Factorization in Break-up and Recombination Processes for Atoms with a Large Scattering Length

TL;DR

This paper develops a factorization approach to analyze break-up and recombination processes in atoms with large scattering lengths, separating short- and long-distance effects to simplify calculations.

Contribution

It introduces a method to factorize rates into short- and long-distance components, applicable to nonperturbative atom interactions with large scattering lengths.

Findings

Factorization separates short- and long-distance effects.

Short-distance factors relate to atom-atom cross sections.

Long-distance factors count atoms in molecules.

Abstract

Break-up and recombination processes for loosely-bound molecules composed of atoms with a large scattering length $a$ necessarily involve interactions that are nonperturbative in the exact 2-body interaction. If these processes involve atoms with relative momenta much larger than $\hbar/|a|$, the leading contributions to their rates can be separated into short-distance factors that are insensitive to $a$ and long-distance factors that are insensitive to the range of the interaction. These factorization contributions can be obtained from the leading term in a perturbation expansion in the exact atom-atom scattering amplitude. The short-distance factors are atom-atom cross sections at a lower collision energy. In the special case of inclusive break-up cross sections for atom-molecule scattering, the long-distance factors simply count the number of atoms in the molecule.