Theoretical description of the method of Continuum Discretized Coupled Channels

Abstract

A quantum mechanical three-body model known as the method of Continuum Discretized Coupled Channels (CDCC) has been a very successful method in explaining physical observables in case of loosely bound light projectile scattering elastically on heavy nuclei[1].and references therein]. However, theoretical foundation was under criticism and the convergence of the solution with respect increasing distance between centers of mass of the projectile and target nuclei and the coupling of higher angular momentum breakup states of the light loosely bound projectile. Convergence property has been already justified in [1] mainly by expanding the model space and using the physical arguments on the validity of the basic assumptions of the model .In this paper ,we are interested in explaining the convergence of the elastic S-matrix element mathematically with respect to increasing angular momentum and the distance between the projectile and the target.