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Title: Probing positive-parity states in 67Ni through one-neutron transfer reactions
Other Titles: Onderzoek naar positieve pariteitstoestanden in 67Ni door middel van één-neutron transfer reacties
Authors: Diriken, Jan
Issue Date: 1-Jul-2013
Abstract: The limited accuracy to which the structure of atomic nuclei can be described and the vast differences in the predicted properties of atomic nuclei far away from the valley of stability are key problems in nuclear physics. Not only the properties of the strong interaction within the nuclear medium are not entirely understood, but also the large number of degrees of freedom associated with this many-body problem do not allow current computers to obtain trustworthy results. By starting from different perspectives, a variety of models has been developed: mean-field calculations incorporating additional correlations, models based on symmetry arguments, shell-model calculations including particle-hole excitations through closed shells and quantum monte-carlo shell-model calculations as to give a few examples. It is of paramount importance to verify these models by comparing their predictions with experimental data. Such comparisons allow the optimization of the models and subsequently improve their predictive capabilities and give new insight in the properties of the strong interaction.The development of energetic radioactive beams provided access to a vast set of new experimental methods which can be used to test the predictions of current state-of-art nuclear models. Besides radioactive decay studies on systems with extreme proton-to-neutron ratios, it is now also possible to perform Coulomb excitation measurements and transfer reactions on these exotic nuclei. These developments allow the nucleus to be studied from different perspectives and explore specific regions of the chart of nuclei as to investigate their distinct properties.The neutron-rich nuclei in the vicinity of the Z=28 closed shell form an interesting region for nuclear structure studies. On one hand this region was used to uncover the importance of specific components of the residual interaction between nucleons, both theoretically and experimentally, while on the other hand it offers crucial information to predict the structure of the double-magic nucleus 78Ni. This nucleus is seen as the corner stone for nuclear structure studies with very exotic proton-to-neutron ratios as well as for astrophysical scenarios. We employed the 66Ni(d,p) reaction to measure the energy position of the neutron orbitals near 68Ni. The energy position of these orbitals near 68Ni can be experimentally obtained. The positions of these orbitals and more specifically the size of the N=50 shell closure are assumed to have a big influence on the structure in the neighborhood of 68Ni and the swift onset of deformation found in the chromium and iron isotopes.The experimental campaign took place at the REX-ISOLDE post-accelerator (CERN Geneva, Switzerland), using the Miniball gamma detector coupled with the T-REX particle detector. By post-accelerating the unstable 66Ni (T1/2 = 54.6 h) isotopes and inducing one-neutron transfer reactions, it was possible to investigate the distribution of the neutron single-particle strength in 67Ni, a direct neighbor of 68Ni. Measuring the angular distribution of the ejectile that remains after the reaction, leads to important information concerning the spin and parity of the populated states, as well as the importance of the one-neutron configuration. In this experiment the (d,p) one-neutron transfer reaction was used (Q value = 3.58 MeV).The experimental set-up for these transfer reaction studies was developed in close collaboration with TU Munich and consists of the coupling between position-sensitive, segmented gamma (Miniball) and particle (T-REX) detectors. The presence of a 1007-keV isomer (T1/2 = 13.3 μs) in 67Ni has led to the development of a delayed coincidence (or isomer tagging) technique. Two meters downstream from the reaction chamber the beam was stopped and monitored using a dedicated germanium detector to detect the delayed transitions.The relatively high beam intensity (4.2 E+6 particles per second) and high level of purity (>99%) delivered a vast amount of data. Gamma radiation up to an energy of 5800 keV was detected and the limited knowledge of the 67Ni level scheme could be significantly improved using the available gamma-gamma coincidence data. In total 17 new excited states were identified, on top of the three known states before this experiment.A good knowledge of both the level and gamma-decay scheme of 67Ni was crucial to extract the proton angular distributions. The energy resolution was in fact insufficient to disentangle the individual excited states populated in the reaction and extract the proton angular distributions based on proton kinematics alone. Hence it was necessary to use the observed proton-gamma coincidences, based on the improved level and decay scheme, to obtain the experimental angular distributions.Proton angular distributions could be determined for seven states in total, incuding the ground state. The 1007-keV 9/2+ state was chosen as reference to determine relative spectroscopic factors (measure for the single-particle purity of a given state). The measured proton angular distributions were compared with DWBA calculations obtained using FRESCO, as to determine the spin and parity of these states. Th proton angular distributions depend on the orbital angular momentum rather than the total spin. However, by also using information from the known gamma decay, the spin and parity of most identified states could be firmly fixed.The proposed spin and parity of 1/2- of the ground state was confirmed, as well as the 9/2+ spin and parity of the isomer at 1007 keV. The small transfer cross section towards the state at 694 keV does not allow the firm determination of both the spin and parity of this state. However, assuming a 5/2- spin and parity based on information from previous experiments, a relative spectroscopic factor for this state was calculated.Besides these negative-parity states, two states at higher excitation energies were characterized with an orbital angular momentum of 2 (hence d orbitals). Based on the characteristic gamma decay of these states, a spin and parity of 5/2+ wasdetermined. The sum of the relative spectroscopic factors of these two 5/2+ states equals 0.5, meaning that 50% of the available νd5/2 single-particle strength (relative to the 9/2+ state at 1007 keV) is contained in these two low-lying 5/2+ states. Systematics of relative spectroscopic factors in the lighter nickel isotopes show that the total νd5/2 single-particle strength contained in the two lowest-lying 5/2+ states gradually increases with the mass of the isotope, reaching a maximum in 67Ni.Based on these measurements the size of the N=50 shell gap was estimated to be 2.6 MeV, which does not, within the limitations of the present data, differ from the constant N=50 shell gap size of 2.6 MeV determined in the lighter nickel isotopes. The results are also compared to the positions of the proton orbitals near 90Zr (Z=40, N=50), a nucleus which can be seen as a mirror nucleus of 68Ni. Despite the fact there is good agreement for both the relative spectroscopic factors and energy of the negative-parity states, clear differences can be noted concerning the distribution of the positive-parity single-particle strength. This is due to a more pronounced Z=50 shell closure (3.9 MeV) compared to the N=50 shell closure (2.6 MeV) near 68Ni.
Table of Contents: Preface
Nederlandstalige samenvatting
Abbreviations
List of Symbols
Contents
List of Figures
List of Tables
1 Structure of Atomic Nuclei
1.1 The atomic nucleus
1.2 The nuclear shell model
1.2.1 The effect of nuclear shells
1.2.2 Calculations in the shell model
1.2.3 Pairing interaction
1.2.4 Evolution of single-particle energies in exotic nuclei
1.2.5 Quadrupole collectivity
1.3 The region around 68Ni
1.3.1 Systematics in the nickel isotopes (Z = 28)
1.3.2 Development of collectivity below Z = 28
1.4 Objectives and motivation
2 Reaction Theory
2.1 Nuclear reactions
2.1.1 Conservation laws
2.1.2 Types of nuclear reactions
2.1.3 Time and energy scales
2.2 Kinematics of nuclear reactions
2.2.1 Direct versus inverse kinematics
2.3 Information from direct nuclear reactions
2.3.1 Differential cross sections
2.3.2 Spectroscopic factors
2.4 Scattering theory
2.4.1 General approach
2.4.2 Partial wave expansion
2.4.3 Multi-channel scattering
2.4.4 Coupled equations
2.4.5 Integral form
2.4.6 Born approximation
2.4.7 Reaction mechanisms
2.4.8 Scattering amplitudes in transfer reactions
2.4.9 Higher-order reactions
2.4.10 Deuteron breakup and nonlocality
2.4.11 Classical view of the angular distributions
2.4.12 Spectroscopic factors and ANC’s
2.5 Calculations for 66Ni(d,p)67Ni
2.5.1 Angular momentum transfer sensitivity
2.5.2 Q value dependence
2.5.3 Beam-energy dependence
2.5.4 Optical-model parameters dependence
2.5.5 Effect of SO coupling
3 Experimental Setup
3.1 Beam production
3.1.1 RILIS
3.1.2 Mass selection
3.1.3 REX-ISOLDE
3.1.4 Beam time structure
3.2 Detection arrays
3.2.1 Reaction chamber
3.2.2 T-REX Particle detectors
3.2.3 Miniball detectors
3.2.4 Delayed coincidence tagging setup
3.3 Data acquisition & structure
3.4 Software analysis procedure
3.4.1 Event building
3.4.2 Calibration
3.4.3 Kinematical reconstruction
4 Paper I (Physical Review Letters)
5 Paper II: Physical Review C
6 Analysis
6.1 Level scheme
6.2 Delayed coincidence analysis
6.3 Feeding pattern
6.4 Angular distributions
6.4.1 Extraction from experimental data
6.4.2 Normalization
6.4.3 Target purity
6.4.4 DWBA calculations
7 Results
8 Discussion
8.1 Systematics in odd-A nickel isotopes
8.2 Positive parity states in 67Ni
8.3 Estimated size of the N = 50 shell gap
8.4 Comparison with 90Zr region (Z = 40,N = 50)
9 Conclusion
A Various spectra
B Cross section tables
Bibliography
Curriculum Vitae
List of Publications
ISBN: 978-90-8649-632-7
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Nuclear and Radiation Physics Section

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