Coupled equations for medium-energy scattering. I

A simple set of coupled equations applicable for medium-energy scattering by composite systems is derived. The scattering function is expanded in the basis functions such that the average inelastic scattering channels simulate both adiabatic and impulse limits. Detailed discussions are given on the construction of the basis functions by the sum-rule technique. A procedure to solve the coupled set of equations by the Green's functions is presented, and the evaluation of the amplitude using the angle-averaging method is outlined.