  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 \textit{signature} of
van der Waals interactions can be directly used in the construction of
approximate pair density and energy functionals including vdW corrections.
