Theory of rotational Raman scattering

Electronic, vibrational and rotational transitions may be involved in Raman scattering but, in this chapter, we consider only rotational transitions. 

Each of these can be assigned to one of the symmetry species of the point group to which the molecule belongs. These assignments are indicated in the right-hand column of each character table given in Appendix A and will be required when we consider vibrational Raman spectra in Section 6.2.3.2. 

When monochromatic radiation falls on a molecular sample in the gas phase, and is not absorbed by it, the oscillating electric field E (see Equation 2.1) of the radiation induces in the molecule an electric dipole which is related to E by the polarizability 

All three terms in this equation represent scattering of the radiation. The first term corresponds to Rayleigh scattering of unchanged wavenumber v, and the second and third terms correspond to anti-Stokes and Stokes Raman scattering, with wavenumbers of (v + 2v () and (v — 2v () respectively. 

Although in a classical system v ( can take any value, in a quantum mechanical system it can take only certain values, and we shall now see what these are for diatomic and linear polyatomic molecules. 

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