Comparison with experiment spherical molecules

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found  

The obtained magnitude of oe 24 A2 differs somewhat from that found by experimentalists themselves because the experimental data (shown in the inset in Fig. 3.15) were fitted in [162] with the perturbation theory formula 

Vibrational broadening in [162] was taken into account under the conventional assumption that contributions of vibrational dephasing and rotational relaxation to contour width are additive as in Eq. (3.49). This approximation provides the largest error at low densities, when the contour is significantly asymmetric and the perturbation theory does not work. In the frame of impact theory these relaxation processes may be separated more correctly under assumption of their statistical independence. Inclusion of dephasing causes appearance of a factor 

The density-dependence of the frequency shift of the Q-branch maximum. The y values for the curves are in the notation of Fig. 3.15. When plotting the experimental data, the cross-section found in the fitting of the density dependence of the width was employed (Fig. 3.15). 

The contribution of dephasing may be easily extracted, if the experiment provides high enough pressures. When the contribution of rotational broadening (3.68) is relatively small, Acoi/2 lAdP is linear over density and the slope is OdP v). On the other hand the true relaxation time of rotational energy xE = W(1 — A) may be expressed via xe and TdP found experimentally as follows  

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