Angular differential scattering

In ion-solid interactions, it is customary to describe the number of particles scattered through different angles, 6C, in terms of a quantity called the angular differential scattering cross-section. Imagine the experiment depicted in Fig. 4.1, where a beam of ions is incident on a thin foil and is scattered into a detector of area A a at a polar angle between 8C and 6C + d0C. Each of the ions in the incident... 

Angular light scattering measurements are sometimes classified as either absolute or relative. In an absolute measurement 7s//(, which is directly related to the differential scattering cross section (13.2), is determined in a relative measurement the irradiance is referred to some arbitrary scattering angle, say 10°, so that (assuming azimuthal symmetry)... 

Fig. 4.1. Experiment for measuring angular differential cross-section. The detector area is Aa = (RA0c)(R sin 6cA(p). By moving the detector to all angular positions for a fixed R, all the scattered particles can be counted, and the detector will have covered an area 4zR2, or a total solid angle of 4 ...

Equations (4.5) and (4.7) give the differential scattering cross-section in the center-of-mass. The equivalent expressions in the laboratory reference frame can be obtained for the scattered projectile and scattered target nucleus by using the angular relationships presented in Table 3.2. 

This final expression is extremely useful since it allows us to determine the differential energy-transfer cross-section if the angular differential cross-section is known, or if the center-of-mass scattering angle and impact parameter are known. 

We define the differential scattering cross-section per unit volume of the scatterer, per unit solid angle ( 2), per unit angular frequency change as... 

The dependence of the radiation pattern from dipoles uniformly distributed within a spherical particle of relative refractive index m = n /n2 = 2.0 upon the particle size is illustrated in Fig.4.9 where the angular distribution in the scattered intensity is plotted in arbitrary units for different values of the size parameter. The exciting radiation incident upon the particle is assumed to be horizontally polarized. There is a sharp increase in the differential scattering... 

In Fig. 3 we report typical total differential scattering data measured for He-NO( n) at two collision energies. The quenching of the quantum diffraction oscillations in the angular dependence of the total DCS with respect to what is expected from a spherical interaction contains information on the anisotropy of the repulsive wall of the potential. The analysis of these.data has permitted us to derive a full anisotropic PES, which represents a significant improvement with respect to a previous determination. Second virial coefficients were also included in the analysis. 

In simplifying the derivation of the paramagnetic differential scattering cross section it is common to assume LS coupling [3, 48]. This assumption states that for individual electrons of spin s and orbital angular momentum 1 ... 

One now has the following expression for the angular differential cross-section for the scattering of light by the kh atom ... 

The angular differential cross-section is calculated by taking dP/dQ, where dP is the time-averaged power scattered into solid angle dQ, and dividing by the intensity of the incident light. This is equivalent to writing da/dQ = r )/ Eq so that... 

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