Does Σ-Σ-α Form a Quasi-Bound State?

We have investigated the possible existence of a quasi-bound state for the Σ-Σ-α system in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T = 2, since for an inert α particle there is no strong conversion to Ξ-N-α or Λ-Λ-α possible. A Σ-α optical potential based on Nijmegen model D and original Σ-Σ interactions of the series of Nijmegen potentials NSC97 as well a simulated Gaussian type versions thereof are used. Our investigation of the Σ-Σ-α system leads to a quasi bound state where, depending on the potential parameters, the energy ranges between −1.4 and −2.4 MeV and the level width is less than 0.4 MeV