Wave-packet dynamics of resonant x-ray Raman scattering: Excitation near the ClLII,IIIedge of HCl

Abstract

A theory of radiative and nonradiative x-ray Raman scattering based on nuclear wave-packet dynamics is presented. The theory is evaluated with special emphasis on the cases when the intermediate and/or final state potentials are dissociative. Different ``one-step'' and ``two-step'' time-dependent wave-packet formalisms are proposed and evaluated, giving different interpretational content and computational efficiency. An interference between the molecular background and the narrow atomiclike contributions is predicted and evaluated. Due to this interference the atomiclike spectral feature manifests itself as a peak or as a spectral hole depending on the circumstances in terms of excitation energy, spectral width of incident radiation, and the form of the interatomic potentials. The counterintuitive situation may even arise that a narrow peak is formed by increasing the spectral photon width. The duration of the resonant x-ray Raman scattering influences in a qualitatively different manner the space distributions of the wave packets in the molecular and the dissociative domains, something that is crucial for the formation of the cross section profile. It is shown that the scattering cross section is proportional to the square of the core excited wave packet and inversely proportional to the derivative of the difference between core excited and final state potentials. The atomiclike profile is shown to consist of a Lorentzian inner part and red or blue wings which give direct information about the long-range regions of the potentials; red wings for diverging potentials, and blue for converging. A technique of mapping of the space distribution of the squared core excited wave packet and the interatomic potentials is suggested. The various features are demonstrated by an ab initio computational study of the resonant Auger spectra of the HCl molecule close to the Cl ${L}_{\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$ edge.