Relativistic mean-field description of the dynamics of giant resonances

The relativistic mean-field theory provides a framework in which the nuclear many-body problem is described as a self-consistent system of nucleons and mesons. In the mean-field approximation, the self-consistent time evolution of the nuclear system describes the dynamics of collective motion: nuclear compressibility from monopole resonances, regular and chaotic dynamics of isoscalar and isovector collective vibrations.Comment: LaTeX, 10 pages, 5 figures, Invited Talk, Topical Conference on Giant resonances, Varenna, May 1998, to be published in Nucl. Phys.

Renormalized relativistic Hartree-Bogoliubov equations with a zero-range pairing interaction

A recently introduced scheme for the renormalization of the Hartree-Fock-Bogoliubov equations in the case of zero-range pairing interaction is extended to the relativistic Hartree-Bogoliubov model. A density-dependent strength parameter of the zero-range pairing is adjusted in such a way that the renormalization procedure reproduces the empirical $^1S_0$ pairing gap in isospin-symmetric nuclear matter. The model is applied to the calculation of ground-state pairing properties of finite spherical nuclei.Comment: 13 pages, 8 figures, accepted for publication in Physical Review

The Proton Electric Pygmy Dipole Resonance

The evolution of the low-lying E1 strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov (RHB) model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton drip-line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.Comment: 7 pages, 4 figures, to be published in Phys. Rev. Let

Beyond the relativistic Hartree mean-field approximation: energy dependent effective mass

The standard relativistic mean-field model is extended by including dynamical effects that arise in the coupling of single-nucleon motion to collective surface vibrations. A phenomenological scheme, based on a linear ansatz for the energy dependence of the scalar and vector components of the nucleon self-energy for states close to the Fermi surface, allows a simultaneous description of binding energies, radii, deformations and single-nucleon spectra in a self-consistent relativistic framework. The model is applied to the spherical, doubly closed-shell nuclei 132Sn and 208Pb.Comment: 14 pages, 2 figures; replaced with revised versio

Random-phase approximation based on relativistic point-coupling models

The matrix equations of the random-phase approximation (RPA) are derived for the point-coupling Lagrangian of the relativistic mean-field (RMF) model. Fully consistent RMF plus (quasiparticle) RPA illustrative calculations of the isoscalar monopole, isovector dipole and isoscalar quadrupole response of spherical medium-heavy and heavy nuclei, test the phenomenological effective interactions of the point-coupling RMF model. A comparison with experiment shows that the best point-coupling effective interactions accurately reproduce not only ground-state properties, but also data on excitation energies of giant resonances.Comment: 24 pages, 4 figures, accepted for publication in Physical Review

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly-periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wavepackets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator which interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.Comment: 4 pages, 3 figures, Optics Letters styl