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

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.

Comments: 17 pages, 5 figures