The structure of the T=1 isotriplet hypernuclei, Λ7He, Λ7Li, and Λ7Be within the framework of an α+Λ+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 αN, αΛ, αNN, and αΛN subsystems. Furthermore, the two-body ΛN interaction is adjusted so as to reproduce the 0+-1+ splitting of Λ4H. Also, a phenomenological ΛN charge symmetry breaking (CSB) interaction is introduced. The Λ binding energy of the ground state in Λ7He 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 Λ7He and Λ7Li are around 0.1MeV. We point out that there is a three-layer structure of the matter distribution, α particle, Λ skin, and proton or neutron halo, in the Λ7He(J=5/2+), Λ7Li(J=5/2+), and Λ7Be(J=1/2+) states.
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