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A theoretical analysis for the resonant hyper-Raman scattering (RHRS) of light in a CdS crystal is presented. The different scattering mechanisms are considered and the cross section of the RHRS by LO phonons are calculated as a function of incident frequency.

A detailed theoretical treatment of the second-order Raman efficiency is given for incident photon energies below an excitonic resonance. The Wannier excitons are considered as intermediate states in the scattering process. By using the Green's function method, the expression for the Raman efficiency is obtained. The contributions of the two sequences of the intermediate states, s-s-s and s-p-s, are analyzed. The second-order Raman efficiency is calculated for CdS.

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