Mass-imbalanced Three-Body Systems in Two Dimensions

TL;DR

This study investigates three-body systems with unequal masses in two dimensions, revealing a rich spectrum of bound states influenced by mass ratios, using numerical solutions and the Born-Oppenheimer approximation.

Contribution

The paper provides a detailed analysis of mass-imbalanced three-body systems in 2D, deriving a Coulomb-like BO potential and quantifying the number of bound states for specific atomic mixtures.

Findings

Mass-imbalanced systems exhibit multiple bound states.

Small light-heavy mass ratios increase the number of bound states.

For 87Rb-87Rb-6Li and 133Cs-133Cs-6Li, 3 and 4 bound states are found.

Abstract

We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The BO expression is derived using separable potentials and yields a concise adiabatic potential between the two heavy particles. The BO potential is Coulomb-like and exponentially decreasing at small and large distances, respectively. While we find similar qualitative features to previous studies, we find important quantitative differences. Our results demonstrate that mass-imbalanced systems that are accessible in the field of ultracold atomic gases can have a rich three-body bound state spectrum in two dimensional geometries. Small light-heavy mass ratios increase the number of bound states. For 87Rb-87Rb-6Li and 133Cs-133Cs-6Li we find respectively 3 and 4 bound states.