Introduction to the theory of x-ray matter interaction

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 out 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.