Resonant states of neutron-rich $Λ$ hypernucleus $^7_Λ$He

The structure of neutron-rich $Λ$ hypernucleus, $^7_Λ$He is studied within the framework of an $α+Λ+n+n$ four-body cluster model. We predict second $3/2^+$ and $5/2^+$ states, corresponding to a $0s$ $Λ$ coupled to the second $2^+$ state of $^6$He, as narrow resonant states with widths $Γ\sim 1$ MeV to be at 0.03 MeV and 0.07 MeV respect to the $α+Λ+n+n$ threshold. From an estimation of the differential cross section for the $^7{\rm Li} (γ,K^+) ^7_Λ$He reaction, there is a possibility to observe these state at JLab in the future. We also calculate the second $2^+$ state of $^6$He as resonant state within the framework of an $α+n+n$ three-body cluster model. Our result is $2.81$ MeV with $Γ=$4.63 MeV with respect to the $α+n+n$ threshold. This energy position is $\sim 1$ MeV higher, and with a much broader decay width, than the recent SPIRAL data. It is suggested that an experiment at JLab to search for the second $3/2^+$ and $5/2^+$ states of $^7_Λ$He would provide an opportunity to confirm the second $2^+$ state of the core nucleus $^6$He.

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