Quasiparticle Lifetime Broadening in Resonant X-ray Scattering of NH₄NO₃

It has been previously shown that two effects cause dramatic changes in the x-ray absorption and emission spectra from the N K edge of the insulating crystal ammonium nitrate. First, vibrational disorder causes major changes in the absorption spectrum, originating not only from the thermal population of phonons, but, significantly, from zero-point motion as well. Second, the anomalously large broadening (~ 4 eV) of the emission originating from nitrate σ states is due to unusually short lifetimes of quasiparticles in an otherwise extremely narrow band. In this work we investigate the coupling of these effects to core and valence excitons that are created as the initial x-ray excitation energy is progressively reduced toward the N edge. Using a GW/Bethe-Salpeter approach, we show the extent to which this anomalous broadening is captured by the GW approximation. The data and calculations demonstrate the importance that the complex self-energies (finite lifetimes) of valence bands have on the interpretation of emission spectra. We produce a scheme to explain why extreme lifetimes should appear in σ states of other similar compounds.