We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential.
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Robert Seiringer, Absence of bound states implies non-negativity of the scattering length. J. Spectr. Theory 2 (2012), no. 3, pp. 321–328DOI 10.4171/JST/31