Explicit dispersive and retardation properties of the dynamical polarization optical potential within a simple model

The dynamical polarization potential corresponding to simple, physical two-channel model is derived and examined paying particular attention to its analytic properties. This enables us to illustrate explicitly the emergence of the general dispersive and retardation features expected from the imposition of causality. The energy dependence of the potential and the associated nonlocality in time, expressed by its Fourier transform, are explored. A physical interpretation of the time nonlocality in terms of the time delay due to the excitation of the inelastic channel will be given.