Precision of finite-difference representation in 3D coordinate-space Hartree-Fock-Bogoliubov calculations

TL;DR

This paper evaluates the accuracy of finite-difference methods in 3D coordinate-space Hartree-Fock-Bogoliubov calculations for nuclear physics, comparing results with harmonic oscillator basis and literature to determine error margins.

Contribution

It provides a detailed analysis of the error introduced by finite-difference discretization in 3D HFB calculations and demonstrates its accuracy relative to established methods.

Findings

Grid spacing ≤0.6 fm yields off-diagonal matrix elements <1 keV.

Quasi-particle spectra differ by only a few keV from HO calculations.

Results are comparable to existing coordinate space and HO basis calculations.

Abstract

The current work plans to study the accuracy due to FD approximation to the 3D nuclear HFB problem. By (1) taking the wave functions solved in harmonic oscillator (HO) basis, (2) representing the HFB problem in coordinate space using FD method, the current work carefully evaluates the error due to box discretization by examining the deviation of the resulted HFB matrix, the total energies in the coordinate space, from those calculated with HO method, the latter of which is free from numerical error within its model configuration. To estimate how the error (given by the box discretization schemes suggested above) accumulates with self-consistent iterations, self-consistent HF and HFB calculations (with two-basis method) has been carried out for doubly magic nuclei, $^{40}$Ca, $^{132}$Sn, and $^{110}$Mo. The resulted total energies are compared with those of HO basis, and 3D coordinate space calculations in literatures. The analysis shows that, for grid spacing $\le$0.6\,fm, the off-diagonal elements of the resulted HFB matrix elements (M.E.) are extremely small ($<$1\,keV). The resulted quasi-particle (q.p.) spectra differ from those of HO calculations by a few keV. Self-consistent HF and HFB calculations within the current FD method with the above box discretizatioin schemes give results similar to those calculations of existing HO basis, and coordinate space method.