Density-dependent Coupling Constants Research Articles

The density- and isospin-dependent Δ-formation cross section and its decay width

The energy-, density-, and isospin-dependent Δ-formation cross section σ*Nπ→Δ and Δ-decay width are calculated based on the relativistic BUU approach in which the effective mass splitting of nucleon and Δ baryons in isospin-asymmetric matter is considered by the inclusion of the δ meson exchange in the effective Lagrangian density and the density-dependent coupling constants of Hofmann et al. The results show that the σ*Nπ→Δ is decreased (increased) moderately with increasing density with (without) the consideration of medium modifications on pion mass. Meanwhile, if the invariant mass of the system is not far from the Δ pole mass, the Δ-decay width is also weakly dependent on density. The mass splitting effect of differently charged nucleon and Δ baryons on σ*Nπ→Δ is found to be more obvious than that of pion mesons but much weaker than the mass splitting in the hard Δ production channel NN → NΔ. Further, the largest mass-splitting influence is seen in the π−p → Δ0 and π+n → Δ+ channels but not in the production of Δ − and Δ++ isobars.

Influence of Density-Dependent Coupling Constants on Equation of State of Infinite Symmetric Nuclear Matter**Supported by the National Natural Science Foundation of China under Grant No. 11275073

In the mean field approximation of nonlinear relativistic σ—ω—ρ model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state (EOS) of infinite symmetric nuclear matter in different conditions. We find that the EOS of nuclear matter will become stiffer as c, d in the self-interaction of σ meson increase when the coefficients except aω in Γω, in which the opposite occurs, are fixed. On the other hand, greater values of aσ, bσ, cσ, aω, dω and smaller values of dσ, bω, cω will lead to stiffer EOS if c and d are fixed. Besides, greater values of Γσ,ω lead to stiffer EOS in high density region for the EOS with same incompressibility coefficient at saturation density.

EffectiveΛNpotential from relativistic Brueckner-Hartree-Fock theory

The effective $\ensuremath{\Lambda}N$ potentials are derived from one-boson-exchange hyperon-nucleon interaction such as Juelich potentials, Juelich94a (Jul94) and Juelich05 (Jul05), within the relativistic Brueckner-Hartree-Fock theory. The Jul94 effective $\ensuremath{\Lambda}N$ potential ${U}_{\ensuremath{\Lambda}}$ (${p}_{\ensuremath{\Lambda}}$) with ${p}_{\ensuremath{\Lambda}}=0$ is $\ensuremath{-}27.63$ MeV at the nuclear saturation density, which is in good agreement with the observed data, whereas for the Jul05 effective $\ensuremath{\Lambda}N$ potential, ${U}_{\ensuremath{\Lambda}}$ is $\ensuremath{-}47.85$ MeV, which is bound more than the observed data. We then compare the effective $\ensuremath{\Lambda}N$ potential energies obtained in nonrelativistic and relativistic frameworks. With the $\ensuremath{\Lambda}$ momentum ${p}_{\ensuremath{\Lambda}}$ increasing, the relativistic effect becomes obvious and provides more repulsive contribution. We also derive the scalar and vector potentials of the $\ensuremath{\Lambda}$ hyperon from the effective $\ensuremath{\Lambda}N$ potential in the relativistic framework. With these potentials, the coupling constants between mesons and the $\ensuremath{\Lambda}$ hyperon are determined for each density in the framework of relativistic mean-field theory. Finally, we calculate the $\ensuremath{\Lambda}$ single-particle energies of hypernuclei with these density-dependent coupling constants in the relativistic mean-field theory. We find that the single $\ensuremath{\Lambda}$ binding energies of $\ensuremath{\Lambda}$ hypernuclei from $_{\ensuremath{\Lambda}}^{16}\mathrm{O}$ to $_{\ensuremath{\Lambda}}^{208}\mathrm{Pb}$ by using the Jul94 potential compare well with the experimental data.

Gamma-ray strength at low energies using relativistic QRPA with exact coupling to the continuum

Continuum-quasiparticle random-phase Approximation (CQRPA) within the relativistic point-coupling model with density-dependent coupling constants is applied to investigate collective excitations in spherical nuclei. In particular we study the impact of the exact continuum on the giant-dipole and pygmy resonance of several Sn isotopes as well as the radiative neutron capture rates of importance for astrophysical calculations.

BCS-BEC crossover and thermodynamics in asymmetric nuclear matter with pairings in isospinI=0andI=1channels

The Bardeen/Cooper/Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover and phase diagram for asymmetric nuclear superfluid with pairings in isospin $I=0$ and $I=1$ channels are investigated at the mean-field level by using a density-dependent nucleon-nucleon potential. Induced by the in-medium nucleon mass and density-dependent coupling constants, neutron-proton Cooper pairs could be in BEC state at sufficiently low density, but there is no chance for the BEC formation of neutron-neutron and proton-proton pairs at any density and asymmetry. We calculate the phase diagram in asymmetry-temperature plane for weakly interacting nuclear superfluid and find that including the $I=1$ channel changes significantly the phase structure at low temperature. There appears a new phase with both $I=0$ and $I=1$ pairings at low temperature and low asymmetry, and the gapless state in any phase with $I=1$ pairing is washed out and all excited nucleons are fully gapped.

Nuclear matter in the crust of neutron stars derived from realisticNNinteractions

Properties of inhomogeneous nuclear matter are evaluated within a relativistic mean-field approximation by using density-dependent coupling constants. A parametrization for these coupling constants is presented that reproduces the properties of the nucleon self-energy obtained in Dirac-Brueckner-Hartree-Fock calculations of asymmetric nuclear matter but also provides a good description for bulk properties of finite nuclei. The inhomogeneous infinite matter is described in terms of cubic Wigner-Seitz cells, which allows for a microscopic description of the structures in the so-called pasta-phase of nuclear configurations and provides a smooth transition to the limit of homogeneous matter. The effects of pairing properties and finite temperature are considered. A comparison is made to corresponding results by employing the phenomenological Skyrme Hartree-Fock approach, and the consequences for the Thomas-Fermi approximation are discussed.

Relativistic Mean Field theory with density dependent meson couplings

Relativistic mean field theory with density dependent coupling constants is used to investigate ground state properties and properties of excited configurations in nuclei far from stability. It turns out that it is very important to consider also a density dependence the isovector channel. This provides not only an improved description of the equation of state for neutron matter and asymmetric nuclear matter but also for isovector properties of finite nuclei far from stability such as the neutron skin thickness, and the isoscalar and isovector giant resonances.

Equation of State of Nuclear Matter in Chiral σ-ω Model**The project supported by National Natural Science Foundation of China under Grant Nos. 10275099, 10347124, and 10175096, and the Natural Science Foundation of Guangdong Province of China under Grant No. 001182

The equation of state of nuclear matter is studied in the 1-loop approximation of chiral linear σ-ω model. By introducing the density-dependent coupling constants, the problem of tachyon pole in the chiral σ-ω model is resolved. The 1-loop contributions of σ and π mesons to the nucleon's binding energy are included, while the empirical properties of nuclear matter such as saturation density, binding energy, and incompressibility are well reproduced.

Incompressibility of strange matter

Strange stars (ReSS) calculated from a realistic equation of state (EOS), that incorporate chiral symmetry restoration as well as deconfinement at high density [Phys. Lett. B 438 (1998) 123; Phys. Lett. B 447 (1999) 352, Addendum; Phys. Lett. B 467 (1999) 303, Erratum; Indian J. Phys. B 73 (1999) 377] show compact objects in the mass radius curve. We compare our calculations of incompressibility for this EOS with that of nuclear matter. One of the nuclear matter EOS has a continuous transition to ud-matter at about five times normal density. Another nuclear matter EOS incorporates density dependent coupling constants. From a look at the consequent velocity of sound, it is found that the transition to ud-matter seems necessary.

Relativistic mean field calculations with density-dependent meson-nucleon coupling

Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for σ-, ω- and ρ-meson coupling is obtained by fitting to properties of nuclear matter and some finite nuclei. The results are compared to density-dependent coupling constants derived from self-energies of Dirac-Brueckner calculations of nuclear matter. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and a centre-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines.

Density dependent hadron field theory.

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used. Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of $^{16}\mathrm{O}$, $^{40,48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new ``Coester line'' in the nuclear matter equation of state.

Relativistic density-dependent Hartree-Fock approach for finite nuclei.

The nucleon self-energy obtained from the Dirac Brueckner-Hartree-Fock calculation is parametrized by introducing density-dependent coupling constants of isoscalar mesons in the relativistic Hartree-Fock (RHF) approach. The RHF calculations with density-dependent coupling constants not only reproduce the nuclear matter saturation properties, but also provide a good starting point to study finite nuclei properties. The relativistic density-dependent Hartree-Fock (RDHF) approach contains the features of the relativistic G matrix and in the meantime simplifies the calculation. The ground state properties of spherical nuclei calculated in the RDHF are in good agreement with the experimental data. The contribution of isovector mesons \ensuremath{\pi} and \ensuremath{\rho}, especially the contribution of the tensor coupling of \ensuremath{\rho} meson, are discussed in this paper.

Finite - Nuclei Properties in Relativistic Density Dependent Hartree - Fock Approach

Finite nucleus properties are studied in a relativistic effective interaction approach. Density dependent coupling constants of the meson-nucleon interactions are adopted to incorporate the relativistic Brueckner-Hartree-Fock results in the relativistic mean field (RMF) or relativistic Hartree-Fock (RHF) approach. It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The calculated ground state properties with the density dependent coupling constants are in a good agreement with experiment. The contribution of isovector mesons in RHF is discussed.

Isovector meson contribution in the relativistic Hartree-Fock approach for finite nuclei.

The properties of finite nuclei are studied in a relativistic effective interaction approach. Density dependent coupling constants of the meson-nucleon interactions are adopted to incorporate the Dirac Brueckner-Hartree-Fock (DBHF) results in the relativistic mean field (RMF) or relativistic Hartree-Fock (RHF) approach. It is desired to remedy the deficiencies of the RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The importance of the nucleon correlations, which are expressed by density-dependent coupling constants, is studied and the contribution of isovector mesons is discussed. It is shown that the calculated ground state properties with the density-dependent coupling constants are in good agreement with experiment.

Thermostatic properties and Coulomb instability of highly excited nuclei.

The nuclear excitation is expressed in terms of an intrinsic temperature. When the temperature is raised beyond a certain limiting value the nucleus becomes unstable due to the Coulomb repulsion and falls apart before the critical temperature of the liquid-vapor phase transition is reached. We isolate the finite nucleus from the surrounding vapor by using a subtracted level occupation probability. Thermo- static and limiting properties are calculated in a relativistic Thomas-Fermi approach using density-dependent coupling constants, adjusted to the outcome of relativistic Brueckner-Hartree-Fock nuclear matter treatments, and, for the purpose of comparison, density-independent coupling constants. The disappearance of fusion-like processes in heavy-ion collisions is related to the limiting excitation energy.

Finite nuclear systems in a relativistic extended Thomas-Fermi approach with density-dependent coupling parameters.

We discuss a relativistic density-dependent Hartree approach, adjusted to the outcome of the relativistic Brueckner-Hartree-Fock nuclear matter treatments with realistic one-boson-exchange (OBE) Lagrangians. The density-dependent coupling constants are then used in the frame of the relativistic extended Thomas-Fermi approximation to determine the properties of finite nuclei. The results are studied for different OBE potentials and compared with experiment. The agreement with the data of this parameter-free treatment is, despite its simplicity, rather satisfactory.

Parametrization of the relativistic Dirac-Brueckner G matrix.

A representation of the relativistic Brueckner G matrix by an effective interaction Lagrangian is proposed. This Lagrangian contains the four mesons \ensuremath{\sigma}, \ensuremath{\omega}, \ensuremath{\pi} (pseudovector), and \ensuremath{\rho} (vector), with density-dependent coupling constants. It is shown that Dirac-Hartree-Fock calculations of nuclear matter using this effective interaction can reproduce well the results of the Dirac-Brueckner Hartree-Fock approach.