A renormalisation-group treatment of two-body scattering

Abstract

Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic power-counting to terms in the potential near each of these fixed points. The expansion around the nontrivial fixed point is shown to be equivalent to the effective-range expansion.

Comments: 6 pages (RevTeX), 1 figure (epsf); picture of RG flow and more discussion of momentum dependence added