uc l - th / 9 70 50 54 v 1 3 0 M ay 1 99 7 An HFB scheme in natural orbitals

We present a formulation of the Hartree-Fock-Bogoliubov (HFB) equations which solves the problem directly in the basis of natural orbitals. This provides a very efficient scheme which is particularly suited for large scale calculations on coordinate-space grids. The production of new nuclei towards the drip lines and in the super-heavy region (for a review see [1]) has raised a growing interest in the refinement of nuclear mean-field models to accommodate the larger body of experimental data. At the level of precision reached nowadays, a correct treatment of pairing becomes a crucial ingredient [2]. This calls for a full variational optimization of the pairing wave function, what is known as the Hartree-FockBogoliubov (HFB) treatment [3,4]. It is the aim of this short note to present an efficient solution scheme for the HFB equations which relies on a direct variational optimization within the natural orbital basis. The following discussion is formulated for one sort of Fermions. Nuclear applications will use that scheme for neutrons and protons separately. A generalization to proton-neutron pairing is obvious. Starting point is the BCS ansatz for the wave function of a pairing many-body system |Φ〉 = ∏ (