On the validity of approximate three-particle scattering models in an exactly soluble theory

Abstract

The approximate equations proposed by Lovelace for three body scattering problems are studied in the V-θ sector of the Lee model, with the view of testing the quantitative validity of the approximations involved. Comparison of the approximate with the exact solution shows that the two can generally differ considerably because the crossedN-pole comes out with a different residue in the approximate theory. This difference is narrowed but still can be considerable, if an arbitrary subtraction is performed at the crossed-pole position. It is concluded that the equations give a much too simplified version of the three-body problem.