Role of relaxation and time-dependent formation of x-ray spectra - art. no. 165115

A fundamental problem of x-ray spectroscopy is the role of relaxation of th e electronic subsystem in the field of the transient core hole. The main in tention of the present study is to explore the dynamics due to core-hole re laxation in the whole time domain, and to find out how it is manifested in finite molecular systems in comparison with solids. A technique is develope d based on a reduction of the Nozieres-De Dominicis equation to a set of li near algebraic equations. The developed time-dependent formalism is applied to a numerical investigation of a one-dimensional tight-binding model. The formation of the x-ray profiles is explored on the real time scale, and th e role of interaction with the core hole, band filling, and the final-state rule are investigated for systems of different size. The fort-nation of sp ectra of the infinite translational invariant system is studied by extensio ns of the finite systems. We found that the dynamics of finite systems, lik e molecules, differs qualitatively from solids: Contrary to the latter the time lapse of the Nozieres-De Dominicis domain for finite systems is squeez ed between the inverse bandwidth and the revival time, which is proportiona l to the system size. For small molecules this means that there is no time for a "Mahan-Nozieres-De Dominicis singularity" to develop. Comparison with the strict solution of the Nozieres-De Dominicis equation shows that the a diabatic approximation describes x-ray absorption and emission considerably better than the fast approximation. This explains the suppression of the r elaxation effects in x-ray emission of, e.g., gas phase and surface adsorbe d molecules, but also that these effects are essential for the absorption c ase. There is still a quantitative distinction between the adiabatic approx imation and the strict approach, which becomes more important for larger sy stems. Adopting the so-called finite state rule by von Barth and Grossman a lso for molecules, an almost complete numerical agreement between this rule and the strict x-ray-absorption and emission profiles for systems of diffe rent sizes is obtained. The simulations indicate that the final-state rule correction is important mainly near the absorption edge and at the top of t he emission band.