Configuration space Faddeev formalism for system of non-identical particles: three-body model for $^6_\Lambda$He

We study structure of energy spectrum of light hyprnucleus $^6_\Lambda$He using cluster $\alpha$+$\Lambda$+$n$ model. In particular, the spin doublet (1$^-$,2$^-$) of $^6_\Lambda$He is of interest for the testing the spin dependence of hyperon-nucleon potentials. Experimental value for 1$^-$ ground state energy of $^6_\Lambda$He has been reported to be -0.17 MeV below the threshold $^5_\Lambda$He+n. Our study is based on the configuration-space Faddeev equations for a system of three non-identical particles. The analytical continuation method in a coupling constant is applied for calculation of resonance parameters. The results of calculations for low-lying spectra of the system $\alpha$+$\Lambda$+$n$ are presented. Within our model, the $\alpha$-n potential is constructed to reproduce the results of $R$-matrix analysis for $\alpha$-n scattering data. This potential simulates the Pauli exception for $\alpha n$ in the s-state with repulsive core. We use phenomenological $\alpha$-$\Lambda$ potential and for the $\Lambda$-n interaction the s-wave potential simulating model NSC97f. We calculated energies of the low-lying 1$^-$, 2$^-$, 2$^+$, 0$^-$ states. Obtained results are discussed and compared with other calculations (T. Motoba et al. Prog. Theor. Phys. 70, 189 (1983)).