A renormalisation-group treatment of two-body scattering

Abstract

A Wilsonian renormalisation group is used to study nonrelativistic two-body scattering by a short-ranged potential. We identify two fixed points: 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: 9 pages (LaTeX, aipproc), 1 figure (epsf); talk presented at the International Workshop on Hadron Physics "Effective Theories of Low Energy QCD", Coimbra, Portugal, September, 1999 (shorter version also presented at MENU'99, Zuoz, Switzerland)