Cross section 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)... 

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. 

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

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 ... 

Another important scattering characteristic is the angular distribution of the scattered field. For an ensemble of randomly oriented particles illuminated by a vector plane wave of unit amplitude and polarization vector Cpoi = epoi,/3e/3 + epoi,a6a, the differential scattering cross-sections in the scattering plane are given by... 

The concept of supermolecules allows a rather rigorous treatment of the aspects of collision-induced light scattering in the binary regime. The frequency dependence of the scattered light is described by the differential photon scattering cross section per unit angular frequency and per pair,... 

Figure 1.6 Angular distribution of the scaled differential cross-section (l/r Kdo 1 VdJ ) of the first harmonic n — 1. Vanishing initial velocity fo = 0 is assumed and tq = 2.82 x 10 13 cm denotes the classical electron radius. The dotted line corresponds to the ordinary Thomson scattering cross-section.

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