SPECTROSCOPY OF NEUTRON{RICH OXYGEN AND FLUORINE NUCLEI VIA SINGLE{NEUTRON KNOCKOUT REACTIONS by Ben Pietras A THESIS Submitted to the University of Liverpool in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 2009 Contents Acknowledgements xii Abstract xiv 1 Introduction 1 1.1 The Nucleus . 1 1.2 The Magic Numbers and Shell Structure . 3 1.3 The Nuclear Shell Model . 3 1.3.1 The Woods Saxon Potential . 4 1.3.2 The Spin{Orbit Interaction . 5 1.4 Evolution of Shell Structure far from Stability . 8 1.4.1 Nuclear Density Profiles . 8 1.4.2 Halo Nuclei . 9 1.4.3 Evolution of Shell Gaps . 10 1.5 New Magic Numbers at N = 14, 16 . 12 1.5.1 Experimental Evidence . 12 1.5.2 The Tensor Force . 15 ii 1.6 Single{Neutron Removal Reactions . 18 1.6.1 Longitudinal Momentum Distributions . 20 1.6.2 Adiabatic Approximation . 23 1.6.3 Serber Reaction Model . 24 1.6.4 Eikonal Theory . 26 2 Experimental Method 33 2.1 Radioactive Ion Beam Production . 33 2.1.1 Primary Beam Production . 34 2.1.2 Projectile Fragmentation . 35 2.1.3 Fragment Separation . 35 2.2 Experimental Detection Setup . 37 2.2.1 Overview of Experimental Setup . 37 2.2.2 The SPEG Spectrometer . 39 2.3 Direct Beam and Fragment Identification . 44 2.3.1 Identification Gates . 46 2.3.2 The Hybrid γ{ray Array . 49 2.3.3 EXOGAM . 50 2.3.4 The NaI Array . 53 2.4 γ{ray Array Calibration . 54 2.4.1 EXOGAM . 54 2.4.2 NaI Array . 57 2.5 SPEG Calibrations . 58 iii 2.6 Drift Chambers . 64 2.7 Ionisation Chamber . 67 2.8 Data Acquisition Trigger . 71 3 Analysis 76 3.1 Target Thickness . 76 3.2 Doppler Shift and Broadening Correction . 77 3.2.1 Lorentz factor calculation . 77 3.2.2 Theta Calculation . 79 3.3 Inclusive Cross Sections . 82 3.4 Exclusive Cross Sections . 87 3.5 Inclusive Momentum Distributions . 91 3.6 Exclusive Momentum Distributions . 92 3.7 Eikonal Calculations . 95 3.7.1 Exclusive Cross Sections . 95 3.7.2 Experimental Spectroscopic factors . 99 3.7.3 Exclusive Momentum Distributions . 99 3.7.3.1 Transformation of Theoretical LMDs . 101 3.7.3.2 Convolution of Theoretical LMDs . 101 3.7.4 Interactions and Model Spaces . 104 4 Results and Discussion 106 4.1 Inclusive One-Neutron Removal Cross Sections . 107 4.2 23O!22O ................................. 108 iv 4.2.1 Discussion . 108 4.2.2 Inclusive One-Neutron Removal Cross Sections . 109 4.2.3 Longitudinal Momentum Distributions . 113 4.3 24F!23F.................................. 115 4.3.1 Discussion . 115 4.3.2 γγ Coincidences . 117 4.3.3 Exclusive One{Neutron Removal Cross Sections and Spectroscopic Factors . 125 4.3.4 Longitudinal Momentum Distributions . 127 4.4 25F!24F.................................. 133 4.4.1 Discussion . 133 4.4.2 Exclusive One-Neutron Removal Cross Sections . 137 4.4.3 Longitudinal Momentum Distributions . 137 4.4.4 Experimental Spectroscopic Factors . 142 4.5 26F!25F.................................. 144 4.5.1 Discussion . 144 4.5.2 Longitudinal Momentum Distributions . 148 Summary 150 References 152 v List of Figures 1.1 The Chart of Nuclides . 2 1.2 The Nuclear Shell Model . 7 1.3 Hartree{Fock calculated neutron and proton density profiles. 8 1.4 Evolution of Shell Gaps. 11 1.5 The effect of Isospin on the Neutron Separation Energy. 13 + 1.6 Evolution of 21 energy in light even{even nuclei. 14 1.7 Neutron effective single particle energies. 15 1.8 Schematics illustrating the tensor interaction. 16 1.9 Neutron effective single{particle energies for 30Si and 24O. 17 1.10 Single{nucleon removal reaction schematic. 19 1.11 Core Fragment Inclusive Longitudinal Momentum Distributions. 21 1.12 Core fragment 25Ne LMD . 22 1.13 Three{body system. 23 1.14 Serber model. 24 1.15 Effect of valence neutron's angular momentum orientation on cross section. 25 vi 1.16 28Mg core fragment Theoretical Longitudinal Momentum Distributions. 26 1.17 One{dimensional Eikonal case. 28 1.18 Nucleon travelling through finite range potential of the target. 28 1.19 Core and valence neutron S{matrices for 26F projectile. 30 2.1 General layout of GANIL, indicating the location of SISSI. 36 2.2 Experimental setup, from secondary beam production to SPEG. 38 2.3 SPEG High{Resolution Mass Spectrometer. 39 2.4 Optics of SPEG. 44 2.5 ∆E vs. E for all ions. 46 2.6 ∆E vs. E for the Fluorine and Oxygen isotopes. 47 2.7 Xf vs. TOF for the Fluorine and Oxygen isotopes. 47 2.8 ∆E vs. Xf for the Fluorine and Oxygen isotopes. 48 2.9 Hybrid γ{ray Array. 49 2.10 One EXOGAM Clover, comprising four segmented coaxial detectors. 50 2.11 Simulated Energy Resolution for EXOGAM. 52 2.12 Schematic of Sodium Iodide detectors. 53 2.13 EXOGAM energy Calibration. 55 2.14 Efficiency vs. Energy for the entire EXOGAM array. 56 2.15 NaI fitting technique for 60Co. 57 2.16 Energy vs Efficiency for the total NaI array. 58 2.17 SPEG focal plane schematic. 59 2.18 Calibration Mask. 61 vii 2.19 Bρref scan with mask. 62 2.20 Bρ scan across SPEG focal plane. 63 2.21 Dispersion calibration. 64 2.22 SPEG Drift Chambers. 66 2.23 Drift chamber TDC calibration. 67 2.24 Ionisation chamber TOF correction. 68 2.25 Ionisation gas pressure correction. 70 2.26 Gas pressure correction effect. 71 2.27 Circuit Diagram of Germanium link to GMT. 73 2.28 Representation of the timing signals used. 74 2.29 Circuit diagram of the Ganil Master Trigger. 75 3.1 The effect of energy loss through half the 12C target. 79 3.2 EXOGAM clover face. 80 3.3 Example of Doppler{correction and Add-back effects. 82 3.4 Incident beam rate, Fluorine. 83 3.5 Incident Beam Rate Scaled Down to Reaction Fragment Rate. 84 3.6 24F Scaledown factors from LDCX1. 85 3.7 24F Scaledown factors from Trifoil. 86 3.8 Forward EXOGAM Array Ratio. 88 3.9 Backward EXOGAM Array Ratio. 88 3.10 Isotropic Forward EXOGAM Array Efficiency. 89 3.11 Isotropic Backward EXOGAM Array Efficiency. 89 viii 3.12 Background Subtraction schematic. 93 3.13 Example of LMD background subtraction. 94 3.14 Dependence of σsp on RMS radius. 97 3.15 Contributions of stripping (nucleon absorbed) and diffraction (nucleon dissociated) mechanisms to the single{particle cross section. 98 3.16 Eikonal distribution for the 24F fragment. 100 3.17 Transformation from centre{of{mass frame to laboratory frame. 102 3.18 Direct{beam{through{target longitudinal momentum distributions. 103 3.19 Convolution of Fragment Theoretical LMDs with the Projectile DBTT LMD. 104 4.1 Level scheme of 22O. 110 4.2 22O γ spectra. 111 4.3 22O Inclusive LMD from this experiment. 114 4.4 22O Inc. LMD taken from [35]. 114 4.5 Comparison of 22O and 23F state energies. 115 4.6 23F γ spectra. 116 4.7 EXOGAM γγ coincidences for 23F..