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

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.

Nonlinear dynamics of giant resonances in atomic nuclei

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.Comment: 24 pages, RevTeX, 15 PS figures, submitted Phys. Rev.

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

Nuclear pairing from chiral pion-nucleon dynamics

We use a recently improved version of the chiral nucleon-nucleon potential at next-to-next-to-leading order to calculate the $^1S_0$ pairing gap in isospin-symmetric nuclear matter. The pairing potential consists of the long-range one- and two-pion exchange terms and two short-distance NN-contact couplings. We find that the inclusion of the two-pion exchange at next-to-next-to-leading order reduces substantially the cut-off dependence of the $^1S_0$ pairing gap determined by solving a regularised BCS equation. Our results are close to those obtained with the universal low-momentum nucleon-nucleon potential $V_{\rm low-k}$ or the phenomenological Gogny D1S force.Comment: 9 pages, 3 eps figures, submitted to PR

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

Signatures of shape phase transitions in odd-mass nuclei

Quantum phase transitions between competing ground-state shapes of atomic nuclei with an odd number of protons or neutrons are investigated in a microscopic framework based on nuclear energy density functional theory and the particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well as the single-particle energies and occupation probabilities of the unpaired nucleon, are completely determined by constrained self-consistent mean-field calculations for a specific choice of the energy density functional and paring interaction, and only the strength parameters of the particle-core coupling are adjusted to reproduce selected spectroscopic properties of the odd-mass system. We apply this method to odd-A Eu and Sm isotopes with neutron number $N \approx 90$, and explore the influence of the single unpaired fermion on the occurrence of a shape phase transition. Collective wave functions of low-energy states are used to compute quantities that can be related to quantum order parameters: deformations, excitation energies, E2 transition rates and separation energies, and their evolution with the control parameter (neutron number) is analysed.Comment: 15 pages, 13 figures; Accepted for publication in Phys. Rev.

Shape-phase transitions in odd-mass γ\gamma-soft nuclei with mass A≈130A\approx 130

Quantum phase transitions between competing equilibrium shapes of nuclei with an odd number of nucleons are explored using a microscopic framework of nuclear energy density functionals and a particle-boson core coupling model. The boson Hamiltonian for the even-even core nucleus, as well as the spherical single-particle energies and occupation probabilities of unpaired nucleons, are completely determined by a constrained self-consistent mean-field calculation for a specific choice of the energy density functional and pairing interaction. Only the strength parameters of the particle-core coupling have to be adjusted to reproduce a few empirical low-energy spectroscopic properties of the corresponding odd-mass system. The model is applied to the odd-A Ba, Xe, La and Cs isotopes with mass $A\approx 130$, for which the corresponding even-even Ba and Xe nuclei present a typical case of $\gamma$-soft nuclear potential. The theoretical results reproduce the experimental low-energy excitation spectra and electromagnetic properties, and confirm that a phase transition between nearly spherical and $\gamma$-soft nuclear shapes occurs also in the odd-A systems.Comment: 13 pages, 15 figures, 9 table

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

Relativistic Random-Phase Approximation with density-dependent meson-nucleon couplings

The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction, that are essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole and isoscalar quadrupole response of $^{208}$Pb, are performed in the fully self-consistent RRPA framework, based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.Comment: RevTeX, 8 eps figures, submitted to Phys. Rev.