UNIFIED CONNECTED THEORY OF FEW-BODY REACTION-MECHANISMS IN N-BODY SCATTERING THEORY

We develop a complete N-body reaction theory that can emphasize any reaction mechanism. Our formalism is based on a system of connected kernel integral equations; one describing the dynamics of the reaction mechanism in a unitary way, one describing the dynamics of the excluded processes in a unitary way, and one combining these to get the full N-body dynamics. To do this we introduce a new democratic decomposition of the full Hamiltonian in terms of proper partition Hamiltonians as follows: H = ∑a Ca Ha where the Ca's are combinatoric coefficients. The set of asymptotic channels, A0, may be divided into the physically important channels A, and the remainder A′. The sets A and A′ of asymptotic channels are referred to as reaction mechanisms (RM's). By making a spectral resolution of each partition Hamiltonian, parts corresponding to each RM may be identified. Using the above expansion this gives a decomposition of the full Hamiltonian by reaction mechanism, H = H(A) + H(A′), depending only on the spectral properties of the partition Hamiltonians. We define the RM resolvents by G(A) = (Z - H(A))-1 and G(A′) = (Z - H(A′))-1. We derive connected kernel equations for these operators using solutions of fewer body problems as input. The full resolvent may then be obtained as the solution of a connected kernel equation involving G(A) and G(A′). Transition operators associated with G(A) and G(A′) are shown to satisfy optical theorems where all of the scattered flux comes through the channels of A and A′ respectively. If A is chosen to only include channels having no more than three or four clusters, the equations for G(A) have the numerical simplicity of a few body problem. This formulation should be useful for serious evaluations of existing reaction models, and in developing new reaction models that can emphasize any given RM including breakup, rearrangement, and those involving overlapping clustering. © 1979.