Scattering cross section Absorption

Scattering cross section, absorption cross section... 

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 peak absorption (scattering) cross sections are thus useful comparative measures of detectivity because the latter is a product of the line strength and the practical line resolution. 

Beryllium has a high x-ray permeabiUty approximately seventeen times greater than that of aluminum. Natural beryUium contains 100% of the Be isotope. The principal isotopes and respective half-life are Be, 0.4 s Be, 53 d Be, 10 5 Be, stable Be, 2.5 x 10 yr. Beryllium can serve as a neutron source through either the (Oi,n) or (n,2n) reactions. Beryllium has alow (9 x 10 ° m°) absorption cross-section and a high (6 x 10 ° m°) scatter cross-section for thermal neutrons making it useful as a moderator and reflector in nuclear reactors (qv). Such appHcation has been limited, however, because of gas-producing reactions and the reactivity of beryUium toward high temperature water. 

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].

Similarly, absorption and scattering cross-sections are defined to give... 

As a pigment, each iron oxide has an optimum particle size which is that with the maximum scattering cross section. This optimum particle size is lower, the higher the refractive index of the mineral. For hematite, the size corresponding to the maximum in scattering/absorption cross section is ca. 1 pm. As the particle size decreases, the relative scattering cross section drops to zero and the relative absorption cross section levels out. As a result, very small particles of hematite are transparent. 

It follows from (3.20) that the extinction cross section Cext may be written as the sum of the absorption cross section Cabs and the scattering cross section Csca ... 

The mathematical basis of the Mie theory is the subject of this chapter. Expressions for absorption and scattering cross sections and angle-dependent scattering functions are derived reference is then made to the computer program in Appendix A, which provides for numerical calculations of these quantities. This is the point of departure for a host of applications in several fields of applied science, which are covered in more detail in Part 3. The mathematics, divorced from physical phenomena, can be somewhat boring. For this reason, a few illustrative examples are sprinkled throughout the chapter. These are just appetizers to help maintain the reader s interest a fuller meal will be served in Part 3. 

A brief treatment of scattering by large, absorbing particles and the concept of absorption and scattering cross sections are presented in Section 5.7 along with two examples of applications of the Mie theory (to absorbing, but small, particles) and a discussion of Tyndall spectra. 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

A significant challenge in using vibrational spectroscopy for explosive detection (especially in the vapor phase) arises because of the combination of low vapor pressures and relatively low cross-section for absorption in the IR and the low scattering cross-section for Raman spectroscopy. For example, typical peak absorption cross-sections, a, for the NOz stretching modes are near 1 x 106 cm2/mole in the IR (for comparison, peak UV absorption cross-sections for TNT approach 50 x 106 cm2/mole). For Raman spectroscopy, scattering cross-sections in the UV may approach 1 x 10 2 cm2/mole [3,7],... 

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