Raman Spectroscopy: Relative intensity of the Stokes and Anti-Stokes lines

Raman Spectroscopy: Relative intensity of the Stokes and Anti-Stokes lines
The Raman effect refers to the shift in the frequency of light scattered by a system. If a light of frequency ? is incident on a system ordinarily the scattered light will also have the same frequency, ?. However, Raman first observed a weak scattered light at a frequency ?±? . The line at a frequency ?-? is called the Stokes line and the one at ?+? is called the anti-Stokes line. The frequency ? is such that h? matches with the vibrational or rotational energy gap of the molecule. The origin of the Raman line may be understood in terms of the transitions depicted in Fig. 2 as follows.








Fig. 2. Transitions involved in (a) Rayleigh; (b) Stokes and (c) Anti-stokes line



a) Rayleigh Line: In this case, the molecule in the ground state g on interaction of the external photon of frequency ? first goes to a non-stationary state, a (fig. 1a) . If from this state the molecule comes back to the same state the scattered (or emitted) photon is of energy, h? and the frequency is ?.
b) Stokes Line: In this case, instead of coming back to the same state the molecule returns to a higher vibrational (or rotational) state, b (fig. 1b). Thus the energy of the scattered light is less than that (h?) of the incident photon by the energy gap Eb-Eg. Since the energy gap Eb-Eg is equal to the vibrational or rotational energy (h? ) the energy of the scattered light is h?- h? and the frequency is ?-? .
c) Anti-Stokes Line: In this case, the transition starts from a higher vibrational or rotational level, b (fig. 1c). From this level, the molecule goes to the virtual state a and then returns to the lowest state g. Thus the energy of the scattered light is more than that (h?) of the incident photon by the energy gap Eb-Eg. Thus, the frequency of the scattered light is ?+? .