Low-Energy Recombination of Identical Bosons by Three-Body Collisions

The threshold recombination coefficient for three bosons whose two-body scattering length $a$ is positive and large compared with the nominal range of the potentials is shown to proceed via a crossing of hyperspherical adiabatic potential curves at $R\approx 2.6a$. The hidden crossing theory gives 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 varies from species to species, however an upper limit to the rate which depends only upon the scattering length emerges from the hidden crossing theory.