Channel coupling arrays and the reduction method in many-body scattering

A differential equation formulation of the multichannel coupled equations of Kouri and Levin describing rearrangement scattering is given. The different channels are linked together in these equations through the presence of the channel coupling array $W$. It is shown that the earlier results of Hahn, derived using the reduction method, follow directly from the multichannel coupled equations by making specific choices of the array $W$. These particular $W\text{'}\mathrm{s}$ guarantee that the iterated kernels of the coupled equations are connected in those channels which are explicitly considered, so that standard numerical techniques can be applied to their solution.