Probing the semi-magicity of $^{68}$Ni via the $^{66}$Ni(t,p)$^{68}$Ni two-neutron transfer reaction in inverse kinematics

The region around the nucleus $^{68}$Ni, with a shell closure for its protons at Z=28 and a harmonic oscillator shell gap for its neutrons at N=40, has drawn considerable interest over the past decades. $^{68}$Ni has properties that are typical for a doubly-magic nucleus, such as a high excitation energy and low B($E2:2^{+} \rightarrow 0^{+}$) transition probability for the first excited 2$^{+}$ level and a 0$^{+}$ level as the first excited state. However, it has been suggested that the magic properties of $^{68}$Ni arise due to the fact that the N=40 separates the negative parity $pf$-shell from the positive parity 1$g_{9/2}$ orbital, and indeed, recent mass measurements have not revealed a clear N = 40 energy gap. Despite all additional information that was acquired over the last decade the specific role of the N=40 is not yet understood and a new experimental approach to study $^{68}$Ni was proposed. Namely, a two-neutron transfer reaction on $^{66}$Ni to characterize and disentangle the structure of the low-lying 0$^{+}$ and 2$^{+}$ states in $^{68}$Ni. The experiment was performed at the ISOLDE facility at CERN, Geneva, Switzerland. A radioactive $^{66}$Ni beam was produced in several steps. It started with an impingement of high energetic protons on a thick uranium-carbide target, after which the desired isotopes were ionized and accelerated to 30 keV and finally, to eliminate contamination of the beam, the beam was passed through a mass separator. However, in order to perform transfer experiments a higher beam energy is required and thus the $^{66}$Ni beam was post-accelerated to 2.6 MeV/u with the REX linear accelerator. The $^{66}$Ni beam was then guided towards a radioactive tritium-loaded titanium foil, where the reaction took place. The reaction products were detected with T-REX and Miniball. T- REX is a position-sensitive particle detection array, consisting out of several silicon detectors, while Miniball is an array of position-sensitive $\gamma$-ray detectors consisting of high-purity germanium detectors. A first step in the analysis was the calibration of the data and performing a particle identification. From proton-$\gamma$ and proton-$\gamma$-$\gamma$ coincidences a level scheme of $^{68}$Ni could be constructed. No new levels were identified in this research, however, the excitation energy of the level that is populated in $^{68}$Ni can be deduced from the detected proton energy. Out of the probability of populating different states, structure information can be derived. By looking at the excitation energy spectra it was clear that most of the feeding in the two-neutron (t,p) transfer reaction to $^{68}$Ni goes to highly excited levels between 5-9MeV. Also, a strong feeding to the ground and a direct population of the first excited 0$^{+}$2 at 1604 keV and 2$^{+}$1 state at 2033 keV was observed, namely respectively 4.2(16) % and 29.3(29) % of the ground state feeding. Direct population of other known 0$^{+}$ and 2$^{+}$ states in $^{68}$Ni was not detected, only upper limits could be determined. In a second step of the analysis the angular distributions constructed for the ground state and first excited 0$^{+}$ and 2$^{+}$ state were compared with theoretical DWBA calculations performed with Fresco, where input from the shell-model code Nushell was used. The predicted magnitude of the angular distributions for the ground and 0$^{+}$2 state is in good agreement with the data, while that for the 2$^{+}$1 state is an order of magnitude too small. This discrepancy is currently not understood. The agreement of the feeding of the 0$^{+}$ states with the calculations indicates that the structure of the 0$^{+}$2 state consists dominantly of two neutrons in the $g_{9/2}$ orbital. Further, the obtained results for $^{68}$Ni were compared to the systematics of the (t,p) reactions on the lighter, stable nickel isotopes and to its valence counterpart $^{90}$Zr, which has a shell closure for its neutrons at N=50 and a harmonic oscillator shell closure for its protons at Z = 40. An outlook for new experiments to study $^{68}$Ni closes the thesis.