Nuclear matter fourth-order symmetry energy in non-relativistic mean-field models

Abstract

Based on systematic analyses of several popular non-relativistic energy density functionals with mean-field approximation, we estimate the value of the fourth-order symmetry energy $E_{\text{sym,4}}(\rho )$ at nuclear normal density ${\rho }_0$ and its density dependence, and explore the correlation between $E_{\text{sym,4}}({\rho }_0)$ and other macroscopic quantities of nuclear matter properties. We use the empirical values of some nuclear macroscopic quantities to construct model parameter sets by Monte Carlo method for the conventional Skyrme-Hartree-Fock (SHF) model, the extended Skyrme-Hartree-Fock (eSHF) model, the Gogny-Hartree-Fock (GHF) model, and the momentum-dependent interaction (MDI) model. The value of $E_{\text{sym,4}}({\rho }_0)$ is estimated to be $1.02\pm 0.49$ MeV for the SHF model, $1.02\pm 0.50$ MeV for the eSHF model, $0.70\pm 0.60$ MeV for the GHF model, and $0.74\pm 0.63$ MeV for the MDI model. Moreover, our results indicate that the density dependence of $E_{\text{sym,4}}(\rho )$ is model dependent, especially at higher densities. Furthermore, we find that the $E_{\text{sym},4}({\rho }_0)$ has strong positive (negative) correlation with isoscalar (isovector) nucleon effective mass $m_{s,0}^{\ast }$ ($m_{v,0}^{\ast }$) at ${\rho }_0$. In particular, for the SHF and eSHF models, the $E_{\text{sym,4}}(\rho )$ is completely determined by the isoscalar and isovector nucleon effective masses $m_s^{\ast }(\rho )$ and $m_v^{\ast }(\rho )$, and the analytical expression is given. In the mean-field models, the magnitude of $E_{\text{sym,4}}({\rho }_0)$ is generally less than $2$ MeV, and its density dependence depends on models, especially at higher densities. $E_{\text{sym,4}}({\rho }_0)$ is strongly correlated with $m_{s,0}^{\ast }$ and $m_{v,0}^{\ast }$.

arXiv comment10 pages, 2 figures, 4 tables. Presentation improved and discussions added. Accepted version to appear in PRC

References in corpus (52)

• Determination of the Equation of State of Dense Matter
• The Physics of Neutron Stars
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Equations of state for supernovae and compact stars
• Isospin Asymmetry in Nuclei and Neutron Stars
• Reaction Dynamics with Exotic Beams
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Isospin Physics in Heavy-Ion Collisions at Intermediate Energies
• Determination of the stiffness of the nuclear symmetry energy from isospin diffusion
• The information content of a new observable: the case of the nuclear neutron skin
• Sound velocity bound and neutron stars
• Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei
• Microscopic determination of the nuclear incompressibility within the non-relativistic framework
• The Nuclear Symmetry Energy
• A way forward in the study of the symmetry energy: experiment, theory, and observation
• Nuclear constraints on properties of neutron star crusts
• Momentum dependence of symmetry potential in asymmetric nuclear matter for transport model calculations
• Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility
• Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter
• Higher-order effects on the incompressibility of isospin asymmetric nuclear matter
• Effects of momentum-dependent symmetry potential on heavy-ion collisions induced by neutron-rich nuclei
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XI: Stabilizing neutron stars against a ferromagnetic collapse
• Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness
• Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models
• Nuclear symmetry energy and its density slope at normal density extracted from global nucleon optical potentials
• Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models
• Momentum dependence of the symmetry potential and nuclear reactions induced by neutron-rich nuclei at RIA
• Unmasking the nuclear matter equation of state
• Locating the inner edge of neutron star crust using terrestrial nuclear laboratory data
• The Giant Monopole Resonance in the Sn Isotopes: Why is Tin so "Fluffy"?
• The long journey from the giant-monopole resonance to the nuclear-matter incompressibility
• Nuclear matter fourth-order symmetry energy in the relativistic mean field models
• The High-Density Symmetry Energy and Direct Urca
• Neutron-proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon-nucleus scattering data within an isospin dependent optical model
• Isovector properties of the Gogny interaction
• Single-nucleon potential decomposition of the nuclear symmetry energy
• Elliptic flow and the symmetry energy at supra-saturation density
• Constraining the density slope of nuclear symmetry energy at subsaturation densities using electric dipole polarizability in ${}^{208}$Pb
• Higher-order symmetry energy of nuclear matter and the inner edge of neutron star crusts
• Extended Skyrme interactions for nuclear matter, finite nuclei and neutron stars
• Isospin splitting of nucleon effective mass from giant resonances in ${}^{208}$Pb
• Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter
• The isospin quartic term in the kinetic energy of neutron-rich nucleonic matter
• Proton fraction in neutron stars
• Higher order bulk characteristic parameters of asymmetric nuclear matter
• Neutron-proton effective mass splitting in neutron-rich matter and its impacts on nuclear reactions
• Low density nuclear matter with quantum molecular dynamics : The role of the symmetry energy
• Mass dependence of symmetry energy coefficients in Skyrme force
• Empirical information on nuclear matter fourth-order symmetry energy from an extended nuclear mass formula
• Limiting symmetry energy elements from empirical evidence
• Effect of Wigner energy on the symmetry energy coefficient in nuclei

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