D. Vautherin

Time-dependent hartree-fock theory with Skyrme's interaction

Abstract The time-dependent Hartree-Fock theory (TDHF) and its adiabatic approximation (ATDHF) are formulated in coordinate space using effective density-dependent interactions of Skyrme type. For this purpose it is necessary to derive the energy density of a Slater determinant without assuming the single-particle states to be invariant under time-reversal. The corresponding Hartree-Fock Hamiltonian is obtained by varying the total energy with respect to the single-particle density matrix. With the Skyrme interaction TDHF theory leads to an equation of continuity for the single-particle density. The ATDHF equation is transformed into a finite set of inhomogeneous differential equations. Hydrodynamic-like expressions for the collective kinetic energy are established in case the single-particle wave functions have certain generalised scaling properties. TDHF and ATDHF are applied to the description of isoscalar monopole vibrations in 16 O and 40 Ca.

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.

Hartree-Fock calculations with Skyrme's interaction

Abstract Hartree-Fock calculations have been made for closed shell nuclei using a form of density dependent nucleon-nucleon interaction suggested by Skyrme. The results are very good for binding-energies, densities and energies of single particle levels near the Fermi level. Calculations have been made in one superheavy nucleus.

A mean-field calculation of the equation of state of supernova matter

Abstract The equation of state for hot dense matter occurring in stellar collapse is calculated using the Hartree-Fock approximation at finite temperature. The effective nucleon-nucleon interaction is a modified Skyrme force which gives a rather good value of the compression modulus in nuclear matter. Results are presented for the adiabat S = 1 per baryon, with a fixed value of the electron fraction Y e = 0.25, in the density range ρ = 0.02 to 0.07 baryons per fm 3 . We find that nuclei are still present in the medium. As a consequence the adiabatic index is slightly less than 4 3 . We also discuss the presence of a transition, around half nuclear matter density, towards a phase made of bubbles.

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.

Self-consistent calculation of the ground state properties of some rare-earth nuclei

Abstract Ground state intrinsic deformation properties of some rare earth nuclei are calculated within the Hartree-Fock approximation using a Skyrme effective interaction. After a careful optimization of basis parameters, calculations have been performed with a basis corresponding to 13 spherical oscillator shells. In order to obtain the multipole moments, good numerical convergence is necessary. Calculated quadrupole and hexadecapole moments are in agreement with available experimental data. Ground state binding energies are also well reproduced.

Temperature dependence of collective states in the random-phase approximation

Abstract We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of 40Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.

Self-consistent calculation of the quadrupole-octupole deformation energy surface of 222Ra

Abstract The Hartree-Fock + BCS quadrupole-octupole deformation energy surface of 222 Ra, calculated with the Skyrme SIII interaction, presents a minimum for a non-zero value of the octupole moment. Our results suggest the existence of a quadrupole coupling which may account for the observed differences between the moments of inertia of the positive- and negative-parity bands.

A Hartree-Fock calculation for the stability of super-heavy nuclei

Spherical Hartree-Fock calculations have been carried out in the super-heavy region with the Skyrme interaction. Shell effects are discussed and stability against alpha and beta-decay are investigated. A strong shell effect is found to occur at N = 228.