Indicatrix of hyper-Raman scattering by internal molecular vibrations

A theoretical investigation is made of the hyper-Raman scattering (HRS) accompanied by the excitation of internal molecular vibrations in a crystal with an inversion center. It is shown that third-order terms contribute to the HRS tensor and these should be allowed for in the second order of the perturbation theory. Formulas are obtained for the scattering indicatrix in the case of the O_h and C_4h symmetry groups and graphs of the indicatrix are given for some special cases.