Unitary Impulse Approximation

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Abstract
With the aid of multiple scattering expansions, Blankenbecler's generalized unitarity relation is derived for a multichannel three-body potential scattering problem. A matrix representation of the scattering amplitudes is obtained in the form of Heitler's integral equation, with the K matrix replaced by a matrix N, so that generalized unitarity is automatically satisfied if N has no physical cut in the total energy variable. A simple, physically resonable, choice for N leads to representations of the inelastic amplitudes which have the form of initial- (or final-) state interaction corrections to the impulse approximation. With the elastic amplitude given, no sums over three-body phase space appear. The elastic amplitude itself is obtained as the solution of an integral equation which sums all diagrams which are iterations of the basic impulse approximation diagram. It is explicitly demonstrated that the partial-wave amplitudes thus obtained must satisfy unitarity even when the impulse (or strip) approximation is nonunitary. A convergent iterative solution is presented which treats the effects of longer ranged forces first and should be appropriate for high-energy diffraction scattering. Rearrangement collisions are treated in a similar way.