Scattering of electromagnetic waves or particles

In a coherent scattering experiment the frequency v is the same for incident and scattered waves. Eq. (3.9) imphes then that = 2. which means that j and 2 have same ampli- 

This eq. (3.11) shows that the amplitude of the scattered wave is proportional to the Eourier transform, defined in eq. (5.A17) of the appendix of Ch. 5, of the density p of scattering centres. This is a particularly favourable situation, because the measurements of the amplitudes of the waves coherently scattered in all directions, that is with all possible wavevec-tors 2, allows in principle to calculate by an inverse Eourier transform, also defined by eq. (5.A17) of the appendix of Ch. 5, the density p(f) of scattering centres. This last equation holds for a one-dimensional (ID) Eourier transform, that is a single coordinate x (or 1) and consequently a single conjugate coordinate k (or v in eq. (5.A17)). The extension to a 3D space defined by f and j, 2 is trivial and can be found in any textbook on X-ray. Without entering the details of calculations of inverse 3D Eourier transforms, we nevertheless have to n te that in a coherent scattering experiment the measured quantities are not amplitudes E (eq. (3.11)) of vectors, which are complex quantities, with real and 

This inverse Fourier transform calculation of the correlations of density of scattering centres of the sample gives particularly precise results when this sample is a crystal. In this case p(f) is periodic. The scattered intensities are then 8 functions , or Dirac s functions, that are zero almost everywhere, except for well-defined values of 2 where they take on great amplitudes. They are known as Bragg peaks for which all scattered waves have the same phase. Interferences of all these waves are consequently constructive in the directions where Bragg s peaks appear. This is the consequence of the mathematical result that the 

A very few highly diluted gases have, however, been the objects of coherent electron scattering experiments. In more dense gases, absorption of electrons rapidly becomes predominant and hinders measuring scattering intensities. Diffraction of electrons thus allowed determining with precision the structure of H-bonded cyclic dimers of carboxylic acids (26-28) that constitute model systems of H-bonds we have already seen in Ch. 2 and shall see later in this book. They nevertheless remain scarcely used methods. 

In the case of H-bonds, a great wealth of stractural data has been obtained, making X-ray and neutron coherent scattering experiments basic methods to determine the geometries of a considerable number of H-bonded systems, as extensively described in excellent books (2,29). 

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