On the reconstruction of coupled two-body channel amplitudes

Abstract

We examine the problem of reconstructing, at a fixed energy, the amplitude of an inelastic reactionAB → CD from its differential cross-section. We furthermore assume that the inelasticity proceeds from the coupling to two-body channels and that we know entirelyone of the two elastic amplitudesAB → AB, CD → CD, but not both. We first prove that, in the case of an infinite number of partial waves, the trivial ambiguities of the reconstructed amplitudes are reduced to a possible complex conjugation eventually combined with a change of sign. Secondly we study the particular case of inelastic amplitudes described with a finite number of partial waves. ForLmax ≤ 5 it is shown that no more than three nontrivially related solutions can exist simultaneously.