Four-body cluster structure ofA=7–10double-Λ hypernuclei

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Abstract

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

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