THE OPTICAL POTENTIAL IN THE CHANNEL COUPLING ARRAY METHOD: A MODEL STUDY

Abstract

Publisher Summary This chapter presents a model study of the optical potential in the channel coupling array method. It reviews an approach to collision problems that leads to new sets of coupled equations for the transition operators associated with a three-body system. A key feature of the method is the introduction of an array whose purpose is to permit one to couple different arrangements in a general fashion. Once the general coupled equations for the transition operator whose matrix elements give the scattering amplitude for going from arrangements is obtained, the channel coupling array may be used to ensure that the kernel of the equations, when iterated a sufficient finite number of times, contains no disconnected diagrams. When iterated a sufficient finite number of times, contains no disconnected diagrams. For sufficiently well-behaved potentials, this leads to a continuous kernel. This then ensures that finite rank approximations to the kernel are elements in a convergent sequence. The chapter focuses on a specific choice of the channel coupling array, called the channel permutting array, which leads to equations whose iterated kernel is connected. The three arrangement analogue of equation for three particles involves a kernel, which is completely connected.