Four-body cluster structure of a = 7-10 double-Λ hypernuclei

Energy levels of the double-Λ hypernuclei _ΛΛ⁷ He, _ΛΛ⁷ Li, _ΛΛ⁸ Li, _ΛΛ⁹ Li, _ΛΛ⁹ Be, and _ΛΛ¹⁰ Be are predicted on the basis of an α+x+Λ+Λ four-body model, where x = n, p, d, t, ³He, and α, respectively. Interactions between the constituent particles are determined so as to reproduce reasonably the observed low-energy properties of the α+x nuclei (⁵He, ⁵Li, ⁶Li, ⁷Li, ⁷Be, ⁸Be) and the existing data for Λ-binding energies of the x + Λ and α+x+Λ systems (_Λ³H, _Λ⁴H, _Λ⁵He, _Λ⁶He, _Λ⁶Li, _Λ⁸Li, _Λ⁸Be, _Λ⁹ Be). An effective ΛΛ interaction is constructed so as to reproduce, within the α+Λ+Λ model, the B_ΛΛ of _ΛΛ⁶ He, which was extracted from the emulsion experiment, the NAGARA event. With no adjustable parameters for the α+x+Λ+Λ system, B_ΛΛ of ground and bound excited states of the double-Λ hypernuclei with A=7-10 are calculated within the Gaussian-basis coupled-rearrangement-channel method. The Demachi-Yanagi event, identified recently as _ΛΛ¹⁰Be, is interpreted as an observation of its 2⁺ excited state on the basis of the present calculation. Structural changes in the α + x core nuclei, due to the interaction of the Λ particles, are found to be substantial, and these play an important role in estimating the ΛΛ bond energies of those hypernuclei.