The few-atom problem

TL;DR

This paper provides a comprehensive theoretical overview of the few-body problem with short-range resonant interactions, covering effective range expansion, Efimov effect, and solution methods like the STM equation.

Contribution

It introduces a detailed analysis of the few-atom problem, including the role of resonance width, quantum symmetry, and mass imbalance, with derivations and solution examples.

Findings

Analysis of the effective range expansion emphasizing resonance width.

Description of the Efimov effect and its dependence on system parameters.

Derivation and application of the STM equation for few-atom systems.

Abstract

These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role of the resonance width. In the second part we review the Efimov effect for three atoms, describe the difference in between the Efimovian and non-Efimovian regimes, and discuss the dependence of three-body observables on quantum symmetry, mass imbalance, and resonance width. In the third part we derive the Skorniakov and Ter-Martirosian equation and give several illustrative examples of its solution.