Does Σ–Σ–α Form Quasi-Bound States?

Abstract

For the Σ–Σ–α system we theoretically look into the possible existence of a quasi-bound state in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T=2, because there is no strong conversion between Ξ–N–α and $${\Lambda-\Lambda-\alpha}$$ . An analytic continuation using the point method is applied to search the eigenvalue in the complex energy plane. In our results the Σ–Σ–α three-body system has two quasi-bound states (J π = 0+) where, depending on the potential parameters in the Nijmegen NSC97 model potential, the energy ranges between −1.4 and −2.4 MeV and the level width is about 0.4 MeV for the ground state. In addition, we obtained the excited state at −0.15 MeV (width 4 MeV).