Scattering Length Scaling Laws for Ultracold Three-Body Collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support $s$-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.

Figure 1

Schematic plot of the three-body effective potentials for $0^{+}$ bosonic systems with (a) $a>0$ and (b) $a<0$, and for all other systems with (c) $a>0$ and (d) $a<0$.