HFB calculations with a microscopic pairing interaction

Hartree-Fock-Bogolyubov (HFB) calculations making use of a recently proposed microscopic effective pairing interaction are presented. The interaction was shown to reproduce the pairing properties provided by the realistic $AV18$ force very accurately in infinite matter. Although finite-ranged and non-local, it makes 3D HFB calculations in coordinate space tractable. As a first application, basic pairing properties of calcium isotopes in their ground-state are studied. By comparing the results with those obtained using a standard Density-Dependent Delta Interaction, the crucial isovector character of the microscopic interaction is highlighted.Comment: 6 pages, 6 figures. Proceedings of the Conference on Nuclei at the Limits, ANL, 2004. They will be published in the AIP Conference Proceedings Serie

Exotic nuclear phases in the inner crust of neutron stars in the light of Skyrme-Hartree-Fock theory

The bottom part of the neutron star crust is investigated using the Skyrme-Hartree-Fock approach with the Coulomb interaction treated beyond the Wigner-Seitz approximation. A variety of nuclear phases is found to coexist in this region. Their stability and relative energies are governed by the Coulomb, surface and shell energies. We have also found that a substantial contribution is coming from the spin-orbit interaction.Comment: 4 pages, 1 eps figure, Talk at the 17th Nuclear Physics Divisional Conference of the EPS: Nuclear Physics in Astrophysics, Debrecen, Hungary, Sept. 30 - Oct. 4, 200

Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis. (II) The program HFODD

We describe the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or non-rotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A~150 nucleus within one CPU hour of the CRAY C-90 supercomputer or within two-three CPU hours of a fast workstation.Comment: 30 LaTeX pages, 9 postscript figures included, submitted to Computer Physics Communication

Pairing schemes for HFB calculations of nuclei

Several pairing schemes currently used to describe superfluid nuclei through Hartree-Fock-Bogolyubov (HFB) calculations are briefly reviewed. We put a particular emphasis on the regularization recipes used in connection with zero-range forces and on the density dependence which usually complement their definition. Regarding the chosen regularization process, the goal is not only to identify the impact it may or may not have on pairing properties of nuclei through spherical 1D HFB calculations but also to assess its tractability for systematic axial 2D and 3D mean-field and beyond-mean-field calculations.Comment: 7 pages, 7 figures, Invited talk at the Workshop on New developments in Nuclear Self-Consistent Mean-Field Theories, Yukawa Institute for Theoretical Physics, Kyoto, Japan, May 30 - June 1, 2005, Yukawa Institute for Theoretical Physics Report Series (Soryushi-ron kenkyu

Configuration mixing of mean-field wave-functions projected on angular momentum and particle number; application to 24Mg

We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.Comment: 26 pages, 7 figures. Submitted to Nuclear Physic

Tetrahedral and Triangular Deformations of Z=NZ=N Nuclei in Mass Region A∼60−80A \sim 60-80

We study static non-axial octupole deformations in proton-rich $Z=N$ nuclei, $^{64}$Ge, $^{68}$Se, $^{72}$Kr, $^{76}$Sr, $^{80}$Zr and $^{84}$Mo, by using the Skyrme Hartree-Fock plus BCS calculation with no restrictions on the nuclear shape. The calculation predicts that the oblate ground state in $^{68}$Se is extremely soft for the $Y_{33}$ triangular deformation, and that in $^{80}$Zr the low-lying local minimum state coexisting with the prolate ground state has the $Y_{32}$ tetrahedral deformation.Comment: 8 pages, 4 Postscript figures, REVTE

Superdeformed Bands of Odd Nuclei in A=190 Region in the Quasiparticle Picture

We study the properties of the superdeformed (SD) bands of 195Pb and 193Hg by the cranked Hartree-Fock-Bogoliubov method. Our calculations reproduce the flat behavior of the dynamical moment of inertia of two of the SD bands of 195Pb measured recently. We discuss possible configuration assignments for the observed bands 3 and 4 of 195Pb. We also calculate the two interacting SD bands of 193Hg. Our analysis confirms the superiority of a density-dependent pairing force over a seniority pairing interaction.Comment: 12 pages, 5 Postscript figures, submitted to Phys.Rev.

GCM Analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of Pb208. In this study, we rely on a coherent approach based on the Generator Coordinate Method including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF+BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations.Comment: 10 pages LATEX, 8 figures, submitted to EPJ

Approximate particle number projection with density dependent forces: Superdeformed bands in the A=150 and A=190 regions

We derive the equations for approximate particle number projection based on mean field wave functions with finite range density dependent forces. As an application ground bands of even-A superdeformed nuclei in the A=150 and A=190 regions are calculated with the Gogny force. We discuss nuclear properties such as quadrupole moments, moments of inertia and quasiparticle spectra, among others, as a function of the angular momentum. We obtain a good overall description.Comment: 31 pages, 10 figures, 3 appendices. In press in Nucl. Phy