Crossover in the Efimov spectrum

A filtering method is introduced for solving the zero-range three-boson problem. This scheme permits solving the original Skorniakov Ter-Martirosian integral equation for an arbitrary large ultraviolet cutoff and avoiding 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 crossover in the Efimov spectrum is found in such systems and a specific regime emerges where Efimov states are long-lived.