Hartree-Fock and Hartree-Fock-Bogoliubov calculations of superdeformed bands

The so-called Higher Tamm–Dancoff Approximation (HTDA) has been designed to describe microscopically correlations within a particle number conserving approach. It relies upon a truncated n particle–n hole expansion of the nuclear wavefunction, where the single particle basis is optimized self-consistently by using the Skyrme mean field associated with the single-particle density matrix of the correlated wavefunction. It is applied here for the first time in a rotating frame, i.e. within a self-consistent cranking approach (cranked HTDA or CHTDA) aimed at describing the collective rotational motion in well-deformed nuclei. Moments of inertia predicted by cranked HTDA in the Yrast superdeformed (SD) bands of some $A\sim 190$ nuclei are compared with those deduced from experimental SD sequences as well as those produced by current cranked Hartree–Fock–Bogoliubov approaches under similar hypotheses.

An overview of a microscopic framework based on the Hartree-Fock description of the mean field is presented which, starting from an effective interaction allows a description of collective motions. A study of the isotope shifts in the Pb region illustrates the importance of the effective interactions and points to their limitations. Such forces should be improved in order to achieve a better description of nuclei properties especially with the coming availability of exotic beam facilities. The coupling of collective quadrupole and octupole degrees of freedom in ¹⁹⁴Pb is analyzed within the Generator Coordinate Method, which represents a step beyond the simple mean-field approximation. As a last example, we present a study of nuclear rotations. First we discuss results on superdeformed rotating bands in ¹⁹²Hg, ¹⁹⁴Hg and ¹⁹⁴Pb obtained without including a treatment of pairing correlations. Preliminary calculations are also presented with these correlations included as well as an approximate projection on nucleon number.

The structure of the yrast superdeformed band of ¹⁹⁴Hg is for the first time studied up to high spin (I≅70) using the Gogny force in self-consistent cranking Hartree-Fock-Bogoliubov calculations. Several properties including pairing correlations, antistretching effects, and dynamic moment of inertia are discussed. A good overall agreement is found between present results and experimental information. A comparison between these cranking model predictions and those we have obtained previously using an adiabatic assumption, is also presented.

The first shape-constrained high-spin Hartree-Fock-Bogoliubov calculations, using the density dependent Gogny interaction, have been carried out to investigate the energy minima in ¹⁸²Os. Deep, well separated minima have been found for shapes with axis ratios of 1.5:1 and 2.2:1. Corrections for rotational zero point energies and for particle number fluctuations are taken into account. Comparisons are made with cranked Strutinsky calculations for this nucleus.