Classical threshold law for the formation of van der Waals molecules

Abstract

We study the role of pairwise long-range interactions in the formation of van der Waals molecules through direct three-body recombination processes A + B + B $\to$ AB + B, based on a classical trajectory method in hyperspherical coordinates developed in our earlier works [J. Chem. Phys. 140, 044307 (2014); J. Chem. Phys. 154, 034305 (2021)]. In particular, we find the effective long-range potential in hyperspherical coordinates with an exact expression in terms of dispersion coefficients of pairwise potentials. Exploiting this relation, we derive a classical threshold law for the total cross section and the three-body recombination rate yielding an analytical expression for the three-body recombination rate as a function of the pairwise long-range coefficients of the involved partners.

arXiv comment9 pages, 5 figures, submitted to The Journal of Chemical Physics

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• Spin hierarchy in van der Waals molecule formation via ultracold three-body recombination
• Hyperradial distribution function of few-body problems: a new arena for extreme value theory
• Spin structure of diatomic van der Waals molecules of alkali atoms
• Isotope study of the nonlinear pressure shifts of ${}^{85}$Rb and ${}^{87}$Rb hyperfine resonances in Ar, Kr, and Xe buffer gases
• Chemistry in a Cryogenic Buffer Gas Cell
• Classical Grand Angular Momentum in N-Body Problems