Many-body and QED effects in electron-atom inelastic scattering in electron energy loss spectroscopy

The elemental composition and electronic structure of materials analyzed by electron energy loss spectroscopy (EELS) are probed by the inner-shell ionization of atoms. This is a localized process that can be approximated by the scattering of an electron beam from a free atom. We calculate the inelastic differential cross section perturbatively within the framework of quantum electrodynamics (QED). The interaction between the incoming electron and the atom factorizes into a high-energy electron term and the atomic transition current. The matrix elements of the transition current are computed within the relaxed Dirac-Hartree-Fock method. We analyze the correlation effects arising from the relaxation of the atomic orbitals induced by the creation of a core hole. These effects are particularly relevant in quantum many-body systems and have a significant impact on the shape of the differential cross section near the ionization threshold in EELS spectra. In addition to the continuum, we calculate the discrete excitation spectrum of DyScO3 using crystal-field multiplet theory. The calculated spectrum shows very good agreement with experimental EELS data.