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

## TL;DR

This paper develops a quasiclassical method to calculate the density of states for ultracold collision complexes, validating it against quantum results and applying it to predict collision times and loss mechanisms in ultracold molecular systems.

## Contribution

It introduces a new quasiclassical approach for DOS calculation in ultracold collisions and applies it to bialkali molecules, providing insights into collision times and loss mechanisms.

## Key findings

- The quasiclassical method agrees well with quantum calculations.
- Calculated DOS for NaK-NaK is 0.124 μK^{-1}.
- Sticking times are much shorter than previous estimates, suggesting different loss mechanisms.

## Abstract

We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, $N$-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the K$_2$-Rb and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 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 all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.