We study the electron density response in gold after excitation with XUV and visible light. We have introduced the concept of occupational nonequilibrium and developed multiband rate equations that track the occupation in each active electron band. The rate equations also track the energy content of the sp- and d-electrons and can be coupled to the phonons. Our results show that visible light excitation leads to an overpopulation of the sp-band, driven primarily by photo-excitation, while XUV irradiation results in an underpopulation of the sp-band, dominated by subsequent impact ionization. However, assuming that the excess energy from the Auger recombination process is transferred to multiple d-electrons, we showcase that XUV-exited gold can lead to an overpopulation of the sp-band. In addition, using a detailed balance of Auger and impact ionization coefficients, we show that a single-rate relaxation time approach is sufficient to describe the imbalance between the impact ionization rate and the Auger recombination rate.
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