Correction to the potential in born approximation arising from direct-channel strips.—II

Abstract

The ππ partial wave ampltude (p.w.a.) is studied in the one-channel approximation for the statel=I=1. The Born approximation to the force operating in the direct channel is assumed to be saturated by σ-exchange in the crossed reactions for this state. This amounts to a “strip approximation” to the force. However, the direct channel strips must also contribute to the potential and there are 2 relatively simple ways to estimate this effect. The first was treated in a previous paper and involved putting an asymptotic constraint on the p.w.a.,B 1 (ν) =A 1 (ν)/ν l which has the threshold factor divided out. The correction to the Born approximation was an attractive force in the statel=I=1. The second method is the subject of this paper and involves working with the p.w.a.,A 1 l (ν), and imposing on it the usual threshold constraint. The correction to the Born approximation in this case is a strong repulsive force. The 2 methods give qualitatively very different effects in ππ scattering, although the present method is probably more reliable. We finally show how to relate the 2 corrections at low energies.