Theory of resonant elastic x-ray scattering by free molecules

A theory of resonant elastic x-ray scattering (REXS) by free molecules is presented. Different scattering channels and their interference on the formation of the spectral profile are identified. It is shown that atomiclike contributions to the cross section are totally eliminated for orthogonal orientations of the polarization vectors of the incident and scattered x-ray photons. A strong deviation from a Lorentzian profile of the spectral bands for REXS resonances is predicted. Numerical applications for the C [Formula Presented] and O [Formula Presented] spectra of carbon monoxide demonstrate the strong dependence of the spectral profile on the excitation energy and the spectral distribution of the incident radiation. Two qualitatively different contributions to the spectral shape are identified in the limit of narrow-band excitation: the first follows the excitation energy, while the second is determined by the absorption resonances. The vibrational progressions are very frequency dependent, and at large detuning frequencies the REXS cross section collapses to a single resonance with the width equal to the width of the photon function. This result is shown to hold for resonant as well as for nonresonant contributions to the REXS cross section.