Resonant Inelastic X-Ray Scattering from Valence Excitations in Insulating Copper-Oxides

We report resonant inelastic x-ray measurements of insulating La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$ taken with the incident energy tuned near the Cu K absorption edge. We show that the spectra are well described in a shakeup picture in 3rd order perturbation theory which exhibits both incoming and outgoing resonances, and demonstrate how to extract a spectral function from the raw data. We conclude by showing {\bf q}-dependent measurements of the charge transfer gap.Comment: minor notational changes, discussion of anderson impurity model fixed, references added; accepted by PR

Temperature dependence and Debye-Waller factors for resonant x-ray Raman scattering in solids

Resonant x-ray Raman scattering is a strongly coherent process. The well defined phase relations between scattering channels through the core excited states localized at different atoms result in a conservation of the electronic crystal momentum. However, as we show here, the zero-point and thermal vibrations dephase these scattering channels and lead to incoherent contributions with different spectral shapes. The relative strength of the coherent and incoherent contributions are found to strongly depend on temperature via a Debye-Waller factor. This results in a characteristic temperature dependence of the spectral profile of the resonant x-ray Raman scattering.</p

Doppler effects in resonant x-ray Raman scattering

Theory for Doppler effects in resonant x-ray Raman scattering (RXS) is presented. It is shown that the "electron" Doppler effect is important in nonradiative RXS for decay transitions between continuum nuclear states lying above the dissociation threshold, and that the averaging of the RXS cross section over molecular orientations can lead to strong non-lorentzian broadenings of the atomiclike resonances. The Doppler effect is found to give a unique possibility to distinguish dissociating identical atoms, because different peaks correspond to atoms with opposite Doppler shifts. Spectral features of the atomiclike profile are predicted and analyzed. Strong oscillations of the RXS cross section will occur as a consequence of the interference of the Auger electrons. Due to the Doppler effect and the interference, the atomiclike profile can be associated with supernarrow spectral features, the width of which goes below the lifetime broadening and is practically independent of the spectral distribution of the incident radiation. As another consequence of the oscillations and strong anisotropy caused by the interference, we predict parity selection rules for Auger decay transitions in both bound and dissociative systems. The corresponding experiments can be realized by measurements of resonant Auger of surface adsorbed molecules and for molecules by the electron-ion coincidence technique.</p

Dynamics of Inner Shell Resonant Raman Scattering

Some recent advances in the theory of the resonant Raman process for atoms, molecules and solids involving inner shell electrons are reviewed. Special emphasis is put on the dynamical aspects and on the notion of a duration time for the x-ray Raman process (RXS), which brings about a distinetion of processes with different time scales responsible for the formation of the spectral profile. This notion has been useful for actual predietions of various phenomena associated with RXS such as "symmetry restoration" "vibrational collapse", and "control of dissociation". The temporal theory of RXS is based on the wave packet formalism. The increase of the broad "molecular" parts relative to the atomic, or fragment, decay upon frequency detuning is demonstrated. The atomic-like resonance and molecular parts are proved to show different dispersion relations. Under certain conditions the interference between the molecular and atomic parts produces conspicuous "spectral holes". These conceptual tools are applicable also in the case of solids; there is an analogous restoration of momentum selection rules and a collapse effect upon detuning the frequency. Thus when the duration of the scattering is shortened by a large detuning, the role of electron-phonon coupling of the core excited states is suppresssed. The shortening of the RXS duration in a certain sense leads to a deloealization of the core hole in a solid. We describe also some new features that derive from the Doppler effect on ejected Auger electrons.</p

Anisotropic EXAFS measured in the Raman mode : a way to determine bond angles in randomly oriented species

It is shown that, contrary to the case of ordinary EXAFS measurements, EXAFS measured in the Raman mode is polarization sensitive for randomly oriented systems. This fact can be used to predict bond angles and gives an opportunity for a complete structural determination of gaseous or amorphous systems.</p

Vibrationally resolved core-photoelectron spectroscopy as an infinite-slit interferometry

During a molecular vibration, an atom changes continuously its position. Just as the emitted photoelectron waves, the electromagnetic waves absorbed by the atom in the different positions are strictly coherent and have different well-defined phases. These phases depend on the relation between the instantaneous internuclear distance and the photoelectron, respectively, photon wavelengths. We predict that the interference of these coherent waves strongly influences the vibrational profile of the photoelectron spectra of core electrons in a molecule. This effect increases with increasing x-ray photon frequency and results in a deformation and broadening of the vibrational profile. In the case of surface adsorbed molecules, the vibrational profile depends strongly on the direction of the photoelectron ejection and photon momentum, and the orientational sensitivity of a vibrational profile can even be used as a tool to define the orientation of adsorbed molecules.</p