Efimov and Thomas effects and the model dependence of three-particle observables in two and three dimensions

It is demonstrated for the three-dimensional three-particle system that a divergence arising from essentially the same singularity structure of the kernel of the scattering integral equation is responsible for both the Efimov and Thomas effects. The above divergence implies that the results of a three-particle dynamical calculation will be sensitive to the details of the two-particle interaction. In two-dimensional systems, the above divergence is absent and consequently the three-particle observables become essentially independent of the two-particle interaction model.