Momentum-dependent lifetime broadening of electron energy loss spectra: Sum rule constraints and an asymmetric rectangle toy model

Electron energy loss spectra enable a detailed quantification of the electronic loss mechanisms in a target solid, particularly in the low-energy region dominated by plasmon excitations. Models of the electronic response in condensed-matter systems are usually derived from free-electron gas or jellium models, which commonly neglect to account for the lifetime broadening of individual plasmon and single-electron excitations in a constrained, physical manner. This can lead to potentially significant errors in electron energy loss spectra and electron inelastic mean-free-path (IMFP) calculations. We develop a toy model of plasmon and single-electron excitations that incorporates lifetime broadening for each excitation in an energyand momentum-dependent fashion. The model is physically constrained using optical and electronic sum rules. We demonstrate the necessity of asymmetric excitation broadening, and show that causally permitted variations in the broadening function can have a significant impact on the dielectric response of the material. Our developments are applied to molybdenum, and compared with previous modeling and high-precision experimental results for the IMFP at electron energies below 120 eV.