Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

BRST-invariant path integral for a spinning relativistic particle

The propagator of a relativistic spinning particle is calculated using the Becchi-Rouet-Stora-Tyutin-(BRST)-invariant path-integral formalism of Fradkin and Vilkovisky. The spinless case is considered as an introduction to the formalism.

Pseudoclassical description of a relativistic spinning particle

A pseudoclassical model for a relativistic spinning particle is studied. The only physically meaningful world line is the one without Zitterbewegung. The Poincar realization for this situation is constructed.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations

Although ab initio calculations of relativistic Brueckner theory lead to large scalar isovector fields in nuclear matter, at present, successful versions of covariant density functional theory neglect the interactions in this channel. A new high-precision density functional DD-MEδ is presented which includes four mesons, σ, ω, δ, and ρ, with density-dependent meson-nucleon couplings. It is based to a large extent on microscopic ab initiocalculations in nuclear matter. Only four of its parameters are determined by adjusting to binding energies and charge radii of finite nuclei. The other parameters, in particular the density dependence of the meson-nucleon vertices, are adjusted to nonrelativistic and relativistic Brueckner calculations of symmetric and asymmetric nuclear matter. The isovector effective mass mp*−mn* derived from relativistic Brueckner theory is used to determine the coupling strength of the δ meson and its density dependence.

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.

The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas-Fermi theory

We analyze the influence of the density dependence of the symmetry energy on the average excitation energy of the isoscalar giant monopole resonance (GMR) in stable and exotic neutron-rich nuclei by applying the relativistic extended Thomas-Fermi method in scaling and constrained calculations. For the effective nuclear interaction, we employ the relativistic mean field model supplemented by an isoscalar-isovector meson coupling that allows one to modify the density dependence of the symmetry energy without compromising the success of the model for binding energies and charge radii. The semiclassical estimates of the average energy of the GMR are known to be in good agreement with the results obtained in full RPA calculations. The present analysis is performed along the Pb and Zr isotopic chains. In the scaling calculations, the excitation energy is larger when the symmetry energy is softer. The same happens in the constrained calculations for nuclei with small and moderate neutron excess. However, for nuclei of large isospin the constrained excitation energy becomes smaller in models having a soft symmetry energy. This effect is mainly due to the presence of loosely-bound outer neutrons in these isotopes. A sharp increase of the estimated width of the resonance is found in largely neutron-rich isotopes, even for heavy nuclei, which is enhanced when the symmetry energy of the model is soft. The results indicate that at large neutron numbers the structure of the low-energy region of the GMR strength distribution changes considerably with the density dependence of the nuclear symmetry energy, which may be worthy of further characterization in RPA calculations of the response function.

Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Scaling in relativistic Thomas-Fermi approach for nuclei

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the ThomasFermi approach. The ThomasFermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Interaccion among systems of finite size in predictive relativistic mechanics I. General framework

We derive a Hamiltonian formulation for the three-dimensional formalism of predictive relativistic mechanics. This Hamiltonian structure is used to derive a set of dynamical equations describing the interaction among systems in perturbation theory.

Interaccion among systems of finite size in predictive relativistic mechanics -II. Electromagnetic and gravitational interactions

We explicitly construct a closed system of differential equations describing the electromagnetic and gravitational interactions among bodies to first order in the coupling constants, retaining terms up to order c-2. The Breit and Barker and O'Connell Hamiltonians are recovered by means of a coordinate transformation. The method used throws light on the meaning of these coordinates.

Interactions among systems of finite size en predictive relativistic mechanics III. Short-range interaction and second-order terms

We compute up to and including all the c-2 terms in the dynamical equations for extended bodies interacting through electromagnetic, gravitational, or short-range fields. We show that these equations can be reduced to those of point particles with intrinsic angular momentum assuming spherical symmetry.