Properties Of Asymmetric Nuclear Matter Research Articles

Relativistic Brueckner–Hartree–Fock Calculations for Cold and Hot Neutron Stars

This study investigates the properties of symmetric and asymmetric nuclear matter using the relativistic Brueckner–Hartree–Fock formalism, examining both zero and finite temperatures up to 70 MeV. Employing the full Dirac space, we incorporate three Bonn potentials (A, B, and C), which account for meson masses, coupling strengths, cutoff parameters, and form factors. The calculated properties of asymmetric nuclear matter form the basis for constructing equation-of-state (EOS) models tailored for neutron stars. These models, in turn, enable the computation of bulk properties for nonrotating, uniformly rotating, and differentially rotating neutron stars. Notably, the EOS models studied in this paper are sufficiently versatile to accommodate the mass of the most massive neutron star ever detected, PSR J0952–0607, estimated to be 2.35 ± 0.17 M ⊙. Furthermore, they yield masses and radii for PSR J0030+451 that align with the confidence intervals established for this pulsar.

Transport properties of asymmetric nuclear matter in the spinodal region

Transport properties of asymmetric nuclear matter in the spinodal region

Basic quantities of the equation of state in isospin asymmetric nuclear matter

Based on the Hugenholtz–Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k), the isospin symmetric and asymmetric parts of the single-nucleon potentials \(U_0(\rho ,k)\) and \(U_{\text {sym},i}(\rho ,k)\). The six basic quantities include the quadratic symmetry energy \(E_{\text {sym,2}}(\rho )\), the quartic symmetry energy \(E_{\text {sym,4}}(\rho )\), their corresponding density slopes \(L_2(\rho )\) and \(L_4(\rho )\), and the incompressibility coefficients \(K_2(\rho )\) and \(K_4(\rho )\). By using four types of well-known effective nucleon–nucleon interaction models, namely the BGBD, MDI, Skyrme, and Gogny forces, the density- and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density \(\rho _0\) are explicitly given. The contributions to these quantities from t(k), \(U_0(\rho ,k)\), and \(U_{\text {sym},i}(\rho ,k)\) are also analyzed at the normal nuclear density \(\rho _0\). It is clearly shown that the first-order asymmetric term \(U_{\text {sym,1}}(\rho ,k)\) (also known as the symmetry potential in the Lane potential) plays a vital role in determining the density dependence of the quadratic symmetry energy \(E_{\text {sym,2}}(\rho )\). It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials (\(U_{\text {sym},i}(\rho ,k)\) with \(i>1\)) cannot be neglected in the calculations of the other five basic quantities. Moreover, by analyzing the properties of asymmetric nuclear matter at the exact saturation density \(\rho _{\text {sat}}(\delta )\), the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation \(K_{\text {sat,2}}=K_{2}(\rho _0)-4.14 L_2(\rho _0)\).

Thermal effects in hot and dilute homogeneous asymmetric nuclear matter

We present a comprehensive analysis of hot and dilute isospin-asymmetric nuclear matter employing the temperature-dependent effective-relativistic mean-field theory (E-RMF). The E-RMF is applied to study the effect of $\delta$ and $\omega-\rho$ meson cross-coupling on the thermal properties of asymmetric nuclear matter using two recently developed IOPB-I and G3 parameter sets. These sets are known to reproduce the nuclear matter properties in agreement with various experimental and observational constraints. We consider the nuclear matter to be homogeneous and study the equation of state (EoS) for densities, temperature and asymmetry which are relevant for astrophysical simulations such as supernovae explosion. The effect of temperature is investigated in reference to the density-dependent free symmetry energy and its higher-order derivatives using the well known parabolic approximation. The larger value of $\lambda_\omega$ cross-coupling in G3 in addition to the $\delta$ meson coupling in G3 smoothen the free symmetry energy. Thermal effects on various state variables are examined at fixed temperature and isospin asymmetry by separating their T=0 and the finite-T expressions. The thermal effects are mainly governed by effective mass with larger effective mass estimating larger thermal contribution. The effect of temperature on isothermal and isentropic incompressibility is discussed which is in harmony with various available microscopic calculations. The liquid-gas phase transition properties are examined in asymmetric matter with two conserved charges in the context of different slope parameter and comparable symmetry energy in IOPB-I and G3 set. The spinodal instability, binodal curve and critical properties are found to be influenced by the slope parameter $L_{sym}$.

Nuclear matter at finite temperature and static properties of proto-neutron star

With the effective chiral model, the finite temperature properties of nuclear matter have been studied at different temperatures. For symmetric nuclear matter, I particularly focused on the possibility of liquid–gas phase transition at low temperature and density. The critical temperature obtained in this context, is consistent with the experimental and empirical findings. The free energy and entropy variation are also studied for different values of temperature. A few asymmetric nuclear matter properties like the equation of state and the speed of sound with respect to temperature are also examined. The work is also extended to obtain the equation of state β stable nuclear matter at finite temperature. For the neutrino free case, the various static proto-neutron star properties are computed for a wide range of temperature, relevant to proto-neutron stars. For all the values of temperature, the obtained estimates of maximum gravitational mass are found to be in good agreement with the observational constraints specified from massive pulsars like PSR J0348 + 0432 and PSR J0740 + 6620. The results of surface redshift for all the temperature also satisfy the maximum surface redshift constraints from EXO 07482-676, 1E 1207.4-5209 and RX J0720.4-3125.

Strongly Interacting Multi-component Fermions: From Ultracold Atomic Fermi Gas to Asymmetric Nuclear Matter in Neutron Stars

We investigate an asymmetric nuclear matter consisting of protons and neutrons with spin degrees of freedom (σ = ↑, ↓). By generalizing the Nozières and Schmitt-Rink theory for two-component Fermi gases to the four-component case, we analyze the critical temperature Tc of the superfluid phase transition. Although the pure neutron matter exhibits the dineutron condensation in the low-density region, the superfluid instability toward the deuteron condensation is found to take place as the proton fraction increases. We clarify the mechanism of the competition between the deuteron condensation and dineutron condensation. Our results would serve for understanding the properties of asymmetric nuclear matter realized in the interior of neutron stars.

The Thermal Properties of Asymmetric Nuclear Matter within the Extended Brueckner–Hartree–Fock Approach

The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole–hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole–hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner–Hartree–Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the press...

Asymmetric nuclear matter and neutron star properties within the extended Brueckner theory

Microscopically, the equation of state (EOS) and other properties of asymmetric nuclear matter at zero temperature have been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF) and the extended BHF approaches by using the self-consistent Green’s function approach or by including a phenomenological three-body force. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. We can calculate the total mass and radius for neutron stars using various equations of state at high densities in $ \beta$ -equilibrium without hyperons. A comparison with other microscopic predictions based on non-relativistic and density-dependent relativistic mean-field calculations has been done. It is found that relativistic EOS yields however larger mass and radius for neutron star than predictions based on non-relativistic approaches. Also the three-body force plays a crucial role to deduce the theoretical value of the maximum mass of neutron stars in agreement with recent measurements of the neutron star mass.

Deformation properties with a finite-range simple effective interaction

Deformed and spherical even–even nuclei are studied using a finite-range simple effective interaction within the Hartree–Fock–Bogoliubov mean-field approach. Different parameter sets of the interaction, corresponding to different incompressibility, are constructed by varying the exponent γ of the density in the traditional density-dependent term. Ten of the 12 parameters of these interactions are determined from properties of asymmetric nuclear matter and spin-polarized pure neutron matter. The two remaining parameters are fitted to reproduce the experimental binding energies known in 620 even–even nuclei using several variants of the rotational energy correction. The rms deviations for the binding energy depend on the value of γ and the way the rotational energy correction is treated but they can be as low as 1.56 MeV, a value competitive with other renowned effective interactions of Skyrme and Gogny type. Charge radii are compared to the experimental values of 313 even–even nuclei and the rms deviation is again comparable and even superior to the one of popular Skyrme and Gogny forces. Emphasis is given to the deformation properties predicted with these interactions by analyzing the potential energy surfaces for several well deformed nuclei and the fission barriers of some nuclei. Comparison of the results with the experimental information, where available, as well as with the results of the Gogny D1S force, shows satisfactory agreement.

Magnetic susceptibility and magnetization properties of asymmetric nuclear matter in a strong magnetic field

We study the effect of a strong magnetic field on the proton and neutron spin polarization and magnetic susceptibility of asymmetric nuclear matter within a relativistic mean-field approach. It is shown that magnetic fields $B \sim 10^{16} - 10^{17}$ G have already noticeable effects on the range of densities of interest for the study of the crust of a neutron star. Although the proton susceptibility is larger for weaker fields, the neutron susceptibility becomes of the same order or even larger for small proton fractions and subsaturation densities for $B > 10^{16}$ G. We expect that neutron superfluidity in the crust will be affected by the presence of magnetic fields.

Thermal properties of asymmetric nuclear matter

The thermal properties of asymmetric nuclear matter are investigated in a relativistic mean-field approach. We start from free-space $NN$ interactions and derive in-medium self-energies by the Dirac-Brueckner theory. By the density-dependent relativistic hadron procedure we derive in a self-consistent approach density-dependent meson-baryon vertices. At the mean-field level, we include isoscalar and isovector-scalar and vector interactions. The nuclear equation of state is investigated for a large range of total baryon densities up to the neutron star regime, the full range of asymmetries $\ensuremath{\xi}=Z/A$ from symmetric nuclear matter to pure neutron matter, and temperatures up to $T\ensuremath{\sim}100$ MeV. The isovector-scalar self-energies are found to modify strongly the thermal properties of asymmetric nuclear matter. A striking result is the change of phase transitions when isovector-scalar self-energies are included.

Thermal properties of asymmetric nuclear matter with an improved isospin- and momentum-dependent interaction

Thermal properties of asymmetric nuclear matter, including the temperature dependence of the symmetry energy, single-particle properties, and differential isospin fractionation, are investigated with different neutron-proton effective mass splittings using an improved isospin- and momentum-dependent interaction. In this improved interaction, the momentum-dependence of the isoscalar single-particle potential at saturation density is well fitted to that extracted from optical model analyses of proton-nucleus scattering data up to nucleon kinetic energy of 1 GeV, and the isovector properties, i.e., the slope of the nuclear symmetry energy, the momentum-dependence of the symmetry potential, and the symmetry energy at saturation density can be flexibly adjusted via three parameters $x$, $y$, and $z$, respectively. Our results indicate that the nucleon phase-space distribution in equilibrium, the temperature dependence of the symmetry energy, and the differential isospin fractionation can be significantly affected by the isospin splitting of nucleon effective mass.

Neutron star properties in density-dependent relativistic mean field theory with consideration of an isovector scalar meson

Based on the density-dependent relativistic mean field theory, the properties for nuclear matter and neutron stars with the effective interaction $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ including the isovector scalar channel which disentangle the effects of isovector scalar and isovector vector channels by fitting microscopic calculations. The influences of the isovector scalar $\ensuremath{\delta}$ meson on properties of asymmetric nuclear matter at high densities are discussed in detail. The results support that the isovector scalar channel can soften the equation of state through the effects on the nucleon effective mass and the scalar $\ensuremath{\sigma}$ field and impact the behavior of the nuclear matter symmetry energy. Because of the influence on the symmetry energy by the $\ensuremath{\delta}$ meson, a larger proton fraction in neutron stars is predicted by the $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ calculation, which strongly affects the cooling process of the star. The maximum masses of neutron stars given by the $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ calculation is $1.97{M}_{⨀}$ which is in reasonable agreement with PSR J1614 \ensuremath{-} 2230 ($1.97 \ifmmode\pm\else\textpm\fi{} 0.04 {M}_{⨀}$) and PSR J0348 + 0432 $(2.01 \ifmmode\pm\else\textpm\fi{} 0.04 {M}_{⨀})$. Among all the selected interactions, $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ gives the smallest radius range. The radius for the 1.4 solar mass neutron star calculated by $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ is in good agreement with the prediction [Astrophys. J. Lett. 765, L5 (2013)] according to the resent observations.

Three-body force effect on nuclear symmetry energy and single-particle properties of asymmetric nuclear matter

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.

Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter

The single-particle potentials for nucleons and hyperons in neutron-rich matter generally depends on the density and isospin asymmetry of the medium as well as the momentum and isospin of the particle. It further depends on the temperature of the matter if the latter is in thermal equilibrium. We review here the extension of a Gogny-type isospin- and momentum-dependent interaction in several aspects made in recent years and their applications in studying intermediate-energy heavy ion collisions, thermal properties of asymmetric nuclear matter and properties of neutron stars. The importance of the isospin- and momentum-dependence of the single-particle potential, especially the momentum dependence of the isovector potential, is clearly revealed throughout these studies.

Nuclear matter and surface clustering

We demonstrate that the binding energy per nucleon of symmetric nuclear matter (SNM) (with Coulomb interaction switched off and N = Z) in the limit of zero density approaches to its value, uv, at the saturation density, where uv is the volume term of the Weizsäcker mass formula. This phenomenon is a direct result of the clustering of nuclei in the low density region of nuclear matter. We study the implications of this result on the properties of nuclei. We also study the properties of asymmetric nuclear matter. Because of clustering a provocative interpretation of the equation of state of asymmetric nuclear matter emerges which is at considerable variance at low densities with hitherto all the previous calculations. For nuclei, as a framework, an extended version of Thomas-Fermi theory is invoked. Calculations are performed for 2149 nuclei with N, Z ≥ 8. The present scheme leads to a forceful interpretation of the low density asymmetry energy data of Natowitz et al. [1].

Applying the "snowplow" model for pulsar glitches to constrain nuclear symmetry energy

Glitches in pulsars are occasional, sudden increases in their rotation frequency as the pulsar otherwise steadily spins down. A broad class of glitch models suppose the sudden spin-ups are due to angular momentum transfer between some of the crustal superfluid neutrons and the rigid crust plus anything that couples to it on timescales shorter than the superfluid-crust coupling time. Using a set of neutron star equations of state (EOS) which span the experimentally constrained range of asymmetric nuclear matter properties, and estimates of the strength of the coupling between the crust and the core superfluid neutrons, we calculate the moment of inertia (MoI) of crustal superfluid neutrons involved in storing angular momentum in the glitch process. Following the recent, microscopically based "snowplow" model for glitches, we restrict the calculation to just those superfluid neutron vortices that are strongly pinned to the crustal lattice, a region which corresponds to an equatorial annulus of the inner crust. We compare calculations to observational estimates of the average rate of angular momentum transfer between superfluid neutrons and the rest of the star in the Vela pulsar, and also the relative acceleration of the crust post-glitch estimated from the 2002 Vela glitch. We found that to match the observations of the glitch sizes and recovery from Vela glitches, a value of L 50 MeV for the density slope of the symmetry energy at saturation density is required and the coupling between core superfluid neutrons and crust is relatively weak.

Nuclear Symmetry Energy in Chiral Model of Nuclear Matter

The physical properties of asymmetric nuclear matter are studied in the Extended Nambou-Jona-Lasinio (ENJL) model formulated directly in the nucleon degrees of freedom. It results that the density dependence of the nuclear symmetry energy and its related quantities are basically in good agreement with data of recent analyses.

Correlations between the nuclear breathing mode energy and properties of asymmetric nuclear matter

Based on microscopic Hartree–Fock + random phase approximation calculations with Skyrme interactions, we study the correlations between the nuclear breathing mode energy EISGMR and properties of asymmetric nuclear matter with a recently developed analysis method. Our results indicate that the EISGMR of 208Pb exhibits moderate correlations with the density slope L of the symmetry energy and the isoscalar nucleon effective mass m*s, 0 besides a strong dependence on the incompressibility K0 of symmetric nuclear matter. Using the present empirical values of L = 60 ± 30 MeV and m*s, 0 = (0.8 ± 0.1)m, we obtain a theoretical uncertainty of about ±16 MeV for the extraction of K0 from the EISGMR of 208Pb. Furthermore, we find that the EISGMR difference between 100Sn and 132Sn strongly correlates with L and thus provides a potentially useful probe of the symmetry energy.

Constraining the symmetry energy from fragment yields

Methods of extraction of the symmetry energy coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. Consistent results are obtained when the hot fragmenting source is well characterized and its excitation energy and isotopic composition are properly taken into account. The results, independent of the mass number of the detected fragments, suggest that their fate is decided very early in the reaction. A comparison to the Statistical Multifragmentation Model (SMM) predictions is also presented. The effort to understand the properties of asymmetric nuclear matter both at normal densities and at densities away from the saturation density has stimulated a growing interest in isospin effects in nuclear reactions. The isotopic distribution of fragments produced in multifragmentation events in central collisions at intermediate energies can probe properties of low density nuclear matter. Different methods to extract the “symmetry energy” coefficient from yield ratios have been proposed. Among those, we focus on three seemingly different approaches: isoscaling [1–4], m-scaling and isobaric yield ratio method [5], and we show that consistent experimental results can be extracted provided that the properties of the hot fragmenting source, such as its isospin composition and excitation energy, are properly taken into account. We remark that experimentally whether the equilibrium process, occurring during the multifragmentation, takes place at constant pressure or volume (freeze-out hypothesis) is not determined. This ambiguity casts some doubts on the derived quantity, i.e. symmetry energy or symmetry enthalpy. Keeping in mind this ambiguity we will refer to the experimentally extracted quantity as the symmetry energy.