Franck-Condon factors as spectral probes of polaron structure

We apply the Merrifield variational method, to the Holstein molecular cryst al model in D dimensions to compute nonadiabatic polaron band energies and Franck-Condon factors at general crystal momenta. We analyze these observab le properties to extract characteristic features related to polaron self-tr apping and potential experimental signatures. These results are combined wi th others obtained by the Global-Local variational method in 1D to construc t a polaron phase diagram encompassing all degrees of adiabaticity and all electron-phonon coupling strengths. The polaron phase diagram so constructe d includes disjoint regimes occupied by small polarons, large polarons, and a newly-defined class of compact polarons, all mutually separated by an in termediate regime occupied by transitional structures.