Correlations in space and time and dynamical diffraction of high-energy electrons by crystals

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Abstract
The problem of scattering of high-energy electrons by solids is formulated on the basis of a kinetic equation (KE) for the one-particle density matrix. This equation provides a general treatment of spatial and temporal coherence of electrons and takes account of both elastic and inelastic scattering for arbitrary geometry of diffraction. Formulating the KE, we prove that if the energy of an electorn is sufficiently high (E∼100 keV), the problem of multiple elastic and inelastic scattering by a solid is entirely determined by two universal functions, namely, the Coulomb potential averaged over the motion of the crystal particles and the mixed dynamic form factor of inelastic excitations, which is related to the time-dependent correlation function of the positions of electrons and nuclei in a solid. We show that in all the diffraction experiments the scattering cross section contains information about both these functions and discuss the possibility of their separate determination. The KE method generalizes previous theoretical approaches to the description of multiple inelastic scattering of high-energy electrons, and in the case of single inelastic interactions the solution of the KE reduces to the distorted-wave approximation. As an illustration, we consider an application of the KE to the problem of multiple scattering of high-energy electrons by collective electronic excitations of a crystal. Numerical solution of the KE is shown to be consistent with experimental observations, and evidence is found for the existence of a mechanism of damping of coherence by small-angle inelastic scattering of high-energy electrons by a crystal.

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