and since in vibrational Raman scattering either gs or g0 can be zero, it follows from Eq. (23) that 0 < p < 3/4. Detailed calculations show that for normal vibrations that do not preserve molecular symmetry during the motion of the nuclei (nontotally symmetric modes), g0 = 0 and hence, from Eq. (23), p = 3/4. For modes that do preserve molecular symmetry neither gs nor g0 is zero, leading to values of p > 3/4 for these modes, and, in fact, p is often found to be substantially less than 3/4 for totally symmetric vibrations.

For totally symmetric modes, p < 0.75 For nontotally symmetric modes, p = 0.75

Under resonance or near-resonance conditions in certain rare instances, ga = 0. This arises because, for certain modes, a can become antisymmetric with apa = -apa, giving rise to "anomalously" polarized bands with p > 3/4. In the limiting case when gs = g0 = 0, but ga = 0, the phenomenon of inverse polarization occurs with, in theory, p = In the usual case when ga = 0, the relative values of the two tensor invariants g0 and gs can be determined from Eq. (23) by the measurement of p. However, for ga = 0 there are three tensor invariants, which, in general, cannot be determined by measurement of p alone. To determine these three invariants, it is necessary to use circularly polarized incident light and to analyze the polarizations of the forward or backscattered radiation.


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