Hubert Flocard

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.

Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line

Abstract We consider the Hartree-Fock-Bogolyubov theory of nuclei in the coordinate representation and derive and solve the HFB equation for the Skyrme effective interaction. Ground-state wave functions and energies of the tin isotopes with 100 ⩽ A ⩽ 176 have been determined and the results have been compared with the predictions of the HF+BCS and macroscopic-microscopic models. The lightest tin isotope which is unstable with respect to a neutron emission is predicted by the HFB method to be 153 Sn. In the region of nuclei where experimental data are not available the macroscopic-microscopic and self-consistent approximations give substantially different results.

Self-consistent study of triaxial deformations: Application to the isotopes of Kr, Sr, Zr and Mo

Abstract Self-consistent mean-field calculations of deformation energy surfaces have been performed for more than 30 exotic isotopes of the Kr, Sr, Zr and Mo elements. Our calculations extend to the proton drip line. We investigate the triaxial stability of the deformed ground states in the deformation regions N ≈ 38 and N ≈ 60. The results are in good agreement with the observed trends.

Nuclear deformation energy curves with the constrained Hartree--Fock method.

Abstract Calculations of the deformation energy curves of relatively heavy deformed nuclei — Ce isotopes — have been performed using the constrained Hartree-Fock technique. The two-body interaction is the Skyrme force, and pairing effects are taken into account. Different possible choices for the external field form are investigated and the advantage of a non-linear dependence of the constraint is shown. One of the advantages of this type of calculation is that deformation energy curves can be calculated without making a complete map of the deformation energy surface. A discussion of the numerical techniques and uncertainties, particularly those connected with truncation effects is given. General trends of the deformation energy curves, calculated for the Ce isotopes as a function of the quadrupole moment, are found to be in good agreement with available experimental information. Associated physical quantities are discussed and a comparison is made with the results of phenomenological calculations using the liquid-drop model and the Strutinsky prescription.

Shape transition in the neutron rich sodium isotopes

Abstract Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at 31Na in the values of the two-neutron separation energies. The spherical shell model naturally predicts a sudden decrease at 32Na after the N = 20 shell closure. We propose that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitais from the 1f 7 2 shell. Hartree-Fock calculations are presented in support of this conjecture.

Analysis of the generator coordinate method in a study of shape isomerism in 194Hg

Abstract We investigate the properties of the generator coordinate method (GCM) on a collective basis of BCS states. The method is applied to a study of large-amplitude quadrupole dynamics in the nucleus 194 Hg. Among the GCM levels, we discuss candidates for a possible shape isomerism associated with a secondary deformed minimum at large deformation ( Q ≈ 45b). We also analyze standard approximation schemes based on the gaussian overlap approximation which lead to a collective Schrodinger equation. We compare their predictions with the exact GCM results for the particular case of 194 Hg.

Deformation of nuclei close to the two-neutron drip line in the Mg region

Abstract We present Hartree-Fock-Bogoliubov (HFB) calculations of the ground states of even Mg isotopes. A Skyrme force is used in the mean-field channel and a density-dependent zero-range force in the pairing channel. 40 Mg and 20 Mg are predicted to be at the two-neutron and two-proton drip lines respectively. A detailed study of the quadrupole deformation properties of all the isotopes shows that the ground states of 36,38,40 Mg are strongly deformed with significantly different deformations for the neutrons and protons. Our study supports the disappearance of the N = 28 shell gap in the Mg and Si isotopes.

Self-consistent calculation of nuclear rotations: The complete yrast line of 24Mg

Abstract We present a method of solution on a three-dimensional mesh of the self-consistent cranked Hartree-Fock + BCS equations. Using several parametrizations of the Skyrme interaction we apply our method to the study of the complete yrast line of 24 Mg. We find that J = 26 is the limiting angular momentum for this nucleus. We have also studied examples of collective rotations along the γ = 60° axis involving hexadecapole deformations. Our work corroborates earlier calculations using the Nilsson-Strutinsky method and extends them to higher spins.

Self-consistent calculation of the fission barrier of 240Pu

Abstract Completely self-consistent calculations using the Skyrme force have been carried out for the fission energy curve of 240 Pu. We use a deformed oscillator basis including 13 major shells and convergence has been checked by extending the size of the basis to 15 shells. We obtain a double humped barrier with energies E A = 9 MeV for the first barrier, E B = 13 MeV for the second barrier and E II = 4 MeV for the isomeric state. Corrections to our calculation, such as inclusion of non-axial and symmetric shapes and zero-point rotational motion, are likely to improve quantitative agreement with experimental data.

3D solution of Hartree-Fock-Bogoliubov equations for drip-line nuclei

Abstract We investigate the possibility of describing triaxial quadrupole deformations for nuclei close to the two-neutron drip line by the Hartree-Fock-Bogoliubov method taking into account resonances in the continuum. We use a Skyrme interaction to describe the Hartree-Fock hamiltonian and a density-dependent zero-range interaction to evaluate the pairing field. The mean-field equations are solved in a three-dimensional cubic mesh. We study the stability of the two-neutron separation energies and of the description of the nuclear surface as a function of the number of active mean-field orbitals and of the size of the mesh. The even Ni isotopes are used as a test case and the accuracy as a function of quadrupole deformation is studied by performing constrained calculations. A first application to the study of the two-neutron separation energies in Ni isotopes up to the drip line is presented.