Nuclei embedded in an electron gas

The properties of nuclei embedded in an electron gas are studied within the relativistic mean-field approach. These studies are relevant for nuclear properties in astrophysical environments such as neutron-star crusts and supernova explosions. The electron gas is treated as a constant background in the Wigner-Seitz cell approximation. We investigate the stability of nuclei with respect to alpha and beta decay. Furthermore, the influence of the electronic background on spontaneous fission of heavy and superheavy nuclei is analyzed. We find that the presence of the electrons leads to stabilizing effects for both $\alpha$ decay and spontaneous fission for high electron densities. Furthermore, the screening effect shifts the proton dripline to more proton-rich nuclei, and the stability line with respect to beta decay is shifted to more neutron-rich nuclei. Implications for the creation and survival of very heavy nuclear systems are discussed.Comment: 35 pages, latex+ep

Calculating the Fierz Transformation for Higher Orders

We consider the higher-order Fierz transformation, which corresponds to expanding a product of $\bar\psi\Gamma\psi$ terms into a sum of products of Dirac densities and currents. It is shown that the Fierz transformation can be obtained by solving a large system of linear equations with fractional complex coefficients, which is practical at least up to fourth power.Comment: 6 pages, 3 table

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

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

Exploring the extended density-dependent Skyrme effective forces for normal and isospin-rich nuclei to neutron stars

We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass ($\sim 1.4 M_\odot$). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the same set of the data as employed to determine the parameters of the GSEF. We find that the GSEF yields larger values for the neutron skin thickness which are closer to the recent predictions based on the isospin diffusion data. The Skyrme parameters so obtained are employed to compute the strength function for the isoscalar giant monopole, dipole and quadrupole resonances. It is found that in the case of GSEF, due to the the larger value of the nucleon effective mass the values of centroid energies for the isoscalar giant resonances are in better agreement with the corresponding experimental data in comparison to those obtained using the SSEF. We also present results for some of the key properties associated with the neutron star of "canonical" mass and for the one with the maximum mass.Comment: 45pages, 16 figure

Nuclear signatures in high-harmonic generation from laser-driven muonic atoms

High-harmonic generation from muonic atoms exposed to intense laser fields is considered. Our particular interest lies in effects arising from the finite nuclear mass and size. We numerically perform a fully quantum mechanical treatment of the muon-nucleus dynamics by employing modified soft-core and hard-core potentials. It is shown that the position of the high-energy cutoff of the harmonic spectrum depends on the nuclear mass, while the height of the spectral plateau is sensitive to the nuclear radius. We also demonstrate that $\gamma$-ray harmonics can be generated from muonic atoms in ultrastrong VUV fields, which have potential to induce photo-nuclear reactions.Comment: 5 pages, 3 figure

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

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