Next-Generation Mass Spectrometry of Exotic Isotopes and Isomers

This cumulative dissertation comprises ISOLTRAP's transition from the well-established Penning-trap mass spectrometry (PTMS) technique, ToF-ICR, to the next-generation PTMS technique, called PI-ICR. First, the highest precision ever achieved at the ISOLTRAP experiment using ToF-ICR allowed for a reduction of the $Q_{EC}$-value uncertainty of the $^{21}$Na → $^{21}$Ne and $^{23}$Mg → $^{23}$Na electron-capture decays by a factor of five compared to their literature values. Within these findings, the most precise $\mathcal{F}t$-values and, in the case of $^{21}$Na → $^{21}$Ne, a new $V_{\rm{ud}}$-element value of the CKM quark-mixing matrix were derived and found to agree with the standard model of particle physics. Second, ISOLTRAP's first publication using PI-ICR demonstrated a supreme relative mass precision of δm/m = 1.4×10$^{–9}$ in only 4 hours of experiment time. The result reduced the uncertainty on the $Q_{EC}$-value of the $^{131}$Cs → $^{131}$Xe decay by a factor of 25 and consequently precluded the decay as a possible candidate for a direct neutrino-mass determination. Third, ultra-high mass resolving powers exceeding 10$^6$ using PI-ICR allowed for the first spatial resolution of isomeric states in neutron-rich cadmium isotopes. Thus, this publication presented the first experimental data describing the $N$ = 82 neutron-shell closure below the proton-magic $Z$ = 50 while implying a drastic weakening of the $N$ = 82 shell. Furthermore, these measurements allowed for sophisticated comparison with state-of-the-art nuclear-theoretical models