Raman, non-Raman, and anti-Raman dispersion in resonant x-ray scattering spectra of molecules

The character of Raman dispersion is investigated for radiative and nonradiative resonant x-ray scattering of systems with vibrational degrees of freedom. It is shown that the center of gravity of the resonantly scattered x-rays and electrons of such systems is strongly dependent on frequency and spectral shape of the incoming x-ray radiation and on the parameters defining the potential surfaces of the states involved in the scattering event. Contrary to nonresonant x-ray and Auger emission, narrow band resonant excitation leads to a strong nonlinear dependence of the center of gravity, with an asymmetrical frequency dependence for this quantity. Contrary to atomic systems it is shown that resonant x-ray scattering of molecules often is guided by an anti-Raman dispersion law.