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

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

2005-01-21

arxiv.org/abs/cond-mat/0501510v2

Physics

Condensed Matter

Other Condensed Matter

7 pages, 3 figures

Scientific paper

10.1103/PhysRevA.73.042707

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.

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