Cluster calculations for the $^6$He and $^9$Be spectra

The $^6$He and $^9$Be nuclei are considered as a mirror cluster systems $\alpha nn$ and $\alpha \alpha n$. The excitation energies of the low-lying levels for $^6$He and $^9$Be nuclei are evaluated. These cluster calculations are based on the configuration-space Faddeev equations. The method of analytical continuation in a coupling constant is used to calculate resonance parameters [1]. Our goal is to show possibility for a reliable description of the $^6$He and $^9$Be within the cluster model using pair local potentials. We focus on the new $\alpha n$ interaction model proposed in [1]. We assume that both, central $p$-wave component and spin-orbital component of $\alpha n$ potential mainly determine the excitation spectra structure of these nuclei. The low-lying spectrum of $^9$Be is well reproduced with this potential. The results for excitation resonance energies of the $\alpha nn$(0+,2+,1+) systems are presented and compared with the experimental data (http://www.tunl.duke.edu/nucldata/chain/06.shtml) and those from other calculations [2]. \\[4pt] [1] I. Filikhin, V.M. Suslov and B. Vlahovic, Few-Body Systems 50, 255 (2011). \\[0pt] [2] S.N. Ershov, T. Rogde, B.V. Danilin, J.S. Vaagen, I.J. Thompson, F.A. Gareev, Phys. Rev. C 56, 1483 (1997).