Paul Bonche

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities

In a first paper Skyrme effective forces were revisited in order to improve their isospin properties away from the β stability line. In this paper, these forces are specifically adjusted to reproduce finite nuclei properties. Spin-orbit terms and center of mass correlations are analyzed. New Skyrme parametrizations are proposed and some of their spectroscopic properties are presented, e.g. S2n, S2p and r.m.s. radii for different isotopic and isotonic series.

A Skyrme parametrization from subnuclear to neutron star densities

Skyrme effective forces are revisited to improve their behavior with respect to the isospin degree of freedom from the stability line to the most exotic nuclei that coming experimental facilities will produce. To achieve the best possible calculation of nuclear properties up to the neutron drip line, it is proposed to fit the neutron matter equation of state of the UV14+UVII theoretical model up to high densities to avoid any collapses or unphysical features of the resulting equation of state in the Skyrme framework. This last and very severe constraint on these interactions allows a prospective study of both neutron rich nuclei and neutron star matter.

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.

Properties of highly excited nuclei

Abstract A prescription is proposed for calculating the contribution of unbound states in nuclear Hartree-Fock calculations at finite temperature. The method is based on the remark that a static Hartree-Fock calculation at finite temperature describes a hot nucleus in equilibrium with an external nucleon vapor. Properties of the hot nucleus including continuum effects are obtained by extracting the contribution of the external gas, which we calculate from a second Hartree-Fock calculation. We show that for a one-body potential this subtraction procedure yields standard formulae for partition functions in terms of phase shifts. Numerical calculations are performed in 56 Fe and 208 Pb. The resuls indicate that continuum contributions are large beyond temperatures of the order of 4 MeV. We also find the existence of a critical temperature, of the order of 10 MeV, beyond which solutions of the equations can no longer be found.

Statistical properties and stability of hot nuclei

Abstract Results of temperature-dependent Hartree-Fock calculations for equilibrated hot nuclei are presented, extending to the highest temperatures at which the nuclei remain stable. A subtraction procedure developed earlier for isolating the properties of the nucleus from the nucleus + vapor system is applied. The temperature dependence of various quantities characterizing hot nuclei is investigated. The influence of different effective interactions in the Hartree-Fock equations is examined. Special attention is devoted to the study of the high-temperature stability limit of hot nuclei. This limit in nuclei with the Coulomb interaction artificially switched off (i.e. uncharged nuclei) is shown to correspond to the critical temperature of the liquid-gas phase transition expected on the basis of hot nuclear matter calculations. In realistic charged nuclei the Coulomb repulsion causes a nucleus to become electrostatically unstable and to fall apart at much lower temperatures than its uncharged partner. The approach to and the temperature of this Coulomb instability are very sensitive to the choice of the nuclear interaction. Studying this instability in compound nuclei with different charge-to-mass ratio provides a sensitive measure of the temperature dependence of the nuclear surface properties as well as of certain features of the nuclear equation of state.

An improved pairing interaction for mean field calculations using skyrme potentials

Abstract A zero-range interaction is proposed to calculate nuclear pairing at the Fermi surface. The results of Skyrme calculations using the zero range pairing interaction are compared with those using the constant G model for the pairing, as well as with those of a finite-range calculation. Particular attention is paid to the region of superdeformation and fission.

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.

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.

Self-consistent calculation of charge radii of Pb isotopes

Abstract Charge radii of lead isotopes are calculated with the HF plus BCS method, using Skyrme forces (SkM∗, SIII and SGII) for the mean field. When these forces are combined with a seniority pairing force, all of them fail to reproduce the experiment. Neither higher-order corrections, nor ground-state correlations due to the collective modes can resolve the discrepancy. However, by introducing a density-dependent pairing force quenched inside the nucleus, one can explain the odd-even staggering as well as the large kink of charge radii at 208Pb when plotted versus A.