Energy scaling of the product state distribution for three-body recombination of ultracold atoms

Three-body recombination is a chemical reaction where the collision of three atoms leads to formation diatomic molecule. In ultracold regime it expected that production rate molecule generally decreases with its binding energy ${E}_{b}$, however, precise dependence and physics governing have been left unclear so far. Here we present comprehensive experimental theoretical study dependency for three-body Rb. For this, determine rates molecules in state-to-state resolved manner, energies ${E}_{b}$ ranging from 0.02 77 $\mathrm{GHz}\ifmmode\times\else\texttimes\fi{}h$. We find approximately scales as ${E}_{b}^{\ensuremath{-}\ensuremath{\alpha}}$, $\ensuremath{\alpha}$ vicinity 1. The typically varies only within factor two different rotational angular momenta molecular product, apart possible centrifugal barrier suppression low energies. addition numerical calculations perturbative model which reveals physical origin scaling rate. Furthermore, show law potentially holds universally broad range interaction potentials.