Conditions for Efimov physics for finite-range potentials

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 nonadiabatic 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.