Three-body recombination of ultra-cold atoms to a weakly bound $s$ level

We discuss three-body recombination of ultra-cold atoms to a weakly bound $s$ level. In this case, characterized by large and positive scattering length $a$ for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability and makes simple Jastrow-like approaches absolutely inadequate. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: ${\alpha }_{\mathrm{r}\mathrm{e}\mathrm{c}}=3.9\mathrm{\hslash }{a}^4\mathrm{/}m$, where $m$ is the atom mass.