Absence of bound states implies non-negativity of the scattering length

TL;DR

This paper demonstrates that if a system of bosons has no bound states, then the scattering length of their interaction potential must be non-negative, linking the spectral properties to scattering characteristics.

Contribution

It establishes a fundamental connection between the absence of bound states in many-boson systems and the non-negativity of the scattering length of the interaction potential.

Findings

Bosons with negative scattering length form bound states with enough particles.

Absence of many-particle bound states implies non-negative scattering length.

Provides a criterion linking spectral properties to scattering parameters.

Abstract

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.