Does \Sigma -\Sigma -\alpha Form a Quasi-Bound State?

Abstract

We have investigated the possible existence of a quasi-bound state for the \Sigma -\Sigma -\alpha system in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T=2, since for an inert \alpha particle there is no strong conversion to \Xi -N-\alpha or \Lambda -\Lambda -\alpha possible. A \Sigma -\alpha optical potential based on Nijmegen model D and original \Sigma -\Sigma interactions of the series of Nijmegen potentials NSC97 as well a simulated Gaussian type versions thereof are used. Our investigation of the \Sigma -\Sigma -\alpha 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 about 0.2MeV.