The nucleon-pair approximation for nuclei from spherical to deformed regions

TL;DR

This paper advances the nucleon-pair approximation (NPA) for modeling low-lying nuclear states across spherical to deformed regions, employing three pair selection methods and achieving good agreement with full shell-model calculations.

Contribution

It introduces and compares three approaches for selecting collective nucleon pairs in NPA, demonstrating their effectiveness across different nuclear shapes and complexities.

Findings

Generalized seniority scheme suits spherical nuclei

Conjugate gradient and Hartree-Fock methods work well for transitional and deformed nuclei

NPA with SDG pairs reproduces shape evolution and matches full CI results

Abstract

In this paper we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provides a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by $SDG$ pairs) reproduce the nuclear shape evolution in the $N=26$ isotones, $^{46}$Ca, $^{48}$Ti, $^{50}$Cr, and $^{52}$Fe, and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: $^{44-48}$Ti, $^{48}$Cr, $^{50}$Cr, $^{52}$Fe, $^{60-64}$Zn, $^{64,66}$Ge, $^{84}$Mo, and $^{108-112}$Xe. Finally, using the $SDGI$-pair approximation we describe low-lying states of $^{112,114}$Ba, cases difficult to reach by conventional configuration-interaction methods.