Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

Neutrino-nucleon scattering rate in proto-neutron star matter

We present a calculation of the neutrino-nucleon scattering cross-section which takes into account the nuclear correlations in the relativistic random phase approximation (RPA). Our approach is based on a quantum-hadrodynamics model with exchange of σ, ω, π, ρ and δ mesons. In view of applications to neutrino transport in the final stages of supernova explosion and proto-neutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-neutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel, coupling to the delta-meson and meson mixing. In contrast with the results of other authors, we find that the neutral-current process is not sensitive to the strength g' of the residual contact interaction. As a consequence, it is found that RPA corrections with respect to the mean-field approximation amount to only 10% to 15% at high density. Received: 27 June 2001 / Accepted: 14 January 2002     

Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Hadron masses in medium and neutron star properties

We investigate the properties of the neutron star with relativistic mean-field models. We incorporate in the quantum hadrodynamics and in the quark-meson coupling models a possible reduction of meson masses in nuclear matter. The equation of state for neutron star matter is obtained and is employed in Oppenheimer-Volkov equation to extract the maximum mass of the stable neutron star. We find that the equation of state, the composition and the properties of the neutron stars are sensitive to the values of the meson masses in medium.     

Propagation of mesons in asymmetric nuclear matter in a density-dependent coupling model

We study the propagation of the light mesons σ,ω,ρ, and a₀(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated. Received: 16 October 2001 / Accepted: 10 January 2002     

Necessity of extra repulsion in hypernuclear systems: Suggestion from neutron stars

Neutron star models with hyperon-mixed core are studied by a realistic approach to use the YN and the YY interactions consistent with hypernuclear data. From the compatibility of the theoretical maximum mass with the observed neutron star mass 1.44 M _⊙ of PSR1913+16, the necessity of some extra repulsion in hypernuclear systems, e.g., a repulsion from three-body force, is stressed. It is noted that the increase of baryon degrees of freedom to avoid the short-range repulsion effectively is an essential mechanism causing the Y-mixed phase. Received: 1 May 2001 / Accepted: 4 December 2001     

Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Momentum distribution of relativistic nuclei with Hartree-Fock mesonic correlations

The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure. Received: 7 June 2002 / Accepted: 24 September 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: juan@nucle.us.es Communicated by G. Orlandini     

Nuclear matter with off-shell propagation

Symmetric nuclear matter is studied within the conserving, self-consistent T-matrix approximation. This approach involves off-shell propagation of nucleons in the ladder diagrams. The binding energy receives contributions from the background part of the spectral function, away from the quasiparticle peak. The Fermi energy at the saturation point fulfills the Hugenholz-Van Hove relation. In comparison to the Brueckner-Hartree-Fock approach, the binding energy is reduced and the equation of state is stiffer. Received: 16 April 2002 / Accepted: 10 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: bozek@sothis.ifj.edu.pl Communicated by A. Molinari     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.     

Effects of δ Meson on Thermal Protoneutron Star Matter

In the framework of the relativistic mean field theory, the effects of the δ meson on protoneutron star matter with hyperons at finite temperature are investigated. In thermal protoneutron star matter, the δ field potential increases with density first and then decreases. Fixing the density, the increase of the temperature suppresses the δ field potential. With the inclusion of the δ meson, the threshold densities for hyperons become lower and the abundance of trapped neutrinos decreases. The most important effect of the δ meson is to increase the abundance of hyperons in the inner core range of protoneutron stars. With the rise of the temperature, the density range where the δ meson plays an important role is narrowed and the effects of the δ meson are suppressed. Moreover, the protoneutron star mass and radius are nearly not affected by the δ meson     

Thermodynamic consistency for nuclear matter calculations

We investigate the relation between the binding energy and the Fermi energy and between different expressions for the pressure in cold nuclear matter. For a self-consistent calculation based on a Φ derivable T-matrix approximation with off-shell propagators, the thermodynamic relations are well satisfied unlike for a G-matrix or a T-matrix approach using quasi-particle propagators in the ladder diagrams. Received: 8 February 2001 / Accepted: 11 June 2001     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Neutron stars with isovector scalar correlations

Neutron stars with the isovector scalar δ-field are studied in the framework of the relativistic mean-field (RMF) approach in a pure-nucleon-plus-lepton scheme. The δ-field leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses. Both features are influencing the stability conditions of the neutron stars. Two parametrizations for the effective nonlinear Lagrangian density are used to calculate the nuclear equation of state (EOS) and the neutron star properties, and compared to correlated Dirac-Brueckner results. We conclude that in order to reproduce reasonable nuclear structure and neutron star properties within a RMF approach, a density dependence of the coupling constants is required.     

Optimized δ expansion for relativistic nuclear models

The optimized δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the λφ⁴ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the δ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations. Received: 17 March 1997 / Revised version: 27 August 1997     

Dynamical response functions in correlated fermionic systems

Response functions in nuclear matter at finite temperature are considered beyond the usual Hartree-Fock plus random phase approximation (RPA) scheme. The contributions due to the propagator for the dressed nucleons and the corresponding vertex corrections are treated in a consistent way. For that purpose a semi-realistic Hamiltonian is developed with parameters adjusted to reproduce the nucleon self-energy as derived from realistic nucleon-nucleon interactions. For a scalar residual interaction the resulting response functions are very close to the RPA response functions. However, the collective modes, if present, get an additional width due to the coupling to multi-pair configurations. For isospin-dependent residual interactions we find strong modifications of isospin response functions due to multi-pair contributions in the response function. Such a modification can lead to the disappearance of collective spin or isospin modes in a correlated system and shall have an effect on the absorption rate of neutrinos in nuclear matter.     

Parity violation,the neutron radius of lead,and neutron stars

The neutron radius of a heavy nucleus is a fundamental nuclear-structure observable that remains elusive. Progress in this arena has been limited by the exclusive use of hadronic probes that are hindered by large and controversial uncertainties in the reaction mechanism. The parity radius experiment at the Jefferson Laboratory offers an attractive electro-weak alternative to the hadronic program and promises to measure the neutron radius of ²⁰⁸Pb accurately and model independently via parity-violating electron scattering. In this contribution we examine the far-reaching implications that such a determination will have in areas as diverse as nuclear structure, atomic parity violation, and astrophysics.     

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 Greens functions when the longitudinal response function and the Coulomb sum rule are calculated. The effects of the and mesons are clearly shown in quasielastic electron scattering, and the isospin-dependent attractive potential between nucleons due to the exchange of the -meson cancels the isospin-dependent repulsive contribution of the -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.     

Nuclear temperature measurements with the double isotope ratio technique: Influence of the experimental conditions

The dependence of the nuclear temperatures of highly excited systems, extracted by means of the double ratios of the emitted isotopes, on the experimental conditions is investigated. Experimental data obtained in the Xe+Cu 30 MeV/nucleon reaction are used to study the sensitivity of the method and the effects of the energy thresholds on the obtained temperature values. We find that the temperatures extracted using the He/Li ratios can be strongly influenced by the experimental energy thresholds which are different for different elements. These distortions depend on the velocity of the emitting system and on the detection angle and therefore particular care is needed in the choice of the detectors in those experiments in which velocities are low and angles are large. The use of four isotopes of the same element make negligible such effects. Received: 6 October 1999 / Accepted: 28 May 2000     

Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998