UC Irvine UC Irvine Electronic Theses and Dissertations Title Demonstration of an Approach to Precisely Measure Long-Lived Gamma-ray Branching Ratios for Beta Emitters Permalink https://escholarship.org/uc/item/8kz8b3cd Author Hennessy, Amber Publication Date 2018 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, IRVINE Demonstration of an Approach to Precisely Measure γ-ray Branching Ratios for Long-Lived β Emitters DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Chemistry by Amber M. Hennessy Dissertation Committee: Professor A.J. Shaka, Chair Professor Emeritus G.E. Miller Professor R.W. Martin 2018 (cid:13)c 2018 Amber M. Hennessy DEDICATION I would like to dedicate this and everything I do to my best friend and my biggest supporter, my husband. I am among those who think that science has great beauty. A scientist in his laboratory is not only a technician: he is also a child placed before natural phenomena which impress him like a fairy tale. We should not allow it to be believed that all scienti(cid:28)c progress can be reduced to mechanisms, machines, gearings, even though such machinery has its own beauty. -Marie Curie ii TABLE OF CONTENTS Page LIST OF FIGURES vi LIST OF TABLES x ACKNOWLEDGMENTS xii CURRICULUM VITAE xiii ABSTRACT OF THE DISSERTATION xv 1 Introduction 1 1.1 Structure of the Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Ionizing Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.1 Quanti(cid:28)cation of Radioactive Decay . . . . . . . . . . . . . . . . . . . 9 1.4.2 Transient Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.3 Secular Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.4 No Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.5 Successive Radioactive Decays . . . . . . . . . . . . . . . . . . . . . . 14 1.4.6 Radioactive Growth, Decay, and Measurement . . . . . . . . . . . . . 14 1.5 The Need for Precision Measurements . . . . . . . . . . . . . . . . . . . . . . 16 1.6 Di(cid:30)culties Associated with Precision Measurements . . . . . . . . . . . . . . 17 1.7 Project Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Experimental Approach 21 2.1 Nuclear Reactor-Produced Test Sources . . . . . . . . . . . . . . . . . . . . . 21 2.2 Fission Fragment Collection at the CARIBU Facility . . . . . . . . . . . . . 23 2.3 TAMU - Source Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.1 HPGe Detector Operation . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.2 HPGe Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.3 Gas Counter Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.4 Gas Counter Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.5 Coincidence Measurement . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4 Analysis of Measured Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 iii 2.4.1 γ-ray Peak Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4.2 βγ Coincidence Peak Fitting . . . . . . . . . . . . . . . . . . . . . . . 48 2.4.3 Gas Counter E(cid:30)ciency . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.4 Simulations using GEANT4 . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.5 β Particle Rate Associated to the Isotope of Interest . . . . . . . . . 55 2.4.6 γ-ray Branching Ration Equation . . . . . . . . . . . . . . . . . . . . 57 2.5 Uncertainty Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.5.1 Uncertainties in γ-ray Peak Area . . . . . . . . . . . . . . . . . . . . 58 2.5.2 Uncertainties in Coincidence Peak Fitting . . . . . . . . . . . . . . . 63 2.5.3 Uncertainties in Measured γ-ray and Gas Counter E(cid:30)ciencies . . . . 63 2.5.4 Uncertainties in Simulated Gas Counter E(cid:30)ciencies . . . . . . . . . . 64 2.5.5 Uncertainty in β Particle Determination . . . . . . . . . . . . . . . . 65 2.5.6 Uncertainty in Correlated Terms . . . . . . . . . . . . . . . . . . . . 66 2.5.7 Uncertainty in the γ-ray Branching Ratio . . . . . . . . . . . . . . . . 67 3 Simulations using GEANT4 68 3.1 Gas Counter Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.1.1 Di(cid:27)erences Between Simulated and Physical Detector Designs . . . . 73 3.2 Evolution of Radiation Source . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.1 The β Decay Code and Fermi Function . . . . . . . . . . . . . . . . . 76 3.2.2 Radiation Size and Geometry . . . . . . . . . . . . . . . . . . . . . . 78 3.3 Simulated Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4 Analysis of Simulated Output . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4 Method Viability - 95Zr 86 4.1 95Zr/95Nb Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.1.1 CARIBU Source Production . . . . . . . . . . . . . . . . . . . . . . . 87 4.1.2 Decay Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.1.3 Simulated β Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . 90 4.1.4 Half-lives of 95Zr/95Nb . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.1.5 Simulated Gas Counter E(cid:30)ciency . . . . . . . . . . . . . . . . . . . . 91 4.1.6 Reactor-Produced Source . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.1.7 CARIBU-Produced Source . . . . . . . . . . . . . . . . . . . . . . . . 92 4.2 95Zr Reactor-Produced Source Measurement . . . . . . . . . . . . . . . . . . 94 4.3 95Zr CARIBU-Produced Source Measurements . . . . . . . . . . . . . . . . . 100 4.3.1 Initial Measurement of 95Zr . . . . . . . . . . . . . . . . . . . . . . . 100 4.3.2 Final Measurement of 95Zr . . . . . . . . . . . . . . . . . . . . . . . . 109 5 Method Application - 144Ce 121 5.1 144Ce/144Pr Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.1.1 CARIBU Source Production . . . . . . . . . . . . . . . . . . . . . . . 122 5.1.2 Decay Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.1.3 Simulated β Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . 125 5.1.4 Half-Lives of 144Ce/144Pr . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.1.5 Simulated Gas Counter E(cid:30)ciency . . . . . . . . . . . . . . . . . . . . 126 iv 5.2 144Ce CARIBU-Produced Source Measurements . . . . . . . . . . . . . . . . 131 5.2.1 Initial Measurement of 144Ce . . . . . . . . . . . . . . . . . . . . . . . 134 5.2.2 Final Measurement of 144Ce . . . . . . . . . . . . . . . . . . . . . . . 135 6 Method Application - 147Nd 144 6.1 147Nd/147Pm Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.1.1 CARIBU Source Production . . . . . . . . . . . . . . . . . . . . . . . 145 6.1.2 Decay Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 6.1.3 Simulated β Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . 148 6.1.4 Half-lives of 147Nd/147Pm . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.1.5 Simulated Gas Counter E(cid:30)ciency . . . . . . . . . . . . . . . . . . . . 150 6.2 147Nd CARIBU-Produced Source Measurement . . . . . . . . . . . . . . . . 156 7 Future Work and Conclusion 170 7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7.1.1 Method Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Bibliography 173 v LIST OF FIGURES Page 1.1 A generic β energy spectrum showing a range of energies for the emitted β particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Fission product yields as a function of mass number for 235U, 238U, 239Pu, and 252Cf1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Theprocessbywhichaconversionelectron,x-ray,andAugerelectronemission occurs. The red line is an emitted γ-ray. . . . . . . . . . . . . . . . . . . . . 8 1.4 The possible types of equilibrium between parent and daughter isotopes. It is also possible for no equilibrium to occur between the pair. Equilibrium relationships are dependent on the relative half-life of parent and daughter isotopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 β energy spectra for (a) a high Q value decay and (b) a low Q value decay showing the relative spread and most probable β energies. For these spectra, a Q = ∼3 MeV results in the most probable energy being roughly 1/3 of the total energy of the reaction whereas a Q = ∼150 keV results in a most probable energy close to 1/30 of the total energy. . . . . . . . . . . . . . . . 18 2.1 Fission product yields for 252Cf showing mass number versus the probability of yield2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Simpli(cid:28)cation of the gas catcher used at CARIBU. Fission products from spontaneous (cid:28)ssion of 252Cf interact with the He gas and are directed toward the RF cone, which concentrates the ions into a beam3. . . . . . . . . . . . . 25 2.3 A simpli(cid:28)ed picture of the components that make up the beam line. Source implantation occurs shortly after beam separation in order to achieve the highest intensity of ions possible4. . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 (a) Placement of the cross on the beam line. The arm which holds Si detec- tors and source foil (cid:28)ts in at the top. (b) Looking directly at the beam on the backside of the cross, one can see the foil positioned in the path of the oncoming beam. The arm that (cid:28)ts into the cross is shown for the side that faces the beam (c) and the side that faces away from the beam (d). . . . . . 27 2.5 Interactions of γ-rays with the germanium crystal inside the HPGe detector5. 30 2.6 Characteristic features of a γ-ray spectrum using a 137Cs source6. . . . . . . 31 2.7 (a) Texas A&M meticulously-calibrated HPGe detector used to measure γ- rays with high precision. (b) Full energy peak e(cid:30)ciency as a function of γ-ray energy of the TAMU HPGe detector7. . . . . . . . . . . . . . . . . . . . . . 33 2.8 The pathway and interactions of an ionizing particle through detection gas in the presence of a bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 vi 2.9 Schematic of the gas counter system. . . . . . . . . . . . . . . . . . . . . . . 37 2.10 (a) A source holder that (cid:28)ts into (b) each half of the detector creating a sealed system (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.11 Generic method by which Radware (cid:28)ts a γ-ray peak. . . . . . . . . . . . . . 46 2.12 ASCII data format of (a) bu(cid:27)er, (b) coincidence, and (c) heavy ion informa- tion. The bu(cid:27)er occurs after the transfer of data. The header appears each 54.93 sec. and signi(cid:28)es the end of a cycle. The coincidence data set occurs each time there is a measurable coincidence event and contains the vital in- formation about timing and energies of the β particle and γ-ray. The heavy ion data set occurs at a speci(cid:28)c rate when the source strength is low. . . . . 49 2.13 Generic source activity over time. Two measurements of this source are taken over this range showing a decay correction for the activity to some reference time, t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 0 2.14 Variations in peak (cid:28)tting result in an uncertainty that is half the midpoint of the two extremes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.15 Spectra from a source and dedicated background measurement overlaid. To align the peaks of interest, background peaks found in both spectra are (cid:28)t to determine their center. The dedicated background is then shifted so that proper alignment is achieved. . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.16 Simpli(cid:28)cation of the qualities that make up a γ-ray peak. . . . . . . . . . . . 62 3.1 Evolution of gas counter designs simulated in GEANT4. . . . . . . . . . . . 71 3.2 Final simulated version of the gas counter representing all the major features of the physical detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3 Source holders for a reactor-made and CARIBU-made sources. The reactor source (a) is held in place with thin wires while the CARIBU source (b) consists of carbon foil (cid:29)oated on top of the source holder. . . . . . . . . . . . 74 3.4 β energy spectra for the main transitions of 144Ce, 95Zr, and 147Nd. . . . . . 75 3.5 (a) Fermi function calculated for non-relativistic and relavistic β particles of 144Ce and (b) the resulting β energy spectra for both relativistic and non- relativistic calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.6 Placement of the simulated radioactive isotopes within the foil. . . . . . . . . 79 3.7 (a) Deposition of energy spectrum produced from GEANT4 simulations. (b) Simulation to determine the material response to radioactive ions and the level of attenuation each imposes on β particles. . . . . . . . . . . . . . . . . 80 3.8 Simpli(cid:28)ed example of a decay scheme and possible pathways to ground state (GS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.1 Mass 95 (cid:28)ssion product yield from 252Cf8. . . . . . . . . . . . . . . . . . . . 87 4.2 A simpli(cid:28)ed decay scheme exhibiting the major transitions of 95Zr decaying to 95Nb decaying to 95Mo. The decay to the isomeric state of 95mNb is also seen at the 235.7 keV energy level. . . . . . . . . . . . . . . . . . . . . . . . . 89 4.3 (a) Major β transitions for 95Zr and 95Nb and (b) decay of the source over time. 90 4.4 (a) Voltage plateau and (b) change in counts per 100V. . . . . . . . . . . . . 96 4.5 (a) Background-subtracted γ-ray spectrum and (b) βγ coincidence spectrum measurement of a reactor-produced source. . . . . . . . . . . . . . . . . . . . 97 vii 4.6 (a) γ-ray spectrum of the CARIBU beam monitoring of mass 95 isotopes. (b) Beam intensity over the length of the measurement. (c) Growth and decay of 95Zr and 95Nb source. The gray section indicates the duration of the measurement performed at TAMU. . . . . . . . . . . . . . . . . . . . . . . . 101 4.7 (a) γ-ray spectra of the source and background measurements overlaid, (b) background-subtracted γ-ray source spectrum, and (c) βγ coincidence spec- trum of a 95Zr/95Nb CARIBU-made source. . . . . . . . . . . . . . . . . . . 103 4.8 (a) γ-ray spectrum of the CARIBU beam monitoring of mass 95 isotopes. (b) Beam strength over the duration of the measurement. (c) Growth and decay of 95Zr and 95Nb. The gray section indicates the length of the measurement. 111 4.9 (a) A measured voltage plateau using a 147Nd source and (b) the change in counts per 100 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.10 (a) γ-ray spectrum, (b) background subtracted γ-ray spectrum, and (c) mea- sured coincidence spectrum of the CARIBU 95Zr/95Nb source. . . . . . . . . 113 4.11 Fits of both (a) γ-ray and (b) βγ coincidence peaks. . . . . . . . . . . . . . . 115 4.12 The TDC spectrum of the source and its individual contributions. . . . . . . 116 4.13 (a) A comparison of the deposition of energy spectra between measured and GEANT4 simulated data for the total 95Zr/95Nb source. The zoomed region shows an average deposited energy of 4.1 keV and a threshold of 1.1 keV. In addition, speci(cid:28)c transition deposition of energy spectra are shown for β particles gated on (b) 724.2, (c) 756.7, and (d) 765.8 keV γ-rays. . . . . . . . 117 5.1 Mass 144 (cid:28)ssion product yield from 252Cf8. . . . . . . . . . . . . . . . . . . . 122 5.2 A simpli(cid:28)ed decay scheme exhibiting the major transitions of 144Ce decaying to 144Pr decaying to 144Nd. The decay to the isomeric state of 144mPr is also seen at the 59 keV energy level. . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.3 (a) Major β transitions for 144Ce and 144Pr and (b) decay of the source over time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.4 (a) γ-ray spectrum of the CARIBU beam monitoring of mass 144 isotopes. (b) Beam strength over the length of the measurement. (c) Growth and decay of 144Ce and 144Pr. The gray section indicates the length of the measurement. 132 5.5 First measurement of βγ coincidences of 144Ce source showing the presence of 103Ru contamination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.6 (a) Voltage plateau and (b) change in counts per 100 V measured during the (cid:28)rst 144Ce source experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.7 (a) γ-ray spectrum, (b) background subtracted γ-ray spectrum, and (c) mea- sured coincidence spectrum of the CARIBU 144Ce/144Pr source after over a year of decay. Each spectrum shows the lack of contamination present within the source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.8 (a) γ-ray and (b) βγ coincidence peak (cid:28)ts of 80.1 and 133.5 keV peaks. . . . 137 5.9 The TDC spectrum generated from βγ coincidence measurement of 144Ce. . 140 5.10 (a) A comparison of the deposition of energy spectra between measured and GEANT4 simulated data. The zoomed region shows an average deposited en- ergy of 2.7 keV and a threshold of 1.1 keV. (b) A transition-speci(cid:28)c deposition of energy spectrum is shown for β particles gated on 133.5 keV γ-ray. . . . . 140 6.1 Mass 147 (cid:28)ssion product yield from 252Cf8. . . . . . . . . . . . . . . . . . . . 145 viii