With only two ingredients, atomic nuclei exhibit a rich structure depending on the ordering of the different proton- and neutron-occupied states. This ordering can give rise to excited states with exceptionally long half-lives, also known as isomers, especially near shell closures. On-line mass spectrometry can often be compromised by the existence of such states that may even be produced in higher proportion than the ground state. This thesis presents the first results obtained from a nuclear spectroscopy setup coupled with the high-resolution Penning-trap mass spectrometer ISOLTRAP, at CERN’s radioactive ion beam facility ISOLDE. The isomerism in the neutron-deficient thallium isotopes was investigated. The data on 184,190,193−195 Tl allow an improvement of existing mass values as well as a mass-spin-state assignment in 190,193,194 Tl. Due to the presence of the ground and isomeric state for 194 Tl the excitation energy of the latter was determined for the first time experimentally. Systematic trends in the vicinity of the Z = 82 shell closure have been discussed.

The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.