IMPROVING THE ENERGY AND TIME RESOLUTION OF THE DRAGON ARRAY by William W. Huang B.Sc. Physics, University of British Columbia, 2016 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICS UNIVERSITY OF NORTHERN BRITISH COLUMBIA December 2022 © William W. Huang, 2022 Abstract DRAGON seeks to replace its BGO detectors with LaBr3:Ce detectors. The Geant4 simu¬ lation estimates gamma ray capture efficiency values of 3.384±0.011% and 1.113±0.007% for the BGO detector and the LaBi'3:Ce detector respectively for 0.6617 MeV gamma rays at 5 cm distance. The latter achieves an experimental efficiency of 1.102±0.042% and an experimental energy resolution of 3.282±0.021% for these gamma rays. The experimental and simulated LaBr3:Ce detector efficiency results agree within error. However, the simula¬ tion may overestimate the detector efficiency at high gamma ray energies, as observed at 4.44 MeV and 6.131 MeV. Furthermore, the timing method is performed to utilize its high time resolution. The average resonance energy is 0.47428±0.00359 MeV/u which agrees with the true value of 0.475 MeV/u. Therefore, the energy and time resolution of the LaBr3:Ce detec¬ tor improve DRAGON’s ability to study radiative capture reactions, with its lower efficiency being its only drawback. ii Contents Abstract ii Contents iii List of Tables vii List of Figures xiii Glossary xxiii Acknowledgements xxvi 1 Introduction 1 1.1 Big Bang Nucleosynthesis 2 1.2 Stellar Nucleosynthesis 2 1.2.1 The Proton-Proton Chain 2 1.2.2 The CNO Cycle 5 iii 1.3 Stellar Evolution 8 1.4 Here Enters the DRAGON 10 11 2 Detector Spectroscopy 2.1 The Photoelectric Effect 12 2.2 Compton Scattering 13 2.3 Pair Production 16 2.4 Gamma Ray Attenuation 18 2.5 The Detector Design 20 2.6 Energy Resolution 29 2.7 Detector Timing Considerations 33 2.8 B GO and LaB^Ce Detector Comparison 34 3 DRAGON 38 3.1 ISAC-I 39 3.2 The Gas Target 41 3.3 The Gamma Detector Array 45 3.4 The Electromagnetic Separator 48 3.5 Double Sided Silicon Strip Detector (DSSSD) 51 3.5.1 The Band Theory of Solids 52 3.5.2 The Pn-Junction 56 iv 3.5.3 The Pn-Junction as a Radiation Detector 58 Summary 61 4 Detector Measurements 62 3.6 4.1 4.2 Simulation Methodology 63 4.1.1 Single Detector Configuration 64 Single LaBr3:Ce Detector Simulation Results 67 4.2.1 “Na 67 4.2.2 60Co 68 4.2.3 137Cs 68 4.2.4 241Am9Be 69 4.2.5 244Cm13C 70 4.2.6 Simulated B GO and LaB^Ce Efficiency Comparison 70 4.3 Other Simulation Errors 73 4.4 Experimental LaBr^Ce Detector Configuration 74 4.4.1 Experimental LaB^Ce Efficiency Analysis 75 4.4.2 22Na 78 4.4.3 60Co 79 4.4.4 137Cs 80 4.4.5 Experimental LaB^Ce Efficiency Data Summary 81 v 4.5 Experimental LaBi‘3:Ce Energy Resolution 82 4.6 Experimental and Simulated Data Comparison 83 4.7 Other Experimental Errors 87 5 The Timing Method 5.1 88 88 Introduction 5.2 Timing Methodology and Results 91 Other Experimental Timing Errors 105 5.3 Conclusion 106 A Data Tables 109 B Gaussian Fitting Program Usage 120 C Geant4 Simulation Usage 127 D References 135 6 vi List of Tables 1.1 The hot CNO cycle reactions 7 1.2 The break out reactions 7 2.1 The properties of the Hamamatsu RI 828-01 model at 25°C 26 2.2 The properties of the ETL 9214B model around room temperature 26 2.3 The properties of the Hamamatsu R2083 model at 25°C 29 2.4 The physical properties of the BGO and LaBr3:Ce crystals 35 3.1 The forward and reverse kinematics of 14N(p, y)15O and 27 Al(y>, y)28Si. ... 48 3.2 The properties of the magnetic dipoles 51 3.3 The properties of the electrostatic dipoles 51 4.1 The external radioactive sources and their gamma ray energies 64 4.2 The simulated efficiency values for the BGO detector and the LaBr3:Ce detector. 71 4.3 The half-lives and branching ratios of the radioactive sources vii 77 4.4 The measured efficiency values for the LaBi'3:Ce detector 81 4.5 The measured energy resolution values for the LaBr3:Ce detector 83 5.1 The values that are used for the calibration run are listed here 98 5.2 The Eout values for the different pressure values are listed here 98 Al The LaBr3:Ce detector’s component materials and positions for the single de¬ tector simulations are provided here. A vacuum is enclosed within the pho¬ tomultiplier tube. These positions are measured relative to the origin which is at the centre of the detector. The photocathode component is inside of the photomultiplier tube, and it is just behind the optical window A2 109 The LaBi’3:Ce detector’s component dimensions for the single detector simu¬ lations are provided here. The photomultiplier tube thickness on its ends allow the photocathode to be inserted on its front end. These values were obtained from the schematic diagrams of the single LaBr3:Ce detector. The photocath¬ ode component is inside of the photomultiplier tube, and it is just behind the 110 optical window A3 The BGO detector’s component materials and positions for the single detec¬ tor simulations are provided here. The positions are measured relative to the origin which is at the centre of the detector. The photocathode is part of the photomultiplier tube, and it is just behind the scintillator crystal viii Ill A4 The DRAGON array’s BGO detector component dimensions that are also used for the single detector simulations are provided here. The materials that are listed in Table A3 are used for the detectors in the hexagonal array. The pho¬ tomultiplier tube thickness on its ends allow the photocathode to be inserted on its front end. The photocathode is part of the photomultiplier tube, and it is just behind the scintillator crystal. The radii refer to the radii of the incircles that would be formed within the hexagonal components. These values were derived from the detector component dimensions in Geant3. Credit is given to Lorenzo Principe and Dario Gigliotti for providing these dimensions A5 112 The dimensions of the gas target box and its components for the simulations are provided here. The trapezoid wall thickness where the entrance and exit holes are placed is given. The trapezoid collimator thickness has been rounded to 3 decimal places A6 113 The positions of the gas target box and its components are provided here with 3 or 4 decimal places. These positions are measured relative to the origin in Figure 3.5 113 ix Al The positions of the left-hand array BGO detectors and their corresponding scintillators in the DRAGON array are provided here. These positions are measured relative to the origin. Detector #1, #2, #8, and #10 straddle the array. Detector #3, #4, #5, #6, #7, and #9 form the crown of the array. The other detectors are on the right-hand positions of the array. Credit is given to Lorenzo Principe for providing the Geant3 scintillator positions A8 114 The positions of the right-hand array BGO detectors and their correspond¬ ing scintillators in the DRAGON array are provided here. These positions are measured relative to the origin. Credit is given to Lorenzo Principe for providing the Geant3 scintillator positions A9 115 The approximate source activities during the experiments along with their cor¬ responding activity uncertainties are provided here. These uncertainties are reported by the manufacturers as percentages of the source activities. The cor¬ responding branching ratio for each gamma decay is shown. The source activ¬ ities have been rounded to 5 decimal places to approximately give the numbers that were actually used to calculate the efficiency values of the LaBr3:Ce de¬ 115 tector x A10 The run time and the number of gates that are produced during each run are provided here. The run time is divided by the internal radiation run time to calculate the "Normalization Factor", where 9 decimal places are given. The counts on the internal radiation spectrum is multiplied by this factor when it is added to a given spectrum to subtract the internal radiation of the 138La 116 isotope from the spectrum All The centroid time stamps that are shown by the LaBi‘3:Ce detectors are given as TDCl&. Likewise, their uncertainties are given as 8TDC^\ 117 A12 The individual delay constants D are given for each LaB^Ce detector. They have been rounded to 5 decimal places 117 Al 3 The Eresc and Zresc values are given along with their uncertainties 8Eresc and 8Zresc 118 A14 The Eresm and Zresm values are given along with their uncertainties 8Eresm and 8Zresm for Detector 0 118 A15 The Eresm and Zresm values are given along with their uncertainties 8Eresm and 8Zresm for Detector 1 118 Al 6 The Eresm and Zresm values are given along with their uncertainties 8Eresm and 8Zresm for Detector 2 118 A17 The Eresm and Zresm values are given along with their uncertainties 8Eresm and 8Zresm for Detector 3 119 xi Al 8 The Eresm and Zresm values are given along with their uncertainties 8Eresm and dZresm for Detector 4 119 xii List of Figures 1.1 The CNO cycles are shown along with additional reaction pathways where broken lines show pathways that lead to the break out reactions 1 .2 6 The central star temperature Tc and central star density pc are listed below each element burning stage. When the element has been consumed in the cen¬ tre, the elements that have been produced form peripheral shells of the star. The downward arrows represent the gravitational contraction of the star be¬ tween stages. The elements that are produced by each stage are shown beside them. When the star explodes as a supernova, the material that is released is the supernova (SN) remnant, and the supernova core leaves behind a residue. 2.1 9 The energy spectrum for mono-energetic gamma rays is shown, assuming that all of them interact with the detector by the photoelectric effect, and this de¬ tector can detect the gamma ray energy perfectly. The number of counts N is being measured with respect to the incident gamma ray energy E xiii 13 2.2 The schematic diagram for Compton scattering is shown. The gamma ray scatters at angle 0 and the electron recoils at angle 0 2.3 14 The energy spectrum for mono-energetic gamma rays is shown, assuming that all of them interact with the detector by the photoelectric effect and Compton scattering. The two extreme cases for 0 are shown, where 0 ~0° corresponds to no energy transfer to the recoil electron, and 0 ~ 180° corresponds to the maximum energy transfer to the recoil electron. This detector is also assumed to detect the gamma ray energy perfectly 2.4 15 The energy spectrum for mono-energetic gamma rays is shown, assuming that all of them interact with the detector through pair production. This detector is also assumed to detect the gamma ray energy perfectly 2.5 17 The regions where the photoelectric effect, Compton scattering, and pair pro¬ duction are most likely to occur are shown. On the curve where a = T, the photoelectric effect and Compton scattering are equally likely to occur. Like¬ wise, on the curve where <7 = K, Compton scattering and pair production are 19 equally likely to occur 2.6 The energy structure of an inorganic scintillator crystal with and without acti¬ vators is shown. GS stands for ground state xiv 22 2.7 The decay scheme of 138La is shown, where it has a 65.5% probability of undergoing electron capture to an excited state of 138Ba which relaxes by re¬ leasing a 1435.8 keV gamma ray. Alternatively, 138La has a 34.5% probability of undergoing jS-minus decay to 138Ce which relaxes by releasing a 788.7 keV gamma ray. The total angular momentum of each state is given as well as the half-life and the parity 23 2.8 A schematic diagram of a detector is shown 24 2.9 The DRAGON BGO detector is shown. This diagram has not been drawn to 28 scale 2.10 The LaBn :Ce detector is shown with the scintillator radius and the aluminium case radius, where the aluminium case covers the scintillator. This diagram has been approximately drawn to scale 29 2.11 A plot of gamma ray energies versus counts shows the concept of energy res¬ olution. Po is the position of the pulse peak. The peak position corresponds to the energy value of the peak channel. The standard deviation a = The energy resolution Er = ^ 2y2/n(2) = 100(FWHM/Po) 31 2.1 2 The energy spectrum for monoenergetic gamma rays which includes the main types of gamma ray interactions is shown. The number of counts N is being measured with respect to the incident gamma ray energy E xv 32 2.13 The 0.662 MeV timing spectrum for the LaB^Ce detector is shown, where the fit function takes into account both the fast and slow decay components. The signal has been normalized so 1 corresponds to the peak value, and the pulse intensity is plotted with respect to the time elapsed in nanoseconds. . . 34 3.1 A section of the ISAC-I accelerators is shown 39 3.2 This figure shows how to study the radiative capture of a proton by 21Na in reverse kinematics in which an accelerated radioactive 21Na beam bombards a proton gas target. A gamma ray and a 22Mg recoil are produced 41 3.3 The major components of the gas target box and the beam direction are shown. 44 3.4 The radioactive beam enters the gas target box and interacts with the gas within the trapezoidal cell. The residual beam and the recoils exit the gas target box. The gamma rays (y) are detected by the BGO detector array. ... 3.5 45 The left side shows the BGO array surrounding the gas target box. The lead shielding surrounds the side of the gas target box where the beam enters it. The detectors are numbered based on their positions. The right side shows a simulation of the gas target box and its components. The beam is propagated along the region that is marked by the purple lines. Gamma rays ( y) and recoils are emitted upon nuclear reactions between the beam and the gas xvi 47 3.6 (a) The left-hand side of the DRAGON array is shown along with the crown detectors and the straddling detectors, (b) The right-hand side of the DRAGON 47 array is shown 3.7 The actions of the first stage dipoles without the quadrupoles are shown. B is 50 coming out of the page 3.8 (a) The general energy structure of a solid, (b) A solid at 0 K. (c) The same solid in (b) at a higher temperature 53 The atomic structure of a doped semiconductor is shown 54 3.10 (a) and (b) Conductor, (c) Insulator, (d) Semiconductor 54 3.9 3.11 The band structure for (a) a p-type semiconductor, and (b) a n-type semicon¬ 56 ductor is shown 3.12 The pn-junction is shown with no bias at the left, forward biased in the middle, 58 and reverse biased at the right 3.13 The Double Sided Silicon Strip Detector is shown with its n-side and p-side. . 60 3.14 The three-dimensional illustration for DRAGON is shown. This diagram has 61 not been drawn to scale 4.1 The simulation arrangement is shown where the source emits 10 gamma rays at a distance 5 cm away from the detector face. The blue oval represents the origin where z = 0. This diagram has been approximately drawn to scale. ... xvii 66 4.2 The simulated Sodium-22 spectrum is shown 67 4.3 The simulated Cobalt-60 spectrum is shown 68 4.4 The simulated Cesium-137 spectrum is shown 68 4.5 (a) The simulated Americium-BeryIlium (AmBe) spectrum is shown, where a single escape peak and a double escape peak are evident, (b) A close-up view of the full energy peak split into two channels is shown, where the histogram has been divided into 10,000 channels. The sum of the two peak counts is used to determine the photopeak efficiency in which 549 entries are shown here. 69 4.6 The simulated Curium-Carbon (CmC) spectrum is shown, where a single es¬ cape peak and a double escape peak form 4.7 The simulated BGO and LaBr3:Ce detector efficiency values are compared at a source-to-detector distance of 5 cm 4.8 72 The simulated BGO and LaBr3:Ce detector efficiency values are compared at a source-to-detector distance of 10 cm 4.9 70 72 The simulated BGO and LaBi‘3:Ce detector efficiency values are compared at a source-to-detector distance of 20 cm 73 4.10 The circuit diagram for the LaBr3:Ce detector is shown. The signals from the detector are paired with gates so they can be accepted by the ADC 75 4.11 The experimental 0.511 MeV spectrum is shown. The Compton scattering counts form a small plateau over the background to the left of this photopeak. xviii 78 4.12 The experimental 1.27 MeV spectrum is shown. The Compton scattering counts form a small plateau over the background to the left of this photopeak. 79 4.13 The experimental 1.17 MeV spectrum is shown 79 4.14 The experimental 1.33 MeV spectrum is shown 80 4.15 The experimental 0.6617 MeV spectrum is shown 80 4.16 The experimental and simulated efficiency values for the LaBi yCe detector are compared at a source-to-detector distance of 5 cm 84 4.17 The experimental and simulated efficiency values for the LaBrs:Ce detector are compared at a source-to-detector distance of 10 cm 85 4.18 (a) The simulated BGO detector efficiency values are compared to previously obtained experimental values at a source-to-detector distance of 10 cm for the 60Co and 137Cs sources, (b) The simulated BGO detector efficiency values are compared to previously obtained experimental values at a source-to-detector distance of 10 cm for the 241Am9Be and 244Cm13C sources 85 4.19 The experimental and simulated efficiency values for the LaB^Ce detector are compared at a source-to-detector distance of 20 cm 5.1 86 The experimental set up for the plastic detector is shown, where the detector is placed perpendicular to the z-axis. The green arrow represents the beam and recoils. This diagram has not been drawn to scale xix 90 5.2 The relationship between the beam energy EBeam and Z is shown along with their uncertainties as shaded regions. The uncertainties have not been drawn 91 to scale 5.3 (a) The detector arrangement for the timing experiments is shown, where the detectors are behind the outline of the gas target box. The gamma rays (y) are being released by the radiative capture reactions between the beam and the gas contained within the trapezoidal cell, (b) The side view for this arrangement is shown. These diagrams have not been drawn to scale 5.4 92 (a) The timing centroid data can be clearly modelled by a Gaussian function in red. (b) The timing centroid data can be modelled by a Gaussian function in red for the outlier. However, the fit is poor 5.5 These timing data could be modelled by a Gaussian function but it would not be accurate due to the low count statistics 5.6 97 97 (a) The measured values for the Z positions and the calculated values are shown for Detector 0. (b) The measured values for the Z positions and the calculated values are shown for Detector 1 5.7 102 (a) The measured values for the Z positions and the calculated values are shown for Detector 2. (b) The measured values for the Z positions and the calculated values are shown for Detector 3 where a significant disagreement is shown at 2.3 Torr 102 xx 5.8 The measured values for the Z positions and the calculated values are shown for Detector 4 where they significantly disagree 5.9 103 (a) The measured resonance energies and the calculated values are shown for Detector 0. (b) The measured resonance energies and the calculated values are shown for Detector 1 103 5.10 (a) The measured resonance energies and the calculated values are shown for Detector 2. (b) The measured resonance energies and the calculated values are shown for Detector 3 104 5.11 The Zresm values cause the Eresm values to be below the true resonance energy value. However, they still agree with the calculated energies and the true value within error for Detector 4 B1 104 The Gaussian fitting program interface is shown with the specified files to be added B2 122 The spectrum that is generated by the addition of two spectra is shown along with the 0.511 MeV photopeak. The warning appears since subtracting the internal radiation counts from each channel may yield a negative number of counts for some channels. However, the program automatically sets these negative numbers to be zero since negative numbers of counts have no physical 123 meaning xxi B3 The Gaussian fit is performed on the 0.511 MeV photopeak B4 The Gaussian fit is performed on the 1.17 MeV photopeak and the 1.33 MeV 125 126 photopeak simultaneously Cl The VMware front interface is shown with the virtual machine shortcut selected. 128 C2 The simulation interface is shown C3 (a) The front view of the LaBryCe detector is shown, (b) The side view of the 129 LaBr3:Ce detector is shown with the photomultiplier tube radius being 2.55 130 cm. These diagrams have not been drawn to scale C4 (a) The front view of the BGO detector is shown, (b) The side view of the BGO detector is shown with the photomultiplier tube radius being 2.95 cm. These diagrams have not been drawn to scale C5 131 The right-hand side of the array along with the crown detectors are shown. Detector #1 and #2 straddle the array as shown. The direction of the beam and recoils is shown for perspective. This diagram has not been drawn to scale. C6 . 132 The left-hand side of the array is shown. Detector #8 and #10 straddle the array as shown and Detector #9 is a crown detector. The direction of the beam and recoils is shown for perspective. This diagram has not been drawn to scale. 132 C7 The major external dimensions of the gas target box are shown. This diagram 133 has not been drawn to scale xxii Glossary Compound Nucleus - A compound nucleus may be formed during a nuclear reaction when a projectile nucleus fuses with a target nucleus [1], Cross-Section - When a beam of projectile nuclei is incident on target nuclei, there is a probability of an interaction between the projectiles and the target. The cross-section is de¬ fined as the ratio of the number of interactions to the product of the number of incident beam projectiles on the target per unit area and the number of target nuclei that the projectile beam comes into contact with. It thereby measures the probability of the occurrence of a nuclear reaction with the units of area. The cross-section may be formulated differently to measure the probability of an interaction such as the photoelectric effect, Compton scattering, and pair production [1], xxiii Isotropic - An isotropic radioactive source emits particles in all directions equally. This means that a detector that is placed at any angle with respect to the source will receive the same amount of particles for the same source-to-detector distance. Lorentzian Distribution - A Lorentzian distribution is also known as a Cauchy distribution. It represents the symmetric distribution about the mean value where the peak is narrow. This distribution is used to represent the numbers of nuclear reaction events at the resonance ener¬ gies, since the event frequencies form sharp peaks at these energies. Particle - In nuclear physics, alpha particles, gamma rays, neutrons, photons, and protons are referred to as particles. However, nuclei in general can also be referred to as particles. Resonance Energy - The discrete energy levels of the compound nucleus correspond to resonance energies in which each individual excited state corresponds to a single resonance energy where the nuclear reactions are likely to occur [1], xxiv Resonance Reaction - In a resonance reaction, the sum of the energy that is released or absorbed in forming the compound nucleus and the projectile energy must match a resonance energy in order for the compound nucleus to reach a resonant excited state. In order for this event to occur, the projectile nuclei have an incident energy that enables them to penetrate the target nuclei. As a result, the reaction cross-section reaches a peak. The compound nucleus relaxes by emitting a particle or by emitting the projectile nucleus, and this event represents the end of the compound nucleus lifetime [1], xxv Acknowledgements I graciously thank the DRAGON group for facilitating the creation of this thesis in which I specifically thank the primary supervisor Dr. Ahmed Hussein for his incredible support, pa¬ tience, and guidance throughout the turbulent process of completing this thesis. Without his help, I would have struggled to understand the required concepts in nuclear astrophysics. I also thank Dario Gigliotti, who helped me set up the electronics for the detector effi¬ ciency calibration experiments, and he also provided the foundation for the Geant4 detector simulation programs. In addition, Dr. Devin Connolly also helped me understand the C++ language when I was new to Geant4. I also thank Konstantin Olchanski, Pierre-Andre Amaudruz, and Thomas Lindgren for their assistance in setting up the detector efficiency calibration experiments. They also provided me with access to MIDAS (Maximum Integrated Data Acquisition System) to acquire data along with the work station. Without them and Dario Gigliotti, these experiments xxvi may not have occurred. Dr. Chris Ruiz and the DRAGON group performed the timing experiments with the LaBra:Ce detectors during the Covid-19 pandemic when I couldn’t be there in person. I specif¬ ically thank Dr. Chris Ruiz for helping me understand the Geant4 simulation and providing feedback on the thesis; in particular, the timing method calculations. He and Dr. Matthew Williams prepared code in ROOT that allows the timing data to be quickly visualized. Dr. Chris Ruiz is an external member of the thesis committee. The co-supervisors are Dr. Ian Hartley and Dr. Mark Shegelski. I thank the external examiner Dr. Barry Davids as well as the entire committee for their support on my thesis and for having the thesis defence. I thank Dr. Dave Hutcheon for also helping me understand the timing method. Further¬ more, Dr. Dave Hutcheon’s advice has been instrumental in describing how DRAGON deter¬ mines the resonance energies of radiative capture reactions. Overall, the DRAGON group has been crucial in completing the thesis work and shaping my learning experience. Many of the data tables could not be written without their AutoCAD files. I thank Dr. Adam Garnsworthy and the GRIFFIN group for letting me borrow a single LaBr'3:Ce detector for the detector efficiency measurements in which Victoria Vedia clarified xxvii the dimensions of this detector. In general, I thank TRIUMF for providing me with a tremen¬ dous scientific research experience. I am truly blessed to be surrounded by amazing people with stellar aspirations. Of course, this thesis is dedicated to my family and friends who have supported me every step of the way. It has been a long journey that has been further prolonged by the global Covid-19 pandemic, which requires tremendous patience to complete. I will always remember these learning moments in the TRIUMF laboratory; the resonance energy measurements and the efficiency calibration runs as well as the DRAGON meetings. I will cherish these memories for a lifetime. xxviii Chapter 1 Introduction The study of nuclear astrophysics involves nuclear reactions that occur within the stars. These reactions produce the elements which make up the universe to ultimately define its existence. This thesis covers the basic details of this field of study, and the role of the DRAGON (Detec¬ tor of Recoils and Gammas of Nuclear Reactions) facility in furthering nuclear astrophysical research. As a contribution, this thesis offers an improvement to the DRAGON facility’s ability to fulfill its role by recommending the replacement of its Bismuth Germanate (BGO) detector array with a Lanthanum Bromide doped with Cerium (LaBr3:Ce) detector array. The corresponding experimental data and Geant4 simulation data have been summarized. 1 1.1 Big Bang Nucleosynthesis The universe is theorized to have been created by a Big Bang in which it expanded from a zero-volume singularity to occupy the current volume over a period of 13.8 billion years. The hydrogen nuclei which are and 2H, and most of the helium nuclei which are 3He and 4He as well as 7Li were created as a result [1]. Nucleosynthesis began when the universal temperature was in between 108 K and 109 K, which occurred between 100 and 1,000 seconds after the Big Bang [2], As the universe cools further, the nuclear reactions "freeze out" of an equilibrium state since they can no longer be reversed. The specific mechanisms by which nucleosynthesis occurs after the Big Bang are described by models in this paper [2], 1.2 Stellar Nucleosynthesis 1.2.1 The Proton-Proton Chain The proton-proton chains that are described here represent the process of nucleosynthesis that occurs within stars such as the Sun. 4He which is known as an alpha particle was mostly produced by the proton-proton (ppi) chain reactions that are shown in Equation 1.1, 2H + e+ + v Q=lA42MeV (Lia) 3He + y Q = 5A93MeV (1-lb) 3He + 3He^ 4He+ XH+ lH Q = 12.861 MeV (1.1c) lH + 2H+ 2 where Q represents the energy that is released during this reaction. Two hydrogen atoms com¬ bine to form deuterium in which a positron and a neutrino are released. Deuterium combines with hydrogen to form 3He and a gamma ray is released. Two 3He nuclei combine to form 4He and two hydrogen nuclei. The total amount of energy produced by this series of reactions is 26.731 MeV because the reactions in Equation 1.1a and Equation 1.1b occur twice for every time the reaction in Equation 1.1c occurs. However, since some energy is carried away by the two neutrinos, the actual amount of energy available in thermal form is about Q = 26.19 MeV [1], 1 H and 4He would be the building blocks for heavier nuclei to ultimately produce the elements that exist today. These heavier nuclei are primarily produced in stars by nuclear reactions along with the further production of 4He. The stars are formed by the gravitational collapse of gaseous clouds which are known as nebulae. As the material of the clouds con¬ tracts, its gravitational potential energy is converted to thermal energy which raises the tem¬ perature of the cloud. At a critical point where the thermal energy enables the nuclei to get close enough to fuse together, nuclear reactions occur. These reactions provide radiative pressure to prevent the material from collapsing further, so the volume of the cloud stabilizes and it becomes a star. This stabilization represents a state of equilibrium. After the hydrogen nuclei have been consumed in these reactions, a new series of nuclear reactions may occur if the amount of thermal energy available is sufficient to facilitate them [1], 3 An alternative nucleosynthesis pathway for the 3He produced by the ppl-chain is the pp2chain which is summarized by Equation 1.2 as follows. 3 He + 4 He 1 Be + y (1.2a) ^Li + v (1.2b) Li+ ]H ~ 4He+ 4He (1.2c) ^Be + e~ 3He combines with 4He to produce 7Be and a gamma ray is released. 7Be undergoes electron capture to become 7Li and a neutrino is released. 7Li combines with hydrogen to produce two alpha particles. When the neutrino energy loss is taken into account, Q = 25.65 MeV [1], An alternative nucleosynthesis pathway for the 7Be produced by the pp2-chain is the pp3-chain which is summarized by Equation 1.3 as follows. ^Be+ {H^ 3B + y (1.3a) 8B^ 8Be + e+ + v (1.3b) *Be^4He+4He (1.3c) 7Be combines with hydrogen to produce 8B and a gamma ray is released. 8B, which has a half-life of 770 milliseconds, undergoes positron emission to release a neutrino to become 8Be. 8Be breaks down into 2 alpha particles and after neutrino energy loss, Q = 19.75 MeV. The pp2 and pp3 chains become more likely to occur than the ppi chain as the temperature rises above 18 x 106 K. Proton capture becomes more favourable at temperatures above 25 x 4 IO6 K for 7Be in which the pp3 chain becomes the most likely outcome [1], Otherwise, the nuclear reactions terminate on the last step of the ppi chain. 1.2.2 The CNO Cycle Most stars contain carbon, nitrogen, and oxygen nuclei in addition to hydrogen and helium, since three alpha particles can combine together to form 12C. Two alpha particles would form 8Be and if the 8Be formation rate equals or exceeds its decay rate, this nuclide could undergo the reaction 8Be(cx,y)12C. Figure 1.1 summarizes the major CNO cycles, which show how 12C would be converted to 14N through its first branch and 16O through its second branch [1]. It is likely for 15N to become 12C through the (p,oc) reaction. The CNO cycle may have a second branch if ,5N undergoes a (p,y) reaction to become 16O instead. The third branch stems from the 17O(p,y)18F reaction, which is an alternative to the l7O(p,a)14N reaction. The fourth branch represents the 18O(p,y)19F reaction, which is an alternative to the 18O(p,a)15N reaction. Figure 1.1 shows the pathways of the CNO cycle, while Table 1.1 lists the hot CNO cycle reactions [1]. As shown in Figure 1.1, carbon, nitrogen, oxygen, or fluorine act as catalysts for these reactions. The typical temperature range for the CNO cycles is on the order ofl06Kto 108K [1,3-5], 5 Stable To N eN Unstable a Na (α,γ) (p,α) 18 (p,γ) (β+ ) Ne 19 Ne 20 17 F 18 F 19 17O 18 18 O 14 14 O 15O 16O 13 13 N 14N 15N 12 13 C e cl cy 20 k ea y Br wa A (α,p) Ne F C Figure 1.1: The CNO cycles are shown along with additional reaction pathways where broken lines show pathways that lead to the break out reactions. A small fraction of 15N nuclei that were produced by the hot CN01 cycle will undergo the 15N(p,y)16O reaction instead of the 15N(p,a)12C to enter the hot CN02 cycle. At temperatures above 1.8 x 108 K, the 17F(p,y)18Ne reaction becomes more frequent over the 17F(jB + v)17O decay which leads to the hot CNO3 cycle [1]. The CNO cycle normally does not produce nuclei with an atomic mass at 20 or above. The break out reaction occurs for temperatures above 108 K because at this temperature range, re¬ actions like 14O(a,p)17F, 150( » 2moc? N 2moc2 N Multiple Compton (ht/~>»^2) E hv Multiple Compton events E events Figure 2.12: The energy spectrum for monoenergetic gamma rays which includes the main types of gamma ray interactions is shown. The number of counts N is being measured with respect to the incident gamma ray energy E. 32 2.7 Detector Timing Considerations The time resolution also depends on the nature of the scintillator crystals [24]. Gamma rays excite the electrons in the scintillator molecules in which photons are emitted upon electron relaxation. This time period is represented as the scintillator rise time R. The differences in the rise times for different gamma ray detection events lead to a spread in the time of these events about a mean time, and the FWHM of this spread is the time resolution. The time spectrum would be similar to what is observed on Figure 2.11, with the number of entries being plotted with respect to time instead of energy. The photons provide a light pulse for the scintillator, and the time required for this light pulse to decrease to|of its maximum value is the decay time D [7]. Equation 2.13 summarizes the scintillator response as follows, — e~^R) I= (2.13) where I is the light yield at a given time, Io is the initial light yield which corresponds to the peak of the light pulse, and t is the elapsed time. Although this equation is used for organic scintillators, similar equations can be used for inorganic scintillators [25]. After gamma ray detection, the detector cannot detect another one until the current gamma ray signal has been mostly processed during the dead time. The intrinsic time resolution of the detector and the accompanying data acquisition system contribute to the dead time [7], Figure 2.13 shows an example of a timing spectrum taken for a LaBr3:Ce detector by using a 137Cs source, which provides 0.662 MeV gamma rays [25]. The decay time may not be Gaussian since the detector 33 has a slow decay component in addition to the relatively fast decay time. However, Equation 2.13 is expected to be a good approximation in most cases since a single decay time dominates although Figure 2.13 shows how this equation can be modified to better model the data. Figure 2.13: The 0.662 MeV timing spectrum for the LaBi^Ce detector is shown, where the fit function takes into account both the fast and slow decay components. The signal has been normalized so 1 corresponds to the peak value, and the pulse intensity is plotted with respect to the time elapsed in nanoseconds. 2.8 BGO and LaBr3:Ce Detector Comparison Table 2.4 summarizes some of the physical properties of the BGO and LaBr^Ce crystals [1 1 , 15, 25-38], The energy resolution values were taken for 0.662 MeV gamma rays, which is the characteristic radiation of 137Cs [12], The BGO detector could have an energy resolution of 11% to 13% at room temperature which worsens as the gamma ray energy decreases [31]. 34 The energy resolution value given at 6.5±0.2% was taken at the temperature of liquid nitro¬ gen [29], On the contrary, the LaB^Ce energy resolution of around 3% was taken at room temperature [34], Table 2.4: The physical properties of the BGO and LaBr^Ce crystals. Material Density (^ ) Effective Atomic Number Decay Time (ns) Time Resolution (ps) Light Output (photons/keV) Band Gap (eV) Peak Emission Wavelength (nm) Overall Energy Resolution (%) Linear Attenuation (jU)(cm-1) Hygroscopic? 35 LaBr3:Ce BGO 5.08 48.3 -16 260 -60 3.24 380 -3 0.47 Yes 7.13 74.2 300 1300 ≥6 4.2 480 6.5±0.2 0.95 No In addition to measuring the rise time, the time resolution can be measured by using the two back-to-back annihilation gamma rays produced by a positron emitting source like “Na in time coincidence. The energy resolution can be measured by using well known gamma rays produced by sources like 60Co and 137Cs. These sources produce gamma rays with well defined energies of 1.17 MeV, 1.33 MeV, and 0.662 MeV. The time resolution of the LaBi^Ce detector doped by 5% Ce was measured in coincidence with a BaF? detector by using 0.511 MeV gamma rays that were provided by 22Na where 260 ps is the FWHM value [34], The time resolution for a BGO crystal was taken in coincidence with a CsF scintillator for the gamma rays emitted by 60Co, which have energies of 1.17 MeV and 1.33 MeV [12]. In this case, the FWHM value is 1300 ps [37]. All of the LaBr3:Ce detector properties apply onto detectors that have been doped with a mole fraction of 5% Cerium, except for the 3.24 eV band gap for detectors that have been doped with a mole fraction of 0.5% Cerium [38], The linear attenuation coefficients are taken in response to 0.511 MeV gamma rays [32], The scintillator crystal should be coupled to the photomultiplier tube through a transparent material that has the same index of refraction as the crystal. This is done to minimize the internal reflection so most of the photons would travel to the photocathode [7], The LaBr3:Ce crystal is hygroscopic, which means it tends to absorb moisture from the air [10], BGO was chosen as the scintillator material for the DRAGON detector array because it was an affordable material with a low decay time and a high density. Its decay time provides a good time resolution, and its high density provides a high interaction probability between 36 the BGO molecules and the gamma rays [3], The latter property is known as the gamma ray capture efficiency. It will be replaced by LaB^Ce to improve the energy and time resolution at the expense of the gamma ray capture efficiency due to its lower density. 37 Chapter 3 DRAGON Although individual detectors can be used to detect charged particles and gamma rays, they usually can only detect one type of particle at a time. A series of detectors is normally required to fully investigate a nuclear reaction. DRAGON is a facility designed to fully investigate reactions of astrophysical importance by taking into account the gamma rays that are produced as well as the residual nuclei which are also known as recoils. The "head of" the DRAGON facility is composed of a gas target box and a BGO detector array. The "body of" DRAGON is a mass separator composed of two pairs of electric and magnetic dipoles, quadrupoles, and adjustable vertical and horizontal slits. At the "tail of" DRAGON, there is a detector for the heavy recoils such as a double sided silicon strip detector (DSSSD) or an ionization chamber (IC) [19]. DRAGON alone is not capable of studying astrophysical nuclear reactions. It needs beams of heavy radioactive ions that are accelerated to energies that correspond to 38 temperatures in the stars. The ISAC (Isotope Separator and Accelerator) facility provides such beams to the DRAGON experiments. Even though ISAC is an integral part of DRAGON, it also serves other experimental facilities. This chapter provides a brief description of the various components of DRAGON. 3.1 ISAC-I The ISAC facility at TRIUMF is composed of two accelerator systems known as ISAC-I and ISAC-II along with beam lines for various types of experiments. This facility is designed to deliver intense radioactive and stable beams with masses and energies suitable for nuclear astrophysics research. ISAC-I delivers radioactive beams of nuclei with atomic masses up to A = 30 and energies in the range of 0.15 - 1.5 MeV/nucleon. ISAC-II provide beams whose masses range up to A = 150 with energies of at least 6.5 MeV/nucleon [39-41]. Figure 3.1 shows a part of the ISAC-I accelerators with all of the optical elements used to transport DTL (106MHz RFQ (35.4MHz) Figure 3.1: A section of the ISAC-I accelerators is shown. 39 and focus the heavy ion bunches [39]. The ISAC system produces and isolates short lived heavy ion bunches by bombarding specific targets with the protons produced by TRIUMF’s main cyclotron. The target choice depends on which particular ion species is required for a particular experiment. The ions are then accelerated to a low energy of about 2 keV/nucleon and directed toward the accelerator components of ISAC. ISAC-Ihas two accelerators; the first is an 8 m long Radio Frequency Quadrupole (RFQ) that uses an electric field created by the quadrupoles and a 35.4 MHz radio frequency electric field to compress the heavy ion bunches. The RFQ accelerates the heavy ion bunch to an energy of 150 keV/nucleon. The ion bunches are then directed to the second stage accelerator called the Drift Tube Linac (DTL). The DTL is composed of 5 drift tube cavities and is capable of accelerating the 150 keV/nucleon ions from the RFQ up to 1.53 MeV/nucleon. The RFQ mass-to-charge acceptance is limited to A/q 30, while the DTL is limited to 3 A/q 6. For ions with A/q larger than 6, a carbon foil is placed between the two accelerators to strip electrons from the ions thus increasing q and reducing A/q to a value within the acceptance of the DTL. As shown in Figure 3.1, the entire ISAC line contains many beam optical elements to direct, focus, and shape the ion beams to suit the various requirements of DRAGON experiments. When the magnetic dipole at the diagnostic station is turned off, the beam proceeds to DRAGON or it can be switched to ISAC-II for further acceleration. In addition, there is an Off Line Ion Source (OLIS) that produces stable beams for experiments that need them [39-41]. 40 3.2 The Gas Target The most common way of studying properties of nuclei and their nuclear interactions is by bombarding a collection of those nuclei (target) with accelerated light particles (projectiles) like p, n, a, etc. This process is called forward kinematics. Many astrophysically important nuclear reactions are of the type (p,y) and (a,y) on ra¬ dioactive nuclei, since they are involved in the pathways of nucleosynthesis. It is not possible to study such nuclear reactions in forward kinematics because the radioactive nuclei under investigation decay rapidly. For instance, the half-life of a 21Na target is 22.49 seconds so it cannot be made into a target [12]. Furthermore, radioactive targets would cause radiation damage to the target containment structure so it would have to be replaced often. To circumvent these issues, such nuclear reactions are performed in reverse kinematics, whereby the radioactive nuclei are used as projectiles rather than a target and the light particles are used as targets. Figure 3.2 illustrates this process [3]. γ 21Na θ P Φ 22Mg Figure 3.2: This figure shows how to study the radiative capture of a proton by 21Na in reverse kinematics in which an accelerated radioactive 2 'Na beam bombards a proton gas target. A gamma ray and a 22Mg recoil are produced. 41 DRAGON is designed to study radiative capture reactions on radioactive nuclei. DRAGON’S target nuclei are either hydrogen or helium in which the hydrogen atom has its electron removed. This explains why the target is made up of protons in Figure 3.2. Gen¬ erally, the chemical and physical conditions of the target in any nuclear reaction experiment are determined by a compromise among many conflicting factors. Its chemical and physical conditions are normally chosen to achieve the best possible experimental results. The most common targets used are solid targets. However, gas and liquid targets have been used in many experiments. In the case of DRAGON, the most important factors are high energy reso¬ lution and high reaction rate. The first factor requires minimum energy loss by the beam while traversing the target. This means that the incoming beam must encounter the least amount of material and that includes the target material itself. High reaction rates require high target density to reduce data collection time and achieve low statistical errors. Further complications arise from the fact that DRAGON’S incoming beams are composed of heavy ions. Heavy ions lose energy very rapidly while travelling in a medium compared to beams of light particles like protons, alpha particles, and neutrons for example. It is then obvious that liquid, solid, very thin selfsupporting foils, and sealed gas targets are unquestionably unsuitable for DRAGON experi¬ ments. A windowless gas target is a target in which the gas is contained in a region with a relatively high pressure in the middle of the beam tube that is under very low pressure. In the DRAGON 42 gas target, the pressure at the center is ~ 5 Torr while the pressure upstream and downstream of the target region is < 10-6 Torr. Figure 3.3 shows the gas target design which includes its trapezoidal component where the nuclear reactions occur [19], Figure 3.4 shows the path of the beam through the gas target [42]. Table A5 in Appendix A provides its dimensions. The gas of the target is contained in a trapezoidal region within the box. The beam enters the trapezoidal region through a 6 mm diameter aperture and exits through an 8 mm diameter aperture. The two apertures are 11 cm apart1 [43], A series of five large Root Blowers and seven turbomolecular pumps along with a trap containing a X-13 (Zeolite) molecular sieve at liquid nitrogen temperature form a system to differentially pump, recirculate, and clean the gas. This system helps maintain the gas pressure inside the trapezoidal region at 0.2-10 Torr and less than 3 x 10-6 Tori' within the gas target box and in the upstream and downstream beam pipes [19], Two silicon detectors (called elastic monitors) are included in the gas target box to detect the hydrogen or helium nuclei that are recoiling from the elastic scattering of beam ions off target particles. One of the silicon detectors observes this at 30° and the other at 57°. The elastic scattering rate is a direct measure of the beam current if the gas pressure is known. In general, the angle of the recoil (j)R is given by Equation 3.1 [43], sin0y = arctan tLy - J cos 0• ’ 'For a detailed description of the entire windowless gas target system see [19,43]. 43 (3.1) Connectors Figure 3.3: The major components of the gas target box and the beam direction are shown. The scattering angle of the gamma ray 9y is given by Equation 3.2 where Ey represents the gamma ray energy. 0y = arccos r z . —e7 i (3.2) The angle of the recoil ^r reaches its maximum when the gamma ray scatters at 90° relative to the beam [43], In Equation 3.3, for the specific cases where 9y = 0° or 180° and ())r = 0°, the recoil momentum pr is expressed in terms of the beam ion momentum: / E \ Pr^P 1±— c\/2mE / \ (3.3) In Equation 3.1, 3.2, and 3.3, m is the mass of the radioactive beam ions, p = y/lmE is the momentum of the beam, E is the kinetic energy of the radioactive beam ions, and c is the speed of light. These equations apply in the lab frame [43], Therefore, the exit aperture must be slightly larger than the entrance aperture to take into account the difference in momenta between the recoils and the radioactive beam as they leave the gas target box. 44 17.15 cm Na 21 Na 21 Beam γ Recoil 22 Mg Figure 3.4: The radioactive beam enters the gas target box and interacts with the gas within the trapezoidal cell. The residual beam and the recoils exit the gas target box. The gamma rays (y) are detected by the BGO detector array. 3.3 The Gamma Detector Array The hexagonal shape of the BGO detectors makes it possible to arrange them in an array without overlaps or gaps. To optimize gamma ray capture, it is important to design the array in such a way to cover the largest possible solid angle around the gas target box. The BGO array covers 89-92% of the solid angle [3]. The scintillator crystals of the array all face the gas target box. Figure 3.5 provides an illustration of the array and the gas target box [43,44]. Each detector has an incircle diameter of 5.58 cm and a length of 28.5 cm [3,43], Each detector in the array is assigned a number from 1 to 30, to indicate their individual positions. Seven of these detectors are made by Bicron, and the other twenty-three as well as a spare detector are made by Scionix [3]. Figure 3.6 shows the detectors in the DRAGON array with 45 their representative numbers. The detectors may be switched around which explains why six Bicron detectors are shown. Table A7 and A8 in Appendix A provide the details on the detector positions. In an experiment, these detectors may be rearranged. To cut down the intensity of the 0.511 MeV gamma rays, lead shielding is placed at the entrance of the gas target box which makes it necessary to move back two detectors. Consequently, about 3% of the array coverage is lost. These background gamma rays are created by the /3 -plus decay of the radioactive beam ions. The positrons that emerge from this decay annihilate electrons in aluminium to produce these gamma rays [3], Gamma rays interact with the BGO detectors through either the photoelectric effect, Comp¬ ton scattering, or pair production [7]. In most cases, the gamma rays can undergo Compton scattering and pair production multiple times to produce multiple electrons before they dis¬ appear. The gamma ray interaction events are separated from the background by using the coincidence timing method with their corresponding recoils. The details of the electronics that are used by DRAGON to obtain the data are described by Christian et al. (2014) [45]. 46 Y X Beam Z γ Beam and Recoils 4 5 6 15 7 21 27 γ 25.718 cm 9 29 10 25 8 17.146 cm 5 cm Figure 3.5: The left side shows the BGO array surrounding the gas target box. The lead shielding surrounds the side of the gas target box where the beam enters it. The detectors are numbered based on their positions. The right side shows a simulation of the gas target box and its components. The beam is propagated along the region that is marked by the purple lines. Gamma rays (y) and recoils are emitted upon nuclear reactions between the beam and the gas. Beam and Recoils 7 6 5 3 9 27 10 29 23 8 Beam and Recoils 4 25 21 15 17 19 13 11 16 12 1 14 22 18 28 24 20 30 26 2 (b) (a) Figure 3.6: (a) The left-hand side of the DRAGON array is shown along with the crown detectors and the straddling detectors, (b) The right-hand side of the DRAGON array is shown. 47 3.4 The Electromagnetic Separator The nuclear reactions of interest at DRAGON have very small cross sections; as a result, the intensity of the product ions are of the order of 1010 - 1016 times lower than that of the incoming beam. In addition, due to the use of reverse kinematics (see Table 3.1), the angular separation between the incoming beam ions and the recoiling ions is extremely small; it can be less than a degree [19]. The electromagnetic separator (EMS) is designed to reduce the beam contamination by at least 1010, and further suppression is provided by the time coincidence between the gamma ray events that are detected by the BGO detectors and the recoil events that are detected by the end detectors placed at the final focus of the mass separator (see section 3.5). Electric and magnetic dipoles are used to separate the recoils from the radioactive beam. Table 3.1 : The forward and reverse kinematics of 14N(p, y) l5O and 27A1(/j, y)28Si. Reverse Kinematics Forward Kinematics 14N(^,y)15O 27A1(^>, y)28Si Ep = 2.0 MeV Ep = 2.0 MeV OnuM = 180° MO) = 8.59° p(14N, y)15O EN = 2.0 MeV = 180° OmaxM = 180° 6max (Si) = 12.7°