Conditions for Efimov Physics for Finite Range Potentials

TL;DR

This paper derives conditions for Efimov physics in three-boson systems with finite-range potentials, highlighting the importance of effective range corrections and non-adiabatic effects near Feshbach resonances.

Contribution

It provides a rigorous large-distance equation for the adiabatic potential considering finite-range interactions and introduces a new effective range correction term.

Findings

Effective range correction requires an additional term of the same order.

Efimov physics is confined between the effective range and scattering length.

Analytical results match numerical calculations for realistic potentials.

Abstract

We consider a system of three identical bosons near a Feshbach resonance in the universal regime with large scattering length usually described by model independent zero-range potentials. We employ the adiabatic hyperspherical approximation and derive the rigorous large-distance equation for the adiabatic potential for finite-range interactions. The effective range correction to the zero-range approximation must be supplemented by a new term of the same order. The non-adiabatic term can be decisive. Efimov physics is always confined to the range between effective range and scattering length. The analytical results agree with numerical calculations for realistic potentials.