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Abstract

Within this thesis, we provide a theoretical description of nuclear decay by elec- tron capture. We discuss the influence of nuclear degrees of freedom and the coupling to the continuous spectrum of the electromagnetic field on the decay rate. Although these contributions are small, we will show that they are impor- tant for metrology and high-precision measurements. Our calculations predict that hyperfine interaction affects the decay rate on the Rydberg energy scale and changes the lifetime on the permille level. As we will show, this highly surprising result originates from selection rules related to the conservation of total angular momentum. In addition, we demonstrate that the coupling of local states to the continuous spectrum of the electromagnetic field leads to an increase of the de- cay rate at high energies. By direct calculations of the second-order decay rate including the decay by electron capture and subsequent fluorescence decay, we describe the process referred to as radiative electron capture. The accurate theo- retical description of nuclear decay rates also requires detailed knowledge of the involved nuclear many-body wave functions. We present an iterative scheme to determine optimized single-particle states based on natural orbitals. Our devel- oped numerical methods are applied to calculate the electron capture decay rate of several isotopes such as Fe-55, Zn-65, Ge-71, Te-118, Cs-131, Nd-140, Ho-163 and Er-165.