Electron linewidths of wide--gap insulators: excitonic effects in LiF

Based on a recent exchange--correlation kernel developed within Time--Dependent--Density--Functional Theory we derive a practical and general expression for the three--point vertex function. We show that excitonic effects in LiF strongly modifies the low--energy electron linewidths leading to linear scaling with quasiparticle energy. We also prove that, in contrast to previous results for the electron gas, simple metals and semiconductors, vertex corrections in the self--energy and in the screening function do not compensate each other.