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The nuclear structure of ²⁹Mg was probed using the d(²⁸Mg,p)²⁹Mg transfer reaction to populate its single-particle states. The ISOLDE facility at CERN provided a 9.473·A beam of ²⁸Mg which was directed at a deuterated target within the ISOLDE solenoidal spectrometer. Exploiting the kinematic advantages of this technique allowed most states up to 5 MeV to be resolved, and angular distributions of the reaction cross section to be obtained. The DWBA code DWUCK5 was used to obtain spectroscopic factors for these states. Additionally, some higher-lying excited states were identified, and their possible properties were proposed. Theoretical calculations in this region broadly reproduced the observed behaviour in ²⁹Mg, as well as matching trends from other nuclides in the N=17 isotones. These calculations indicate that the nucleon-nucleon interaction between protons and neutrons, with the tensor interaction as a key component, is driving the evolution of shell structure, with the filling of the πd5/2 orbital of particular importance in this region. Finite geometry effects also play an important role in this evolution as the p orbitals approach the neutron-separation threshold, and the energy spacing between them reduces. The information gained from the nuclear structure will help to continue refining these interactions, and provide a valuable benchmark for nuclear-structure studies around the border of the island of inversion. Similar experiments to study ³⁰Al and ³¹Mg carried out recently will help to further the understanding of nuclear structure in this exotic region of the nuclear chart.

A systematic study of the change in proton single-particle occupancies in two neutrinoless double beta decay candidates, 130Te to 130Xe and 136Xe to 136Ba, has been performed. Final states in 129Sb, 129I, 135I and 135Cs have been populated using the (d,3He) single proton removal reaction. The deuterons were accelerated to 101 MeV using the coupled azimuthally varying field and Ring cyclotrons at the Research Center for Nuclear Physics, University of Osaka. The outgoing ejectiles were momentum analysed using the Grand Raiden magnetic spectrometer. Absolute cross sections were measured for states up to 7 MeV in excitation. Transferred angular momenta were identified through a comparison of angular distributions with those calculated using the distorted-wave Born approximation. Spectroscopic factors were extracted from the experimental cross sections. In addition to the 0v2B decay candidates the reaction was also performed on 128Te, 132Xe, 134Xe and 138Ba as a consistency check. The occupancies of the nuclei were determined from the spectroscopic factors, the reaction model was normalised using a common normalisation factor across all targets. The change in occupancies between the 0v2B decay candidates and their daughters were then determined. The change in occupancies were then compared with those calculated by interacting shell model, interacting boson model and quasiparticle random phase approximation. This comparison showed that whilst the three theories were qualitatively able to reproduce the change in occupancies, quantitatively there are significant discrepancies. These are the same models that are used to determine the nuclear matrix elements governing the rate of 0v2B decay.