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 µK −1 , with an associated Rice-Ramsperger-Kassel-Marcus (RRKM) sticking time of 6.0 µs. 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. * gerritg@theochem.ru.nl arXiv:1905.06691v2 [cond-mat.quant-gas]
Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three-and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK) 2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm −1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.
We consider losses in collisions of ultracold molecules described by a simple statistical short-range model that explicitly accounts for the limited lifetime of classically chaotic collision complexes. This confirms that thermally sampling many isolated resonances leads to a loss cross section equal to the elastic cross section derived by Mayle et al. [Phys. Rev. A 85, 062712 (2012)] and this makes precise the conditions under which this is the case. Surprisingly, we find that the loss is nonuniversal. We also consider the case that loss broadens the short-range resonances to the point that they become overlapping. The overlapping resonances can be treated statistically even if the resonances are sparse compared to k B T , which may be the case for many molecules. The overlap results in Ericson fluctuations which yield a nonuniversal short-range boundary condition that is independent of energy over a range much wider than is sampled thermally. Deviations of experimental loss rates from the present theory beyond statistical fluctuations and the dependence on a background phase shift are interpreted as nonchaotic dynamics of short-range collision complexes.
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