Low-energy recombination of identical bosons by three-body collisions

The threshold recombination coefficient for three bosons whose two-body sca ttering length a is positive and large compared with the nominal range of t he potentials is shown to proceed via a crossing of hyperspherical adiabati c potential curves at R approximate to 2.6a. The hidden crossing theory giv es a simple expression for the rate in terms of the scattering length and a phase Delta. The phase depends upon the details of the interaction, and va ries from species to species, however an upper limit to the rate which depe nds only upon the scattering length emerges from the hidden crossing theory .