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

Abstract

The structure of the T=1 iso-triplet hypernuclei, $^7_Λ$He, $^7_Λ$Li and $^7_Λ$Be 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 $^4_Λ$H. Also a phenomenological $ΛN$ charge symmetry breaking(CSB) interaction is introduced. The $Λ$ binding energy of the ground state in $^7_Λ$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 $^7_Λ$He and $^7_Λ$Li are around 0.1 MeV. We point out that there is a three-layer structure of the matter distribution, $α$ particle, $Λ$ skin, proton or neutron halo, in the $^7_Λ{\rm He}(J=5/2^+)$, $^7_Λ{\rm Li}(J=5/2^+)$ and $^7_Λ{\rm Be}(J=1/2^+)$ states.

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