Upper and lower bounds to multichannel-scattering parameters

Abstract

We derive rigorous calculable upper and lower bounds to the scattering parameters that arise in coupled channel problems. The method is based on integral identities and equations that are satisfied by the (unknown) exact and (approximate) trial solutions. We illustrate the method on the Huck model (coupled square wells) and the scattering of positrons by hydrogen atoms in a two-state (1s – 2s) approximation.