Nonlinear Walecka Research Articles

Dynamical instabilities in density-dependent hadronic relativistic models

Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities are studied in the framework of relativistic mean-field density-dependent hadron models. The size of the instabilities that drive the system are calculated and a comparison with results obtained within the nonlinear Walecka model is presented. The distillation and antidistillation effects are discussed.

Metastability of hadronic compact stars

Pure hadronic compact stars, above a threshold value of their gravitational mass (central pressure), are metastable to the conversion to quark stars (hybrid or strange stars). In this paper, we present a systematic study of the metastability of pure hadronic compact stars using different relativistic models for the equation of state. In particular, we compare results for the quark-meson coupling model with those for the Glendenning-Moszkowski parametrization of the nonlinear Walecka model. For the quark-meson coupling model, we find large values (${M}_{\mathrm{cr}}=1.6--1.9{M}_{\ensuremath{\bigodot}}$) for the critical mass of the hadronic star sequence and we find that the formation of a quark star is only possible with a soft quark matter equation of state. For the Glendenning-Moszkowski parametrization of the nonlinear Walecka model, we explore the effect of different hyperon couplings on the critical mass and on the stellar conversion energy. We find that increasing the value of the hyperon coupling constants shifts the bulk transition point for quark deconfinement to higher densities, increases the stellar metastability threshold mass and the value of the critical mass, and thus makes the formation of quark stars less likely. For the largest values of the hyperon couplings we find a critical mass which may be as high as $1.9--2.1{M}_{\ensuremath{\bigodot}}$. These stellar configurations, which contain a large central hyperon fraction (${f}_{Y,\mathrm{cr}}\ensuremath{\sim}30%$), would be able to describe highly massive compact stars, such as the one associated with the millisecond pulsar PSR $\mathrm{B}1516+02\mathrm{B}$ with a mass $M={1.94}_{\ensuremath{-}0.19}^{+0.17}{M}_{\ensuremath{\bigodot}}$.

Reexamining the neutron skin thickness within a density dependent hadronic model

In the present work, we calculate the $^{208}\mathrm{Pb}$ neutron skin thickness, binding energy, surface energy, and density profiles within the Dirac solution of a density dependent hadronic model. The same calculation is performed with the NL3 parametrization of the nonlinear Walecka model. The asymmetry of a polarized electron scattered from a heavy target is also obtained within a partial wave expansion calculation. The theoretical results are then ready to be compared with the experimental results expected to be available very soon at the Thomas Jefferson National Accelerator Facility. For completeness, other nuclei such as $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{66}\mathrm{Ni}$, and $^{90}\mathrm{Zr}$ are also investigated.

POINT-COUPLING AND NONLINEAR WALECKA MODELS CONNECTION

In the context of infinite nuclear matter, the equation of states obtained from the Walecka model turn out to be the same as those constructed from point-coupling models in which the nucleons interact with each other only when they are in contact.1 Nonlinear point-coupling models have been applied sucessfully to describe infinite nuclear matter and finite nuclei spectra properties.2 A theoretical support for this was presented on the basis of naturalness and naive dimensional analysis.3 For the usual linear Walecka model the infinite meson masses limit leads to a point-coupling model. From this, a quite natural question arises, whether the same kind of masses limit taken in a nonlinear Walecka model would provide a point-coupling model. We construct a modified nonlinear Walecka model Lagrangian in which the infinite meson masses limit can be taken exactly and leads to the contact nonlinear model. This modified nonlinear Walecka model includes higher order couplings. Although the modified and the nonlinear Walecka model at a mean field approach lead to distinct equations of state, the physically relevant content of the models are the same.

NEUTRON SKIN THICKNESS AND NEUTRON STARS WITHIN A DENSITY DEPENDENT HADRONIC MODEL

A density dependent hadronic model and a common parametrization of the nonlinear Walecka model are used to obtain the lead neutron skin thickness through its proton and neutron density profiles. Our results are obtained within the Thomas–Fermi approximation. The neutron skin thickness is known to reflect the equation of state properties.

Density dependent hadronic models and the relation between neutron stars and neutron skin thickness

In the present work, we investigate the main differences in the lead neutron skin thickness, binding energy, surface energy, and density profiles obtained with two different density dependent hadron models. Our results are calculated within the Thomas-Fermi approximation with two different numerical prescriptions and compared with results obtained with a common parametrization of the nonlinear Walecka model. The neutron skin thickness is a reflex of the equation of state properties. Hence, a direct correlation is found between the neutron skin thickness and the slope of the symmetry energy. We show that within the present approximations, the asymmetry parameter for low momentum transfer polarized electron scattering is not sensitive to the model differences.

γ-ray bursts and the QCD phase diagram

The quantum chromodynamics phase diagram shows the phase transitions that can take place in matter at different temperatures and densities. In this work we discuss the possibility that \ensuremath{\gamma}-ray bursts might result from a phase change in the interior of a neutron star and calculate the energy released in the conversion of a metastable star into a stable star. We consider several different initial and several different final configurations. Initial metastable stars are taken as hadronic, hybrid, and quark stars with unpaired quarks; possible stable stars are hybrid and quark stars, taken both with unpaired and paired phases to study the deconfinement phase transition and normal quark matter--superconducting quark matter phase transition within a large number of relativistic models used to describe compact stars. The models used for the hadron matter are the nonlinear Walecka model and the quark-meson coupling model with and without hyperons. For the quark matter we have used the MIT bag model, the bag model with paired quarks to which we refer as the color-flavor-locked phase model, and the Nambu--Jona-Lasinio model. Within this mechanism we obtain energies of the order of ${10}^{50}\ensuremath{-}{10}^{53}$ erg, accounting for both long and short \ensuremath{\gamma}-ray bursts.

Kaon condensation in the quark-meson coupling model and compact stars

The properties of neutron stars, consisting of a crust of hadrons and an internal part of hadrons and kaon condensate, are calculated within the quark-meson-coupling model. We considered stars with nucleons only in the hadron phase and also stars with hyperons as well. The results are compared with the ones obtained from the nonlinear Walecka model for the hadronic phase.

Quasielastic electron scattering in relativistic mean-field theory

The density-dependent relativistic hadron (DDRH) field theory proposed recently is extended to investigate the longitudinal response function and the Coulomb sum rule in quasielastic electron scattering in the relativistic random phase approximation (RPA). The results in the DDRH model are compared with those in other models systematically. It is found that meson effective masses induced by the nonlinear terms in the nonlinear Walecka model should be used to obtain the meson Green’s functions when the longitudinal response function and the Coulomb sum rule are calculated. The effects of the δ and ρ mesons are clearly shown in quasielastic electron scattering, and the isospin-dependent attractive potential between nucleons due to the exchange of the δ-meson cancels the isospin-dependent repulsive contribution of the ρ-meson to a certain extent. The obtained results in the DDRH model are in good agreement with experimental data except for the Coulomb sum rule in 208Pb.

In‐Medium Kaon and Antikaon Production and Antikaon Condensation in Neutron Star Matter

Kaon and antikaon production and antikaon condensation in neutron star matter are investigated in a chiral hadronic model proposed by Furnstahl, Tang, & Serot (FST model). Results calculated in the FST model are compared with those in the nonlinear Walecka model. Antikaon condensation decreases the maximum masses of neutron stars with a composition of (n, p, e, μ, K) compared with those of (n, p, e, μ), without antikaon condensation. The FST model predicts that Σ+ and Ξ0 do not occur in neutron stars. Moreover, it has been shown that antikaon condensation in the FST model does not exist in neutron star matter with compositions of both (n, p, e, μ, K, H) if hyperons are considered and (n, p, e, μ, νe, K, H) if hyperons plus neutrino tripping are considered. The Q-values for K+ and K- production are not sensitive to antikaon condensation and the presence of hyperons. In-medium effects decrease the Q-values for NN → NNK+K- and ΛN → NNK- and increase those for NN → NΛK+, K-p → Λπ0, and K-n → Λπ- as the density of neutron star matter increases.

Lambda Hypernuclei in a Chiral Hadronic Model

Nuclear matter calculations in a chiral hadronic model have beenperformed. It has been found that the scalar and the vector potentialsand binding energies per nucleon in the chiral hadronic model are veryclose to those of the microscopic relativistic Brueckner–Hartree–Fockcalculations. The good results for finite nuclei can be obtained in themean field approximation only if scalar mass ms and coupling constantgs have been improved with the fixed values of cs2≡gs2(M/ms)2 as those given by the original parameter sets of the chiralhadronic model. Then the chiral hadronic model is extended to lambdahypernuclei. Our results predicted by the chiral hadronic model arecompared with those by the nonlinear Walecka model. It has been shownthat the hadronic model can also be used to describe lambda hypernucleisuccessfully.

δmeson effects on stellar matter

The consequences for compact star properties of including the $\ensuremath{\delta}$ mesons in the Lagrangian density of the nonlinear Walecka model are investigated. The equations of state for neutrino free and neutrino trapped with and without the $\ensuremath{\delta}$ mesons are compared. We conclude that the sensitivity to the $\ensuremath{\delta}$ mesons depends on the hadronic contents of the star, i.e., stars with only protons and neutrons behave in a different way than stars with protons, neutrons, and hyperons. Moreover, although the properties of maximum mass stable protoneutron stars with trapped neutrinos are essentially equivalent when the $\ensuremath{\delta}$ meson is included, the neutrino content is affected by its presence.

NUCLEAR MATTER AND PROTON HALO NUCLEI IN A CHIRAL HADRONIC MODEL

The results for the nuclear-matter properties in a chiral hadronic model have been compared with those in the nonlinear Walecka model. It has been found that the scalar and the vector potentials and binding energies per nucleon for nuclear matter in the chiral hadronic model are very close to those of the RBHF. Two-proton halo in 27 S and one-proton halo in 26 P are predicted when the chiral hadronic model is extended to study proton halos in light proton-rich nuclei. Comparison between the results obtained in the chiral hadronic model and in the nonlinear Walecka model has been made, it has been shown that the chiral hadronic model can also be used to describe the properties of light proton-rich nuclei.

Equations of state for mixed stars

We investigate the properties of mixed stars formed by hadronic and quark matter in fl-equilibrium described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. We use the non-linear Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The calculations were performed for T = 0 and for finite temperatures in order to describe neutron and proto-neutron stars. The star properties are discussed. Both the Bag model and the NJL model predict a mixed phase in the interior of the star.

Dense and hot matter within the nonlinear Walecka model

In this work we study the effects of temperature on the equations of state obtained within a relativistic model, with and without $\ensuremath{\beta}$ equilibrium over a wide range of densities. We also compare the results of the equation of state, effective mass, and strangeness fraction for the TM1, NL3, and GL sets of parameters. We have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars.

Warm stellar matter with neutrino trapping

The properties of hybrid stars formed by hadronic and quark matter in beta-equilibrium at fixed entropies are described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. In this work we include the possibility of neutrino trapped EOS and compare the star properties with the ones obtained after deleptonization, when neutrinos have already diffused out. We use the nonlinear Walecka model for the hadron matter with two different sets for the hyperon couplings and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a deconfined quark phase is investigated. Depending on the model and the parameter set used, the mixed phase may or may not exist in the EOS at high densities. The star properties are calculated for each equation of state. The maximum mass stellar configurations obtained within the NJL have larger masses than the ones obtained within the Bag model. The Bag model predicts a mixed phase in the interior of the most massive stable stars while, depending on the hyperon couplings, the NJL model predicts a mixed phase or pure quark matter. Comparing with neutrino free stars, the maximum allowed baryonic masses for protoneutron stars are $\sim 0.4 M_\odot$ larger for the Bag model and $\sim 0.1 M_\odot$ larger for the NJL model when neutrino trapping is imposed.

Warm stellar matter with deconfinement: Application to compact stars

We investigate the properties of mixed stars formed by hadronic and quark matter in $\ensuremath{\beta}$ equilibrium described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. We use the nonlinear Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio (NJL) models for the quark matter. The phase transition to a deconfined quark phase is investigated. In particular, we study the dependence of the onset of a mixed phase and a pure quark phase on the hyperon couplings, quark model, and properties of the hadronic model. We calculate the strangeness fraction with baryonic density for the different EOS. With the NJL model the strangeness content in the mixed phase decreases. The calculations were performed for $T=0$ and for finite temperatures in order to describe neutron and proto-neutron stars. The star properties are discussed. Both the Bag model and the NJL model predict a mixed phase in the interior of the star. Maximum allowed masses for proto-neutron stars are larger for the NJL model $(\ensuremath{\sim}{1.9M}_{\ensuremath{\bigodot}})$ than that for the Bag model $(\ensuremath{\sim}{1.6M}_{\ensuremath{\bigodot}}).$

Warm asymmetric matter in the quark-meson coupling model

In this work we study the warm equation of state of asymmetric nuclear matter in the quark-meson coupling model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar, vector, and isovector mesons. Mechanical and chemical instabilities are discussed as a function of density and isospin asymmetry. The binodal section, essential in the study of the liquid-gas phase transition is also constructed and discussed. The main results for the equation of state are compared with two common parametrizations used in the nonlinear Walecka model and the differences are outlined.

Δ excitation and its influences on neutron stars in relativistic mean field theory

The relativistic mean field models with the different parameter sets are extended to investigate the properties of $\ensuremath{\Delta}$-excited nuclear matter. The calculated results show that the critical densities for the $\ensuremath{\Delta}$-excited nuclear matter predicted in a chiral hadronic model are larger than those obtained in the nonlinear Walecka model with the parameter sets Tm1 and NL1. The inclusion of the $\ensuremath{\Delta}$ leads to the decrease in the maximum mass of neutron stars in a chiral hadronic model, while the opposite behavior is shown in the nonlinear Walecka model.

ρ−ωmixing in the nonlinear Walecka model

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo>−</mml:mo><mml:mi>ω</mml:mi></mml:math>mixing in the nonlinear Walecka model