Coherent elastic scattering

Bragg scattering Coherent elastic scattering of monochromatic neutrons by a set of crystal planes. 

Figure 2.4 Different types of interactions of electrons with a solid 1, X-ray or optical photons 2, back-scattered electrons 3, secondary electrons 4, coherent elastic scattering 5, inelastic scattering 6, incoherent elastic scattering.

In the case of electron diffraction, we consider the coherent, elastically scattered electrons only, so that the time-independent, static correlation function G(r, o) is obtained in terms of the number density Q(r) of atoms on the surface of a sphere a certain distance r from an atom at the origin ... 

The coherent, elastically scattered electrons contain all the high resolution information... 

In diffraction mode, the projector lens system is adjusted in order to image the electron wave located at the back focal plane of the objective lens. What is seen on the screen is the intensity of this electron wave, which for coherent elastic scattering is called an electron diffraction pattern. 

The general form of the equation giving the dependence of the intensity Iq of the coherently (elastically) scattered beam of electrons on the angle of scattering d is identical with that... 

Figure 29. Time-of-flight spectra for a series of temperatures at the specular angle (45°) for NaCl(001), transformed to energy transfer distributions. The laige peak at zero energy transfer is the coherent elastic scattering (specular beam) which diminishes in intensity with temperature according to the Debye-Waller factor. The solid curves fitting the multiphonon foot of the elastic peaks are calculated from the Manson theory as described in the text. The incident helium wavevector for these experiments was 9.25 A , corresponding to an incident energy of 44 meV. (Reproduced from Fig. 1 of Ref. 96, with permission.)...

A qualitatively new approach to the extended fine structure in the secondary electron spectrum was proposed in [33-35]. Bearing in mind the autoionization mechanism, the authors suggested allowing for the coherent elastic scattering of electrons of both intermediate state of autoionization and the final state, i.e., the electrons detected in an experiment. In the context of this approach, the secondary electron extended fine structure results from superposition of two interference terms, both of which are determined by the local atomic environment of the ionized atom. One of them is determined by the wave number of the intermediate-state electron of autoionization, and the other by the wave number of the final-state electron detected in the experiment. 

Table 3 Coherent elastic scattering lengths of the isotopes of nickel.

Brief Theoretical Background In the case of coherent elastic scattering, a macroscopic ensemble of scattering atoms can be replaced by a continuous medium characterized by an index of refraction n [39] ... 

RAYLEIGH SCATTERING Coherent elastic scattering of photons by bound electrons. Energy is not lost by the photon. 

The delta function of Equation [28], d(Q-Thki), shows that coherent elastic scattering only occurs when the following condition is satisfied... 

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