Some Aspects of Group Theory

Abstract

In the discussion offered in Chapters I and II, no mention has been made of the impact of the symmetry of the scattering entity, e.g. atom, ion or molecule, on the properties of the scattered light. Yet, intuitively it can be felt that the properties of, for instance, the Raman radiation of a molecule like CCl₄ could be different from that of the CHCl₃, not because a hydrogen atom replaces a chlorine atom of CCl₄ but because the symmetry of the latter molecule is different from that of the former. The symmetry difference is reflected, for example, through the absence of a three-fold rotational axis around any of the C-Cl bonds of the CHCl₃ molecule, while four of such rotational axes are present for the CCl₄ molecule. The effect of symmetry on the Rayleigh and Raman processes should, of course, be reflected in the scattering tensor — not to such extent that a separation of symmetric and antisymmetric tensors may occur, (they are associated with the type of Rayleigh and Raman process) — but more importantly, it determines which of the six elements of the symmetric tensor and three elements of the anti-symmetric tensor are different from zero. It may be remarked here that the trend is that the scattering tensor will become more simple (more elements will be equal to zero) if the symmetry of the scattering entity becomes higher. The interesting aspect of application of group theory is that a considerable amount of information on the tensor is obtained without going into details, about the mathematical formulation of the elements of the scattering tensor.