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Currently, quantum scattering calculations cannot be used for quantitativepredictions of molecular scattering observables at ultralow temperatures. Thisis a result of two problems: the extreme sensitivity of the scatteringobservables to details of potential energy surfaces (PES) for interactionsbetween the collision partners, and the exceedingly large size of molecularbasis sets required for the numerically exact integration of theSchr\"{o}dinger equation in the presence of external fields. Here, we suggest anew statistical approach to address both of the above problems. We show thatensembles of scattering calculations with different PESs are characterized bycumulative probability distributions, which are insensitive to the size of themolecular basis sets and can, therefore, be obtained from calculations withrestricted basis sets. This opens the possibility of making predictions ofexperimentally relevant observables for a wide variety of molecular systems,currently considered out of reach of quantum dynamics theory. We demonstratethe method by computing the success probability of sympathetic cooling of CaHand SrOH molecules by Li atoms and SrF molecules by Rb atoms.

Universal probability distributions of scattering observables in ultracold molecular collisions