Realistic calculations of K-NN, K-NNN, and K-K-NN quasibound states

Binding energies and widths of three-body K-NN, and of four-body K-NNN and K-K-NN nuclear quasibound states are calculated in the hyperspherical basis, using realistic NN potentials and subthreshold energy dependent chiral K-N interactions. Results of previous K ^-pp calculations are reproduced and an upper bound is placed on the binding energy of a K ^-d quasibound state. A self-consistent handling of energy dependence is found to restrain binding, keeping the calculated four-body ground-state binding energies to relatively low values of about 30 MeV. The lightest strangeness -2 particle-stable K- nuclear cluster is most probably K-K-NN. The calculated K-N→πY conversion widths range from approximately 30 MeV for the K-NNN ground state to approximately 80 MeV for the K-K-NN ground state.