Correlation-induced collapse of many-body systems with zero-range potentials - art. no. 063608

The zero-range potential is customarily employed in various mean-field calc ulations of many-body systems in atomic and nuclear physics within, corresp ondingly, Gross-Pitaevskii and Skyrme-Hartree-Fock approaches. We argue, ho wever, that a many-body system with zero-range potentials is unstable again st clusterization into collapsed three-body subsystems. We show that neithe r the density dependence of the potential nor an additional repulsive three -body potential can prevent this unexpected correlational collapse if the p otentials are of zero range. Therefore, the zero-range potential can only b e used in many-body calculations where all three-body correlations are expl icitly excluded.