Distribution properties of the channel interactions in N-body scattering and applications

We derive several classes of distribution properties for the channel internal and external interactions, as well as for generalized residual interactions, in the framework of the N-body scattering theory An essential feature of our distribution properties is that all coefficients are unity (natural distributions). We give several examples of the great advantages coming from the employment of the natural distributions in practical applications. Several classes of cluster expansions are derived for the channel resolvent operators and the Hepp-Narodetskiî-Yakubovskiî expansion is proved in a simple algebraic way. We present compact procedures leading to both the Sloan-Bencze-Redish equations and the Faddeev-Yakubovskiî equations with artificial indexes in the unknowns. We consider also many types of decompositions for the full N-body scattering wave functions and, finally, we present general reversion properties for linked-cluster strings of resolvents and interactions.