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

Classical threshold law for the formation of van der Waals molecules