Optical Analysis of Potential Well Resonances

As a contribution toward the understanding of resonant scattering in general, we examine the potential-barrier resonances which occur in a variety of simple one- and two-channel $S$-wave scattering problems. The models chosen have familiar optical analogs which, together with the appealingly simple analytic properties of their scattering amplitudes, facilitate a unified discussion of such diverse phenomena as the peculiar $S$-wave "resonances" of a square potential well, the occurrence of "resonance circles" in both elastic and inelastic scattering amplitudes, and the large nonresonant maxima which the descent of the background phase (as a function of energy) can produce in total cross sections.