On the validity of the Franck-Condon principle in the optical   spectroscopy: optical conductivity of the Fr\"{o}hlich polaron
  The optical absorption of the Fr\"{o}hlich polaron model is obtained by an approximation-free Diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: i) a strong coupling expansion, based on the the Franck-Condon principle, well describes the optical conductivity for large coupling strengths ($\alpha >10$); ii) a Memory Function Formalism with phonon broadened levels reproduces the optical response for weak coupling strengths ($\alpha <6$) taking the dynamic lattice relaxation into account. In the coupling regime $6<\alpha<10$ the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions. 
G. De Filippis, V. Cataudella, A. S. Mishchenko, C. A. Perroni, and J.   T. Devreese