Solving the three-dimensional Skyrme Hartree-Fock-Bogoliubov problem using the mixed-basis method

TL;DR

This paper introduces an efficient 3D Skyrme Hartree-Fock-Bogoliubov code using a mixed-basis approach, enabling accurate simulations of complex nuclear systems without symmetry constraints.

Contribution

The authors develop and validate a novel mixed-basis 3D HFB code that improves numerical efficiency for nuclear structure calculations without symmetry restrictions.

Findings

Excellent agreement with existing codes in total energies and quadrupole moments.

Successfully applied to various nuclear shapes including spherical, prolate, and triaxial.

Demonstrated feasibility in fission barrier calculations for 240Pu.

Abstract

Background: The symmetry-unrestricted Hartree-Fock-Bogoliubov (HFB) simulation is important for describing various quantum many-body systems. However, the HFB problem in Cartesian coordinate space is numerically challenging. Purpose: For describing ground states without imposing axial symmetry and looking ahead to future extension for dynamics with full time dependence, we present a numerically efficient implementation of the three-dimensional (3D) HFB code. Methods: We develop a 3D Skyrme HFB code based on the mixed-basis representation (HFBmix) which consists of two harmonic-oscillator (HO) bases in the x- and y-directions, and finite-difference (FD) basis in the z-direction in solving the nuclear 3D HFB problem. Results: The results show very well agreement among all the three codes (HFBmix, HO3D, and hfodd). Especially for the HF calculations, the differences in total energies are on the order of a few keV for the lightest O and Mg nuclei. The HFBmix is applied to spherical, prolate, and triaxial systems, and gives the same quadrupole moments for the deformed nuclei as those of the HO-based calculations. Feasibility of the HFBmix is demonstrated in the fission isomer and barrier calculations of 240Pu. Conclusions: The HFBmix is useful for solving the nuclear 3D HFB problem for its numerical efficiency. Future work will include the analysis of deformed drip-line systems and systematic potential-energy surface calculation for fission-path analysis as well as the time-dependent extension of the HFBmix code for dynamics calculations.