Hartree-Fock-Bogoliubov calculations for nuclei far from stability

Abstract

The description of the properties of nuclei far from stability presents a big challenge in Nuclear Physics theory. It demands the development of sophisticated algorithms suitable for describing the complex many-body nuclear problem, specially for nuclei under extreme conditions. This thesis addresses the study of nuclei far from stability by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction.

Calculations for even-even nuclei are carried out on a two-dimensional axially symmetric lattice, in coordinate space. The Bogoliubov transformation gives place to quasiparticle states. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei.

The first part of this thesis deals with the HFB theory in nuclear structure. The standard HFB formalism is introduced. The detailed representation of the HFB equations in axial symmetry is discussed, as well.

The numerical techniques involved are also described. The numerical algorithm is implemented to work iteratively, since the nature of the nuclear problem in the HFB scheme is self-consistent. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines.

Calculations of observables for nuclei far from the stability are presented to demonstrate the reliability of the method. Results for oxygen, zirconium, tin and sulfur isotopes are shown.