Dynamical properties of X-ray Raman scattering

This paper reviews theory for resonant X-ray scattering, emphasizing the dynamical aspects related to the nuclear motion during the scattering process. Various features of the theory are illustrated by simulations on small molecules in the gaseous phase. After the introduction defining the X-ray Raman scattering process, we briefly describe some central concepts of its theory: the Raman law, the time hierarchy of X-ray scattering and the generalized Kramers-Heisenberg relation. We then go into some detail of various theoretical aspects of the process: transition moments and light polarization, time-dependent formulation and wave packets. We review two aspects of recent experimental focus: Doppler effects and generalized Franck-Condon factors. In the last part of the paper we discuss X-ray Raman scattering of dissociative core excited states, and the intriguing concept of a duration time for the scattering. We address dissociative resonant photoemission from first principles, with particular emphasis on the conditions for observing so-called "atomic peaks" and "atomic holes". The atomic holes are the results of continuum-continuum interference effects between the atomic and molecular channels which may act destructively under certain conditions. We demonstrate that the resonant contribution and the evolution of the atomic peaks can be subject to strong dynamical suppression caused by nuclear motion. In general, the molecular geometry dependence of the electronic transition moments can change the scattering cross section quite dramatically. This is exemplified here by an unusual spectral flattening for the B state of N₂, and by a breakdown of the spectator versus participator classification in a part of the non-radiative resonant photoemission spectrum of HF. The notion of a duration time in resonant X-ray scattering is put forward as a powerful concept for predicting and understanding qualitative aspects of many of the effects or processes treated in this paper. The role of the pulse shape for short pulse X-ray excitation is also discussed.