Rayleigh scattering revisited: From gases to crystals
Scattering of an incident field by particles aligned along the axis. The figure is not drawn to scale because . The bold arrow gives the propagation direction of the incident field, which is polarized in the direction. The origin of the coordinate system is at the midpoint of the line of scatterers.
Particles placed on a line at random with nearest neighbors removed. It is clear from the figure that removal of nearest neighbors builds in correlation between particle positions.
Graphs of the structure function as a function of for several values of : (a) , (b) , (c) , (d) . The approximate expression (24) is used for (a)–(c) and the exact expression (21) with is used for (d). A region of the order of about the origin is excluded because it is assumed that .
Experimental curves of the structure factor for x-ray diffraction from rubidium (Ref. 16) [ corresponds to our ]. The lowest curve corresponds to a dense gas and the other curves to the liquid phase.
The particles are divided into bins, each bin containing a large number of oscillators. The spatial phase factor is approximately constant for each particle within a given bin.
particles randomly distributed over a wavelength distance. The sine wave is replaced by a square wave to illustrate the importance of the scattered signal on particle fluctuations.
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