Form factor approach to N-body scattering theory

We develop the form factor approach to N-body scattering theory. By combining certain Green's function identities with the two-Hilbert space description of N-body scattering theory we find an exact coupled integral equation for the N-body problem. The momemtum space on-shell solutions give the physical amplitudes appearing in the N-body S-matrix. In this equation all possible stable clusters are represented by their associated form factors. The mechanism producing scattering in this formalism is an effective interaction that acts between clusters. These effective potentials are simple in that they contain only the degrees of freedom that describe relative cluster motion. None of the amplitudes of a rearrangement character appear in the integral equation, but instead are determined by quadrature formulas. It is found that this form factor description of scattering imbeds the resonating group method. A simple truncation of the full set of our equations leads to the resonating group equation for the collision of two clusters