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

We calculated the energy spectra of the neutron-rich He $\Lambda$ hypernuclei with $A=6$ to 9 within the framework of an $\alpha + \Lambda +Xn$ ($X=1$--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 $^6_{\Lambda}$He and $^7_{\Lambda}$He are in good agreement with published data. The energy levels of $^8_{\Lambda}$He and $^9_{\Lambda}$He are predicted. In $^9_{\Lambda}$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.