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## Mutual control of x-rays and nuclear transitions

Gunst, Jonas Friedrich

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In the course of this Thesis the mutual control between x-rays and nuclear transitions is investigated theoretically. In the first Part, we study the nuclear photoexcitation with the highly brilliant and coherent x-ray free-electron lasers (XFELs). Apart from amplifying the direct resonant interaction with nuclear transitions, the super-intense XFEL can produce new states of matter like cold, high-density plasmas where secondary nuclear excitation channels may come into play, e.g., nuclear excitation by electron capture (NEEC). Our results predict that in the case of ${}^{57}$Fe targets secondary NEEC can be safely neglected, whereas it is surprisingly the dominating contribution (in comparison to the direct photoexcitation) for the XFEL-induced ${}^{93\rm{m}}$Mo isomer triggering. Based on these case studies, we elaborate a general set of criteria to identify the prevailing excitation channel for a certain nuclear isotope. These criteria may be most relevant for future nuclear resonance experiments at XFEL facilities. On the opposite frontier, the interplay between single x-ray photons and nuclear transitions offer potential storage and processing applications for information science in their most compact form. In the second Part of this Thesis, we show that nuclear forward scattering off ${}^{57}$Fe targets can be employed to process polarization-encoded single x-rays via timed magnetic field rotations. Apart from the realization of logical gates with x-rays, the polarization encoding is used to design an x-ray quantum eraser scheme where the interference between scattering paths can be switched off and on in a controlled manner. Such setups may advance time-energy complementarity tests to so far unexplored paramater regimes, e.g., to the domain of x-ray quanta.