Crossover in the Efimov spectrum

TL;DR

This paper introduces a new filtering method to solve the zero-range three-boson problem, revealing a crossover in the Efimov spectrum and identifying regimes where Efimov states are long-lived.

Contribution

A novel filtering scheme for solving the Skorniakov Ter-Martirosian equation that handles large UV cut-offs and avoids Thomas collapse, applied to generalized models including finite background scattering.

Findings

Identified a crossover in the Efimov spectrum.

Discovered regimes with long-lived Efimov states.

Extended the model to include finite background scattering and effective range.

Abstract

A filtering method is introduced for solving the zero-range three-boson problem. This scheme permits to solve the original Skorniakov Ter-Martirosian integral equation for an arbitrary large Ultra-Violet cut-off and to avoid the Thomas collapse of the three particles. The method is applied to a more general zero-range model including a finite background two-body scattering length and the effective range. A cross-over in the Efimov spectrum is found in such systems and a specific regime emerges where Efimov states are long-lived.