Normalized scattering cross section

Figure 6. Normalized scattering cross section for an air bubble and a rigid sphere.

The normalized scattering cross-sections versus size parameter for a particle in fixed or random orientation... 

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

In Eq. (7.21) the normalization to the scattering cross-section r2 leads to the definition of absolute intensity in electron units which is common in materials science. If omitted [90,91], the fundamental definition based on scattering length density is obtained (cf. Sect. 7.10.1). 

Figure 8.7 Scattering cross section per unit particle volume for normally incident light polarized parallel (---) and perpendicular (...) to the axis of an infinite cylinder in air.

Figure 11.15 shows Asano s calculations of extinction by nonabsorbing spheroids for an incident beam parallel to the symmetry axis, which is the major axis for prolate and the minor axis for oblate spheroids. Because of axial symmetry extinction in this instance is independent of polarization. Calculations of the scattering efficiency Qsca, defined as the scattering cross section divided by the particle s cross-sectional area projected onto a plane normal to the incident beam, are shown for various degrees of elongation specified by the ratio of the major to minor axes (a/b) the size parameter x = 2ira/ is determined by the semimajor axis a. 

Relative measurements are considerably easier to make and are the type most commonly reported. However, absolute measurements are of importance, for example, in comparing measured scattering cross sections of nonspherical particles with calculations for equivalent spheres. Note that absolute as we are using the term here means that scattering is not normalized to some arbitrary reference angle it does not mean that absolute irradiances are measured, as with calibrated detectors. In both relative and absolute measurements, it is relative (i.e., dimensionless) irradiances that are determined. 

Gs°(r, t) and Gsc(r, t) determine the incoherent differential scattering cross section for slow neutrons from CO through a weighted sum of their space-time Fourier transforms. Each of these functions is normalized to unity when integrated over all space. 

Raman spectra have been observed wherein the signals obtained are of the order of lO -lO greater than one would predict on the basis of the normal Raman scattering cross section of bulk molecules (11, J2). The latter effect has sometimes been termed "enhanced Raman scattering" and has been the subject of intensive theoretical and experimental investigation. We will first discuss the normal or general situation. 

In order to obtain an absolute scale for the measurements, the elastic scattering cross section was normalized to the total cross sections of Stein et al. (1978) at energies below EPs. 

It is very difficult to experimentally obtain the values of the scattering cross section. However, it is relatively easy to obtain the intensity of given normal mode k relative to that of another mode k. A simple expression relating the relative intensities has been derived for the special conditions of harmonic oscillators, no Duschinsky rotation, no change in normal mode frequencies, and pre-resonance (short time) condition spectra. Under these conditions the relative intensities of two modes is given by... 

Redefining h as the reference frequency, and - dividing this equation by u,ef h), affords the absolute normalized Raman scattering cross section (Eq. 3.5-13). It has been tabulated for several compounds by Schrotter and Klockner, 1979. Typical values for liquids excited by radiation from an argon ion laser at 488 nm are listed in Table 3.5-1. Raman scattering cross sections of gases are discussed by Schrotter in Sec. 4.3.2.3. 

Table 3.5-1 Integrated absolute normalized Raman scattering cross sections of liquids, excited with radiation of A,e/ = 487.99 nm = hef = 20487 cm (Schrotter and Klockner, 1979)...

Eysel and Bertie (1988) considered the absolute normalized Raman scattering cross section of the ring breathing vibration of liquid benzene at 992 cm a standard for the measurement of relative Raman scattering cross sections of a number of compounds. When applying it as standard they made use of a divided spinning cell , developed by Kiefer and Topp (1974). 

Most scattering cross sections of other Raman bands were measured against the nitrogen 2-branch as standard. Therefore the relative normalized differential Raman scattering cross section ... 

The time-independent probability for the occurrence of a particular collision process is represented by the corresponding scattering cross section. It characterises the scattering process and is well defined in most scattering experiments. There are some situations when a time-dependent probability must be considered and the normal definition of a scattering cross section is not applicable. 

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