Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations

TL;DR

This paper introduces an advanced 2D lattice Skyrme-HFB solver, { exthfbax}, for accurately modeling weakly bound, deformed, neutron-rich nuclei, improving computational performance and benchmarking against existing methods.

Contribution

The paper presents a new, efficient 2D Skyrme-HFB solver with improved performance and benchmarking, enabling detailed studies of weakly bound and deformed nuclei.

Findings

Validated { exthfbax} against other HFB solvers.

Accurately modeled neutron-rich, deformed nuclei.

Provided insights into nuclear structure near drip lines.

Abstract

The coordinate space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables 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 2D lattice Skyrme-HFB solver {\hfbax} based on B-splines. Compared to previous implementations, we made a number of improvements aimed at boosting the solver's performance. These include: explicit imposition of axiality and space inversion, use of the modified Broyden's method to solve self-consistent equations, and a partial parallelization of the code. {\hfbax} has been benchmarked against other HFB solvers, 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, {\hfbax} can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB solvers, both existing and in development.