Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

TL;DR

This paper introduces a new three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver in coordinate space, enabling detailed studies of weakly bound nuclei without symmetry restrictions, with improved accuracy and performance.

Contribution

The authors developed HFBFFT, a parallelized 3D solver based on Sky3D, solving HFB equations directly in the canonical basis using Fourier transforms, with enhancements for convergence and pairing stability.

Findings

Validated against existing HFB codes for various nuclei.

Demonstrated improved convergence and accuracy.

Effective handling of weakly bound nuclei.

Abstract

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. The accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.