Three-Body Recombination of Ultracold Atoms to a Weakly Bound<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">s</mml:mi></mml:math>Level

Abstract

We discuss three-body recombination of ultracold 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. 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: ${\ensuremath{\alpha}}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.9\ensuremath{\Elzxh}{a}^{4}/m$, where $m$ is the atom mass.