Analytic expression for three-body recombination rates into deep dimers

TL;DR

This paper derives analytic formulas for three-body recombination rates into deep dimers in cold atomic gases, accounting for universal behavior and effects of short-range absorption and mass ratio variations.

Contribution

It provides the first closed-form expressions for recombination rates into deep dimers using a hyper-spherical approach with a short-range absorption parameter.

Findings

Recombination rates follow a universal fourth power law with log-periodic peaks.

Short-range absorption broadens and eventually smears out the peaks.

Higher heavy-to-light mass ratios decrease peak spacing and increase overall recombination rate.

Abstract

We investigate three-body recombination rates into deep dimers in cold atomic gases with large scattering length within hyper-spherical adiabatic zero-range approach. We derive closed analytic expressions for the rates for one- and two-species gases. Although the deep dimers are beyond the zero-range theory the latter can still describe the recombination into deep dimers by use of one additional short-range absorption parameter. The recombination rate, as function of the scattering length, retains the known universal behavior --- the fourth power trend with characteristic log-periodic peaks --- however increasing the short-range absorption broadens the peaks until they are eventually completely smeared out. Increasing the heavy-to-light mass ratio in a two-species system decreases the distance between the peaks and increases the overal scale of the recombination rate.