Rotational Structure of a Novel Raman Effect in Quantized Symmetric- and Spherical-Top Molecules

Abstract

By angular momentum techniques, the theoretical line intensities of a higher-order odd-parity Raman effect have been derived. This effect may be used as an alternative mechanism to study the silent modes forbidden in the infrared spectra, and in the conventional lower-order Raman effect which is of even parity. It can be compared with the recently discovered (three-photon) hyper-Radman effect which is also of odd parity and contrasted with the recently studied electronic Raman effect using the antisymmetric scattering tensor which is of even parity: It has different selection rules (Secs. IV, V) and angular characteristics (Sec. III and Appendix B). It is Raman scattering in which one photon is in an electric dipole mode, whereas the other photon is in a magnetic dipole (or electric quadrupole) mode. The scattering tensor is of odd parity. The intensities along the perpendicular direction of observation of the scattering by symmetric-top molecules in their transition from the state | J′K′〉 to | JK〉 and by spherical-top molecules in their transition from the state | J〉 to | J′〉 have been derived (Sec. II and Appendix A). Depolarization ratios for linearly polarized and for unpolarized incident light may be computed from these intensities. Similar intensities for scattering of circularly polarized light into forward as well as into arbitrary observation directions were derived (Sec. III and Appendix B). These allow the computation of the reversal coefficients. In the limit when both photons are in the electric dipole mode the results will agree with those for the conventional even-parity Raman effect studied by Placzek and by Teller. The total intensity for the scattering of unpolarized light into an arbitrary direction and the integrated intensity for scattering into all directions have been obtained (Appendix B). Explicit forms of the new scattering tensors, which are bipolar harmonics, in Cartesian coordinates are given (Sec. IV and Appendix C). Their similarity to, as well as difference from, spherical harmonics are shown. Special features are pointed out for the tensors. Their transformation under the C3υ point group, to which a symmetric-top molecule may belong, and under the T point group, to which a spherical-top molecule may belong, have been derived and tabulated (Tables I and II). The scattering tensor may connect different electronic states of opposite parities in an electronic Raman effect, or may give rise to a rotational and vibrational Raman effect with different selection rules (Sec. V) from the conventional Raman effect, and thereby may serve as a supplement for the study of molecular structure.