Resonant states of the neutron-rich Λ hypernucleus He Λ7

The structure of the neutron-rich Λ hypernucleus, ⁷_ΛHe 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 0sΛ coupled to the second 2⁺ state of 6He, as narrow resonant states with widths of Γ∼1 MeV to be at 0.03 and 0.07 MeV with respect to the α+Λ+n+n threshold. From a separate estimate of the differential cross section for the ⁷Li(γ,K⁺)⁷_ΛHe reaction, we suggest a possibility to observe these states at the Thomas Jefferson National Accelerator Facility (JLab) in the future. We also calculate the second 2⁺ state of ⁶He as a 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 ∼1 MeV higher, and with a much broader decay width, than the recent SPIRAL data. We suggest that an experiment at JLab to search for the second 3/2⁺ and 5/2⁺ states of ⁷_ΛHe would provide an opportunity to confirm the second 2⁺ state of the core nucleus ⁶He.