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Abstract

In this thesis, different measurement and data evaluation approaches for the detection and characterization of collective nuclear level schemes arising in the low-excitation regime of thin-film x-ray cavities are discussed. The first approach uses Fourier transforms to analyze time- and frequency-resolved spectra recorded using nuclear reference absorbers. This allows for the extraction of the phase-resolved nuclear resonant response of the sample under investigation. Next, to study the dynamics of nuclear ensembles upon suitably-shaped x-ray light, a density matrix perturbation theory is presented that allows for the study of multi-level and many-body dynamics in the low-excitation regime of the x-ray-nuclei interaction. This method is used to interpret numerical data simulating several experimental scenarios: First, it is used to derive an equivalence between coherently and incoherently scattered x-ray intensity detectable in nuclear resonant scattering experiments, which serves as a criterion for nonlinear excitation of nuclear ensembles at coherent x-ray sources. Second, signatures of couplings between collective excited nuclear states in thin-film cavities upon differently-shaped x-ray pulses are proposed and identified in time-frequency-spectra. Finally, the feasibility of a specific coherent double pulse spectroscopic method under low-excitation conditions is discussed and numerically simulated spectra upon different double pulse sequences are compared.