Study of the 66Ni(t,d)67Ni Transfer Reaction in Inverse Kinematics

The nickel isotopes with 28 protons are an interesting series in the study of nuclear structure. In the framework of the shell model nickel has a closed proton shell and the number of neutrons ranges from the magic numbers 20 to 50. The neutron-rich isotope $^{78}$Ni, is a waiting point in the nucleosynthesis r-process. In this process an intense neutron flux such as in supernovae results in the rapid capture of neutrons. The reaction sequence halts at $^{78}$Ni and waits for this nucleus to decay [Hea05]. For several decades the nickel isotopes have been studied extensively, particularly how the nuclear structure evolves when moving to the exotic boundaries of the nuclear chart. A remarkable feature was observed in $^{68}$Ni. This nucleus with 40 neutrons exhibits properties that are characteristic for doubly magic nuclei. Such as the energy of the first 2$^+$ state lies significantly higher than in neighbouring even-A isotopes, and is also higher than the energy of the second 0$^+$ state. Moreover also the B(E2 : $0^+_1 \rightarrow 2^+_1$) transition probability is lower than in neighbouring isotopes. These observations may indicate that the energy gap between the $2p_{1/2}$ and $1g_{9/2}$ shell model orbitals on both sides of the N = 40 gap is large and $^{68}$Ni could be called a semi-magic nucleus. To test this hypothesis mass measurements of the nickel isotopes have been performed. From these measurements however $^{68}$Ni does not behave as would be expected for a magic nucleus. Besides these mass measurements, also large scale shell model calculations point out $^{68}$Ni is no magic nucleus. Due to the parity change in the pf and dg orbitals, $^{68}$Ni mimics typical features of doubly-magic nuclei. To gain more insight in the nature of the internal states of $^{68}$Ni a transfer reaction experiment was performed at the REX-ISOLDE facility in CERN. A radioactive beam of $^{66}$Ni produced at the ISOLDE facility impinges on a target containing $^{3}$H. The reaction channels of interest are $^{67}$Ni + $^{2}$H (Q = $-$0.45 MeV) and $^{68}$Ni + $^{1}$H (Q = 5.12 MeV). The latter offers a means to directly populate excited states of $^{68}$Ni. This way the energy of the nuclear states can be determined. Moreover from conservation of spin and parity in the reaction the possible spin and parity configurations of the energy levels can be deduced from the angular distribution of the emitted protons. The angular distribution is intimately related to the transferred angular momentum. In this thesis the $^{67}$Ni + $^{2}$H partition has been analysed. This reaction provides insight in the low energy structure of $^{67}$Ni. In addition, the structure of this nucleus offers a means to study the magic character of $^{68}$Ni. One nucleon transfer reactions are excellent probes for the single-particle character of nuclei. In these studies the differential cross section as function of the angle is of ample importance. The experimental differential cross section can be compared to theoretical DWBA calculations from which spectroscopic factors can be deduced. The spectroscopic factor represents how well the populated state in $^{67}$Ni correspond to $^{66}$Ni plus a neutron in a particular shell model orbital. Nuclei which differ from doubly-magic nuclei are very well described by the independent single-particle model. In this perspective the single-particle character of 67Ni is an indirect probe of the magicity of $^{68}$Ni. The experiment has been performed at the ISOLDE facility at CERN, this facility is dedicated to the study of exotic nuclei. A large variety of exotic radioactive beams can be produced. At the REX-ISOLDE beamline a beam of $^{66}$Ni is shaped, pulsed an postaccelerated to 2.6 MeV/A. This energy is needed to penetrate through the Coulomb barrier and induce transfer reactions through the strong, short-ranged nuclear force. The detection system is equipped with the T-REX and Miniball setup. T-REX is an array of silicon strip detectors to detect charged particles. The detectors are placed inside the target chamber both in forward and backward direction from the target and cover about 66% of the total solid angle. This wide detection range is necessary in transfer experiments in inverse kinematics. The silicon detectors are segmented such that the angular distribution can be reconstructed. Furthermore the detectors have a telescope configuration which allows to identify protons, deuterons, tritons and other light charged particles. The identifications is based on the position in $\Delta$E-E plots. This way one can discriminate different reaction channels in the experiment. Besides the T-REX array there is the Miniball setup, Miniball is an array of eight clusters of three six-fold segmented HPGe detectors. The germanium detectors are placed outside the target chamber and surround the target, the total detection effciency of a 1 MeV $\gamma$ ray is about 6%. The detectors are used to detect $\gamma$ rays from the decay of $^{67}$Ni and $^{68}$Ni. These nuclei move through the target chamber with high velocities of about 0.07$c$. Consequently it is necessary to Doppler correct the $\gamma$ spectrum to increase the energy resolution. The data analysis in this thesis focuses on the $^{67}$Ni + $^{2}$H partition. By means of d-$\gamma$ and d-$\gamma$-$\gamma$ coincidence gates the decay of $^{67}$Ni is investigated. Low energy states of $^{67}$Ni could be identified. From the energy of the deuterons it can be seen that excited states up to 3.6 MeV are populated. The observations are in agreement with the literature [Jea05] and the proposed level scheme based on the $^{66}$Ni(d,p)$^{67}$Ni reaction [Dir13]. The angular distribution of the ground state and three low excited states has been reconstructed. From the elastic channel $^{66}$Ni(t,t)$^{66}$Ni the normalization factor and average beam intensity has been calculated, i.e. 2.5(3) 10$^6$ pps. The differential cross section has been compared to DWBA calculations performed with Fresco [Tho88]. The experimental data on the (t,d) reaction is limited to high CM angles. At these angles, far from the position of the first maximum, it is impossible to determine the transferred angular momentum. Consequently no spin and parity assignments are done and no spectroscopic factors could be deduced. This thesis consists of five chapters. In the first chapter the motivation for this experiment is described. In the second chapter the experimental setup at ISOLDE and the detection setup are presented. The third chapter gives an introduction to scattering theory and reaction theory with a focus on transfer reactions. In the fourth chapter the data analysis is described and the obtained results are presented. In the last chapter the conclusions of this experiment are given.