Multichannel Approach to High-Energy Peripheral Collisions

In the peripheral model for high-energy, two-body inelastic collisions, the Born-approximation amplitudes are modified to take into account absorption effects due to other open channels. This is done to reduce the partial-wave amplitudes, which may otherwise exceed unitarity limits, especially in the lower partial waves. We estimate each off-diagonal element of the $S$ matrix in terms of the Born amplitude and elastic-scattering parameters, using a formula applied by many authors. Using the fact that the $S$ matrix is unitary we obtain a set of equations which relates the diagonal and off-diagonal parts. Additional assumptions about the phases involved then enable us to determine the elastic-scattering parameters. Thus we obtain the angular distributions for elastic scattering as well as the modified inelastic angular distributions. This procedure differs from that of previous authors who used an experimental elastic differential cross section to obtain the absorption parameters.