Unified treatment of recoil and Doppler broadening in molecular high-energy photoemission

Doppler and recoil effects are an integral part of the photoemission process at the high kinetic energies reached in hard x-ray photo-electron spectroscopy (HAXPES) and have a major effect on the observed lineshape, resulting in broadening, energy losses and discrete excitations. These effects can be modeled with a high degree of detail for small systems like diatomic molecules, for larger systems such treatment is often superfluous as the fine spectral features are not observable. We present a united description of the Doppler and recoil effects for arbitrary polyatomic systems and offer an approximate description of the recoil- and Doppler-modified photoemission spectral lineshape as a practical tool in the analysis of HAXPES spectra of core-level photoemission. The approach is tested on the examples of carbon dioxide and pentane molecules. The C and O 1s photoelectron spectra of CO _2 in gas phase were also measured at 2.3 and 7.0 keV photon energy at Synchrotron SOLEIL and the spectra were analyzed using the model description. The limitations and applicability of the approach to adsorbates, interfaces and solids is briefly discussed.