS matter. However, since the density region where constraints are required are well above densities in finite nuclei, the largest uncertainty originates from the density dependence of the energy density functional (EDF), which remains largely unknown.

The radii and tidal deformabilities of neutron stars are investigated in the framework of the relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, $\omega$ meson and $\rho$ meson coupling terms are included in a popular RMF Lagrangian, i.e., the TM1 parameter set, which is adopted for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector–isovector meson, $\rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii in the intermediate-mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number, which is related to the quadrupole deformation of the star in a static external tidal field and can be extracted from the observation of a gravitational wave generated by a binary star merger. We find that its value at $1.4 \mathrm{M}_\odot$ has a linear correlation to the slope of symmetry energy, unlike that previously studied. With the latest constraints of tidal deformabilities from the GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of a lower symmetry energy slope for the updated supernova EoS, which is applicable to simulations of neutron star mergers. Furthermore, an analogous analysis is also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 \mathrm{M}_\odot$ have very similar linear relations in these RMF models.

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system [R. Abbott et al., ApJ Lett., 896, L44 (2020)]? This is the central question animating this letter. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (a) account for a 2.6 Msun neutron star, (b) satisfy the original constraint on the tidal deformability of a 1.4 Msun neutron star, and (c) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support super-massive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Thus, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 Msun compact object is likely to be the lightest black hole ever discovered.

The main goal of the present contribution is a pedagogical introduction to the fascinating world of neutron stars by relying on relativistic density functional theory. Density functional theory provides a powerful--and perhaps unique--framework for the calculation of both the properties of finite nuclei and neutron stars. Given the enormous densities that may be reached in the core of neutron stars, it is essential that such theoretical framework incorporates from the outset the basic principles of Lorentz covariance and special relativity. After a brief historical perspective, we present the necessary details required to compute the equation of state of dense, neutron-rich matter. As the equation of state is all that is needed to compute the structure of neutron stars, we discuss how nuclear physics--particularly certain kind of laboratory experiments--can provide significant constrains on the behavior of neutron-rich matter.

Significant progress has been made in recent years in constraining nuclear symmetry energy at and below the saturation density of nuclear matter using data from both terrestrial nuclear experiments and astrophysical observations. However, many interesting questions remain to be studied especially at supra-saturation densities. In this lecture note, after a brief summary of the currently available constraints on nuclear symmetry energy near the saturation density we first discuss the relationship between the symmetry energy and the isopin and momentum dependence of the single-nucleon potential in isospin-asymmetric nuclear medium. We then discuss several open issues regarding effects of the tensor force induced neutron-proton short-range correlation (SRC) on nuclear symmetry energy. Finally, as an example of the impacts of nuclear symmetry energy on properties of neutron stars and gravitational waves, we illustrate effects of the high-density symmetry energy on the tidal polarizability of neutron stars in coalescing binaries.