Adjustment studies in self-consistent relativistic mean-field models

We investigate the influence of the adjustment procedure and the set of measured observables on the properties and predictive power of relativistic self-consistent mean-field models for the nuclear ground state. These studies are performed with the point-coupling variant of the relativistic mean-field model. We recommend optimal adjustment algorithms for the general two-part problem and we identify various trends and dependencies as well as deficiencies of current models. Consequences for model improvements are presented.Comment: 18 pages, 6 figures, revised version, accepted for publication in Nuclear Physics

Density distributions of superheavy nuclei

We employed the Skyrme-Hartree-Fock model to investigate the density distributions and their dependence on nuclear shapes and isospins in the superheavy mass region. Different Skyrme forces were used for the calculations with a special comparison to the experimental data in $^{208}$Pb. The ground-state deformations, nuclear radii, neutron skin thicknesses and $\alpha$-decay energies were also calculated. Density distributions were discussed with the calculations of single-particle wavefunctions and shell fillings. Calculations show that deformations have considerable effects on the density distributions, with a detailed discussion on the $^{292}$120 nucleus. Earlier predictions of remarkably low central density are not supported when deformation is allowed for.Comment: 7 pages, 10 figure

On the Isovector Channels in Relativistic Point Coupling Models within the Hartree and Hartree-Fock Approximations

We investigate the consequences of Fierz transformations acting upon the contact interactions for nucleon fields occurring in relativistic point coupling models in Hartree approximation, which yield the same models but in Hartree-Fock approximation instead. We find for four-fermion interactions occurring in two existing relativistic point coupling phenomenologies that whereas in Hartree the isovector-scalar strength, corresponding to delta-meson exchange, is unnaturally small, indicating a possible new symmetry, in Hartree-Fock it is instead comparable to the isovector-vector strength corresponding to rho-meson exchange, but the sum of the two isovector coupling constants appears to be preserved in both approaches. Furthermore, in Hartree-Fock approximation, both QCD-scaled isovector coupling constants are natural (dimensionless and of order 1) whereas in Hartree approximation only that of the isovector-vector channel is natural. This indicates that it is not necessary to search for a new symmetry and, moreover, that the role of the delta-meson should be reexamined.Comment: 10 pages; accepted for publication in Nuclear Physics

The nonrelativistic limit of the relativistic point coupling model

We relate the relativistic finite range mean-field model (RMF-FR) to the point-coupling variant and compare the nonlinear density dependence. From this, the effective Hamiltonian of the nonlinear point-coupling model in the nonrelativistic limit is derived. Different from the nonrelativistic models, the nonlinearity in the relativistic models automatically yields contributions in the form of a weak density dependence not only in the central potential but also in the spin-orbit potential. The central potential affects the bulk and surface properties while the spin-orbit potential is crucial for the shell structure of finite nuclei. A modification in the Skyrme-Hartree-Fock model with a density-dependent spin-orbit potential inspired by the point-coupling model is suggested.Comment: 21 pages, latex, 1 eps figure. accepted for publication in annals of physic

The two-proton shell gap in Sn isotopes

We present an analysis of two-proton shell gaps in Sn isotopes. As the theoretical tool we use self-consistent mean-field models, namely the relativistic mean-field model and the Skyrme-Hartree-Fock approach, both with two different pairing forces, a delta interaction (DI) model and a density-dependent delta interaction (DDDI). We investigate the influence of nuclear deformation as well as collective correlations and find that both effects contribute significantly. Moreover, we find a further significant dependence on the pairing force used. The inclusion of deformation plus correlation effects and the use of DDDI pairing provides agreement with the data.Comment: gzipped tar archiv containing LaTeX source, bibliography file (*.bbl), all figures as *.eps, and the style file

Description of nuclear systems within the relativistic Hartree-Fock method with zero range self-interactions of the scalar field

An exact method is suggested to treat the nonlinear self-interactions (NLSI) in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We consider here the NLSI constructed from the relativistic scalar nucleon densities and including products of six and eight fermion fields. This type of NLSI corresponds to the zero range limit of the standard cubic and quartic self-interactions of the scalar field. The method to treat the NLSI uses the Fierz transformation, which enables one to express the exchange (Fock) components in terms of the direct (Hartree) ones. The method is applied to nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the NLSI, which are explicitly isovector-independent, generate scalar, vector and tensor nucleon self-energies strongly density-dependent. This strong isovector structure of the self-energies is due to the exchange terms of the RHF method. Calculations are carried out with a parametrization containing five free parameters. The model allows a description of both types of systems compatible with experimental data.Comment: 23 pages, 14 figures (v2: major quantitative changes

Comment on ``Structure of exotic nuclei and superheavy elements in a relativistic shell model''

A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the new parameterization NL-RA1 of the relativistic mean-field model which is claimed to give a better description of nuclear properties than earlier ones. Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will be shown in this comment these findings are to be doubted as they are obtained with an unrealistic parameterization of the pairing interaction and neglecting ground-state deformation.Comment: 2 pages REVTEX, 3 figures, submitted to comment section of Phys. Rev. C. shortened and revised versio

Skyrme mean-field study of rotational bands in transfermium isotopes

Self-consistent mean field calculations with the SLy4 interaction and a density-dependent pairing force are presented for nuclei in the Nobelium mass region. Predicted quasi-particle spectra are compared with experiment for the heaviest known odd N and odd Z nuclei. Spectra and rotational bands are presented for nuclei around No252,4 for which experiments are either planned or already running.Comment: 13 pages LATEX, elsart style, 6 embedded eps figure

Shell stabilization of super- and hyperheavy nuclei without magic gaps

Quantum stabilization of superheavy elements is quantified in terms of the shell-correction energy. We compute the shell correction using self-consistent nuclear models: the non-relativistic Skyrme-Hartree-Fock approach and the relativistic mean-field model, for a number of parametrizations. All the forces applied predict a broad valley of shell stabilization around Z=120 and N=172-184. We also predict two broad regions of shell stabilization in hyperheavy elements with N approx 258 and N approx 308. Due to the large single-particle level density, shell corrections in the superheavy elements differ markedly from those in lighter nuclei. With increasing proton and neutron numbers, the regions of nuclei stabilized by shell effects become poorly localized in particle number, and the familiar pattern of shells separated by magic gaps is basically gone.Comment: 6 pages REVTEX, 4 eps figures, submitted to Phys. Lett.