We report on studies of state-populations during the two-photon absorption process\nusing intense X-ray pulses. The calculations were performed in a time-dependent manner using a\nsimple three-level model expressed by coupled rate equations. We show that the proposed approach\ndescribes well the measured rates of X-rays excited in the one-photon and two-photon absorption\nprocesses, and allows detailed investigation of the state population dynamics during the course\nof the incident X-ray pulse. Finally, we demonstrate that the nonlinear interaction of X-ray pulses\nwith atoms leads to a time-narrowing of state populations. This narrowing-effect is attributed to a\nquadratic incidence X-ray intensity dependence characteristic for nonlinear interactions of photons\nwith matter.
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