We investigate the polarization anisotropy of resonant x-ray emission
using one-step, two-step, and classical formulations. It is shown, ana
lytically and numerically, that these models in general give different
polarization anisotropies. We compare also the results of the one- an
d two-step models for the integrated unpolarized cross sections over t
he same set of test molecules. These include two of the chlorofluorome
thanes used originally to experimentally verify the polarization aniso
tropy in resonant x-ray emission. The test molecules also represent sp
ecies with core-level chemical shifts and species with symmetry-adapte
d and quasidegenerate core levels. It is shown that only in the case o
f energy-isolated and localized symmetry-non-adapted core levels do th
e two-step model and the - in that case identical-classical model appl
y, while in all other cases, the one-step model is required either for
the polarization anisotropy or for the total cross section, or for bo
th these quantities.