Ground state properties of neutron-rich Mg isotopes: the "island of inversion" studied with laser and $\beta$-NMR spectroscopy

Studies in regions of the nuclear chart in which the model predictions of properties of nuclei fail can bring a better understanding of the strong interaction in the nuclear medium. To such regions belongs the so called "island of inversion" centered around Ne, Na and Mg isotopes with 20 neutrons in which unexpected ground-state spins, large deformations and dense low-energy spectra appear. This is a strong argument that the magic N=20 is not a closed shell in this area. In this thesis investigations of isotope shifts of stable $^{24-26}$Mg, as well as spins and magnetic moments of short-lived $^{29,31}$Mg are presented. The successful studies were performed at the ISOLDE facility at CERN using collinear laser and $\beta$-NMR spectroscopy techniques. The isotopes were investigated as single-charged ions in the 280 nm transition from the atomic ground state $^2\!$S$_{1/2}$ to one of the two lowest excited states $^2\!$P$_{1/2 ,\,3/2}$ using continuous wave laser beams. The isotope-shift measurements with fluorescence detection for the three stable isotopes show that it is feasible to perform the same studies on radioactive Mg isotopes up to the "island of inversion". This will allow to determine differences in the mean charge square radii $\delta\langle r^2\rangle$ and interpret them in terms of deformation. The high detection efficiency for $\beta$- particles and optical pumping close to saturation allowed to obtain very good $\beta$-asymmetry signals for $^{29}\!$Mg and $^{31}\!$Mg with half-lives around 1 s and production yields about 10$^5$ ions/s. For this purpose the ions were implanted into a host crystal lattice. Such detection of the atomic resonances revealed their hyperfine structure, which gives the sign and a first estimate of the value of the magnetic moment. The nuclear magnetic resonance gave also their $g$-factors with the relative uncertainty smaller than 0.2%. By combining the two techniques also the nuclear spin of both isotopes could be unambiguously determined. The measured spins and $g$-factors show that $^{29}\!$Mg with 17 neutrons lies outside the ``island of inversion". On the other hand, $^{31}\!$Mg with 19 neutrons has an unexpected ground-state spin which can be explained only by promoting at least two neutrons across the N=20 shell gap. This places the above nucleus inside the "island". However, modern shell-model approaches cannot predict this level as the ground state but only as one of the low-lying states, even though they reproduce very well the experimental $g$-factor. This indicates that modifications to the available interactions are required. Future measurements include isotope shift measurements on radioactive Mg isotopes and $\beta$-NMR studies on $^{33}\!$Mg.