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Modeling of the structure of hypernuclei and dynamics of many-body systems comprising nucleons and hyperons is critical to understand hyperon-nucleon and hyperon-hyperon interactions and the role that hyperons can play in the state of matter. We have made significant progress towards this goal by developing our cluster approach for light hypernuclei like 7He and 9Be. The 7He hypernucleus is considered within the 5He +n+n cluster model and 9Be is considered as 5He +. We also significantly improved existing computer algorithms by including the spin orbit interaction and by developing a new phenomenological αΛ potential. This set includes the Ali-Bodmer potential of model "e" for and modified Tang-Herdon potential for interactions. The spin-orbit component of the interaction is given by modified Scheerbaum potential. In the LS basis used in this work the potential is represented by diagonal matrix.

Both improvements, inclusion of the spin orbit interaction in few body reactions and developed new αΛ potential, resulted in higher accuracy in calculating physical observables. In particular we have calculated energies of low-lying levels of these nuclei. For the ground state of the hypernucleus we have been obtained result (5.35 MeV) which is in well agreement with preliminary experimental data (5.4 MeV). We compared our results for low-lying excited states of this nucleus with the corresponding states of the nuclear core ( nucleus) to get classification of the levels and develop role of Λ-hyperon in formation of theresonance states. We have also shown that the spectral properties of can be classified as an analog of spectrum, with the exception of several "genuine hypernuclear states". Energy splitting (5/2+, 3/2+) have been evaluated and energy space of the spin-flip doublet (9/2+,7/2+) was predicted.

The calculations were based on the configuration space Faddeev equations within the framework of three cluster models for these nuclei.

Energies of resonance states have been evaluated by applying a variant of the method of analytical continuation in coupling constant. To realize this method an attractive three-body potential is added to the Hamiltonian of system. The strength parameter of the potential defines a number of bound states existing in system. This parameter is considered as a variational parameter for analytical continuation of energy of bound state to complex plane using the Pade approximates. Energy of corresponding resonance is calculated for zero value of the parameter. The experimental data for excitation energies are well reproduced by our calculations.