Minlos-Faddeev regularization of zero-range interactions in the three-body problem

Abstract

To regularize the three-body problem, Minlos and Faddeev suggested a modification of zero-range model, which diminishes interaction at the triple-collision point. The analysis reveals that this regularization results in four alternatives depending on the regularization parameter σ. Explicitly, Efimov or Thomas effects remain for σ < σ c , the additional boundary conditions of two types should be imposed at the triple-collision point for σ c ≤ σ < σ e and σ e < σ < σ r , and the problem is regularized for σ ≥ σ r . Critical values σ c < σ e < σ r separating different alternatives are determined both for a two-component three-body system and for three identical bosons.