Self-consistent inclusion of pion polarisation in the relativistic Dirac-Brueckner approach to nuclear matter

We investigate the influence of pion polarisation effects in the Dirac-Brueckner approach. The pion polarisation is included preserving the self-consistency of the DB approach. Results for single-particle properties, equation of state, and total effective cross sections in symmetric nuclear matter are presented. Also, we calculated the pion condensation threshold.     

On the effective σ-boson exchange in the relativistic Dirac-Brueckner approach to nuclear matter

A relativistic form of the Brueckner theory of nuclear matter is applied to an extended meson-exchange model for the NN-interaction which contains explicit 2π-and π-exchange. This model avoids the effective σ-boson which is characteristic of the simplified meson exchange, as e.g. the one-boson-exchange (OBE) potential. It turns out that the relativistic saturation. effects found earlier within the OBE model are confirmed by the extended and more realistic model. In particular it is found that the relativistic effects caused by the explicit 2π-and π-exchange are well simulated by the effective σ-boson of the OBE model.     

Density dependence of the single-particle potential in nuclear matter

The single-particle potential in infinite nuclear matter is computed as a function of density and energy in a variety of relativistic mean-field models of nuclear matter. A comparison of this potential is made with that computed by Friedman and Pandharipande using the variational method. We also show that the self-consistent mean-field Hartree approximation satisfies the Hugenholtz-van Hove theorem. High-density behavior of the single-particle potential is considered.     

The single-particle potential of nuclear matter in the LOCV framework

The density and momentum dependence of single-particle potential (SPP) and effective mass of symmetric nuclear matter are studied in the framework of lowest order constrained variational (LOCV) method. The Reid68, the Reid68-Δ and the ₁₈Av interactions are considered as the input nucleon-nucleon potentials. It is shown that the SPP of nuclear matter, at fixed density, is an increasing function of nucleon momentum, and it has different behavior for the Reid type potentials with respect to ₁₈Av interaction. We find good agreements between our LOCV SPP and those coming from others many-body techniques such as the (Dirac-)Brueckner-Hartree-Foch ((D)BHF), the fermion hypernetted chain (FHNC), mean field (MF), etc. On the other hand SPP dramatically depends on the density at low and high nucleon momentums. While the effective mass of nuclear matter increases as we increase the nucleon momentum, it decreases at the Fermi surface. Again, good agreements are observed between our calculated effective mass and those coming from the methods mentioned above.     

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and to the AV₁₄interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the a² \alpha^{2}_{} law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} instead of its non-relativistic version, i.e. the AV₁₄interaction. The results are compared with other many-body calculations.     

The tensor interaction and nuclear matter

The separation method of Moszkowski-Scott has been applied to the calculation of the properties of nuclear matter using two different nucleon-nucleon potentials, both in reasonable agreement with two-body data. Calculations with the potential of Brueckner-Gammel gave $\text{A}\text{E}\text{= ?14.2}\text{Mev}$ at an equilibrium densitty corresponding to k_f = 1.5 f^?1. The difference from the results of B and G may be caused by slow convergence of the series (especially in the triplet-even state where the tensor interaction has a large second order contribution). An important factor in obtaining nuclear saturation is shown to be the weakening of tensor interaction effects by the Fermi sea. Evidence for this may also be seen from the results obtained using a different two nucleon potential which, however, still gives good fits to two body data. The potential chosen has a much weaker tensor component and shows no sign of saturation at normal densities (at k_f = 1.5 f^?1, $\text{A}\text{E}\text{= ?23.4}\text{Mev}$). The difference in the two results appears to be much larger than can be accounted for either by higher order terms or by differences in the phase shift approximation to the reaction matrix.     

Instability in relativistic mean-field theories of nuclear matter

We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly.     

Modifications of single-particle properties in nuclear matter induced by three-body forces

Within the self-consistent Green’s function formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.     

On relativistic approaches to the pion self-energy in nuclear matter

We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon-hole and delta-isobar-nucleon-hole contributions to the pion self-energy incorporates the s-wave scattering, whose magnitude within the RPA is in conflict with the near-threshold behavior imposed by chiral symmetry. As a result, a relativistic approach to the pion self-energy in isospin-symmetric nuclear matter, containing only these diagrams, does not satisfy the known experimental results on the near-threshold behavior of the -nucleon (forward) scattering amplitude.Received: 12 December 2003, Revised: 16 March 2004, Published online: 26 May 2004PACS: 24.10.Cn Many-body theory - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.65. + f Nuclear matter - 25.70.-z Low and intermediate energy heavy-ion reactions     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

Systematics of nuclear matter and finite nuclei properties in a non-linear relativistic mean field approach

A phenomenological non-linear relativistic mean field approach is used to investigate primarily the properties of nuclear matter. The dimensionless parameters are adjusted using different empirical quantities which are discussed in detail: saturation conditions, the incompressibility parameter, symmetry energy and surface energy. Particular attention is paid to the cubic and quartic terms in the self-interaction part of the scalar field. The effective parameters are then used to study doubly magic finite nuclei in the Dirac-Hartree approximation. Different ground-state properties, binding energies, rms radii, density distributions, are then systematically analyzed and discussed. A remarkable agreement with experimental quantities is found and further possibilities are suggested.     

Pulsating blobs of quark matter in relativistic nuclear collisions

The formation of hot, dense quark matter in violent high energy heavy ion collisions is discussed in a relativistic hydrodynamical model. Rapidly pulsating blobs of quark matter (treated in the bag model) are predicted to appear as a result of the expansive flow of the compressed quark matter against the contracting influence of confinement. The radial oscillations may result in pulsed matter emission.     

Strongly interacting low-viscosity matter created in relativistic nuclear collisions

Substantial collective flow is observed in collisions between large nuclei at BNL RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity eta to entropy density s by Kovtun, Son, and Starinets within anti-de Sitter space/conformal field theory yields eta/s=variant Planck's over 2pi/4pikB, which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio eta/s. We suggest that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD.     

Fractional exclusion statistics applied to relativistic nuclear matter

The effect of statistics of the quasiparticles in the nuclear matter at extreme conditions of density and temperature is evaluated in the relativistic mean-field model generalized to the framework of the fractional exclusion statistics (FES). In the model, the nucleons are described as quasiparticles obeying FES and the model parameters were chosen to reproduce the ground state properties of the isospin-symmetric nuclear matter. In this case, the statistics of the quasiparticles is related to the strengths of the nucleon-nucleon interaction mediated by the neutral scalar and vector meson fields. The relevant thermodynamic quantities were calculated as functions of the nucleons density, temperature and fractional exclusion statistics parameter α. It has been shown that at high temperatures and densities the thermodynamics of the system has a strong dependence on the statistics of the particles. The scenario in which the nucleon-nucleon interaction strength is independent of the statistics of particles was also calculated, but it leads in general to unstable thermodynamics.     

LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (H_R) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and the non-relativistic two-body Hamiltonian, i.e. the Argonne V₁₄ interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and AV₁₄ interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at r \rho = 0.253 (fm^-3) with [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.     

Incompressibility and single-particle potential for asymmetric nuclear matter with Skyrme potential

The incompressibility and the single-particle potential of asymmetric nuclear matter have been investigated in the framework of the Skyrme interaction. These parameters have been studied as functions of the nuclear density, the neutron excess parameter, and the temperature. The ratio of the isothermal incompressibility of hot nuclear matter to the incompressibility of cold nuclear matter for different values of neutron excess as a function of temperature is calculated. It is observed that this ratio decreases with temperature increasing apart from pure neutron matter when the growth of temperature leads to the growth of incompressibility. The symmetry incompressibility has been calculated as a function of density for different values of temperature. The text was submitted by the authors in English.