New exact solutions of the standard pairing model for well-deformed nuclei

TL;DR

This paper introduces a new step-by-step diagonalization method using Bethe ansatz to find exact solutions of the standard pairing model in deformed nuclei, revealing similarities with extended models.

Contribution

A novel diagonalization procedure based on Bethe ansatz for solving the nuclear pairing model exactly, linking it to extended models with a simplified first step approximation.

Findings

The new method provides exact eigenvalues and eigenstates.

The extended pairing model is similar to the standard model with a first step approximation.

The approach simplifies solving complex nuclear pairing interactions.

Abstract

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a $k$-particle Hilbert subspace can be mapped unto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Phys. Rev. Lett. 92, 112503 (2004) ] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis show that the standard pairing model with the first step approximation displays similar pair structures of first few exact low-lying states of the model, which, therefore, provides a link between the two models.