Search for Bound States in \(\boldsymbol{\Xi^{-}nn}\)-, \(\boldsymbol{\Xi^{-}pn}\)- and \(\boldsymbol{\Xi^{-}pp}\)- Systems

Search for bound states in @, @, and @ systems is performed by employing coupled homogeneous integral Faddeev equations written in terms of 
-matrix components. Instead of the traditional partial-wave expansion, a direct integration with respect to angular variables is used in these equations, and three-body coupling in the phase space of each of the @–@–@, @–@–@, and @–@–@ systems is taken precisely into account within this approach. Two-body 
 matrices are the only ingredient of the proposed method. In the case of two-body @ interaction, they are found by solving the coupled Lippmann–Schwinger integral equations for the @–@–@ system in the (@, @) state, the @ system in the (@, @) state, the @–@ systemin the (@, @) state, and the @–@–@ system in the (@,@) state. An updated version of the ESC16 microscopic model is used to obtain two-body @, YY, and YN interactions generating @ matrices. Two-body NN @ nteraction is reconstructed on the basis of the charge-dependent Bonn model. Direct numerical calculations of the binding energy for the systems being considered clearly indicate that either of the @ and @ systems has one bound state with binding energies of 4.5 and 5.5 MeV, respectively, and that the @ system has two bound states with binding energies of 2.7 and 4.4 MeV.