Zero Energy Bound States in Many--Particle Systems

TL;DR

This paper proves that in many-particle quantum systems, eigenvalues merge at zero energy if no subsystems are bound and no pairs have zero-energy resonances, allowing for both attractive and repulsive potentials.

Contribution

It establishes conditions under which eigenvalues in many-particle systems are absorbed at zero energy, extending previous results to include potentials of both signs.

Findings

Eigenvalues are absorbed at zero energy under specified conditions.

No bound subsystems or zero-energy resonances are required.

Results apply to systems with both attractive and repulsive pair potentials.

Abstract

It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs.