Solution of the multichannel collision problem by the quasiparticle method without the use of Faddeev's theory

Abstract

Exact effective two-particle equations are derived for the composite particle collision problem without reference to the Faddeev theory. This is accomplished by application of the quasiparticle idea to the subsystem operators occuring in the kernel of the multiparticle resolvent (Lippmann-Schwinger) equation. Similar treatments have been put forward already in the framework of Faddeev's theory. Our present investigation, however shows that the method is neither restricted to this starting point, nor even typical for this approach. Being closely related to the separable potential approximation it generalizes this model rather directly by including “small” nonseparable rest parts of the potentials iteratively.