Zero Energy Bound States in Three--Particle Systems

TL;DR

This paper proves that in specific three-particle systems, eigenvalues merge at zero energy if no negative bound states or resonances exist in pairs, under certain potential restrictions.

Contribution

It establishes conditions under which three-particle eigenvalues are absorbed at zero energy, advancing understanding of spectral behavior in quantum systems.

Findings

Eigenvalues merge at zero energy under specified conditions

No negative bound states or resonances in pairs lead to eigenvalue absorption

Provides mathematical proof under potential restrictions

Abstract

Under certain restrictions on pair--potentials it is proved that the eigenvalues in the three--particle system are absorbed at zero energy threshold if there is no negative energy bound states and zero energy resonances in particle pairs.