Satellites in electronic spectra are pure many-body effects, and their study has been of increasing interest in both experiment and theory. The presence of satellites due to plasmon excitations can be understood with simple models of electron-boson coupling. It is far from obvious how to match such a model to real spectra, where more than one kind of quasi-particle and of satellite excitation coexist. Our joint experimental and theoretical study shows that satellites in the angle-resolved photoemission spectra of the prototype simple metal aluminum consist of a superposition of dispersing and non-dispersing features. Both are due to electron-electron interaction, but the non-dispersing satellites also reflect the thermal motion of the atoms. Moreover, besides their energy dispersion, we also show and explain a strong shape dispersion of the satellites. By taking into account these effects, our first principles calculations using the GW+C approach of many-body perturbation theory reproduce and explain the experimental spectra to an unprecedented extent.
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