Reduction Method and Distortion Potentials for Many-Particle Scattering Equations

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Abstract
A general procedure is formulated by which the hierarchy of many-particle scattering equations of the Faddeev types can be reduced systematically to matrix equations of lower dimensions. As illustrations, such reduced sets are derived explicitly for the three-particle system by rearranging different components of the total Green's function. The resulting equations iterate with connected kernels only in the explicit channels. Using the reduction method, the connection between the various versions of scattering equations derived earlier have been exhibited. The effect of implicit channels may be taken into account noniteratively using the channel projection operators. It is also shown that an arbitrary set of distortion potentials may be introduced for the purpose of minimizing the coupling between the rearrangement channels, thus improving the convergence of the multiple-scattering series.