Generality of anomalous broadening in $\sigma$ peaks of low-Z compounds

X-ray emission spectra originating from N 1s core holes in some nitrates have displayed extreme broadening($>$~4~eV) of a feature identified with the NO $\sigma$ state. Simple band structure calculations of the valence band derived from this bond in a crystal show it to be quite narrow. Calculations of transitions that take into account many-body corrections in the {\it GW} approximation indicate that the final state has a large imaginary self-energy. We have discovered other compounds that demonstrate this effect experimentally, and we are able to show that they display giant lifetime fluctuations of a similar valence state. We have formulated a criterion of compounds for which this effect should be present.