Variational approach for pair optimization in the nucleon pair approximation

TL;DR

The paper introduces a variational method to identify key collective pairs in atomic nuclei, improving the nucleon-pair approximation's accuracy for low-lying states and shape transitions.

Contribution

A novel pair-condensate variational approach that determines critical collective pairs, enhancing nucleon-pair approximation calculations for transitional nuclei.

Findings

Accurately describes quadrupole-deformation evolution in Ba isotopes

Concludes neutron negative-parity pairs are not favored for $^{132}$Ba

Produces level structures and B(E2) values consistent with experiments

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.