Polarization anisotropy in resonant x-ray emission from molecules

We investigate the polarization anisotropy of resonant x-ray emission using one-step, two-step, and classical formulations. It is shown, analytically and numerically, that these models in general give different polarization anisotropies. We compare also the results of the one- and two-step models for the integrated unpolarized cross sections over the same set of test molecules. These include two of the chlorofluoromethanes used originally to experimentally verify the polarization anisotropy in resonant x-ray emission. The test molecules also represent species with core-level chemical shifts and species with symmetry-adapted and quasidegenerate core levels. It is shown that only in the case of energy-isolated and localized symmetry-non-adapted core levels do the two-step model and the - in that case identical-classical model apply, while in all other cases, the one-step model is required either for the polarization anisotropy or for the total cross section, or for both these quantities.