Structure ofA=7iso-tripletΛhypernuclei studied with the four-body cluster model

Abstract

The structure of the $T=1$ isotriplet hypernuclei, ${}_{\ensuremath{\Lambda}}^{7}\mathrm{He}$, ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Li}$, and ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Be}$ within the framework of an $\ensuremath{\alpha}+\ensuremath{\Lambda}+N+N$ four-body cluster model is studied. Interactions between the constituent subunits are determined so as to reproduce reasonably well the observed low-energy properties of the $\ensuremath{\alpha}N$, $\ensuremath{\alpha}\ensuremath{\Lambda}$, $\ensuremath{\alpha}\mathit{NN}$, and $\ensuremath{\alpha}\ensuremath{\Lambda}N$ subsystems. Furthermore, the two-body $\ensuremath{\Lambda}N$ interaction is adjusted so as to reproduce the ${0}^{+}--{1}^{+}$ splitting of ${}_{\ensuremath{\Lambda}}^{4}\mathrm{H}$. Also, a phenomenological $\ensuremath{\Lambda}N$ charge symmetry breaking (CSB) interaction is introduced. The $\ensuremath{\Lambda}$ binding energy of the ground state in ${}_{\ensuremath{\Lambda}}^{7}\mathrm{He}$ is predicted to be $5.16(5.36)$ MeV with (without) the CSB interaction. The calculated energy splittings of the $3/{2}^{+}--5/{2}^{+}$ states in ${}_{\ensuremath{\Lambda}}^{7}\mathrm{He}$ and ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Li}$ are around 0.1 MeV. We point out that there is a three-layer structure of the matter distribution, $\ensuremath{\alpha}$ particle, $\ensuremath{\Lambda}$ skin, and proton or neutron halo, in the ${}_{\ensuremath{\Lambda}}^{7}\mathrm{He}(J=5/{2}^{+})$, ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Li}(J=5/{2}^{+})$, and ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Be}(J=1/{2}^{+})$ states.