A Zero-Range Model for the Efimov Effect in the Born-Oppenheimer Approximation

TL;DR

This paper demonstrates that a three-particle quantum system with zero-range interactions, under the Born-Oppenheimer approximation, exhibits the Efimov effect with infinitely many bound states accumulating at zero energy.

Contribution

It extends previous results by showing the Efimov effect in a specific three-particle system with zero-range interactions under the Born-Oppenheimer approximation.

Findings

Infinite negative eigenvalues accumulate at zero energy.

The eigenvalues follow the universal geometric law of the Efimov effect.

Generalizes earlier results on Efimov states in similar systems.

Abstract

In this note we discuss the Efimov effect emerging in a three-particle quantum system with zero-range interactions. In particular, we consider two non-interacting identical bosons plus a different lighter particle such that the interaction between a boson and the light particle is resonant. We also assume the validity of the Born-Oppenheimer approximation. Under these conditions, we show that the three-particle system exhibits infinitely many negative eigenvalues which accumulate at zero and satisfy the universal geometrical law characterising the Efimov effect. The result we find is a generalisation of previous results recently obtained in [13, 24].