Raman scattering isotropic spectrum

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

In the conclusion of the present chapter we show how comparison of NMR and Raman scattering data allows one to test formulae (3.23) and (3.24) and extract information about the relative effectiveness of dephasing and rotational relaxation. In particular, spectral broadening in nitrogen caused by dephasing is so small that it may be ignored in a relatively rarefied gas when spectrum collapse proceeds. This is just what we are going to do in the next sections devoted to the impact theory of the isotropic Raman spectrum transformation. 

In the pioneering work the same information was extracted from the extremum position assuming it is independent of y [143]. This is actually the case when isotropic scattering is studied by the CARS spectroscopy method [134]. The characteristic feature of the method is that it measures o(ico) 2 not the real part of Ko(icu), as conventional Raman scattering does. This is insignificant for symmetric Lorentzian contours, but not for the asymmetric spectra observed in rarefied gas. These CARS spectra are different from Raman ones both in shape and width until the spectrum collapses and its asymmetry disappears. In particular, it turns out that... 

Burshtein A. I., Storozhev A. V. The quantum theory of collapse of the isotropic Raman scattering spectrum, Chem. Phys. 135, 381-9 (1989). 

Figure 8. Two-body isotropic scattering Stokes spectrum of the Vi Raman band of gaseous CF4 in absolute units at 294.5 K. Full circles ( ) indicate experimental data together with error bars.

ROA and Raman intensity are proportional to the square of a tensor quantity, as expressed in Equation [1]. For Raman scattering only the square of the polarizability is needed, whereas ROA intensity arises from the product of the polarizability and an ROA tensor. The ROA tensor are approximately three orders of magnitude smaller than the polarizability, and hence an ROA spectrum is approximately three orders of magnitude smaller than its parent Raman spectrum. As noted above, the Greek subscripts of the tensor refer to the molecular axis system. However, for both Raman and ROA, linear combinations of products of tensors can be found that do not vary with the choice of the molecular coordinate frame. Such combinations are called invariants. All Raman intensities from samples of randomly oriented molecules can be expressed in terms of only three invariants, called the isotropic invariant, the symmetric... 

Fig. 0.3. Raman spectrum of liquid oxygen [6]. The positions of the free rotator s. /-components are shown by vertical lines and the isotropic scattering contour is presented by the dashed line.

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