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 \le σ< σ_e $ and $ σ_e < σ< σ_r $, and the problem is regularized for $ σ\ge 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.