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Register a new userSymmetry energy softening in nuclear matter with non-nucleonic constituents
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We study the trend of the nuclear symmetry energy in relativistic mean-field models with appearance of the hyperon and quark degrees of freedom at high densities. On the pure hadron level, we focus on the role of $Lambda$ hyperons in influencing the symmetry energy both at given fractions and at charge and chemical equilibriums. The softening of the nuclear symmetry energy is observed with the inclusion of the $Lambda$ hyperons that suppresses the nucleon fraction. In the phase with the admixture of quarks and hadrons, the equation of state is established on the Gibbs conditions. With the increase of the quark volume fraction in denser and denser matter, the apparent nuclear symmetry energy decreases till to disappear. This softening would have associations with the observations which need detailed discriminations in dense matter with the admixture of new degrees of freedom created by heavy-ion collisions.
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We present a study of the symmetry energy (a_s) and its slope parameter (L) of nuclear matter in the general framework of the Landau-Migdal theory. We derive an exact relation between a_s and L, which involves the nucleon effective mass and three-particle Landau-Migdal parameters. We also present simple estimates which show that there are two main mechanisms to explain the empirical values of L: The proton-neutron effective mass difference in isospin asymmetric matter, and the isovector three-body Landau-Migdal parameter H_0. We give simple estimates of both effects and show that they are of similar magnitude.
The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.
We study relativistic nuclear matter in the $sigma - omega$ model including the ring-sum correlation energy. The model parameters are adjusted self-consistently to give the canonical saturation density and binding energy per nucleon with the ring energy included. Two models are considered, mean-field-theory where we neglect vacuum effects, and the relativistic Hartree approximation where such effects are included but in an approximate way. In both cases we find self-consistent solutions and present equations of state. In the mean-field case the ring energy completely dominates the attractive part of the energy density and the elegant saturation mechanism of the standard approach is lost, namely relativistic quenching of the scalar attraction. In the relativistic Hartree approach the vacuum effects are included in an approximate manner using vertex form factors with a cutoff of 1 - 2 GeV, the range expected from QCD. Due to the cutoff, the ring energy for this case is significantlysmaller, and we obtain self-consistent solutions which preserve the basic saturation mechanism of the standard relativistic approach.
The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduced by Kaiser [Phys.~Rev.~C textbf{91}, 065201 (2015)]. Our results suggest that the quartic contribution to the symmetry energy can be robustly determined from the various Hamiltonians employed, and we obtain 1.00(8) MeV (or 0.55(8) MeV for the potential part) at saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We finally employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a small 5% correction.
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.
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