Variational Upper and Lower Bounds for Multichannel Scattering

Upper and lower variational bounds are given for all elements of the reaction matrix. These, in turn, lead to upper and lower bounds on the elastic and inelastic cross sections. We explicitly discuss two-particle scattering, coupled two-particle channels, and three-particle scattering situations, and our methods will work for any number of particles. Numerical examples are given, including phase shift bounds for $s$-wave electron-hydrogen scattering. It is hoped that this approach will lead to a tractable calculational scheme for strongly interacting relativistic particles.