Spectroscopy of $^7_{\Lambda}$He hypernucleus in three-body model

The $^7_{\Lambda}$He hypernucleus is considered as three-body cluster system $^5_{\Lambda}$He+$N$+$N$ [1]. Configuration space Faddeev calculations are performed for the hyperon binding energy. In particular we obtained the binding energy 5.35 MeV, which agrees with preliminary theoretical predictions (5.4 MeV) [2]. Note that this value differs from the recent experimental data [3]. Discussed is the recipe for extracting hyperon binding energy from the three-body calculations. The value obtained in previous E. Hiyama's et al.[4] calculation has to be corrected. A variant of the method of analytical continuation in coupling constant is applied to calculate the energies of resonance levels of the $^7_{\Lambda}$He. The second bound state of $^7_{\Lambda}$He with total angular momentum $J=3/2^+(5/2^+)$ was found. The bound states and low-lying resonances of $^7_{\Lambda}$He can be classified as an analog of the $^6$He ground band. 1. I. Filikhin, V. M. Suslov and B. Vlahovic, J. Phys. G31 389 2005. 2. O. Hashimoto, HYP2006 Mainz, October 11-14, 2006. 3. L. Tang, {\it Spectroscopy of $\Lambda$-Hypernuclei by Electroproduction, HNSS/HKS Experiments at JLAB}, FB18, Brazil, August 21-26 (2006); http://www.fb18.com.br 4. E. Hiyama, et al., PRC53 2078 1996.