Multiple electron scattering forward

We have just described electron scattering by a single atom. The main feature to remember is the pronounced forward scattering within a more or less narrow forward cone, which occurs especially at the higher energies. The implications for multiple scattering are as follows. 

We now consider an atom instead of a stationary electron. The majority of atoms and ions consist of multiple electrons distributed around a nucleus as shown schematically in Figure 2.24. It is easy to see that no path difference is introduced between the waves for the forward scattered x-rays. Thus, intensity scattered in the direction of the propagation vector of the incident wavefront is proportional to the total number of core electrons, Z, in the atom. For any other angle, 20 > 0, i.e. when the propagation vector of the scattered waves, k , is different from the propagation vector of the incident waves, k, the presence of core electrons results in the introduction of a certain path difference, 5, between the individual waves in the resultant wavefront. 

The first term clearly relates to the nucleus, whereas the second term is due to the electron cloud. The interaction with matter is stronger (x 10 ) for electrons than for X rays or neutrons, which interact only with the electron cloud or with the nucleus, respectively. As a result multiple scattering will not be negligible in electron diffraction experiments. Moreover, electron scattering is oriented mainly in the forward direction. Tables of/e(0) for different atoms are given in [140]. 

Several reasons have been put forward to explain the change in the angular intensity pattern of the photoelectrons. One explanation is that intermediate neutral energy levels are ac-Stark shifted into resonance and contribute new selection rules to the photoionization process [53,54], Another possibility is that the electrons of the Kr or D2 are driven into the core Kr+ or D2 in a scattering-like process that creates interference fringes in the photoelectron angular distribution due to interference between multiple scattering channels [55],... 

Third, while these Ideas were developed (36) In the context of molecular photolonlzatlon, the continuum elgenchannel concept carries over without any fundamental change to electron-molecule scattering. Finally, while we have used one-electron wavefunctlons here, obtained with the multiple-scattering model, we emphasize that the elgenchannel concept Is a general one and we look forward to Its use In the analysis of more sophisticated, many-electron molecular continuum wavefunctlons. 

It was established by X-ray [9.15], neutron [9.16], and electron diffraction, and by high resolution electron microscopy (HREM) [9.17] that the deviation from the average structure of Bi/2212 is reasonably well described by the introduction of a displacement field. However, in electron diffraction superstructure reflections are seen also near the forward direction, Fig. 9.3(a), and they should not be there in a kinematieal diffraction pattern unless the displacements are extremely large. Unfortunately electron diffraction is prone to multiple scattering. Thus, we cannot rule out the possibility that the superstrueture reflections near the center of these diffraction patterns are caused by the other reflections further out in reciproeal space these may aet as new incident beams bringing superstructure spots caused by displacement into the central region of the diffraction pattern. 

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