A revised formula for 3-body recombination that cannot exceed the unitarity limit

Abstract

We discuss the recent developments in theory and experiment that bear on our understanding of three-body recombination at ultracold temperatures. Some of these predictions include the fourth-power dependence of the three-body rate on the two-body scattering lenght a, the appearance of quantum mechanical shape resonance and Feshbach resonances, and the existence of destructive interference minima at large positive scattering lenghts. At very large scattering lenghts, however, the a 4 dependence of the recombination rate eventually will exceed the unitarity limit. We propose in this paper a simple way to correct this problem, permitting an approximate extension of previous predictions to slightly higher energies above the three-body fragmentation threshold. A preliminary comparison is carried out with a very recent experiment by Grimm and coworkers, showing reasonable agreement.