Nuclear curvature energy in relativistic models

The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curvature energy are in good agreement.

Nuclear curvature energy in relativistic models

The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curvature energy are in good agreement.

Rho-omega mixing and the Nolen-Schiffer anomaly in relativistic nuclear models

We calculate within the framework of relativistic nuclear models the contribution of the ρ0 - ω mixing interaction to the binding energy differences of the mirror nuclei in the neighborhood of A = 16 and A = 40. We use two relativistic models for the nuclear structure, one with scalar and vector Woods-Saxon potentials, and the Walecka model. The ρ0 - ω interaction is treated in first order perturbation theory. When using the Walecka model the ρ- and ω-nucleon coupling constants are the same for calculating bound state wave functions and the perturbation due to the mixing. We find that the relativistic results on the average are of the same order as the ones obtained with nonrelativistic calculations.

Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

We study whether the neutron skin thickness Δrnp of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to Δrnp arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in Δrnp of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that Δrnp of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of Δrnp of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of Δrnp. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.

Statistical quark models for the nucleon structure functions

We consider some existing relativistic models for the nucleon structure functions, relying on statistical approaches instead of perturbative ones. These models are based on the Fermi-Dirac distribution for the confined quarks, where a density of energy levels is obtained from an effective confining potential. In this context, it is presented some results obtained with a recent statistical quark model for the sea-quark asymmetry in the nucleon. It is shown, within this model, that experimental available observables, such as the ratio and difference between proton and neutron structure functions, are quite well reproduced with just three parameters: two chemical potentials used to reproduce the valence up and down quark numbers in the nucleon, and a temperature that is being used to reproduce the Gottfried sum rule violation. © 2010 American Institute of Physics.

NOLEN-SCHIFFER ANOMALY AND RHO(0)-OMEGA MIXING

The Nolen-Schiffer anomaly is the long standing discrepancy between theory and experiment of binding energy differences of mirror nuclei. It appears that the anomaly is largely explained by the charge symmetry breaking force generated by the rho(0)-omega mixing. In this paper I discuss the effect of the rho(0)-omega mixing to the binding energy differences in relativistic models of the nucleus. I also discuss the issue of momentum dependence of rho(0)-omega mixing amplitude and present an alternative explanation of the anomaly based on the partial restoration of chiral symmetry in the nucleus.

Rho-omega mixing and neutron-proton self-energies in the Walecka model

We use the Walecka model to investigate the influence of the charge symmetry breaking ρ0-ω mixing interaction on the neutron-proton self-energy difference in nuclear matter. Using 2mρ〈ρ0|H|ω〉 = -4500 MeV2, and employing the Dirac-Hartree-Fock approximation, we find that the neutron-proton self-energy difference is a decreasing function of the nuclear matter density, and that it has a value of the order of 700 keV at the normal density. The results indicate that the Nolen-Schiffer anomaly might be explained by means of relativistic nuclear models in a similar way as it is explained by means of non-relativistic models.

Droplet formation in cold asymmetric nuclear matter in the quark-meson-coupling model

The quark-meson-coupling model is used to study droplet formation from the liquid-gas phase transition in cold asymmetric nuclear matter. The critical density and proton fraction for the phase transition are determined in the mean field approximation. Droplet properties are calculated in the Thomas-Fermi approximation. The electromagnetic field is explicitly included and its effects on droplet properties are studied. The results are compared with the ones obtained with the NL1 parametrization of the non-linear Walecka model. © 2000 Elsevier Science B.V.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition. © Springer-Verlag 1996.

Optimized delta expansion for relativistic nuclear models: Renormalization of vacuum fluctuations

We use the optimized linear δ expansion and functional methods to study vacuum contributions in nuclear matter up to the lowest non-trivial order which includes exchange terms. We show that well known results (MFT, RHA and HF) can be easily reproduced when appropriate limits are taken. Neglecting vacuum contributions we explicitly show that the δ expansion goes beyond the traditional loop approximation previously used to study two loop vacuum contributions in nuclear matter. We then evaluate and renormalize vacuum exchange contributions showing that they are numerically very large, as predicted by the ordinary loop approximation.

Optimized delta expansion for relativistic nuclear models

The optimized delta-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 lambda phi(4) model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the delta expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.