Spin-flip doublets of $^9$Be spectrum within a cluster model

TL;DR

This paper models the low-lying spectrum of $^9$Be using a cluster approach with fixed orbital momentum, successfully reproducing experimental data and revealing spin-flip doublets within a three-body framework.

Contribution

It introduces a cluster model with fixed orbital momentum to analyze $^9$Be spectrum, employing Faddeev equations and a novel application of analytical continuation for resonance energies.

Findings

Reproduces $^9$Be spectral data accurately

Identifies spin-flip doublets in the spectrum

Calculates bound and resonance states with good agreement

Abstract

The structure of the $^9$Be low-lying spectrum is studied within the cluster model $\alpha+\alpha+n$. In the model the total orbital momentum is fixed for each energy level. Thus each level is determined as a member of the spin-flip doublet corresponding to the total orbital momentum ($L^\pi=0^+, 2^+,4^+, 1^-, 2^-,3^-, 4^-$) of the system. The Ali-Bodmer potential (model E) is applied for the $\alpha\alpha$ interaction. We employ a local $\alpha n$ potential which was constructed to reproduce the $\alpha-n$ scattering data. The Pauli blocking is simulated by the repulsive core of the $s$-wave components of these potentials. Configuration space Faddeev equations are used to calculate the energy of the bound state ($E_{cal.}$=-1.493 MeV v.s. $E_{exp.}$=-1.5735 MeV) and resonances. A variant of the method of analytical continuation in the coupling constant is applied to calculate the energies of low-lying levels. Available $^9$Be spectral data are satisfactorily reproduced by the proposed model.