Variational approach for pair optimization in the nucleon pair approximation

Abstract

We propose a pair-condensate variational approach (PCV) to determine a set of the most important collective pairs in the description of low-lying states in atomic nuclei. Having available the precise details on these key collective pairs -- their spin, parity, and structure -- can be particularly useful in calculations based on the nucleon-pair approximation (NPA), helping to reduce their uncertainties. In trial calculations for the transitional Ba isotopes, our variational approach describes the evolution of quadrupole-deformation properties similar to Hartree-Fock treatments, while at the same time highlighting the $\gamma$ softness of ${}^{132}$Ba. Our approach can conclusively determine which collective pairs are critical for obtaining the lowest possible yrast, quasi-beta, quasi-gamma bands, producing both the level structure of these bands and related B(E2) values in reasonable consistency with experiment. These trial calculations suggest that with our PCV approach the NPA can be meaningfully applied to transitional nuclei with a wide spectrum of shapes. We also show that while neutron negative-parity pairs could in principle have an important impact on backbending in ${}^{132}$Ba, they are not favored for this nucleus.

16 pages, 6 figures

References in corpus (6)

• RPA vs. exact shell-model correlation energies
• Shell Model Monte Carlo Investigation of Rare Earth Nuclei
• Measurable bounds for Entanglement of Formation
• Gamow-Teller transitions and deformation in the proton-neutron random phase approximation
• Tests of the random phase approximation for transition strengths
• $(h_{11/2}{)}^2$ alignments in neutron-rich ${}^{132}$Ba with negative-parity pairs

Cited by in corpus (6)

• Recent progress in configuration-interaction shell model
• Nuclear states projected from a pair condensate
• The nucleon-pair approximation for nuclei from spherical to deformed regions
• The pervasiveness of shape coexistence in nuclear pair condensates
• Algebraic description of the triaxially to axially rotational shape phase transition
• Systematic analysis of double Gamow-Teller sum rules