Nuclear Matter Equation Of State Research Articles

Effects of quantum statistics near the critical point of nuclear matter

Effects of quantum statistics for nuclear matter equation of state are analyzed in terms of the recently proposed quantum van der Waals model. The system pressure is expanded over a small parameter $\delta \propto n(mT)^{-3/2}[g(1-bn)]^{-1}$, where $n$ and $T$ are, respectively, the particle number density and temperature, $m$ and $g$ the particle mass and degeneracy factor. The parameter $b$ corresponds to the van der Waals excluded volume. The corrections due to quantum statistics for the critical point values of $T_c$, $n_c$, and the critical pressure $P_c$ are found within the linear and quadratic orders over $\delta $. These approximate analytical results appear to be in a good agreement with exact numerical calculations in the quantum van der Waals model for interacting Fermi particles: the symmetric nuclear matter ($g=4$) and the pure neutron matter ($g=2$). They can be also applied to the system of interacting Bose particles like the matter composed of $\alpha$ nuclei.

Interpretation of the anomaly in the diffuseness parameter of the Woods–Saxon potential for light fusion reactions using the effects of nuclear matter equation of state

The present study has been aimed at understanding the role of nuclear matter (NM) incompressibility effects on the description of the problem of the abnormally large diffuseness parameter of the Woods–Saxon (WS) potential for the fusion reactions induced by the light-mass nuclei. In order to assess this aim, we simulate theoretically the saturation properties of NM within the framework of the double-folding (DF) model for a total of 26 colliding systems with condition 64 ≤ Z1Z2≤ 204 for charge product of their participant nuclei. It is shown that the DF model supplemented with the effects of nuclear matter equation of state (EOS) provides an appropriate description for measured fusion cross sections of our selected systems at around and above barrier energies. We find that the diffuseness parameters of the equivalent WS potential fitted to the DF model in the fusion barrier region are ranging from 0.62 to 0.71 fm, whereas this range is increased to aWS=0.66−0.81 fm after modeling the incompressibility effects. Our results show that the extracted values of the diffuseness parameter based on the modified form of the DF model follow an increasing trend with the charge product Z1Z2. We also present for the first time a discussion on a decreasing linear dependence of the diffuseness parameter of the nucleus–nucleus potential on the nuclear incompressibility constant K.

Cold dilute nuclear matter with α -particle condensation in a generalized nonlinear relativistic mean-field model

We explore the thermodynamic properties of homogeneous cold (zero-temperature) nuclear matter including nucleons and $\alpha$-particle condensation at low densities by using a generalized nonlinear relativistic mean-field (gNL-RMF) model. In the gNL-RMF model, the $\alpha$-particle is included as explicit degree of freedom and treated as point-like particle with its interaction described by meson exchanges and the in-medium effects on the $\alpha$ binding energy is described by density- and temperature-dependent energy shift with the parameters obtained by fitting the experimental Mott density. We find that below the dropping density $n_{\rm{drop}}$ ($\sim 3\times 10^{-3}$ fm$^{-3}$), the zero-temperature symmetric nuclear matter is in the state of pure Bose-Einstein condensate (BEC) of $\alpha$ particles while the neutron-rich nuclear matter is composed of $\alpha$-BEC and neutrons. Above the $n_{\rm{drop}}$, the fraction of $\alpha$-BEC decreases with density and vanishes at the transition density $n_t$ ($\sim 8\times 10^{-3}$ fm$^{-3}$). Above the $n_t$, the nuclear matter becomes pure nucleonic matter. Our results indicate that the empirical parabolic law for the isospin asymmetry dependence of nuclear matter equation of state is heavily violated by the $\alpha$-particle condensation in the zero-temperature dilute nuclear matter, making the conventional definition of the symmetry energy meaningless. We investigate the symmetry energy defined under parabolic approximation for the zero-temperature dilute nuclear matter with $\alpha$-particle condensation, and find it is significantly enhanced compared to the case without clusters and becomes saturated at about $7$ MeV at very low densities ($\lesssim 10^{-3}$ fm$^{-3}$). The critical temperature for $\alpha$-condensation in homogeneous dilute nuclear matter is also discussed.

On Relation between Bulk, Surface and Curvature Parts of Nuclear Binding Energy within the Model of Hexagonal Clusters

Using the model of hexagonal clusters we express the surface, curvature and Gauss curvature coefficients of the nuclear binding energy in terms of its bulk coefficient. Using the derived values of these coefficients and a single fitting parameter we are able to reasonably well describe the experimental binding energies of nuclei with more than 100 nucleons. To improve the description of lighter nuclei we introduce the same correction for all the coefficients. In this way we determine the apparent values of the surface, curvature and Gauss curvature coefficients which may be used for infinite nuclear matter equation of state. This simple model allows us to fix the temperature dependence of all these coefficients, if the temperature dependence for the bulk term is known. The found estimates for critical temperature are well consistent both with experimental and with theoretical findings.

Finite-temperature equations of state for neutron star mergers

The detection of gravitational waves from a neutron star merger has opened up the possibility of detecting the presence or creation of deconfined quark matter using the gravitational wave signal. To investigate this possibility, we construct a family of neutron star matter equations of state at nonzero density and temperature by combining state-of-the-art nuclear matter equations of state with holographic equations of state for strongly interacting quark matter. The emerging picture consistently points toward a strong first order deconfinement transition, with a temperature-dependent critical density and latent heat that we quantitatively examine. Recent neutron star mass measurements are further used to discriminate between the different equations of state obtained, leaving a tightly constrained family of preferred equations of state.

Accretion-induced Collapse of Dark Matter Admixed White Dwarfs. II. Rotation and Gravitational-wave Signals

Abstract We present axisymmetric hydrodynamical simulations of accretion-induced collapse (AIC) of dark matter (DM) admixed rotating white dwarfs (WD) and their burst gravitational-wave (GW) signals. For initial WD models with the same central baryon density, the admixed DM is found to delay the plunge and bounce phases of AIC, and decrease the central density and mass of the protoneutron star (PNS) produced. The bounce time, central density, and PNS mass generally depend on two parameters, the admixed DM mass M DM and the ratio between the rotational kinetic and gravitational energies of the inner core at bounce . The emitted GWs have generic waveform shapes and the variation of their amplitudes h + show a degeneracy on and M DM. We found that the ratios between the GW amplitude peaks around bounce allow breaking of the degeneracy and extraction of both and M DM. Even within the uncertainties of the nuclear matter equation of state, a DM core can be inferred if its mass is greater than 0.03 M ⊙. We also discuss possible DM effects on the GW signals emitted by PNS g-mode oscillations. GWs may boost the possibility for the detection of AIC, as well as open a new window into the indirect detection of DM.

Nuclear physics aspects of the GW170817 neutron star merger event

The detection of the GW170817 neutron star merger event by the Advanced LIGO and Virgo collaborations has stimulated an intense research activity regarding novel aspects of nuclear physics, which may play an essential role in the understanding of the merger dynamics. Among those, one of the most relevant regards the nuclear-matter equation of state. The analysis of the gravitational wave signal has shown that the upper limit on the average tidal deformability rules out very stiff equations of state, whereas a lower limit can be extracted from the analysis of the kilonova AT2017gfo signal. Those limits translate into an allowed range for the radius R1.5 of a 1.5 solar mass neutron star, 11.8 km ≲ R1.5 ≲ 13.1 km. On the other hand, radii significantly smaller than 12 km have been suggested by X-ray observations. This clash can be solved if the event GW170817/AT2017gfo would originate from the merger of a hadronic star and a star containing quark matter, as in the two-families and in the twin-stars scenarios.

Neutron stars in general relativity and scalar-tensor theory of gravity

The masses and radii of neutron stars are discussed in general relativity and scalar-tensor theory of gravity and the differences are compared with the current uncertainties stemming from the nuclear equation of state in the relativistic mean-field framework. It is shown that astrophysical and gravitational wave observations of radii of neutron stars with masses M lesssim 1.4 M_{odot } constrain only the nuclear equation of state, and in particular the density dependence of the nuclear symmetry energy. Future observations of massive neutron stars may constrain the coupling parameters of the scalar-tensor theory provided that a general consensus on the dense nuclear matter equation of state is reached.

The fourth-order symmetry energy of nuclear matter and symmetry energy coefficients of finite nuclei using extended semi-empirical mass formula

An extended nuclear mass formula has been used by considering the bulk, surface and coulomb contributions to the nuclear mass. In this mass formula, the fourth-order symmetry energy coefficient [Formula: see text] of finite nuclei and fourth-order symmetry energy [Formula: see text] of nuclear matter (NM) are related explicitly to the characteristic parameters of NM equation of state (EOS) using finite range effective interaction. The calculations are carried out with Yukawa form of exchange interaction having the same range but with different strengths for interaction between like and unlike nucleon. In this extended mass formula, by approximating [Formula: see text] to a constant [Formula: see text] an explicit relation between [Formula: see text] and fourth-order symmetry energy [Formula: see text] is obtained, which provides the possibility to extract information on [Formula: see text].

Hard-Core Radius of Nucleons within the Induced Surface Tension Approach

We review the recent approach to model the hadronic and nuclear matter equations of state using the induced surface tension concept, which allows one to go far beyond the usual Van der Waals approximation. Since the obtained equations of state, classical and quantum, are among the most successful ones in describing the properties of low density phases of strongly interacting matter, they set strong restrictions on the possible value of the hard-core radius of nucleons, which is widely used in phenomenological equations of state. We summarize the latest results obtained within this novel approach and perform a new detailed analysis of the hard-core radius of nucleons, which follows from hadronic and nuclear matter properties. Such an analysis allows us to find the most trustworthy range of its values: the hard-core radius of nucleons is 0.3–0.36 fm. A comparison with the phenomenology of neutron stars implies that the hard-core radius of nucleons has to be temperature and density dependent. Such a finding is supported when the eigenvolume of composite particles like hadrons originates from their fermionic substructure due to the Pauli blocking effect.

Tidal Love numbers of neutron stars in f(R) gravity

The recent detection of gravitational waves from a neutron star merger was a significant step towards constraining the nuclear matter equation of state by using the tidal Love numbers (TLNs) of the merging neutron stars. Measuring or constraining the neutron star TLNs allows us in principle to exclude or constraint many equations of state. This approach, however, has the drawback that many modified theories of gravity could produce deviations from General Relativity similar to the deviations coming from the uncertainties in the equation of state. The first and the most natural step in resolving the mentioned problem is to quantify the effects on the TLNs from the modifications of General Relativity. With this motivation in mind, in the present paper we calculate the TLNs of (non-rotating) neutron stars in R^2-gravity. More precisely, by solving numerically the perturbation equations, we calculate explicitly the polar and the axial l=2 TLNs for three characteristic realistic equations of state and compare the results to General Relativity. Our results show that while the polar TLNs are slightly influenced by the R^2 modification of General Relativity, the axial TLNs can be several times larger (in terms of the absolute value) compared to the general relativistic case.

GW170817: Constraining the nuclear matter equation of state from the neutron star tidal deformability

Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $\sim 2 ~ {\rm M}_\odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest that a precise value of the tidal deformability can put tight bounds on several EoS parameters, in particular, on the slope of the incompressibility and the curvature of the symmetry energy. The tidal deformability obtained from the GW170817 and its UV/optical/infrared counterpart sets the radius of a canonical $1.4~ {\rm M}_{\odot}$ neutron star to be $11.82\leqslant R_{1.4}\leqslant13.72$ km.

Universal Relations for Innermost Stable Circular Orbits around Rapidly Rotating Neutron Stars

Abstract We study the innermost stable circular orbit (ISCO) of a test particle around rapidly rotating neutron stars. Based on 12 different nuclear-matter equations of state (EOS), we find numerically two approximately EOS-insensitive universal relations that connect the radius and orbital frequency of the ISCO to the spin frequency f and mass M of rotating neutron stars. The relations are EOS-insensitive to about the 2% level for a large range of Mf. We also find that the universal relation for the ISCO radius agrees with the corresponding relation for the Kerr black hole to within 6% up to Mf = 5000 M ⊙ Hz. Our relations can be applied to accreting neutron stars in low-mass X-ray binaries. Using the spin frequency f = 414 Hz and the highest kilohertz quasi-periodic oscillations (kHz QPOs) at 1220 Hz observed in the system 4U 0614+09, we determine the mass of the neutron star to be 2.0 M ⊙. Our conclusion only makes a minimal assumption that the highest kHz QPO frequency is the ISCO frequency, bypassing the assumption of slow rotation and the uncertainty related to the dimensionless spin parameter, which are commonly required in the literature.

Influence of the nuclear matter equation of state on the r-mode instability using the finite-range simple effective interaction

The characteristic physical properties of rotating neutron stars under the r-mode oscillation are evaluated using the finite-range simple effective interaction. Emphasis is given on examining the influence of the stiffness of both the symmetric and asymmetric parts of the nuclear equation of state on these properties. The amplitude of the r-mode at saturation is calculated using the data of particular neutron stars from the considerations of ‘spin equilibrium’ and ‘thermal equilibrium’. The upper limit of the r-mode saturation amplitude is found to lie in the range 10−8–10−6, in agreement with the predictions of earlier work.

Effects of the nucleon radius on neutron stars in a quark mean field model

We study the effects of free space nucleon radius on nuclear matter and neutron stars within the framework of quark mean field model. The nucleon radius is treated self-consistently with this model, where quark confinement is adjusted to fit different values of nucleon radius. Corrections due to center-of-mass motion, quark-pion coupling, and one gluon exchange are included to obtain the nucleon mass in vacuum. The meson coupling constants that describe the behavior of many-body nucleonic system are newly-constructed by reproducing the empirical saturation properties of nuclear matter, including the recent determinations of symmetry energy parameters. Our results show that the nucleon radius in free space have negligible effects on nuclear matter equation of state and neutron star mass-radius relations, which is different from the conclusion drawn in previous studies. We further explore that the sensitivity of star radius on the nucleon radius found in earlier publications is actually from the symmetry energy and its slope.

Classifications of twin star solutions for a constant speed of sound parameterized equation of state

We explore the possible mass radius relation of compact stars for the equation of states with a first order phase transition. The low density matter is described by a nuclear matter equation of state resulting from fits to nuclear properties. A constant speed of sound parametrization is used to describe the high density matter phase with the speed of sound $c_s^2=1$. A classification scheme of four distinct categories including twin star solutions, i. e. solutions with the same mass but differing radii, is found which are compatible with the $M \ge 2M_\odot$ pulsar mass constraint. We show the dependence of the mass and radius differences on the transition parameters and delineate that higher twin star masses are more likely to be accompanied by large radius differences. These massive twin stars are generated by high values of the discontinuity in the energy density and the lowest possible values of the transition pressure that still result in masses of $M \geq 2M_\odot$ at the maximum of the hadronic branch.

Thomas–Fermi approximation for the equation of state of nuclear matter: A semi-classical approach from the Landau Fermi-Liquid theory

The equation of state (EOS) of nuclear matter is investigated in a semi-classical mean-field (MF) approach. Starting from the phase-space NN-interaction of Myers and Swiatecki [Nucl. Phys. A 601 (1996) 141], the EOS of nuclear matter by the Thomas–Fermi approximation is derived. A self-consistent semi-classical approach is presented by employing the Landau Fermi-Liquid theory (LFT). In our statistical approach, the phase-space occupation number can be expressed in terms of an extended effective mass which is affected by both temperature and nucleonic density. Accordingly, an explicit expression of the nucleonic chemical potential inside the nucleonic occupation number can be obtained. Special attention is also devoted to the density dependence of the nuclear symmetry free energy at different temperatures. The results of this model are compared with other theoretical predictions.

The CSS parametrization for Hybrid Stars with the Field Correlator Method

We explore the structure of hybrid stars based on a nuclear matter equation of state (EoS) built with the microscopic Brueckner-Hartree-Fock many-body theory, and a quark matter EoS derived with the Field Correlator Method (FCM), which can be accurately represented by the CSS (constant speed of sound) parametrization. We find that the main features of the hadron-quark phase transition are directly related to the FCM parameters, i.e. the quark-antiquark potential V1, the gluon condensate G2 and the color-flavour superconducting gap ∆, whose values range can be determined by the observational data on neutron star (NS) masses.

Effects of Induced Surface Tension in Nuclear and Hadron Matter

Short range particle repulsion is rather important property of the hadronic and nuclear matter equations of state. We present a novel equation of state which is based on the virial expansion for the multicomponent mixtures with hard-core repulsion. In addition to the hard-core repulsion taken into account by the proper volumes of particles, this equation of state explicitly contains the surface tension which is induced by another part of the hard-core repulsion between particles. At high densities the induced surface tension vanishes and the excluded volume treatment of hard-core repulsion is switched to its proper volume treatment. Possible applications of this equation of state to a description of hadronic multiplicities measured in A+A collisions, to an investigation of the nuclear matter phase diagram properties and to the neutron star interior modeling are discussed.

Escape and trapping of low-frequency gravitationally lensed rays by compact objects within plasma

We consider the gravitational lensing of rays emitted by a compact object (CO) within a distribution of plasma with power-law density $\propto r^{-h}$. For the simplest case of a cloud of spherically symmetric cold non-magnetized plasma, the diverging effect of the plasma and the converging effect of gravitational lensing compete with one another. When $h<2$, the plasma effect dominates over the vacuum Schwarzschild curvature, potentially shifting the radius of the unstable circular photon orbit outside the surface of the CO. When this occurs, we define two relatively narrow radio-frequency bands in which plasma effects are particularly significant. Rays in the escape window have $\omega_{0} < \omega \leq \omega_{+}$ and are free to propagate to infinity from the CO surface. To a distant observer, the visible portion of the CO surface appears to shrink as the observed frequency is reduced, and vanishes entirely at $\omega_{0}$, in excess of the plasma frequency at the CO surface. We define the anomalous propagation window for frequencies $\omega_{-}< \omega \leq \omega_{0}$. Rays emitted from the CO surface within this frequency range are dominated by optical effects from the plasma and curve back to the surface of the CO, effectively cloaking the star from distant observers. We conclude with a study of neutron star (NS) compactness ratios for a variety of nuclear matter equations of state (EoS). For $h=1$, NSs generated from stiff EoS should display significant frequency dependence in the EW, and lower values of $h$ with softer EoS can also show these effects.