Scattering by a macroscopic sample

Let us consider a sample intended for a scattering experiment. It is made up of a large number of scattering centres. We can associate a cross-section with each isolated centre. We saw 

It is observed that the interference effects are strongly dependent on the scatterer concentration and on the collision amplitudes. There are two extreme cases  

Radiation scattering by an assembly of centres is also characterized by another effect related to time fluctuations concerning either the sample or the incident radiation. In fact, in the course of time, the total spin state of the neutron-nuclei system may change, and the same remark applies to the orientations of the anisotropic polarizable elements. Thus, the cross-section of the assembly of scattering centres is averaged over a period of time. Two contributions appear. The first one, which is called coherent, reveals interference effects between scattered rays. The second one, which is called incoherent, is the sum of the cross-section of the various centres (considered as isolated). 

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Many radioactive materials in the natural decay series and in the nuclear fuel cycle are a emitters for which very little radiation escapes a macroscopic sample. If radiochemistry is used to isolate a particular element, and its mass is small, the solid can be deposited on a metal planchet (e.g., by evaporating a small volume of liquid containing the purified material) and counted with the planchet forming the bottom of the gas chamber such as shown in O Fig. 48.3. Under these conditions, the a detection efficiency can be about 52% and the P detection efficiency about 80%. (Some p particles that are emitted toward the planchet are scattered into the gas volume.)... 

For a macroscopic sample with a volume V and very large dimensions compared to the X-ray wavelength, the first integral yields non-zero values only over an extremely small q range, around q = 0, that is not reached in typical SAXS experiments. Thus, the scattering intensity, I q) = Aq) Aq) -, over the accessible q range, is given by... 

We consider a macroscopically isotropic system composed of /V-like molecules in an active scattering volume V illuminated by laser radiation of frequency oa linearly polarized in the direction e. We analyze the secondary electromagnetic radiation emitted by the system in response to that perturbation. At a point R distant from the center of the sample, the radiation scattered at ft) is measured on traversal of an analyzer with polarization n. The pair doubledifferential cross sections for scattered interaction-induced radiation becomes... 

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