Scattering Length Scaling Laws for Ultracold Three-Body Collisions

TL;DR

This paper derives universal scaling laws for inelastic three-body collision rates in ultracold systems with short-range interactions, covering various particle combinations and providing a comprehensive framework.

Contribution

It introduces a unified, simple model that reproduces known results and predicts new scaling laws for three-body collision processes in ultracold physics.

Findings

Provides general scaling laws for vibrational relaxation, recombination, and dissociation.

Applies to systems with different particle symmetries, including bosons and fermions.

Reproduces previous results and extends to new cases.

Abstract

We present a simple picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short range two-body interactions. In particular, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons (BBB), two identical bosons (BBB'), and two identical fermions (FFF'). Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.