Spin doublet $(1^-,2^-)$ of ${ }_\Lambda ^6 $He within three-body cluster model

The spin doublets $(1^-,2^-)$ of ${ }_\Lambda ^6 $He are of great interest for testing theoretical models of the hyperon-nucleon interaction. The experimental value -0.17 MeV is known for the binding energy of the state $1^-$ (singlet spin state) of ${ }_\Lambda ^6 $He [1]. The experimental data for the $2^-$ state (triplet spin state) were not yet reported. Theoretical considerations for the state $2^-$of ${ }_\Lambda ^6 $He have been attempted by Motoba et al. [2] and Hiyama et al. [3]. Indirect prediction for this state has been given in [4]. Results obtained in these works are quite different. Our goal is to obtain a new prediction for the hyper nucleus $_\Lambda ^6 $He, which is considered as the cluster system$\alpha n\Lambda $, by using new proposed potentials for$\alpha \Lambda $and $\alpha n$ interactions [5]. Our cluster calculation is based on the configuration-space Faddeev equations for a system of three non-identical particles. The energies of the ($1^-2^-)$ spin doublets are calculated for different $n\Lambda $ and $\alpha \Lambda $ potentials [4-6]. Our results are compared with those from other calculations and experimental data. \\[4pt] [1] L. Majling, Proc. Natl. Conf. on Phys. of Few-Body and Quark-Hadronic Syst. (Kharkov, Ukraine, 1992). \\[0pt] [2] T. Motoba et al. Prog. Theor. Phys. \textbf{70} 189 (1983). \\[0pt] [3] E. Hiyama et al. Phys. Rev. C \textbf{59} 2351 (1999). \\[0pt] [4] I. Filikhin, et al. J. Phys. G: \textbf{31}, 389 (2005). \\[0pt] [5] I. Filikhin et al. EPJ Web of Conferences \textbf{3}, 07004 (2010); \\[0pt] [6] I. Filikhin, A. Gal, Phys. Rev. C \textbf{65} 041001R (2002).