Background: Formal optical model theory shows that coupling to vibrational nuclear states generates a nonlocal and l-dependent dynamical polarization potential (DPP). Little is established concerning the DPP, yet its properties are crucial for explaining the departures of optical model potentials (OMPs) from global behavior and for the rigorous extraction of spectroscopic information from direct reactions.Purpose: To appraise the application of channel coupling followed by S-matrix inversion for the systematic exploration of the contribution of the coupling of collective states to the nucleon OMP and to identify properties of nuclear potentials indicative of l-dependence. Methods: S-matrix to potential, Slj→V(r )+l .sVSO(r), inversion provides local potentials that precisely reproduce the elastic channel S-matrix from coupled channel (CC) calculations. Subtracting the elastic channel uncoupled (bare) potential yields a local and l-independent representation of the DPP. The dependence of this local DPP upon the nature of the coupled states and upon other parameters can be studied. Results: All components of the DPP arising from coupling to vibrational states are substantially undulatory with a point-by-point magnitude therefore disproportionate to their contribution to volume integrals. Information relating to dynamical nonlocality is found. The proton charge leads to a substantial difference between DPPs for protons and neutrons. Conclusions: Undulatory features in potentials found in precision fits to elastic scattering data are significant, are a consequence of coupling to inelastic channels and must be allowed for in phenomenology; they are indirect evidence of l-dependence. Within the model, coupling to excited states magnifies the effect of the proton charge on the difference between proton-nucleus and neutron-nucleus interactions. Coupled channel plus inversion is a procedure of wide applicability, complementary to evaluation of the Feshbach formalism.