Differential scattering cross-sections

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

When the exciting frequency is nonresonant (distant from any electronic transition), the differential scattering cross section at wavelength X is as in equation 8 ... 

The relative number of particles backscattered from a target atom into a given solid angle for a given number of incident particles is related to the differential scattering cross section ... 

For more general interactions - i.e. not necessarily between two hard-spheres - we introduce a differential scattering cross section a v,8), defined by b db d(j> a u,8)dU. Boltzman s equation (equation 9.32) becomes... 

If the force between the beam particle and the target nucleus is assumed to be the Coulomb force, the basic equation for the differential scattering cross-section is given by Rutherford s formula ... 

In the scattering theory approach, the stopping power, or energy loss per unit length for a projectile of energy Ep, can be written in terms of a differential scattering cross section da/dQ as... 

Plots of each of these quantities as a function of particle size would look quite different and, therefore, would tell different stories. Except for a scale factor, each of them plotted as a function of wavelength for the same particle size would be identical. In our first example of extinction (Fig. 4.6) we displayed the efficiency Qext, as we shall often do in this chapter. In Chapter 12, however, our preference switches to the extinction cross section per unit particle volume. Unnormalized extinction cross sections (strictly speaking, the differential scattering cross section integrated over the acceptance angle of the detector) are more appropriate in Section 13.5 on particle sizing. 

The differential scattering cross section dCsc /dQ, a familiar quantity in atomic physics, is defined as the energy scattered per unit time into a unit solid angle about a direction —which may be specified by two angles, the scattering angle 6 and the azimuthal angle (see Fig. 3.3)—for unit incident irradiance. It is expressed in terms of the scattered irradiance Is(0, ), the incident irradiance /, and the distance r to the detector as... 

For an isotropic medium such as a collection of many randomly oriented particles, which may themselves be anisotropic, the scattered irradiance and hence the differential scattering cross section is independent of . 

The differential scattering cross section divided by the total scattering cross section... 

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)... 

We define a scattering (or deflection) angle, x, as in Fig. 2.2, an azimuth, solid angle, Q, so that d2Q = sin dx dq>. The differential scattering cross section is defined as the number AN of particles scattered every second into the solid angle A 2 around x,

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Units of the differential scattering cross section are area per steradian. 

Differential scattering cross sections may be specified in the laboratory frame or, alternatively, in the center of mass frame each may be transformed into the other by well-known relationships (Levine and Bernstein 1974). 

Quantum theory of scattering. The differential scattering cross section for isotropic potentials is given by the scattering phase shifts r e as... 

We note that bdb is related to the classical differential scattering cross section. It is a short-hand notation for b(x) di>/d/ dx the magnitude of the derivative di>/dx falls off to zero quickly so that the integral over bdb is actually finite. 

The most important experiment of this type is thermal neutron scattering A complete determination of the differential scattering cross section for the scattering of neutrons from liquids completely determines the Van Hove scattering function.18 This function is related through a space-time Fourier transform to the autocorrelation function of the number density at two... 

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