Efimov Trimers near the Zero-crossing of a Feshbach Resonance

TL;DR

This paper investigates whether Efimov-like three-boson states can exist near a Feshbach resonance where the two-body scattering length approaches zero, concluding that higher-order effects do not support Efimov physics in this regime.

Contribution

The study demonstrates that, within a zero-range model, no Efimov-like solutions arise when the scattering length approaches zero, challenging previous assumptions about Efimov states near this point.

Findings

No Efimov solutions near zero scattering length

Higher-order terms do not support Efimov physics in this regime

Zero-range model shows absence of anomalous three-boson states

Abstract

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schr\"odinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.