Multipole expansion of densities in the deformed relativistic Hartree-Bogoliubov theory in continuum

TL;DR

This paper investigates how the multipole expansion of potentials and densities in the deformed relativistic Hartree-Bogoliubov theory in continuum affects the accuracy of nuclear structure calculations, highlighting differences between light and heavy nuclei.

Contribution

It provides a detailed analysis of the multipole expansion dependence in DRHBc for both light and heavy nuclei, including convergence behavior and the role of higher-order components.

Findings

Total energy converges well with expansion truncation.

Heavy nuclei require larger truncation for same accuracy.

Higher deformation increases dependence on high-order components.

Abstract

The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has been proved one of the best models to probe the exotic structures in deformed nuclei. In DRHBc, the potentials and densities are expressed in terms of the multipole expansion with Legendre polynomials, the dependence on which has only been touched for light nuclei so far. In this paper, taking a light nucleus $^{20}$Ne and a heavy nucleus $^{242}$U as examples, we investigated the dependence on the multipole expansion of the potentials and densities in DRHBc. It is shown that the total energy converges well with the expansion truncation both in the absence of and presence of the pairing correlation, either in the ground state or at a constrained quadrupole deformation. It is found that to reach a same accuracy of the total energy, even to a same relative accuracy by percent, a larger truncation is required by a heavy nucleus than a light one. The dependence of the total energy on the truncation increases with deformation. By decompositions of the neutron density distribution, it is shown that a higher-order component has a smaller contribution. With the increase of deformation, the high-order components get larger, while at the same deformation, the high-order components of a heavy nucleus play a more important role than that of a light one.