Three-body resonant states of ${}_{\Lambda }^9$Be with $\alpha +\alpha +\Lambda$ cluster model

Abstract

We study the structure of ${}_{\Lambda }^9$Be in the framework of three body $\alpha +\alpha +\Lambda$ cluster model using YNG-NF interaction with the Gaussian expansion method. Employing the complex scaling method, we obtain the energies of bound states as well as energies and decay widths of the resonant states. By analyzing our wave functions of bound states and resonant states, we confirm three analogue states of ${}_{\Lambda }^9$Be pointed out by Band$\bar{\mathrm{o}}$ and Motoba {\it et al.} \cite{motoba1983,motoba1985,bando1983}, ${}^8$Be analogue states, ${}_{\Lambda }^9$Be genuine states and ${}^9$Be analogue states. The new states of ${}_{\Lambda }^9$Be are also obtained at a high energy region with broader decay widths.