Depolarized line shapes

IR line shapes for this system have been measured at room and other temperatures. Isotropic, depolarized, and unpolarized Raman line shapes have also been measured. For this system all Raman line shapes are similar, peaking at about 3430 cm 1, with a shoulder at about 3625 cm 1 (at room temperature). The IR line shape is red-shifted by about 30 cm 1 and does not show the blue shoulder. Experimental IR [10] and unpolarized Raman [12] line shapes are shown in Fig. 3. 

N. Meinander and G. C. Tabisz. Information theory and line shape engineering approaches to spectral profiles of collision induced depolarized light scattering. Chem. Phys. Lett., 110 388, 1984. 

Out-of-plane vibrations of type B2 were assigned based on the fact that they possess depolarized lines in the Raman spectra and bands characterized by band shapes of type C in the IR spectra of the vapor. 

U. Baffle, R. Magli, F. Barocchi, M. Zoppi, and L. Frommhold. Line shape and moment analysis in depolarized collision induced light scattering. Molec. Phys., 49A149-1166 (1983). 

N. Meinander and G. C. Tabisz. Moment analysis and line shape calculations in depolarized induced light scattering Modeling empirical pair polarizability anisotropy. J. Quant. Spectres. Rad. Transfer, 55 39-52 (1986). 

V. D. Ovsyannikov. Asymptotic line shape for collision induced depolarized light scattering in atomic gases. Phys, Lett. A, 55 275-277 (1981). 

B. Hegemann, K. Baker, and J, Jonas. Temperature and density effects on the collision induced depolarized Rayleigh line shapes of liquid carbon disulfide. J. Chem. Phys., 0 570-571 (1984). 

P. A. Madden. The line shape of the depolarized Rayleigh scattering from liquid argon. Chem. Phys. Lett., 47 174-178 (1977). 

Here, T is the observed line width (Av << F), 7d is the peak-to-valley intensity in the difference spectrum, and To is the peak height of the Raman line. Although this equation is for Lorentzian-shaped bands, the results are approximately the same for Gaussian-shaped bands (the constant 0.385 becomes 0.350). In the case of carbon disulfide-benzene mixtures, the smallest shift observed was -0.06 cm-1, and the associated error was 0.02 cm-1 (77). A convenient rotating system that can be used for (1) difference spectroscopy, (2) normal rotating sample techniques (solid and solution), and (3) automatic scanning of the depolarization ratios as a function of the wave number has been designed (45). 

What are the consequences of these considerations for depolarized light scattering In a dilute gas where reorientation is predominantly inertial, we expect the spectrum to be what is normally called the pure rotational Raman spectrum of the molecule. As higher densities are approached, the discrete spectral lines broaden and overlap to form a continuous band. We show how the band shape can be computed for freely rotating linear molecules and spherical top molecules and then indicate the assumptions that have been used by several authors to include collisions in the theory. 

The conversion factors g and g contain the so-called form factors which account for shape anisotropies. In an ellipsoidal molecule the form factors (sometimes called depolarizing factors, which are the components of the depolarizing tensor) of the main polarization axes are Ag = Aa, Ai, A, In line with the vectorial character of the internal and directing fields the g factors of anisotropic molecules are tensors. If the environment of the molecules (which are characterized by the polarizability tensor a and the permanent dipole moment p), can be considered as nonpolar and the overall dielectric permittivity is s, the g factor of the q axis is given by... 

Calculated depolarization ratios and differential scattering cross sections (do/dn)i for propyne are presented in Table 9.10. The simulated Raman spectrum is compared with the experimental gas-phase spectral ciuve [317] in Fig. 9.4. The band half-widths are taken from the experiment. The lines of A] transitions have sharp features, while E-vibrations are characterized with much broader bands. Since no quantitative intensity data for this molecule exist, a qualitative assessment of the results obtained can be done only. Fig. 9.4 reveals that the overall shape of the Raman spectrum is reproduced correctly. The most intense Raman lines are calculated to be those positioned at 2941, 2142 and 930 cm with intensities decreasing in the same order in agreement with the experimental spectrum. These lines are highly polarized. The other vibrational transitions giving rise to low- or medium-intensity lines in the spectrum are predicted to have intensities of the same order. The most significant difference between calculated and... 

It is important to note that although optical radiation is being used in these experiments both for excitation and detection, the width of the depolarization signal is determined by the natural linewidth of the excited level rather than by the Doppler width o the optical line. The detection system is in fact equally sensitive to all frequencies within the line profile and the shape of the optical line is not resolved. The depolarization signal appears effectively at zero (d.c.) frequency and hence we may say that Doppler broadening is theoretically impossible. 

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