Faddeev Equations with Inelastic Processes
Abstract
Starting from the general LippmannSchwinger equation, we study the effect of inelastic processes on the scattering of threebody states. We show that it is possible to incorporate the inelastic effects into Faddeevtype equations in two different ways. The first approach is a straightforward generalization of the singlechannel Faddeev equations to the multichannel form. However, we have to introduce the concepts of position and particle labeling in order to obtain a meaningful generalization. The second approach, which is derived from an extension of the concept of a complex potential, yields singlechannel Faddeev equations with a modified input. The essential difference between this input and the input for the elastic case is the presence of a completely connected term. The two approaches are shown to be equivalent in their common region of validity. Under the resonance approximation, both approaches yield onedimensional equations. The structure of the completely connected term is investigated for certain specific models and further simplifications on it are obtained. We also observe that the concept of the inelasticity parameter in the twobody case does not seem to have a natural generalization.
 Publication:

Physical Review
 Pub Date:
 December 1966
 DOI:
 10.1103/PhysRev.152.1475
 Bibcode:
 1966PhRv..152.1475K