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We derive a quasiclassical expression for the density of states (DOS) of anarbitrary, ultracold, $N$-atom collision complex, for a general potentialenergy surface (PES). We establish the accuracy of our quasiclassical method bycomparing to exact quantum results for the K$_2$-Rb and NaK-NaK systems, withisotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES tobe 0.124~$\mu$K$^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus (RRKM)sticking time of 6.0~$\mu$s. We extrapolate the DOS and sticking times to allother polar bialkali-bialkali collision complexes by scaling with atomicmasses, equilibrium bond lengths, dissociation energies, and dispersioncoefficients. The sticking times calculated here are two to three orders ofmagnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712(2012)]. We estimate dispersion coefficients and collision rates betweenmolecules and complexes. We find that the sticking-amplified three-body lossmechanism is not likely the cause of the losses observed in the experiments.

A quasiclassical method for calculating the density of states of ultracold collision complexes