Energy levels of the double-Λ hypernuclei ${}_{\Lambda \Lambda }^7\mathrm{He},$ ${}_{\Lambda \Lambda }^7\mathrm{Li},$ ${}_{\Lambda \Lambda }^8\mathrm{Li},$ ${}_{\Lambda \Lambda }^9\mathrm{Li},$ ${}_{\Lambda \Lambda }^9\mathrm{Be},$ and ${}_{\Lambda \Lambda }^{10}\mathrm{Be}$ are predicted on the basis of an $\alpha +x+\Lambda +\Lambda$ four-body model, where ${x=n,p,d,t,}^3\mathrm{He},$ and $\alpha ,$ respectively. Interactions between the constituent particles are determined so as to reproduce reasonably the observed low-energy properties of the $\alpha +x$ nuclei ${(}^5\mathrm{He},{}^5\mathrm{Li},{}^6\mathrm{Li},{}^7\mathrm{Li},{}^7\mathrm{Be},{}^8\mathrm{Be})$ and the existing data for Λ-binding energies of the $x+\Lambda$ and $\alpha +x+\Lambda$ systems ${(}_{\Lambda }^3\mathrm{H},{}_{\Lambda }^4\mathrm{H},{}_{\Lambda }^5\mathrm{He},{}_{\Lambda }^6\mathrm{He},{}_{\Lambda }^6\mathrm{Li},{}_{\Lambda }^7\mathrm{Li},{}_{\Lambda }^8\mathrm{Li},{}_{\Lambda }^8\mathrm{Be},{}_{\Lambda }^9\mathrm{Be}).\mathrm{}$ An effective ΛΛ interaction is constructed so as to reproduce, within the α+Λ+Λ model, the $B_{\Lambda \Lambda }$ of ${}_{\Lambda \Lambda }^6\mathrm{He},$ which was extracted from the emulsion experiment, the NAGARA event. With no adjustable parameters for the $\alpha +x+\Lambda +\Lambda$ system, $B_{\Lambda \Lambda }$ of ground and bound excited states of the double-Λ hypernuclei with $A=7\mathrm{}–10$ are calculated within the Gaussian-basis coupled-rearrangement-channel method. The Demachi-Yanagi event, identified recently as ${}_{\Lambda \Lambda }^{10}\mathrm{Be},$ is interpreted as an observation of its $2^{+}$ excited state on the basis of the present calculation. Structural changes in the $\alpha +x$ 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.

• Received 21 April 2002

DOI:https://doi.org/10.1103/PhysRevC.66.024007