Resonant inelastic x-ray scattering with symmetry-selective excitation

We present a theoretical formulation of resonant inelastic x-ray scattering (RIXS) of molecules with an element of symmetry, and study the consequences of this formulation both with respect to short and long lifetimes of the intermediate core-excited scattering states and with respect to localized versus delocalized descriptions for these states. Strong polarization and excitation energy dependencies are predicted. The ``core-hole localization'' problem is explored also from the point of view of diffractional scattering of an x-ray photon showing that x-ray photons distinguish core holes in the short-wavelength limit only. By analyzing the properties of the x-ray scattering tensor, strict selection rules for the RIXS process are derived. The local decomposition model (one-center approximation) frequently employed in ordinary x-ray emission is generalized for the calculation of intensities and polarization dependence of the RIXS process, assuming either localized or delocalized core holes. It is argued that Stokes doubling should be a commonly observable feature in RIXS spectra. By means of model calculations we demonstrate the crucial role of RIXS selection rules, of channel interferences, of Stokes doubling, and of the form of the excitation frequency function for the appearance of RIXS spectra.