Hyperspherical few-body model calculation for cascade $\Xi$ exotic hypernuclei with reference to nuclear drip lines

In this paper, we presented the ground state energies calculated for some single and double cascade hyperon(${\Xi}^{-}$) hypernuclei. For hypernuclei of the type $_{\Xi}^{A_c+1}$X we applied $\Xi+^A_c$X two-body model and for hypernuclei of the type $_{\Xi\Xi}^{A_c+2}$X we adopted $\Xi+\Xi+^A_c$X three-body model. A two-term Gaussian (Isle type) potential with adjustable parameters is chosen as the $\Xi$-nucleus interaction, while a two-term Yukawa-type potential has been chosen for the $\Xi\Xi$ pair. In the three-body model calculation, we adopted the hyperspherical harmonics expansion (HHE) formalism. The resulting two- and three-body Schr{\"o}dinger equations subject to appropriate boundary condition's have been solved numerically to get the ground-state energies and wavefunctions. Computed values are in excellent agreement with the observed ones as found in the literature. Analysis of the calculated observables indicates that the hyperons stay close to the core-nucleus. Hypernuclei formed as a result of absorption of one or more $\Xi$-hyperon(s) by a normal nucleus (bound or unbound) are found to have more stability than those formed as a result of absorption of one or more $\Lambda$ hyperon(s) by the same nucleus. This fact flashes towards the possibility of the existence of a valley of strange hypernuclei near the drip lines.