Universal Probability Distributions of Scattering Observables in Ultracold Molecular Collisions

Currently, quantum dynamics theory cannot be used for quantitative predictions of molecular scattering observables at low temperatures because of two problems. The first problem is the extreme sensitivity of the low-temperature observables to details of potential energy surfaces (PESs) parametrizing the nuclear Schrödinger equation. The second problem is the large size of the basis sets required for the numerical integration of the Schrödinger equation for strongly interacting molecules in the presence of fields, which precludes the application of rigorous quantum theory to all but a few atom-molecule systems. Here, we show that, if the scattering problem is formulated as a probabilistic prediction, quantum theory can provide reliable results with exponentially reduced numerical effort. Specifically, we show that the probability distributions that an observable is in a certain range of values can be obtained by averaging the results of scattering calculations with much smaller basis sets than required for calculations of individual scattering cross sections. Moreover, we show that such distributions do not rely on the precise knowledge of the PES. This opens the possibility of making probabilistic predictions of experimentally relevant observables for a wide variety of molecular systems, currently considered out of reach of quantum dynamics theory. We demonstrate the approach by computing the probability for elastic scattering of CaH and SrOH molecules by Li atoms and SrF molecules by Rb atoms.