Structure of neutron-rich He $\mathrm{\Lambda }$ hypernuclei using the cluster orbital shell model

We calculated the energy spectra of the neutron-rich He $\mathrm{\Lambda }$ hypernuclei with $A=6$ to 9 within the framework of an $\alpha +\mathrm{\Lambda }+Xn$ ($X=1$–4) cluster model using the cluster orbital shell model. The employed constituent particles reproduce their observed properties. For resonant states of core nuclei such as ${}^5$He, ${}^6$He, and ${}^7$He, the complex scaling method is employed to obtain energies and decay widths. The calculated ground states of ${}_{\mathrm{\Lambda }}^6$He and ${}_{\mathrm{\Lambda }}^7$He are in good agreement with published data. The energy levels of ${}_{\mathrm{\Lambda }}^8$He and ${}_{\mathrm{\Lambda }}^9$He are predicted. In ${}_{\mathrm{\Lambda }}^9$He, we find one deeply bound state and two excited resonant states, which are proposed to be produced at the Japan proton accelerator research complex (J-PARC) by the double-charge-exchange reaction $({\pi }^{-},K^{+})$ using a ${}^9$Be target.