Limits on the Domain of Coupling Constants for Binding N-Body Systems with No Bound Subsystems

Abstract

We study the domain of coupling constants for which a 3-body or 4-body system is bound while none of its subsystems is bound. Limits on the size of the domain are derived from a variant of the Hall--Post inequalities which relate $N$-body to $(N-1)$-body energies at given coupling. Possible applications to halo nuclei and hypernuclei are briefly outlined.