Relation between the projection operator formalism and the Faddeev theory

Abstract

In an earlier paper it was shown by means of the Faddeev equations that the reduction of the three-body problem to formal two-body equations with energy-dependent complex potentials — a procedure which was already well known for separable potentials — can be generalized rigorously to arbitrary potentials. In the present paper we show that the projection operator approach of Feshbach appears as a special, and in a certain sense singular case of our general treatment. Optical potentials for rearrangement scattering are given explicitly and questions of how to calculate them are discussed, showing that the Faddeev approach is better suited in these respects.