Solution of quantum kinetic equation in the locally eikonal approximation

A stationary quantum kinetic equation is derived for the density matrix of fast charged particles in an inhomogeneous medium (a crystal or an amorphous medium) in the approximation of slowly varying amplitudes. This equation is used to derive the mutual coherence function of the wave field for scattering in a plate of an amorphous material with a sharp boundary. The longitudinal coherence is determined by the mean free path of the particles in the medium. Equations are derived for the orientational dependence of the total reflection coefficient of a single crystal for electrons with energies on the order of a few tens of keV in the case of incoherent multiple scattering (the channeling pattern). The diffraction fine structure of the angular distribution of back-scattered particles near Bragg directions (the back-scattering pattern) is derived analytically in the two-wave approximation. The results are found to correspond to experimental data