Rayleigh intensity

Case 2 Constant Rayleigh Cross Section - In this case, variations in the Rayleigh scattering intensity are attributed to variations in temperature. A natural compliment to the isothermal mixing investigations identified in Case 1 would be to measure the time-resolved temperature in a submerged jet of heated air. For premixed flames, the variation of Rayleigh intensity is primarily due to variation in temperature, which can vary by a factor of 7. 

Fig. 15.8 Confocal Raman microscopy and SNOM images of a locally stressed SiC crystal (a) Rayleigh intensity map. (b), (c) Spectral position maps of fitted TO and LO phonon lines obtained by fitting a Lorentzian peak, (d) Topography of the indent, (e) SNOM amplitude for cOiR = 924 cm. (f) SNOM amplitude for (0 = 944 cm (Reprinted from [68])...

As pointed out in section 3 the total depolarized Rayleigh intensity provides information on the orientational pair correlation factor 92 defined by equation (20). Equation (19) indicates, however, that the total intensity is made up not only of an orientational but also of a collision induced contribution, which must be removed. As an example as to how 92 can be... 

Cl2 and CO2 and used the DID model for the induced polarizability. They showed that for CO2 the collision induced contribution to the depolarised Rayleigh intensity was 25% of the total intensity and that the second moment was increased by about 50% by induced effects. The timescale separation was examined in N2 and C02 In their terminology is the collision induced contribution it was found to relax in a very similar way to the orientational function <°M(t).°M> and the spectra of the two terms were indistinguishable for practical purposes. Furthermore the cross-term was quite large. The net effect of the non-orientational terms was to reduce the amplitude of the spectrum at low frequencies and to increase it in the wings. Frenkel and McTague s results on nitrogen have been carefully compared with experiment by Sampoli de Santis and co-workers(54). 

Rayleigh intensity one must determine the local field factors (c.f eqn 6.1) In the dielectric case it seems that one must calculate this quantity (normally an approximate formula of the Frohlich type is used), but in the case of g2 it is possible to avoid this by combining the results of several experiments in order to eliminate. the local field effects (see also the lectures of Versmold). 

EJ Stansbury, MF Crawford, HL Welsh. Determination of rates of change of polarizability from Raman and Rayleigh intensities. Can J Phys 31 954-961, 1953. 

Due to the rather stringent requirements placed on the monochromator, a double or triple monocln-omator is typically employed. Because the vibrational frequencies are only several hundred to several thousand cm and the linewidths are only tens of cm it is necessary to use a monochromator with reasonably high resolution. In addition to linewidth issues, it is necessary to suppress the very intense Rayleigh scattering. If a high resolution spectrum is not needed, however, then it is possible to use narrow-band interference filters to block the excitation line, and a low resolution monocln-omator to collect the spectrum. In fact, this is the approach taken with Fourier transfonn Raman spectrometers. 

The second method to calculate the scattered intensity or R the Rayleigh ratio) is to square the sum in I... 

The Rayleigh ratio combines the intensity factors with those associated with the geometry of the experiment ... 

Thus Rg is a constant in any particular experiment where Rayleigh scattering is obtained, since the entire angular dependence of the light intensity is correctly contained in the 1 + cos 6 term. 

We assume that there exists a function which we represent by P(0)-in recognition of the fact that it is angle dependent-which can be multiplied by the scattered intensity as predicted by the Rayleigh theory to give the correct value for i, even in the presence of interference. That is. 

Since P(0) is Rayleigh observed scattering intensity at 0-the value that... 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

In the low frequency region, the calculations predict nanotube-specifiic Eig and E g modes around 116 cm and 377 cm respectively, for (10,10) armchair naiiotubes, but their intensities are expected to be lower than that for the A g mode. However, these Eig and E2g modes are important, since they also show a diameter dependence of their mode frequencies. In the very low frequency region below 30 cm a strong low frequency Raman-active E2g mode is expected. However, it is difficult to observe Raman lines in the very low frequency region, where the background Rayleigh scattered is very strong. 

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