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Break-up and recombination processes for loosely-bound molecules composed ofatoms with a large scattering length $a$ necessarily involve interactions thatare nonperturbative in the exact 2-body interaction. If these processes involveatoms with relative momenta much larger than $\hbar/|a|$, the leadingcontributions to their rates can be separated into short-distance factors thatare insensitive to $a$ and long-distance factors that are insensitive to therange of the interaction. These factorization contributions can be obtainedfrom the leading term in a perturbation expansion in the exact atom-atomscattering amplitude. The short-distance factors are atom-atom cross sectionsat a lower collision energy. In the special case of inclusive break-up crosssections for atom-molecule scattering, the long-distance factors simply countthe number of atoms in the molecule.Comment: 7 pages, 3 figure

Factorization in breakup and recombination processes for atoms with a large scattering length