Role of electron-phonon interaction in resonant x-ray Raman scattering by polymers and solids

• We present a theory of radiative resonant x-ray Raman scattering by solids and polymers beyond the Born-Oppenheimer approximation. The role of electron-phonon coupling of the intermediate core excited and final electronic states is analyzed in detail for π-electron systems and solids assuming the frozen-orbital approximation. The momentum exchange processes between valence electrons and phonons and with x-ray photons are analyzed, showing the similarities and differences between the two processes. The resonant inelastic x-ray scattering by a π-electron system is quenched up to zero in the Born-Oppenheimer approximation with frozen orbitals if the momentum exchange between valence electrons and x-ray photons is neglected. The electron-phonon and electron-photon interactions open the scattering channels for all occupied states in π systems. The frequency dependence of these effects is analyzed, showing that when the duration of the scattering is shortened by a large detuning of the excitation frequency, the role of electron-phonon coupling of both core-excited and final states is suppressed, depleting the cross section for π systems up to zero. The detuning quenches the symmetry breaking of the core-excited electronic states and results in a restoration of the selection rules and a conservation of electron momentum. Specific selection rules for the zero-phonon line in x-ray Raman spectra of linear polyenes are found. A detailed investigation of the narrowing, or collapse, of the electron-vibrational bands is given. When the detuning is large, the spectral profile is described by a joint density of states. It is predicted that the singularities of this joint density of states follows the Raman-Stokes dispersion law, something that allows a mapping of the band structure. We found that the phonon broadening of these singularities is completely quenched by detuning. A detailed investigation of the spectral shape versus detuning of the so-called excitonic band is given.

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