Abstract
We now turn to the case of a low-energy collision, such that kb1, where k is the relative wave vector of the two collision partners and b the range of the interaction potential. This problem is of great importance for cold atom physics. It will bring about a considerable mathematical simplification: only the lowest partial waves (L=0 or 1) contribute significantly, and when they do play a role, they can be characterized by just one or two physical parameters such as the scattering length or the effective range. In particular, this simplification makes it possible to replace the real potential between atoms, which can be complicated to determine as we saw in lecture 1, with a much simpler potential leading to the same set of physical parameters.
