The development of high power pulsed lasers has permitted the observation of nonlinear light scattering phenomena, in particular the molecular hyper-Raman effect. The wave numbers of hyper-Raman transitions can be predicted simply from the energy differences between known levels. For the intensities, however, it is necessary to devise a well-adapted method of calculation.Hilico, Berger, and Loete have developed a tensor formalism in the (m)O(3) × (F)O(3) group, for the calculation of microwave, infrared, and Raman intensities from XY4 tetrahedral molecules. In this paper, we extend the formalism to a G × (F)O(3) subgroup and make it applicable to the case of hyper-Raman transitions.A general expression for the hyper-Raman intensities of any molecule is given. In the case of XY4 tetrahedral molecules, where a tensor extension to the (m)O(3) × (F)O(3) group is possible, we give the intensity formulas line by line and band by band for the simplest cases.[Journal translation]
