Low-energy universality and scaling of van der Waals forces

At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion in terms of the scattering length alpha(0) and the effective range r(0). We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem r(0) = A + B/alpha(0) + C/alpha(2)(0), where A, B, and C depend on the dispersion coefficients C-n and the reduced diatom mass. We confront this formula to about 100 determinations of r(0) and alpha(0) and show why the result is dominated by the leading dispersion coefficient C-6. Universality and scaling extend much beyond naive dimensional analysis estimates.