Structure of A=7 iso-triplet $\Lambda$ hypernuclei studied with he four-body model

Abstract

The structure of the T=1 iso-triplet hypernuclei, ${}_{\Lambda }^7$He, ${}_{\Lambda }^7$Li and ${}_{\Lambda }^7$Be within the framework of an $\alpha +\Lambda +N+N$ 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 $\alpha N$, $\alpha \Lambda$, $\alpha NN$ and $\alpha \Lambda N$ subsystems. Furthermore, the two-body $\Lambda N$ interaction is adjusted so as to reproduce the $0^{+}$-$1^{+}$ splitting of ${}_{\Lambda }^4$H. Also a phenomenological $\Lambda N$ charge symmetry breaking(CSB) interaction is introduced. The $\Lambda$ binding energy of the ground state in ${}_{\Lambda }^7$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 ${}_{\Lambda }^7$He and ${}_{\Lambda }^7$Li are around 0.1 MeV. We point out that there is a three-layer structure of the matter distribution, $\alpha$ particle, $\Lambda$ skin, proton or neutron halo, in the ${}_{\Lambda }^7\mathrm{He}(J=5/2^{+})$, ${}_{\Lambda }^7\mathrm{Li}(J=5/2^{+})$ and ${}_{\Lambda }^7\mathrm{Be}(J=1/2^{+})$ states.

12 pages, 9 figures, To be published in Phys. Rev. C

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