Quantum electrodynamical study of bimolecular scattering effects in Raman spectroscopy

In this paper a quantum electrodynamical theory of cooperative Raman scattering in fluids is developed. The process is one in which pairs of molecules undergo concerted Raman transitions via an intermolecular energy transfer mechanism. The formalism is also extended to chromophore pairs in which intramolecular energy transfer is involved. Using the Power-Zienau-Woolley multipolar Hamiltonian, intensity equations of the Kramers-Heisenberg type are derived which are valid over all regions of molecular separation. In the near zone it is illustrated how the intensity of cooperative scattering is simply that obtained by consideration of the instantaneous response of one molecule to the scalar field generated by another. Within this regime it is shown that the rate of scattering has the familiar $R^{\mathrm{-}6}$ dependence on intermolecular separation R associated with interacting induced dipoles. In the far zone it is demonstrated that the fully retarded and causal interaction between molecules is mediated through virtual photon coupling, and that this leads to a result for the intensity that dies off with $R^{\mathrm{-}2}$. This long-range-interaction contribution to the overall scattering intensity is generally ignored in collisional treatments of intermolecular interactions, yet is likely to be of more significance than higher-order multipole terms in near-zone calculations. Finally it is shown how bands in a Raman spectrum due to cooperative scattering effects may be identified by their unique pressure characteristics, or by observation of light scattering that occurs outside the interaction volume of the laser beam. In the case where the scattering occurs between molecules or chromophores held in a fixed orientation with respect to one another, it is demonstrated how detection may be facilitated through the manifestation of a differential scattering effect.