Realistic calculations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:math> 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.

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