Search for Bound States in Ξ-nn, Ξ-pn, and Ξ-pp Systems

Search for bound states in Xi(-)nn, Xi pn, and Xi(-) pp systems is performed by employing coupled homogeneous integral Faddeev equations written in terms of T-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 Xi(-) nn-Delta Sigma(-)n-Sigma- Sigma(0)n, Xi(-)np-Lambda Lambda n(-)Lambda Sigma(0)n, and Xi(-)pp-Lambda Lambda p-Lambda Sigma(0)p systems is taken precisely into account within this approach. Two-body t matrices are the only ingredient of the proposed method. In the case of two-body Xi(-) N interaction, they are found by solving the coupled Lippmann-Schwinger integral equations for the Xi N-Lambda Lambda-Sigma Sigma system in the (I = 0, S-1(0)) state, the Xi N system in the (I = 0, S-3(1)) state, the Xi N-Lambda Sigma system in the (I = 1, S-1(0)) state, and the Xi N-Lambda Sigma-Sigma Sigma system in the (I = 1, S-3(1)) state. An updated version of the ESC16 microscopic model is used to obtain two-body Xi N-, YY, and YN interactions generating t matrices. Two-body NN interaction 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 Xi(-) nn and Xi(-) np systems has one bound state with binding energies of 4.5 and 5.5MeV, respectively, and that the Xi(-) pp system has two bound states with binding energies of 2.7 and 4.4 MeV.