Core-hole excitation and decay for continuum-coupled systems: The adsorbate case

In isolated atoms and molecules the resonant excitation and the subsequent decay of core-electron excitations are appropriately described as a coherent one-step process. Narrow-band excitation brings out its distinct features (linear dispersion and line narrowing for decay spectra in atoms; detuning effects such as vibrational collapse and turn-on and atomic versus molecular lines in molecules). Using the example of adsorbates on metal surfaces, we address the question if and how this is modified for systems in which discrete intermediate (core-excited) states are coupled to a continuum. The basic question of coherent versus incoherent processes is considered, and the more practical question is addressed as to what is the correct interpretation of the observed detuning effects for adsorbates. We demonstrate the inappropriateness of the usual wave function description based on the perturbative treatment of the time-dependent Schrödinger equation which leads to unphysical interferences and physically unacceptable features of the decay electron spectra and develop an appropriate density matrix approach. While its complications make a general solution impossible, we show that this approach leads in a systematic way to a picture in which coherent and incoherent excitation-decay channels compete but do not interfere with each other. The two-step description of the incoherent channel and the one-step character of the coherent one emerge from this analysis. The earlier interpretation of the observed variations of the relative strengths of the two channels upon detuning as the variation of the delocalization probability of the intermediate core excitation is justified by our treatment.