Differential scattering cross-section polarizations

Hug and Surbeck 35) have proposed the use of Ada. = daL — daR, the difference of the Raman differential scattering cross sections in left and right circularly polarized incident light. This is the Raman equivalent of the circular dichroism Ae = el — eR, where s is the decadic molar extinction coefficient and, unlike the measured (but not the theoretical) IR — IL which depends on both sample and instrumental factors, is solely a molecular parameter. They introduced a chirality number q defined by... 

FIGURE 14.3 Polar and Cartesian plots of Rayleigh scattering for both /w and /jjh-Then the differential scattering cross section is... 

The Rayleigh-Debye-Gans differential scattering cross section in the scattering plane for vertically polarized light (Eigure 14.1) is... 

In ion-solid interactions, it is customary to describe the number of particles scattered through different angles, 6C, in terms of a quantity called the angular differential scattering cross-section. Imagine the experiment depicted in Fig. 4.1, where a beam of ions is incident on a thin foil and is scattered into a detector of area A a at a polar angle between 8C and 6C + d0C. Each of the ions in the incident... 

Raman scattering is a two photon process in which a photon changes its frequency co, wavevector k, and polarization via scattering from the values (coj, kj, i) to the values (cos> ks, s) while the scattering material experiences a transition from i) to f). The associated photon differential scattering cross section for this process is [46] ... 

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... 

Another important scattering characteristic is the angular distribution of the scattered field. For an ensemble of randomly oriented particles illuminated by a vector plane wave of unit amplitude and polarization vector Cpoi = epoi,/3e/3 + epoi,a6a, the differential scattering cross-sections in the scattering plane are given by... 

In Figs. 3.14-3.17 we plot the normalized differential scattering cross-sections together with the results computed with the discrete sources method for parallel and perpendicular polarizations, and for the case of normal incidence. It is apparent that the agreement between the curves is acceptable. 

Fig. 3.32. Normalized differential scattering cross-sections for parallel polarization...

RS process is intrinsically weak. Since only a very small fraction of light is inelastically scattered, the intensity ratio of Rayleigh line and Raman lines is approximately 10 -10. The efficiency of particular molecule (with a random orientation with respect to the incident field polarization) to scatter light by RS can be determined by a differential Raman cross-section ... 

One of the main goals of the crossed-beam experiment is to measure the internal energy AEvlh rol transferred to the molecule. In principle, this is possible in either of two ways. First, the scattered molecules could be detected and their product-state population analyzed. Infrared emission or absorption techniques may be considered, similar to those used in cell experiments.13 21 Although such studies would lead to the most detailed results (at least for polar molecules), under crossed-beam conditions they are impossible for intensity reasons, even if the possibility of measuring differential cross sections is renounced and the molecules in the scattering volume itself are detected. Detection via electronic molecular transitions may be invisaged. Unfortunately, the availability of tunable lasers limits this possibility to some exotic molecules such as alkali dimers. The future development of UV lasers could improve the situation. Hyper-Raman... 

Figure 33. Experimental scattering geometry for observation of polarization effects in differential quenching process F may be varied to determine ratio of maximum (/raax) to minimum (/mirL) partial quenching cross section.

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