Density matrix of inelastically scattered fast electrons

Abstract

The kinetic equation for the evolution of a fast electron's density matrix $\ensuremath{\rho}$ after single inelastic scattering is solved in the one-beam approximation. The solution holds for any type of inelastic interaction and for any scatterer. It relates $\ensuremath{\rho}$ directly to the mixed dynamic form factor (MDFF) for inelastic scattering, which in turn is the Fourier transform of an energy-loss dependent density correlation function. This approach allows simulations 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 attainable resolution in ESI is derived. As an example, we discuss dipole-allowed atomic transitions for the Si-K ionization.