From deformed Hartree-Fock to the nucleon-pair approximation

TL;DR

This paper introduces a new method for selecting pairs in the nucleon-pair approximation by deriving pairs from deformed Hartree-Fock states, improving accuracy for deformed nuclei.

Contribution

It proposes a novel approach to generate pairs from deformed Hartree-Fock states, enhancing the NPA's effectiveness for deformed nuclear systems.

Findings

NPA with pairs from deformed Hartree-Fock states agrees well with FCI results.

The method improves modeling of deformed nuclei with strong rotational bands.

Pairs of good angular momentum are successfully projected from Slater determinants.

Abstract

The nucleon-pair approximation (NPA) can be a compact alternative to full configuration-interaction (FCI) diagonalization in nuclear shell-model spaces, but selecting good pairs is a long-standing problem. While seniority-based pairs work well for near-spherical nuclides, they do not work well for deformed nuclides with strong rotational bands. We propose an alternate approach. We show how one can write any Slater determinant for an even number of particles as a general pair condensate, from which one can project out pairs of good angular momentum. We implement this by generating unconstrained Hartree-Fock states in a shell model basis and extracting $S$, $D$, and $G$ pairs. The subsequent NPA calculations yield good agreement with FCI results using the same effective interactions.