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We review recent progress in S=−2 hypernuclei such as double-Λ hypernuclei and Ξ hypernuclei, which are composed of a nucleus and one or two hyperons, such as a Λ or a Ξ particle. Through observations of He, such as the Nagara event, we obtain important information about the ΛΛ interaction. Using this information, we perform a four-body calculation of ααΛΛ for
Be, which was observed at KEK as the Demachi–Yanagi event. We interpret this event as the
excited state. We calculate energy levels of
Be within the framework of an ααnΛΛ five-body cluster model, and then interpret the Hida event, which was observed at KEK as the ground state of
Be. Motivated by observation of the Kiso event of
C, by using the Skyrme–Hartree–Fock and relativistic mean-field frameworks, we calculate the energy spectra of this hypernucleus. We interpret this event as the 14N(g.s.)+Ξ−(0p) state. Finally, we propose an experiment on
H and
Li to extract information about the spin- and isospin-averaged parts of the ΞN interaction.
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