Deformed coordinate-space Hartree-Fock-Bogoliubov approach to weakly bound nuclei and large deformations

Abstract

The coordinate-space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables the self-consistent treatment of mean field and pairing in weakly bound systems whose properties are affected by the particle continuum space. Of particular interest are neutron-rich, deformed drip-line nuclei, which can exhibit novel properties associated with neutron skin. To describe such systems theoretically, we developed an accurate two-dimensional lattice Skyrme-HFB solver HFB-AX based on basis (or B)-splines. Compared to previous implementations, ours incorporated a number of improvements aimed at boosting the solver's performance. These include the explicit imposition of axiality and space inversion, use of the modified Broyden method to solve self-consistent equations, and a partial parallelization of the code. HFB-AX has been compared with other HFB codes, both spherical and deformed, and the accuracy of the B-spline expansion was tested by employing the multiresolution wavelet method. Illustrative calculations are carried out for stable and weakly bound nuclei at spherical and very deformed shapes, including constrained fission pathways. In addition to providing new physics insights, HFB-AX can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB frameworks, both existing and in development.