[en] We discuss the unified reaction theory of Polyzou and Redish [Ann. Phys. (N.Y.) 119, 1(1979)] with regard to the freedom to perturb the approximate Hamiltonian by a connected operator. A proper treatment of this freedom is crucial for a good treatment of the dynamics. We show how to construct an effective N-body force so the approximate Hamiltonian is a projection of the exact Hamiltonian on an appropriate infinite dimensional subspace. Because this operator is connected it should not alter the unitarity considerations in the above paper. The methods used in constructing this effective interaction can also be used to reformulate the scattering integral equations as equivalent equations with noncompact contractive kennels. This reduces the scattering problem to uniformly convergent perturbation theory