Cluster-dynamical approach to N-body scattering

A formulation of the quantum-mechanical nonrelativistic N-body problem is derived using as guiding principle the dynamical evolution of two-cluster partitions of the N particles during the scattering process. This concept is realized by first making a certain choice for the basic subcluster-exchange potentials and then requiring consistency at all subsystem levels to generate the detailed structure. A decoupling is performed which divides the two-cluster partitions into primary and secondary ones, thus leading to a generalized optical potential-type formulation which makes the description of the reaction mechanisms very detailed and transparent and allows for a convenient graphical visualization. The resulting effective two-body equations of Lippmann-Schwinger form take full account of the Pauli principle and involve as input only physical subsystem transition amplitudes. The present approach may be understood as an off-shell transformation of the corresponding Alt-Grassberger-Sandhas N-body equations which eliminates some off-shell dependence of the latter. As a direct consequence of the compound nature of spectator clusters, the final equations turn out to be four-dimensional, involving one off-shell energy and one vector momentum as integration variables. Implications of this finding for a possible relativistic generalization are discussed