Single–particle spectra of Λ and Σ hypernuclei are calculated within a relativistic mean–field theory. The hyperon couplings used are compatible with the Λ binding in saturated nuclear matter, neutron-star masses and experimental data on Λ levels in hypernuclei. Special attention is devoted to the spin-orbit potential for the hyperons and the influence of the ρ-meson field (isospin dependent interaction). PACS number: 21.80.+a

A new effective two-body interaction of the Gogny type (DIP) is presented. While the merits of the currently used parametrizations (D1 and D1S) remain practically untouched, significant improvements are achieved with respect to three of their main deficiencies: (i) the depth of the optical potential agrees with experiments to energies beyond 200 MeV, (ii) sum rules of Landau parameters are better fulfilled and cleaned from instabilities due to the isovector breathing mode at physical values of the density and (iii) a realistic behaviour for the neutron matter equation of state at high densities is achieved.

The variational content of the Wigner–Kirkwood ℏ expansion of the density matrix is analyzed in mean field approximation. A new variational method based on a strict expansion of the energy density in powers of ℏ is established. It is applied to the case of fermions moving in an external potential, as well as to the self-consistent problem in semi-infinite matter. The standard density functional theory is reviewed and contrasted with the new method.

Lambda, Sigma, and Xi (multi-)hypernuclei are investigated within a density-dependent relativistic Hartree approach. To this end, the covariant field theory recently developed by Lenske and Fuchs is extended to hypernuclear systems, leading to rearrangement self-energies in the baryonic field equations. Self-consistent solutions, including omega-hyperon tensor couplings, are obtained in the Hartree limit with the sigma- and omega-nucleon couplings adjusted to Dirac-Brueckner-Hartree-Fock results for infinite nuclear matter, utilizing a local density approximation. With the meson-nucleon couplings compatible with realistic nucleon-nucleon potentials, the description remains free of adjustable parameters on the nucleonic side, while meson-hyperon couplings are fixed by SU(6) symmetry or fitted to available experimental data. In addition, results for A hypernuclei are presented within a purely phenomenological relativistic mean-field model including sigma and omega self-interactions. Special attention is devoted to the impact of the rho-meson field in Sigma and Xi hypernuclei. Finally, the 'hyperon-halo' of multi-hypernuclei and the way it is affected by rearrangement effects is studied.

In this study we appraise the capability of the relativistic density-dependent Hartree theory to reproduce the properties of finite nuclei by using parametrizations of relativistic Brueckner-Hartree-Fock calculations for infinite nuclear matter, performed in the full Dirac space. We apply the density-dependent relativistic Hartree approach of Brockmann and Toki as well as its covariant extension including rearrangement contributions, recently developed by Lenske and Fuchs. Within this parameter-free theory the results for finite systems are satisfactory. We used the one-boson-exchange potentials A and B constructed by Brockmann and Machleidt.

The relativistic spin-orbit force and its dependence on neutron excess are studied using the σ-ω-ϱ model. By working within the schematic model of asymmetric semi-infinite nuclear matter we are able to isolate the spin-orbit potential and to investigate the following aspects: (i) the influence of the spin-orbit force on nuclear surface properties as a function of neutron excess, (ii) the local variation of the spin-orbit strength at various asymmetries, and (iii) the dependence of the spin-orbit force on the nucleonic isospin. Calculations have been performed for the currently used parameter sets NL1 and NL-SH up to the corresponding neutron-drip line. We conclude that with increasing neutron excess the spin-orbit strength drastically decreases while its impact on nuclear surface properties depends only slightly on asymmetry. The isospin dependence of the relativistic spin-orbit force is negligible.

Relativistic Thomas-Fermi calculations of asymmetric semi-infinite nuclear matter have been performed using some current parameter sets of the sigma - omega - rho model. Symmetric semi-infinite nuclear matter is also calculated in the Hartree approximation. We present and discuss the results for various macroscopic coefficients with special emphasis on the surface-symmetry properties and compare them with values from non-relativistic Skyrme calculations and from semi-empirical mass formulae.

Calculations for semi-infinite nuclear matter within the relativistic Hartree approximation have been performed utilizing the nonlinear sigma-omega model. We investigate the structure of the nuclear surface, i.e., the surface energy and the surface thickness, in its dependence on the properties of uniform nuclear matter in a systematic manner. We establish criterions for the selection of a relativistic mean-held parametrization following from the experimentally well determined, nuclear surface properties. In this respect, we discuss some currently used parameter sets. In addition, the accuracy of the semiclassical Thomas-Fermi approximation compared with the fully quantal approach is investigated. We close with some studies on density distributions (skewness parameter, Friedel oscillations, and the influence of the spin-orbit potential) and the nuclear curvature energy.

Using the scaling model, we calculate within the framework of relativistic Hartree theory the nuclear breathing-mode energies corresponding to the NL1 and NL-SH parameter sets of the nonlinear sigma-omega-rho model. Both of these sets are found to be in disagreement with experiment and there is a clear need for an improved fit. However, as far as the nuclear-matter incompressibility K(upsilon) is concerned, neither the NL1 value, 212 MeV, nor the NL-SH value, 356 MeV, can be excluded.

Relativistic Thomas-Fermi calculations for finite nuclei including quantum corrections up to second order in \ensuremath{\Elzxh}, i.e., Wigner-Kirkwood and exchange corrections, have been performed. A linear \ensuremath{\sigma}-\ensuremath{\omega} model is used, in case of exchange-corrected calculations extended by \ensuremath{\pi}-nucleon and tensor \ensuremath{\rho}-nucleon contributions. A detailed discussion of the outcome shows that the inclusion of quantum corrections improves the description of the nuclear surface and the classical forbidden region in comparison to the standard relativistic Thomas-Fermi model. Furthermore, special attention is devoted to the investigation of the spin-orbit interaction and the influence of the \ensuremath{\sigma}-meson mass on nuclear properties.

Relativistic thermal Thomas-Fermi calculations for equilibrated hot nuclei have been performed for a nonlinear sigma-omega model. To isolate the properties of the hot nucleus from the contributions of the surrounding nucleon vapor, a subtraction procedure based on the "equivalent sharp radius" is applied. Various quantities describing hot nuclei and their temperature dependence are investigated. Special attention is devoted to the study of the level density parameter; we compare our results with those of a recently published nonrelativistic investigation.

We present an extension of the semiclassical Thomas-Fermi model to relativistic systems. These are obtained by application of the gradient expansion scheme on the Wigner transformed Dyson equation. Explicitly we give the expansion of the Green's functions, phase-space densities, and densities for a system of nucleons in a vector and scalar potential to second order.

A derivation of the relativistic Hartree-Fock-Approximation for finite temperatures is given by utilizing a thermodynamic extremum principle for the construction of an approximate (thermal HF-) hamiltonian of single-particle structure. By use of the Wigner transform one can obtain the so-called quasi-classical expansion of the theory; i.e. the thermal Thomas-Fermi theory plus quantum corrections. The details are illustrated for the Walecka Lagrangian density.