Bounds on Scattering Phase Shifts for Compound Systems

An extension of recently developed methods determines a rigorous upper bound on ${(-kcot\eta )}^{-1\mathrm{}}$, where $\eta$ is the phase shift, for the general one-channel scattering process. The method, unfortunately, requires truncation of the various potentials, but it should generally be possible, in practice, to so truncate the potentials that the difference between the phase shifts of the original problem and of the problem for which a bound is obtained is insignificant.