Density matrix of inelastically scattered fast electrons

The kinetic equation for the evolution of a fast electron's density matrix rho after single inelastic scattering is solved in the one-beam approximati on. The solution holds for any type of inelastic interaction and for any sc atterer. It relates rho directly to the mixed dynamic form factor (MDFF) fo r inelastic scattering, which in turn is the Fourier transform of an energy -loss dependent density correlation function. This approach allows simulati ons of both energy-filtered diffraction patterns and high-resolution energy spectroscopic imaging (ESI), as well as access to the mutual coherence and the density autocorrelation function of the probe electron, all under the same formalism and the same approximation. A criterion for the maximum atta inable resolution in ESI is derived. As an example, we discuss dipole-allow ed atomic transitions for the Si-K ionization. [S0163-1829(99)08615-4].