In this doctoral work, a novel method for simultaneous measurement of masses, isomer excitation energies, half-lives, and decay branching ratios of exotic nuclei has been developed, implemented, and used at the FRS Ion Catcher (FRS-IC) experiment located at the GSI accelerator facility in Darmstadt, Germany. The method utilizes the advantages of in-flight production and separation of exotic nuclei at relativistic energies in the fragment separator (FRS), controllable storage of the ions of interest and retrapping of their decay recoils in a gas-filled cryogenic stopping cell (CSC), and fast, accurate and broadband measurement with a multiple reflection time-of-flight mass spectrometer (MR-TOF-MS).The feasibility of the method has been demonstrated in pilot measurements with the FRS Ion Catcher. The measurements have been performed with the nuclide 216Po produced by an internal alpha-recoil source and with the nuclide 119Sb and its isomer produced by fragmentation of 238U primary beam at an energy of 300 MeV/u. It has been shown that the ions can be stored in the CSC for controllable durations of up to 10 seconds without non-nuclear-decay losses. The alpha-decay of 216Po and the internal transition of the 119m2Sb isomer produced in the FRS have been investigated by observing simultaneous decay of the mother nuclides and growth of the daughter nuclides. The measured half-life value for 216Po of (145 ± 11) ms is consistent with the literature value of (145 ± 2) ms; and the measured half-life of 119m2Sb of (776 ± 181) ms is consistent with the literature value of (850 ± 90) ms. For the 119m2Sb isomer, for which it is energetically possible to undergo three different types of decay, the decay branching ratios have been measured directly for the first time. It has been experimentally confirmed that the isomer decays by internal transition, whereas the probabilities for beta+- and beta- -decays are consistent with 0. The masses of the ground and isomeric states of 119Sb have been measured directly for the first time, as well. Previously, the excitation energy and the spin assignment of the 119m2Sb isomer had not been unambiguously established. The results of gamma-ray spectroscopy experiments contradicted each other. In this work, it has been confirmed that the 119m2Sb isomeric state has an energy level of 2841.7 keV. The obtained results indicate that the adopted assignment for the excitation energy and the spin of 119m2Sb is not correct.In addition, within the frame of this thesis, a number of technical improvements and upgrades have been introduced to the FRS Ion Catcher setup. (i) A new calibration 228Th recoil ion source has been installed inside the CSC. This source and a discharge source have been extensively characterized. (ii) The vacuum system has been upgraded, which, in combination with the extended RFQ beamline, has resulted in higher possible areal densities of the CSC operation. The safe long-term operation of the CSC at areal densities of helium buffer gas of up to 10 mg/cm2 has been demonstrated, which is almost a factor of two higher than in the past. The increase in the buffer gas areal density leads to the corresponding increase in the stopping efficiency of the CSC. (iii) In order to increase the selectivity of ion transport, two new techniques have been developed and implemented: the isolation-dissociation-isolation (IDI) method in the RFQ beamline and the separation by ion mobility at the RF carpet. Also, in this work, characterization studies have been conducted. (i) The cleanliness of the CSC and the charge states of the thermalized and extracted ions have been investigated. It has been confirmed from the measurements of ions of more than 25 different chemical elements that the charge states are governed by the ionization potential of N2 molecules, which are the dominant contaminant of the helium buffer gas in the present setup. (ii) Rate capability studies of the CSC have been conducted. (iii) In addition, the homogeneity of the matter in the beamline of the FRS has been studied with the FRS Ion Catcher. It has been observed that, for 238U primary beam with an initial energy of 300 MeV/u, the measured width of the range distribution of the ions sigma = (7.8 ± 0.4) mg/cm2 is more than a factor of five larger than the calculated collisional straggling. The results indicate that the the range distribution of the ions for these experimental conditions is dominated by the contribution of the charge-exchange range straggling. A thickness variation of the matter in the beamline of the FRS corresponding to ~ 20-30 µ of aluminum has also been measured.
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