Scattering intensity definition

Measurements at low angles are subject to considerable error, and for this reason it is often preferred to apply appropriate corrections to scattering intensities measured at larger angles. The observed intensity ie in a direction 0 will be reduced on account of intraparticle interference by a factor cusomarily designated by P(0), which depends on the size and shape of the particle as well as on the angle 0. Thus, by definition... 

The fundamental scattering mechanism responsible for ROA was discovered by Atkins and Barron (1969), who showed that interference between the waves scattered via the polarizability and optical activity tensors of the molecule yields a dependence of the scattered intensity on the degree of circular polarization of the incident light and to a circular component in the scattered light. Barron and Buckingham (1971) subsequently developed a more definitive version of the theory and introduced a definition of the dimensionless circular intensity difference (CID),... 

Definition Submatrix. We choose a deliberate pixel from our scattering image. The pixel and its neighboring pixels are the submatrix. For the example we choose a submatrix size of 3 x 3 elements. There is scattering intensity in each pixel, e.g. 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

Definition Pole Figure. A pole figure, ghki(scattering intensity of the reflection... 

With these definitions the scattering intensity of a single particle maybe split into three terms [23,24,34-37] ... 

Similarly to IR, classical theories have also been proposed in the literature for Raman intensities in solution [29,32-38], The starting point is again the definition of the local field Eso1 acting on the molecule. In all cases the local field factor is defined as / = S-i/S-c, with 5 sc being the scattering intensity. 

Anisotropic Particle Scattering Varying Intensity Decay in Different Directions. In case of anisotropy the decay of the scattering intensity I (s) is a function of the direction chosen. The intensity extending from 5 = 0 outward in a deliberately chosen direction i is mathematically the definition of a slice (cf. Sect. 2.7.1, p. 22). Thus, the Fourier-Slice theorem, Eq. (2.38), turns the particle density function Ap (r) into a projection Ap (r) j (r,) and the scattering intensity is related to structure by... 

The value of the product of the definite integrals is 167t/3, so that we obtain the relationship between the turbidity and the total scattered intensity as... 

Miyaki, Einaga, and Fujita3 represented their measured scattered intensities in the form (15.1.24) and their results are reproduced in Fig. 15.2. Their sample was a dilute solution of long chains (Mw = 8.78 x 106) of polystyrene in cyclohexane at 34.6 °C [the temperature TF corresponds to 34 °C see (14.2.13) for the definition of jTf], In this situation, the polystyrene chains have a conformation close to that of equivalent Brownian chains. It is then possible to recognize the three correlation ranges in Fig. 15.2, using (15.1.25). 

FIGURE 7.11 Relation between the incident and scattered intensities and the definition of scattering angle. 

Fig. 9. Smearing of scattering intensity by sUt-coUimation Definition of geometry and variables...

Figure 9-4. The scattering profile of small particles with vertically (v) and horizontally h) polarized incident light. Upper row the oscillating dipole position and definition of the angles dv and h. Lower row polar plot of the light-scattering intensity (indicated by arrows) in the xy plane.

Note that Secs. 2.2 to 2.6 dealing with scattered intensities are the only places in this book where the strict definition of intensity is implied. Most diffraction and scattering theories have been developed around the strict definition of intensity [48]. This must be kept in mind when applying the results of such theories to single-photon-counting detectors. 

The extrapolation of scattering intensity to the lower limit of scattering angles gives the Hory-Huggins interaction parameter. The experimental definition of this value is... 

Note that both relations (6.26a) and (6.26b) hold only if d < d, or equivalently if t > 2. If d( = d, ot t = 2, both masses become proportional to each other, and in our definitions, there is only one mass present in the problem. This will prove to be important in the discussion for the scattered intensity for dilute solutions below. 

Projections are integral operators which map functions onto subspaces of their definition domain. They shall be denoted by a pair of curly parentheses. The best known projection in the field of scattering theory maps the scattering intensity I ( ) onto a zero-dimensional subspace, which is the number Q, known as "invariant or scattering power ... 

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