Nguyen Van Giai

Nuclear ground-state properties and self-consistent calculations with the skyrme interaction: (I). Spherical description

Abstract The parameters of the effective Skyrme interaction are determined by requiring that they accurately reproduce the total binding energies and charge radii of magic nuclei in spherical self-consistent calculations. It is shown that many parameter sets can satisfy these requirements. They differ essentially by the single-particle spectra they give. A detailed study of the influence of the force parameters on the binding energies, charge densities, radii and single-particle energies of magic nuclei is made. Extensive self-consistent calculations covering over two hundred nuclei have been performed in a spherical scheme using one of the parameter sets. The effects of pairing correlations are discussed. The magnitude of the corrections due to the deformation in the rare earth region is indicated. The good overall agreement of the results with experimental data shows that the Skyrme parametrisation of the effective interaction is adequate. The remaining discrepancies may be attributed essentially to dynamic collective effects not included in the present approach.

Spin-isospin and pairing properties of modified Skyrme interactions

Abstract New sets of parameters for Skyrme interactions have been determined. In addition to the ground-state properties, they give satisfactory values for the compression modulus, spin and spin-isospin Landau parameters, and pairing matrix elements. Gamow-Teller states are calculated and compared with experimental data.

Monopole and dipole compression modes in nuclei

Abstract The isoscalar monopole and dipole strength distributions are calculated in the framework of the self-consistent RPA. The single-particle continuum is exactly treated. A comparison of results obtained with various interactions having different values of the compression modulus is made. The mass number dependence of excitation energies and widths of the monopole and dipole giant resonances are discussed.

Effects of collective modes on the single-particle states and the effective mass in 208Pb

Abstract A microscopic particle-vibration model is used to study the single-particle energies, spectroscopic factors and nucleon effective mass in 208 Pb. The relevant quantities are deduced from the knowledge of the mass operator which is the sum of a Hartree-Fock term and an energy-dependent term coming from the coupling to RPA vibrations. The results are discussed and compared with experimental data. The main conclusions are: (i) the gap between the occupied and unoccupied shells is substantially decreased by the coupling to the vibrations; (ii) the spectroscopic factors in the valence shells are of the order of 0.7–0.8, and in some cases smaller; (iii) the value of the effective mass near the Fermi level is about 1.1–1.2.

New effective interactions in RMF theory with nonlinear terms and density dependent meson nucleon coupling

New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1 with nonlinear sigma- and omega-meson self-coupling, PK1R with nonlinear sigma-, omega-, and rho-meson self-coupling, and PKDD with the density-dependent meson-nucleon coupling are proposed. They are able to provide an excellent description not only for the properties of nuclear matter but also for the nuclei in and far from the valley of beta stability. For the first time in the parametrization of the RMF Lagrangian density, the center-of-mass correction is treated by a microscopic way, which is essential to unify the description of nuclei from light to heavy regions with one effective interaction.

A self-consistent microscopic description of the giant resonances including the particle continuum

Abstract The distribution of strength for the isovector dipole and isoscalar quadrupole modes in 16 O and 208 Pb is calculated in the framework of the RPA. Effects due to the self-consistency as well as the single-particle continuum are included. The various collective models and the coupled-channel reaction theory are related through the RPA sum rules.

The nucleon-nucleus potential in the Hartree-Fock approximation with Skyrme's interaction

Abstract We investigate the connection between the self-consistent nuclear field in the Hartree-Fock (HF) approximation with the Skyrme interaction and the real part of the phenomenological nucleon-nucleus optical potential. We show that a simple local transformation u(r) = ( m ∗ (r) m ) 1 2 u L (r) of the radial wave function u(r) leads to an ordinary Schrodinger equation for uL(r). The energy-dependent potential VL(r, E) which appears in this equation is identified with the real part of the nucleon optical potential. We decompose VL(r, E) into a central part Vav, a symmetry part Vsym and a spin-orbit part Vs.o.. The radial form factors which characterize Vav, Vsym and Vs.o. are expressed in closed form in terms of the total nuclear density ϱ(r) and the neutron excess density Δϱ(r). Using force parameters obtained by fitting bound-state properties of closed-shell nuclei, we calculate VL numerically and compare to empirical potentials. We find that Vav strongly resembles a Woods-Saxon form, with depth V0 ≈ − 43 MeV, radius R 0 = 1.10A 1 3 + 0.75 fm and diffuseness a ≈ 0.55 fm ; V av also contains an energy-dependent part of depth 0.43 E and radius R0E = R0 − 0.25 fm. It is shown that Vsym is proportional to Δϱ(r) times a smooth function of the density. The calculated symmetry potential changes from a surface form for medium nuclei (Ca) to a surface plus volume for heavier nuclei (Zr, Sn, Pb). The form factor for Vs.o. is close to a Thomas form, but peaks at a radius inside that of the central potential.

Pairing and continuum effects in nuclei close to the drip line

The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are performed with effective Skyrme interactions. The exact HFB solutions are compared with HFB calculations based on box boundary conditions and with resonant continuum Hartree-Fock-BCS (HF-BCS) results. The comparison is done for the neutron-rich Ni isotopes. It is shown that close to the drip line the amount of pairing correlations depends on how the continuum coupling is treated. On the other hand, the resonant continuum HF-BCS results are generally close to those of HFB even in neutron-rich nuclei.

Spin-Isospin Resonances : A Self-Consistent Covariant Description

For the first time a fully self-consistent charge-exchange relativistic RPA based on the relativistic Hartree-Fock (RHF) approach is established. The self-consistency is verified by the so-called isobaric analog state (IAS) check. The excitation properties and the nonenergy weighted sum rules of two important charge-exchange excitation modes, the Gamow-Teller resonance (GTR) and the spin-dipole resonance (SDR), are well reproduced in the doubly magic nuclei 48Ca, 90Zr and 208Pb without readjustment of the particle-hole residual interaction. The dominant contribution of the exchange diagrams is demonstrated.

Density-dependent relativistic Hartree–Fock approach

A new relativistic Hartree-Fock approach with density-dependent sigma, omega, rho and pi meson-nucleon couplings for finite nuclei and nuclear matter is presented. Good description for finite nuclei and nuclear matter is achieved with a number of adjustable parameters comparable to that of the relativistic mean field approach. With the Fock terms, the contribution of the pi-meson is included and the description for the nucleon effective mass and its isospin and energy dependence is improved. (c) 2006 Elsevier B.V. All rights reserved.