Resonances and bound states

Resonances manifest as the sharp peaks observed in graphs of scattering cross section versus energy. Resonances in binary collisions are closely related to twobody bound or quasi-bound states, which are the discrete quantum states whose amplitudes fall off (usually exponentially) in space as the separation r → ∞. In the case of a single channel, a bound state is formed at a specific negative energy; that is, below the channel threshold. In the multichannel case, as mentioned in the preceding chapter, a bound state occurs when all the channels are closed; that is, below the threshold of the lowest channel. Under specific circumstances, a bound state may occur at zero energy; that is, right at the lowest threshold. Quasi-bound states are also discrete quantum states that are formed temporarily at a discrete positive energy (above the lowest threshold). Both resonant and bound states (including quasibound ones) can be described by a unified approach to cold collisions. The temporary binding of a quasi-bound state at a discrete energy enhances the scattering cross section at that energy. This occurs because the quasi-bound state eventually decays into the continuum of scattering states whose central energy equals the binding energy. The resonance width is determined by the coupling between the bound and continuum states.