A renormalisation-group approach to two-body scattering with long-range forces

We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of distorted waves for the long range potential. We illustrate the method by applying it to scattering in the presence of a repulsive 1/r2 potential. We find a trivial fixed point, describing systems with weak short-range interactions, and a unstable fixed point. The expansion around the latter corresponds to a distorted-wave effective-range expansion.