Mass-imbalanced Three-body Systems in 2D: bound states and the analytical approach to the adiabatic potential

TL;DR

This paper investigates three-body bound states in two-dimensional systems with zero-range interactions, revealing how the number of bound states depends on mass ratios and providing an analytical approximation to the adiabatic potential.

Contribution

It introduces an analytical approach to approximate the adiabatic potential in 2D three-body systems, enhancing understanding of mass-dependent bound state properties.

Findings

Number of bound states increases as one particle becomes lighter.

Universal bound state boundaries are mapped in a mass-mass diagram.

Analytical approximation successfully describes the adiabatic potential.

Abstract

Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to study universal properties of such systems with respect to the bound-state energies. The number of universal bound states is represented in a form of boundaries in a mass-mass diagram. The number of bound states is strongly mass dependent and increases as one particle becomes much lighter than the other ones. This behavior is understood through an accurate analytical approximation to the adiabatic potential for one light particle and two heavy ones.