Check out the introduction of e.g. this paper for an example of long range Van der Waals forces, which are encountered in cold atom experiments. These forces occur between highly excited atoms called Rydberg atoms and behave as $n^{11}/r^6$, where $n$ is the principal quantum number, which is extraordinary high for these atoms.
This post imported from StackExchange Physics at 2014-03-24 04:15 (UCT), posted by SE-user Funzies