Raman Cross Sections

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

It should be noted that this technique is not without some disadvantages. The blackbody emission background in the near IR limits the upper temperature of the sample to about 200°C [43]. Then there is the dependence of the Raman cross-section ( equation (B 1.3.16) and equation ( B1.3.20)-equation ( B 1.3.21)) which calls for an order of magnitude greater excitation intensity when exciting in the near-IR rather than in the visible to produce the same signal intensity [39]. 

We have seen that the strength of Raman scattered radiation is directly related to the Raman scattering cross-section (Oj ). The fact that this cross-section for Raman scattering is typically much weaker than that for absorption (oj limits conventional SR as a sensitive analytical tool compared to (Imear) absorption... 

The metal substrate evidently affords a huge ( 10 and even as high as 10 [84, 85]) increase in the cross-section for Raman scattering of the adsorbate. There are two broad classes of mechanisms which are said to contribute to this enhancenient [, and Ml- The first is based on electromagnetic effects and the second on cheniicaT effects. Of these two classes the fomier is better understood and, for the most part, the specific mechanisms are agreed upon the latter is more complicated and is less well understood. SERS enhancenient can take place in either physisorbed or chemisorbed situations, with the chemisorbed case typically characterized by larger Raman frequency shifts from the bulk phase. 

Flere we examine the viewing angle dependence of the differential Raman cross-section for the cases of... 

For a circularly polarized light experiment, one can measure the cross sections for either right (r) or left (1) polarized scattered light. Suppose that right polarized light is made incident on a Raman active sample. The general expressions for the Raman cross sections are [176]... 

Laser stimulation of a silver surface results in a reflected signal over a million times stronger than that of other metals. Called laser-enhanced Raman spectroscopy, this procedure is useful in catalysis. The large neutron cross section of silver (see Fig. 2), makes this element useful as a thermal neutron flux monitor for reactor surveillance programs (see Nuclearreactors). 

Because the Raman cross-section of molecules is usually low, intense light sources and low-noise detectors must be used, and high sensitivities - as required for surface analysis - are difficult to achieve. Different approaches, singly and in combination, enable the detection of Raman spectroscopy bands from surfaces. 

Resonant Excitation Excitation by a laser, which is resonant with an electronic transition of the material under investigation, can increase the Raman cross-section by approximately 10. The transitions and thus the resonance wavelengths are specific for the substances. Resonance excitation thus leads to selectivity that can be useful for suppressing bulk bands, but can also complicate the detection of mixtures of substance with different absorption spectra. 

Bonamy L., Bonamy J., Robert D., Temkin S. I. Consequences of angular momenta coupling on generalized spectroscopic relaxation cross-sections collisional narrowing in isotropic and anisotropic Raman CO2 branches, Proc. 13th ICORS. (Wiley Sons, New York) (1992). 

Figures 8 and 9 shows a part of the bending region at low temperature containing the components of Vg (150-160 cm ) and Vs (190-200 cm ). The Vg vibration, IR active in the free molecule, has weak components in the Raman spectrum. According to theoretically calculated Raman intensities, which almost perfectly fit the experimental spectrum, the big component has a very low scattering cross-section [87] and is accidentally degenerate with the b2g component at ca. 188 cm. The IR active components of Vg cause strong absorptions in the IR spectrum even if the crystalline sample used for transmission studies is as thin as 400 pm [107, 109].

However, as Raman scattering is a two-photon process, the probability of the Raman scattering process is lower than that of fluorescence and IR absorption processes. The cross section of Raman scattering is 10 cm, which is much smaller than that of fluorescence ( 10 cm ) and IR absorption ( 10 °cm ). When we detect Raman scattering at the nanoscale, the number of photons obtained is less than with the usual micro-Raman spectroscopy due to reduction in the detection area or the number of molecules. To overcome this problem, we need to devise a method for amplification of Raman scattering. 

A spontaneous Raman spectra is shown in Figure 2.8d in which the on- and off-resonant frequencies are indicated. The DNA bundles are observed at the resonant frequency, as shown in Figure 2.8a, while they cannot be seen at the off-resonant frequency in Figure 2.8b. This indicates that the observed contrast is dominated by the vibrationally resonant CARS signals. Figure 2.8c shows a cross-section of Figure 2.8a denoted by two solid arrows, which were acquired with a 5 nm step. The FWHM of... 

The hyper-Raman scattering cross section is extremely small, typically of the order of 10 cm per molecule [24]. Therefore, an enhancement of signal intensity is essential in order to utilize this phenomenon as a practical spectroscopic tool in the field of molecular science. In a similar marmer to the enhancement of Raman scattering... 

The TED and XRD patterns revealed that the deposit is not amorphous carbon but nanocrystalline diamond. Nonetheless, the 514-nm excited Raman spectra do not exhibit a clear diamond peak at 1332 cm though the peak due to the sp -bonded carbon network appears at 1150 cm The Raman cross section of the sp -bonded carbon network with visible excitation is resonantly enhanced [43, 48-50]. It consequently makes the 1332 cm diamond peak overlap with the peaks due to sp -bonded carbon. 

The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman-anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman-Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117] ... 

The probability of Raman scattering from an arbitrary initial state I to a final state F is related to the Raman cross section of a molecule that is described as follows ... 

The interactions of photons with molecules are described by molecular cross-sections. For IR spectroscopy the cross-section is some two orders of magnitude smaller with respect to UV or fluorescence spectroscopy but about 10 orders of magnitude bigger than for Raman scattering. The peaks in IR spectra represent the excitation of vibrational modes of the molecules in the sample and thus are associated with the various chemical bonds and functional groups present in the molecules. The frequencies of the characteristic absorption bands lie within a relatively narrow range, almost independent of the composition of the rest of the molecule. The relative constancy of these group frequencies allows determination of the characteristic... 

---