The resonant Raman scattering diagram shown in Figure 8.7(a) can be compared to the results of Section 7.8 by taking the initial state |i〉 as Ni photons in state qvector) and the final state as N_i − 1 photons in state q(vector)  and a phonon in state p(vector).

(a) Calculate the rate of transitions for the matrix element (8.5.4), and show that it is independent of the volume V and proportional to the total number of incoming photons (assuming no stimulated photon emission).

b) Using (7.8.8), calculate the Raman scattering cross-section for this process. Verify that your answer has the units of area, and is proportional to the volume of the illuminated scattering medium.

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