Salient signature of van der Waals interactions

van der Waals interactions govern the physics of a plethora of molecular structures. It is well known that the leading term in the distance-based London expansion of the van der Waals energy for atomic and molecular dimers decays as 1/R-6, where R is the dimer distance. Using perturbation theory, we find the leading term in the distance-based expansion of the intracule pair density at the interatomic distance. Our results unveil a universal 1/R-3 decay, which is less prone to numerical errors than the 1/R-6 dependency, and it is confirmed numerically in H-2 and He-2 molecules. This signature of van der Waals interactions can be directly used in the construction of approximate pair density and energy functionals including vdW corrections.