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

Abstract

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 ${}_{\Lambda }^6$He and ${}_{\Lambda }^7$He are in good agreement with published data. The energy levels of ${}_{\Lambda }^8$He and ${}_{\Lambda }^9$He are predicted. In ${}_{\Lambda }^9$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.

6 pages, 4 figures, typos corrected

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