On the inner and outer scattering tensor for vibrational Raman effect

Vibrational Raman intensities are proportional to matrix elements of the type < v vertical bar Q(n)vertical bar v + n >: n = 1 for a first order transition and n = 2 for an overtone. Employing pure harmonic oscillator type wave functions it is shown that the same tensor links the successive vibrational levels of one particular normal coordinate. These tensors are called inner tensors. On the other haad are the tensors which are associated with the various normal coordinates of the molecule, they may be called outer tensors. The temperature dependent intensity of Raman lines is only given by the Boltzmann factor if the inner tensors are indeed identical.