Knowledge Bank

Raman Scattering was treated as a two-photon process in quantum electrodynamics. A novel scattering mechanism that involves one photon in an electric dipole mode of radiation (R) and one photon in a magnetic dipole mode (M, or electric quadrupole mode) has been worked out. Because the electric dipole transition operator has odd parity and the magnetic dipole (or electric quadrupole) operator has even parity, the initial and final electronic states in this mechanism are of opposite parities. This is in contrast to the conventional vibrational or rotational Raman Effect which involves both photons in the electric dipole mode and in which the initial and final electronic states are the same (and of the same parity). When the initial and final electronic states are of different energies, this mechanism gives rise to an odd-parity electronic Raman Effect. When the initial and final electronic states are the same, this mechanism can give rise to the vibrational and rotational Raman Effect for optically active molecules for which the second order transition matrix element $(O|R|b)(b|M|O)$ is non-vanishing. For random molecular system, the depolarization ratios for linearly polarized light and the reversal coefficients for circularly polarized light have been derived for arbitrary observation directions. For quantized symmetric top and spherical top molecules, the rotational structure for this novel Raman Scattering has also been derived. The derivation made use of the coupling of irreducible tensor, the properties of the rotation matrices and the symmetry and sum rules of Clebsch-Gordan $coefficients.1$ Such use of modern angular momentum techniques shows an improvement of clarity over the early use of circular coordinates and direction consines by Placzek and Teller. These new techniques yield results expressible in terms of well known tabulated functions and are capable of extension to multi-photon (hyper)Raman Effects.