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

Abstract

Binding of two heavy fermions interacting with a light particle via the contact interaction is possible only for sufficiently large heavy-light mass ratio. In this work, the two-variable inequality is derived to determine a specific value ${\mu }^{\ast }$ providing that there are no three-body bound states for the mass ratio smaller than ${\mu }^{\ast }$. The value ${\mu }^{\ast }=5.26$ is obtained by analyzing this inequality for a total angular momentum and parity $L^P=1^{-}$. For other $L^P$ sectors, the specific mass-ratio values providing an absence of the three-body bound states are found in a similar way. For generality, the method is extended to determine corresponding mass-ratio values for the system consisting of two identical bosons and a distinct particle for different $L^P$ ($L>0$) sectors.

11 pages, 1 figure

References in corpus (5)

• Low-energy three-body dynamics in binary quantum gases
• Models of zero-range interaction for the bosonic trimer at unitarity
• Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
• Minlos-Faddeev regularization of zero-range interactions in the three-body problem
• Three two-component fermions with contact interactions: correct formulation and energy spectrum