Absence of bound states implies non-negativity of the scattering length
  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. 
Robert Seiringer
math-ph cond-mat.quant-gas math.MP math.SP