This contribution summarises the theoretical basics for the theory of X-ray matter interaction and is based on a quantised description of the electromagnetic field. In view of a formally transparent presentation, we adopt the approach of second quantisation for the electronic degrees of freedom. We start from the minimal-coupling Hamiltonian that in principle contains all levels of electron correlation and treat the X-ray matter interaction in lowest-order perturbation theory. We give the explicit derivation of the photoionisation (X-ray absorption) cross section and the doubly differential cross sections for elastic and inelastic Thomson scattering, as well as resonant inelastic X-ray scattering. A connection to relevant experimental techniques is attempted. At some instances, the electronic Hamiltonian is approximated by a mean-field Hamiltonian, in order to facilitate the interpretation of the results and connect experimental observables with the underlying fundamental quantities of the quantum system under study.
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