Abstract
Previous lectures have been devoted to the general formalism for studying the interaction between two particles. Among the main results, we established that at low energies and for a potential decreasing fast enough to infinity, the interaction could be characterized by a single number, the scattering length. The aim of this lecture is to concretize this notion for a realistic atomic potential, varying as 1/r6 at large distances. For species commonly used in cold atom experiments, the potential well describing the interaction between two atoms contains many vibrational states. It follows that the theoretical study of the problem can be carried out using a semi-classical approach, based on the WKB (Wentzel - Kramers - Brillouin) method, with a few subtleties that we'll describe below. The WKB approach leads to a remarkable universality of result, linking the value of the scattering length to the energy of the weakest bound states in the interatomic potential.
