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 $\sigma$. Explicitly, Efimov or Thomas effects remain for $\sigma <{\sigma }_c$, the additional boundary conditions of two types should be imposed at the triple-collision point for ${\sigma }_c\le \sigma <{\sigma }_e$ and ${\sigma }_e<\sigma <{\sigma }_r$, and the problem is regularized for $\sigma \ge {\sigma }_r$. Critical values ${\sigma }_c<{\sigma }_e<{\sigma }_r$ separating different alternatives are determined both for a two-component three-body system and for three identical bosons.

12 pages, 3 figures. Accepted in JETP Letters

References in corpus (5)

• Scattering in Mixed Dimensions with Ultracold Gases
• Low-energy three-body dynamics in binary quantum gases
• Universal Fermi gases in mixed dimensions
• Universal low-energy properties of three two-dimensional particles
• Efimov physics and universal trimer in spin-orbit coupled ultracold atomic mixtures

Cited by in corpus (1)

• Mass-ratio condition for non-binding of three two-component particles with contact interactions