Assessing the accuracy of Hartree-Fock-Bogoliubov calculations by use of mass relations

TL;DR

This paper systematically evaluates the accuracy of Hartree-Fock-Bogoliubov nuclear binding energy calculations using mass relations to identify discrepancies and structural differences, especially in regions of rapid deformation change.

Contribution

It introduces a second order four-point mass relation to highlight non-smooth energy components and compares structural features between measured and calculated energies.

Findings

Detection of missing substructures in calculations around specific nuclei.

Observation of decreasing odd-even effects with neutron excess.

Identification of discrepancies in regions of rapid deformation change.

Abstract

The accuracy of three different sets of Hartree-Fock-Bogoliubov calculations of nuclear binding energies is systematically evaluated. To emphasize minor fluctuations, a second order, four-point mass relation, which almost completely eliminates smooth aspects of the binding energy, is introduced. Applying this mass relation yields more scattered results for the calculated binding energies. By examining the Gaussian distributions of the non-smooth aspects which remain, structural differences can be detected between measured and calculated binding energies. Substructures in regions of rapidly changing deformation, specifically around $(N,Z)=(60,40)$ and $(90,60)$, are clearly seen for the measured values, but are missing from the calculations. A similar three-point mass relation is used to emphasize odd-even effects. A clear decrease with neutron excess is seen continuing outside the experimentally known region for the calculations.