The first direct Q_EC measurement in ¹⁶³Ho and the development of the high-precision mass spectrometer PENTATRAP for neutrino physics

An improvement of the upper limit of the electron neutrino mass to a sub eV/c² level is the goal of the ECHo collaboration. The upper limit of the neutrino mass will be determined with cryogenic microcalorimetry from the analysis of the atomic de-excitation spectrum of ¹⁶³Dy after the EC in ¹⁶³Ho. To check for systematic errors an independent measurement of the Q-value of the EC in ¹⁶³Ho is required. For the first phase of ECHo the issue with the discrepancy between the latest microcalorimetry measurements of the Q-value and its literature value needed to be fixed. For this, a first direct measurement of the Q-value of the EC in ¹⁶³Ho with the Penning-trap mass spectrometer SHIPTRAP was accomplished in the context of this thesis using the novel PI-ICR technique. Within the uncertainty, it agrees with the latest microcalorimetry measurements. Furthermore, the achieved precision is sufficient for ECHo-1k to be able to improve the upper limit of the electron neutrino mass to 10 eV/c² (95% C.L.). For further improvements on the neutrino mass, the Q-value needs to be improved, too. For this, the novel high precision Penning-trap mass spectrometer PENTATRAP has been developed and commissioned. PENTATRAP will utilize five Penning traps to test new measurement schemes, which could make it possible to reach unv certainties in the 10^-12 regime. Currently, first mass-ratio measurements of the nuclei pair ¹³²Xe and ¹³¹Xe with known masses were carried out to test the performance of PENTATRAP.