The structure of light hypernuclei with strangeness S= -2 is investigated with the three-, four-, and five-body cluster model and the Gaussian Expansion method (GEM). Energy levels of the double-Λ hypernuclei ΛΛ7He, ΛΛ 7Li, ΛΛ8Li, ΛΛ9Li, ΛΛ 9Be, and ΛΛ10Be are predicted with the framework of αxΛΛ four-body model, where x = n,p,d,t, 3He, and α, respectively. Also, energy levels of the double Λ hypernucleus, ΛΛ11Be are calculated within the framework of a ααnΛΛ five-body model. The Demachi-Yanagi event, identified as ΛΛ 10Be, is interpreted as an observation of its 2+ state excited state. The Hida event, recently observed at KEK-E373 experiment, is interpreted as an observation of the ground state of the ΛΛ11Be. Detailed structure calculations in Ξ12-Be, Ξ5-H, Ξ9-Li, Ξ7-H and Ξ10-Li are performed within the framework of the microscopic two-, three- and four-body cluster models. Ξ 7-H and Ξ10-Li are predicted to have bound states.
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