Application of Gaussian expansion method to nuclear mean-field calculations with deformation

TL;DR

This paper introduces a Gaussian expansion method (GEM) for mean-field calculations of deformed nuclei, offering efficiency, versatility, and broad applicability across nuclear species.

Contribution

The paper develops and demonstrates a GEM-based algorithm for deformed nuclear mean-field calculations, capable of handling various interactions with a single basis set.

Findings

Efficient description of wave function asymptotics at large distances.

Applicable to various effective interactions including finite-range ones.

Identification of a neutron halo structure in $^{40}$Mg.

Abstract

We extensively develop a method of implementing mean-field calculations for deformed nuclei, using the Gaussian expansion method (GEM). This GEM algorithm has the following advantages: (i) it can efficiently describe the energy-dependent asymptotics of the wave functions at large $r$, (ii) it is applicable to various effective interactions including those with finite ranges, and (iii) the basis parameters are insensitive to nuclide, thereby many nuclei in wide mass range can be handled by a single set of bases. Superposing the spherical GEM bases with feasible truncation for the orbital angular momentum of the single-particle bases, we obtain deformed single-particle wave-functions to reasonable precision. We apply the new algorithm to the Hartree-Fock and the Hartree-Fock-Bogolyubov calculations of Mg nuclei with the Gogny interaction, by which neck structure of a deformed neutron halo is suggested for $^{40}$Mg.