How different is the resonating-group method from the integral-equation approach to few-particle scattering

In the last decade, a quantum mechanical scattering theory for few-particle systems has been developed which is based on exact integral equations. Of course, for more than three particles there is no hope for solving these equations directly on the computer. Besides, there is no interest in a complete solution as a function of 3N variables. It is important, therefore, to reduce the equations to effective two-particle equations. This can be achieved by approximating the kernels by pole terms which represent the dominant subsystem properties. Such a procedure leads into the neighbourhood of conventional reaction theories as far as they are designed for a quantitative description of reaction phenomena from a microscopic point of view. There are essentially two theories of this kind: the shell-model reaction theory, which is well suited for the description of the scattering of a single particle from a heavy nucleus, and the cluster-model reaction theory or resonating-group method, which has been applied successfully in the calculation of scattering data of composite projectiles from light nuclei. Unfortunately little attention has been paid as yet to the relation between the integral-equation approach and the customary reaction theories. In the hope that such a comparison may be helpful for a further development of either approach, an outline of some essential points is given in this contribution. (Auth.)