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 ${\mathrm{DyScO}}_3$ using crystal-field multiplet theory. The calculated spectrum shows very good agreement with experimental EELS data.

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• Electronic structure of atoms & molecules
• Diagrammatic methods
• Electron energy loss spectroscopy
• Many-body techniques