Neutron Activation Analyses and Half-Life Measurements at the Usgs Triga Reactor

NEUTRON ACTIVATION ANALYSES AND HALF-LIFE MEASUREMENTS AT THE USGS TRIGA REACTOR

by Robert E. Larson A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy (Applied Physics).

Golden, Colorado Date

Signed: Robert E. Larson

Signed: Dr. Uwe Greife Thesis Advisor

Golden, Colorado Date

Signed: Dr. Thomas E. Furtak Professor and Head Department of Physics

ii ABSTRACT

Neutron activation of materials followed by gamma spectroscopy using high-purity germanium detectors is an e↵ective method for making measurements of nuclear beta decay half-lives and for detecting trace amounts of elements present in materials. This research explores applications of neutron activation analysis (NAA) in two parts. Part 1. High Precision Methods for Measuring Decay Half-Lives, Chapters 1 through 8 Part one develops research methods and data analysis techniques for making high precision measurements of nuclear beta decay half-lives. The change in the electron capture half-life of 51Cr in pure chromium versus chromium mixed in a gold lattice structure is explored, and the 97Ru electron capture decay half-life are compared for ruthenium in a pure crystal versus ruthenium in a rutile oxide state, RuO2.Inaddition,thebeta-minusdecay half-life of 71mZn is measured and compared with new high precision ﬁndings. Density Func- tional Theory is used to explain the measured magnitude of changes in electron capture half-life from changes in the surrounding lattice electron conﬁguration. Part 2. Debris Collection Nuclear Diagnostic at the National Ignition Facility, Chapters 9 through 11 Part two explores the design and development of a solid debris collector for use as a diagnostic tool at the National Ignition Facility (NIF). NAA measurements are performed

on NIF post-shot debris collected on witness plates in the NIF chamber. In this application

NAA is used to detect and quantify the amount of trace amounts of gold from the hohlraum

and germanium from the pellet present in the debris collected after a NIF shot. The design of

asoliddebriscollectorbasedonmaterialx-rayablationpropertiesisgiven,andcalculations

are done to predict performance and results for the collection and measurements of trace amounts of gold and germanium from dissociated hohlraum debris.

iii TABLE OF CONTENTS

ABSTRACT ...... iii

LIST OF FIGURES ...... xii

LISTOFTABLES...... xix

LISTOFSYMBOLS...... xx

LIST OF ABBREVIATIONS ...... xxi

ACKNOWLEDGMENTS ...... xxii

DEDICATION ...... xxiii

CHAPTER 1 THE DEVELOPMENT OF HIGH PRECISION METHODS FOR MEASURING BETA DECAY HALF-LIFE ...... 1

1.1 Nuclear Beta Decay ...... 2

1.1.1 Electron Capture Beta Decay ...... 2

1.2 Measurement Campaigns ...... 3

1.3 Theoretical Descriptions ...... 4

1.4 NeutronActivationLaboratory ...... 4

1.5 Summary of Chapters for Part 1 ...... 5

CHAPTER 2 PREVIOUS RESEARCH INTO CHANGES IN ELECTRON CAPTURE HALF-LIFE ...... 6

2.1 Earliest Research ...... 6

2.2 Later Research ...... 8

2.3 Recent Measurements ...... 9

2.4 Recent High Z Research, a Motivation for this Research ...... 10

iv CHAPTER 3 DATA COLLECTION METHODS ...... 12

3.1 Decay Half-life Measurement Apparatus ...... 12

3.1.1 The USGS TRIGA Reactor ...... 12

3.1.2 ORTEC HPGe Detectors ...... 13

3.1.3 MAESTRO Software ...... 15

3.1.4 PC Clock Synchronization ...... 15

3.2 Pure Chromium Campaign ...... 15

3.2.1 51Cr Decay Scheme ...... 15

3.2.2 Chromium Sample Preparation ...... 17

3.2.3 Irradiation and Decay Count Spectrum ...... 17

3.3 Gold/Chromium Campaign ...... 17

3.3.1 Sample Preparation for Sputtering ...... 17

3.3.2 Irradiation and Decay Spectrum ...... 23

3.3.3 Mass from Activity Analysis ...... 26

3.4 Ruthenium Crystal and Ruthenium Oxide Campaigns ...... 26

3.4.1 Electron Capture Decay Scheme of 97Ru ...... 26

3.4.2 Irradiation and Decay Count Spectra ...... 26

3.4.3 Ruthenium Crystal ...... 28

3.4.4 Ruthenium Oxide ...... 30

3.5 Zinc Campaign ...... 32

3.5.1 Decay Scheme of 71Zn ...... 33

3.5.2 Irradiation and Decay Count Spectrum ...... 33

CHAPTER 4 HALF-LIFE ANALYSIS METHODS ...... 37

v 4.1 Radioactive Decay Equation ...... 37

4.1.1 Linearization Method Not Adequate for High Precision ...... 37

4.2 Protocol for Uncertainty Assessment of Half-lives ...... 38

4.2.1 Uncertainty Deviation Models ...... 38

4.3 Data Processing Methods ...... 39

4.3.1 Half-life Data Collection using ORTEC MAESTRO Software ...... 39

4.3.2 Method for Analyzing Gamma-ray Spectra Using gf3 ...... 41

4.3.3 RStudio, a Statistical Computational Tool ...... 44

4.4 Data Analysis Methods ...... 44

4.4.1 Autocorrelation as a Data Acceptance Criterion ...... 45

4.4.2 The Breusch-Godfrey Autocorrelation Test ...... 46

4.4.3 Simulated Data Used as a Reference for Statistical Consistency . . . . 47

4.4.4 Half-life Measurements and Uncertainty Analysis ...... 49

4.4.5 Examining the Data for Possible Medium Term Periodic Patterns . . . 50

4.4.6 Systematic Error Estimation ...... 50

4.5 Dead Time Measurement Studies Using a Precision Pulse Generator ...... 54

CHAPTER 5 RESULTS OF ELECTRON CAPTURE HALF-LIFE MEASUREMENTS ...... 58

5.1 Pure Chromium 51Cr Results ...... 58

5.1.1 Pure Chromium 51Cr Decay Count Plot ...... 58

5.1.2 Half-life Values for Full Pure Chromium Campaign ...... 59

5.1.3 Breusch-Godfrey Plot for Pure Chromium Data ...... 59

5.1.4 Half-life Results for Pure Chromium for the Accepted Data ...... 61

vi 5.1.5 Estimate of Systematic Standard Error for the Pure Chromium Measurement ...... 64

5.1.6 Pure Chromium Campaign Data Judged to be Spurious ...... 64

5.2 51Cr in a Gold Lattice: AuCr Results ...... 66

5.2.1 AuCr 51Cr Decay Count Plot ...... 66

5.2.2 Breusch-Godfrey Plot for Gold Chromium ...... 67

5.2.3 Half-life Results for AuCr for the Accepted Data ...... 67

5.2.4 Estimate of Systematic Standard Error for the Gold Chromium Measurement ...... 70

5.2.5 198Au Half-life Measurement ...... 72

5.2.6 Comparison with Established Chromium Results ...... 74

5.2.7 Comparison to Previous 51Cr Measurements ...... 76

5.3 Ruthenium Crystal Results ...... 78

5.3.1 Ruthenium Crystal 97Ru Decay Count Plot ...... 78

5.3.2 Ru Crystal Half-life Values ...... 79

5.3.3 Breusch-Godfrey Plot for the Ruthenium Crystal ...... 79

5.3.4 Half-life Results for the Ruthenium Crystal Campaign ...... 79

5.3.5 Estimate of Systematic Standard Error: Ruthenium Crystal Measurement ...... 82

5.3.6 Comparison to Previous 97Ru Measurements ...... 84

5.3.7 Results for 103Ru 497 keV Line ...... 84

5.4 Ruthenium Oxide Results ...... 89

5.4.1 Ruthenium Oxide 97Ru Decay Count Plot ...... 89

5.4.2 Ru Oxide Half-life Values ...... 91

vii 5.4.3 Breusch-Godfrey Plot for Ruthenium Oxide ...... 91

5.4.4 Half-life Results for the Ruthenium Oxide Campaign ...... 91

5.4.5 Estimate of Systematic Standard Error for the Ruthenium Oxide Measurement ...... 95

5.4.6 Comparison with Ruthenium Crystal Results ...... 95

CHAPTER 6 RESULTS OF ZINC MEASUREMENTS ...... 98

6.1 Enriched 71mZn Decay Count Plots ...... 99

6.2 Half-life Plots for 71mZn Lines ...... 99

6.3 Breusch-Godfrey 71mZn Plots ...... 102

6.4 Half-life Results for the Zinc Campaign ...... 104

6.4.1 Residual and Autocorrelation Plots ...... 107

6.4.2 Estimate of Systematic Error for the Zinc Data ...... 111

6.4.3 WeightedAverage...... 112

6.5 Comparison to Previous 71mZn Measurements ...... 114

CHAPTER 7 THEORETICAL ANALYSIS OF CHANGES IN ELECTRON CAPTURE DECAY HALF-LIFE ...... 116

7.1 Theoretical Approaches ...... 116

7.1.1 Thomas-Fermi Theory ...... 116

7.1.2 Hartree-Fock-Slater Method ...... 117

7.1.3 Density Functional Theory ...... 118

7.2 Density Functional Theory Calculations ...... 119

7.2.1 The WIEN2k Program Package for DFT Calculations of Solids . . . . 119

7.2.2 Linear Relationship Between Nuclear Electron Density and Half-life . 120

7.2.3 The Location of the Chromium Atoms in the Gold Lattice ...... 121

viii 7.2.4 Chromium in Gold Lattice Calculation ...... 122

7.2.5 AuCr Comparison to Theoretical Analysis ...... 123

7.2.6 Ruthenium Oxide Calculation ...... 124

7.2.7 Ruthenium Comparison to Theoretical Analysis ...... 125

7.2.8 WIEN2k Results ...... 125

CHAPTER 8 PART 1 SUMMARY AND CONCLUSIONS HIGH PRECISION HALF-LIFE MEASUREMENTS ...... 126

8.1 Research Motivation ...... 126

8.2 Detector Dead Time ...... 127

8.3 51Cr in Gold Lattice ...... 129

8.4 97Ru in Ruthenium Oxide ...... 131

8.5 71mZn Beta-minus Decay Half-life Measurement ...... 131

8.6 Overall Conclusions, Part 1 ...... 132

8.7 Areas of Continuing Research ...... 133

8.7.1 Changes in Electron Capture Half-life from Electronic Structure Compression ...... 133

CHAPTER 9 DEBRIS COLLECTION NUCLEAR DIAGNOSTIC AT THE NATIONAL IGNITION FACILITY ...... 136

9.1 Introduction ...... 136

CHAPTER 10 COLLECTOR DESIGN CONSIDERATIONS ...... 140

10.1 Geometry and Scale ...... 140

10.2 Preliminary Vessel Design ...... 140

10.3 X-ray/Debris Source Characterization ...... 140

10.4 Candidate Material Analysis ...... 141

ix 10.4.1 Original Material Candidates ...... 142

10.4.2 Proposed Ablation E↵ects Experiments ...... 143

10.4.3 Material X-ray Response Analysis and X-ray Ablation Predictions . . 144

10.4.4 Grazing Incidence Predictions ...... 147

10.4.5 HydrodynamicAnalysis ...... 147

10.4.6 Material Transport Process ...... 148

CHAPTER 11 NIF NEUTRON ACTIVATION ANALYSIS RESULTS ...... 152

11.1 Neutron Activation Analysis Procedure ...... 152

11.2 Detector Setup ...... 154

11.3TestsandAnalysis ...... 154

11.4 Summary and Conclusions, Part 2 ...... 155

11.5 Ideas for Continuing Research ...... 156

REFERENCES CITED ...... 157

APPENDIX A - COMPUTER PROGRAM LISTINGS ...... 163

A.1 MAESTRO data acquisition script ...... 163

A.2 The rwspec code ...... 163

A.3 Therptpythoncode ...... 165

A.4 Thegﬁnit.datﬁle ...... 167

A.5 Thesum.pypythoncode ...... 168

A.6 Theﬁt.pypythoncode ...... 168

A.7 Thesto.pypythoncode...... 169

A.8 RScriptforPlotting ...... 171

A.9 R Script for Looping over Contiguous Points ...... 173

x A.10 R Script for Generating Monte Carlo Data ...... 176

A.11 R Script for Generating Results at Regular Intervals ...... 177

APPENDIX B - AUCR SPUTTER SAMPLE DATA ...... 180

APPENDIX C - PROPERTIES OF MATERIALS ANALYZED SOURCE: NIST-JANAF THERMOCHEMICAL TABLES 4TH EDITION . . . 182

xi LIST OF FIGURES

Figure 1.1 HPGe Detectors ...... 5

Figure 2.1 Balanced Ionization Chambers ...... 7

Figure 3.1 ORTEC HPGe Interface Boards ...... 14

Figure 3.2 HPGe Detector Block Diagram ...... 14

Figure 3.3 WWVB Receiver ...... 16

Figure 3.4 51Cr Decay Scheme ...... 16

Figure 3.5 Full Pure Chromium Campaign Spectrum ...... 18

Figure 3.6 Pure Chromium Spectrum in Region of 320 keV ...... 19

Figure 3.7 198Au Decay Scheme ...... 20

Figure3.8 SputterApparatus ...... 21

Figure 3.9 Sputter Target Preparation ...... 22

Figure3.10 ProﬁlerMachine ...... 22

Figure 3.11 AuCr Sample Preparation ...... 23

Figure3.12 FullAuCrSpectrum ...... 24

Figure 3.13 AuCr Spectrum in Measurement Region ...... 25

Figure 3.14 97Ru Decay Scheme ...... 27

Figure3.15 RutheniumSamples ...... 27

Figure 3.16 Full Ruthenium Crystal Spectrum ...... 28

Figure 3.17 Ruthenium Crystal Spectrum in Region of Measurements ...... 29

Figure3.18 RutheniumOxideFullSpectrum ...... 30

xii Figure 3.19 Ruthenium Oxide Spectrum in Region of Measurements ...... 31

Figure 3.20 Enriched 70Zn Sample (Powder) ...... 32

Figure 3.21 71Zn Decay Scheme ...... 33

Figure 3.22 Full 71mZn Sample Spectrum ...... 34

Figure 3.23 71mZn Spectrum in Region of Measurements ...... 35

Figure 4.1 Uncertainty Sources (from Pomm´eet al.) ...... 40

Figure 4.2 gf3 Fit Components ...... 42

Figure 4.3 AuCr Monte Carlo Half-lives for Varying Starting Point ...... 48

Figure 4.4 Pure Chromium Week Correlation Study ...... 51

Figure 4.5 Ruthenium Crystal Daily Correlation Study ...... 51

Figure 4.6 Pure Chromium Systematic Error Study ...... 53

Figure 4.7 Pure Chromium Monte Carlo Systematic Error Study ...... 53

Figure 4.8 ORTEC Precision Pulse Generator ...... 55

Figure 4.9 Zinc Pulser Study Results ...... 56

Figure 4.10 Europium Pulser Study Results ...... 56

Figure 5.1 Pure Chromium 51Cr Decay Count Data ...... 59

Figure 5.2 Pure Chromium Half-life Values for Later Starting Points ...... 60

Figure 5.3 Pure Chromium Campaign Breusch-Godfrey P-Values ...... 60

Figure 5.4 Pure Chromium Campaign Half-life Values ...... 61

Figure 5.5 Pure Chromium Monte Carlo Data ...... 62

Figure 5.6 Pure Chromium 51Cr Exponential Fit Residuals ...... 63

Figure 5.7 Pure Chromium Autocorrelation Lags ...... 63

Figure 5.8 Pure Chromium Seven Day Correlation Study ...... 64

xiii Figure 5.9 Pure Chromium Systematic Error Study ...... 65

Figure 5.10 Pure Chromium Systematic Error Monte Carlo Study ...... 65

Figure 5.11 AuCr 51Cr Count Data ...... 66

Figure 5.12 AuCr Breusch-Godfrey P-values ...... 67

Figure 5.13 AuCr Campaign Half-life Values for Later Starting Points ...... 68

Figure 5.14 AuCr Campaign Half-life Values for Monte Carlo Simulation ...... 68

Figure 5.15 AuCr Residuals ...... 69

Figure 5.16 AuCr Autocorrelation Lags ...... 69

Figure 5.17 AuCr Seven Day Correlation Study ...... 70

Figure 5.18 AuCr Systematic Error Study ...... 71

Figure 5.19 AuCr Systematic Error Monte Carlo Study ...... 71

Figure 5.20 198Au Half-life Values for Starting Point ...... 72

Figure 5.21 198Au Breusch-Godfrey P-values ...... 73

Figure 5.22 198Au Half-life Values for Later Starting Point ...... 73

Figure 5.23 198Au Data Half-life Monte Carlo Values ...... 74

Figure 5.24 198Au 24 Hour Correlation Study ...... 75

Figure 5.25 Au Systematic Error Study ...... 75

Figure 5.26 Au Systematic Error Monte Carlo Study ...... 76

Figure 5.27 51Cr Half-life Measurement History ...... 78

Figure 5.28 Ruthenium Crystal 97RuActivityData ...... 79

Figure 5.29 Ruthenium Crystal Half-life Values ...... 80

Figure 5.30 Ruthenium Crystal Breusch-Godfrey P-values ...... 80

Figure 5.31 Ruthenium Crystal Half-life Values for Accepted Data ...... 81

xiv Figure 5.32 Ruthenium Crystal Campaign Half-life Monte Carlo Values ...... 81

Figure 5.33 Ruthenium Crystal Residuals ...... 82

Figure 5.34 Ruthenium Crystal Autocorrelation Lags ...... 83

Figure5.35 RutheniumOxide24HourCorrelationStudy ...... 83

Figure 5.36 Ruthenium Crystal Systematic Error Study ...... 84

Figure 5.37 Ru Systematic Error Monte Carlo Study ...... 85

Figure 5.38 97Ru Half-life Measurements ...... 86

Figure 5.39 103Ru Half-life Values ...... 87

Figure 5.40 103Ru Breusch-Godfrey P-values ...... 87

Figure 5.41 103Ru Half-life Values for Accepted Data ...... 88

Figure 5.42 103Ru Half-life Monte Carlo Values ...... 88

Figure 5.43 103Ru Systematic Error Study ...... 89

Figure 5.44 103Ru Systematic Error Monte Carlo Study ...... 90

Figure 5.45 Ruthenium Oxide 97RuActivityData ...... 90

Figure 5.46 Ruthenium Oxide Half-life Values ...... 91

Figure 5.47 Ruthenium Oxide Breusch-Godfrey P-values ...... 92

Figure 5.48 Ruthenium Oxide Half-lives ...... 92

Figure 5.49 Ruthenium Oxide Campaign Half-life Monte Carlo Values ...... 93

Figure5.50 RutheniumOxide24HourCorrelationStudy ...... 94

Figure5.51 RutheniumOxideResiduals...... 94

Figure5.52 RutheniumOxideAutocorrelationLags ...... 95

Figure5.53 RutheniumOxideSystematicErrorStudy ...... 96

Figure 5.54 Ruthenium Oxide Systematic Error Monte Carlo Study ...... 96

xv Figure 6.1 71mZn 386 keV Decay Counts ...... 99

Figure 6.2 71mZn 487 keV Decay Counts ...... 100

Figure 6.3 71mZn 620 keV Decay Counts ...... 100

Figure 6.4 71mZn 386 keV Line Half-life Values for Later Starting Points . . . . . 101

Figure 6.5 71mZn 487 keV Line Half-life Values for Later Starting Points . . . . . 101

Figure 6.6 71mZn 620 keV Line Half-life Values for Later Starting Points . . . . . 102

Figure 6.7 71mZn 386 keV Line Breusch-Godfrey P-values ...... 103

Figure 6.8 71mZn 487 keV Line Breusch-Godfrey P-values ...... 103

Figure 6.9 71mZn 620 keV Line Breusch-Godfrey P-value ...... 104

Figure 6.10 71mZn 386 keV Line Half-life Values ...... 105

Figure 6.11 71mZn 386 keV Line Half-life Monte Carlo Values ...... 105

Figure 6.12 71mZn 487 keV Line Half-life Values ...... 106

Figure 6.13 71mZn 487 keV Line Half-life Monte Carlo Values ...... 106

Figure 6.14 71mZn 620 keV Line Half-life Values ...... 107

Figure 6.15 71mZn 386 keV Residuals ...... 108

Figure 6.16 71mZn 487 keV Residuals ...... 108

Figure 6.17 71mZn 620 keV Residuals ...... 109

Figure 6.18 71mZn 386 keV Autocorrelation Lags ...... 109

Figure 6.19 71mZn 487 keV Autocorrelation Lags ...... 110

Figure 6.20 71mZn 620 keV Autocorrelation Lags ...... 110

Figure 6.21 Zinc 386 keV Line Systematic Error Study ...... 111

Figure 6.22 Zinc 386 keV Systematic Error Monte Carlo Study ...... 112

Figure 6.23 Zinc 487 keV Line Systematic Error Study ...... 113

xvi Figure 6.24 Zinc 487 keV Systematic Error Monte Carlo Study ...... 113

Figure 6.25 71mZn Half-life Measurements ...... 115

Figure 7.1 AuCr Phase Diagram ...... 122

Figure 7.2 AuCr Lattice Structure ...... 123

Figure 7.3 RuO2 RutileLatticeStructure ...... 124

Figure 8.1 Dead time versus Statistical Error ...... 128

Figure 8.2 Dead time versus Systematic Error ...... 128

Figure8.3 DeadtimeversusTotalStandardError ...... 129

Figure9.1 TheNationalIgnitionFacility...... 137

Figure 10.1 Debris Collection Vessel Design ...... 141

Figure 10.2 X-ray Deposition Proﬁle ...... 144

Figure 10.3 X-ray Energy Deposition Proﬁle for Aluminum 6061 ...... 145

Figure 10.4 X-ray Energy Deposition Proﬁle for Aluminum Grafoil ...... 146

Figure 10.5 X-ray Energy Deposition Proﬁle for Aluminum Titanium ...... 146

Figure 10.6 X-ray Energy Deposition Proﬁle for Aluminum Tantalum ...... 147

Figure 10.7 Al Max Particle Velocity ...... 148

Figure 10.8 Ti Max Particle Velocity ...... 149

Figure 10.9 Grafoil Max Particle Velocity ...... 149

Figure 10.10 Hohlraum and Debris Collector ...... 150

Figure 10.11 Disassociated Hohlraum ...... 151

Figure 10.12 Hohlraum Debris and Ablated Material Interaction ...... 151

Figure11.1 ExampleCouponSample21...... 153

Figure 11.2 Loaner 4 Detector Setup ...... 154

xvii Figure 11.3 Gold Versus Shot Energy ...... 155

xviii LIST OF TABLES

Table 3.1 Enriched 70Zn Sample Isotopic Composition ...... 32

Table 5.1 Comparison of Established 51Cr Half-life versus AuCr Results ...... 76

Table 5.2 51Cr Half-life Measurement Results ...... 77

Table 5.3 97Ru Half-life Measurement Results ...... 85

Table 5.4 Comparison of Ruthenium Crystal versus Ruthenium Oxide ...... 96

Table 6.1 Results for 71mZn ...... 114

Table 6.2 71mZn Half-life Measurement Results ...... 114

Table 7.1 Theoretical Calculations of Half-life Change ...... 125

Table 8.1 Comparison of Established 51Cr Half-life versus AuCr Results ...... 130

Table 8.2 Comparison of Ruthenium Crystal versus Ruthenium Oxide ...... 131

Table 8.3 Results for 71mZn ...... 132

Table 10.1 X-ray Ablation Predictions ...... 145

Table 11.1 Test Descriptions for NIF Shots ...... 152

TableB.1 SputterData ...... 181

TableC.1 JanafTable ...... 183

xix LIST OF SYMBOLS

duration of a measurement campaign ...... T

electron density at the nucleus ...... ⇢

InteractionHamiltonian ...... Hint

Kohn–Sham orbital ...... i(r)

Kohn–Sham potential ...... eff

radioactive decay constant ...... radioactive half-life ...... T1/2

xx LIST OF ABBREVIATIONS

AtomicRydbergUnits...... ARU

Breusch-Godfrey ...... BG

Density Functional Theory ...... DFT

Durbin-Watson ...... DW

Electron Capture ...... EC

High-Purity Germanium ...... HPGe

Inertial Conﬁnement Fusion ...... ICF

Integrated Development Environment ...... IDE

Levenberg-Marquardt ...... LM

Linearized Augmented Plane Wave ...... LAPW

Multi-Channel Analyzer ...... MCA

National Ignition Facility ...... NIF

Neutron Activation Analysis ...... NAA

National Institute of Standards and Technology ...... NIST

Self Consistent Field ...... SCF

Tight Binding, Linear Mun-Tin Orbital ...... TB-LMTO

Training,Research,Isotopes,GeneralAtomic ...... TRIGA

X-ray Di↵raction...... XRD

xxi ACKNOWLEDGMENTS

I am very grateful to Dr. Uwe Greife for providing the overall guidance and direction of this research. I would also like to thank Dr. Marty Hudson for his invaluable help and good ideas. I would like to thank my committee: Dr. Cory Ahrens, Dr. Tim Ohno, Dr. Fred Sarazin, and Dr. Lawrence Wiencke. I would especially like to thank Dr. Sarazin for valuable discussions regrading data uncertainty analysis. Special thanks goes to Dan Shields for his help in making the gold/chromium sputtering sample and to Dr. Randy Zombola of Exelis for his support. Tim Debey and the sta↵ of the USGS TRIGA reactor were very helpful for their prompt assistance in processing activation samples. Thanks to Ryan and Josh for your support, and to my grandson Sam, a bright shining star. And of course, special thanks to my wife Bren for her encouragement and love.

xxii For my children: Annie, Michael, and Jenna. You inspire me with your dedication and hard work in service to others.

xxiii CHAPTER 1 THE DEVELOPMENT OF HIGH PRECISION METHODS FOR MEASURING BETA DECAY HALF-LIFE

Activation of materials using thermal neutron environments in a TRIGA research reactor with subsequent gamma decay analysis using high-purity germanium detectors is an e↵ective method for measuring decay half-lives and for detecting trace amounts of elements present in materials. This research investigates applications of such neutron activation analysis (NAA) in two parts. Part one, Chapters 1 through 8, develops high precision half-life measurement methods and data analysis techniques to 1) investigate changes in the electron capture decay half-lives of 51Cr and 97Ru nuclei in di↵erent host lattice structures and to 2) corroborate recent high precision beta-minus half-life measurements of 71mZn using zinc enriched in 70Zn. Density Functional Theory is used to analyze changes in electron capture half lives from changes in surrounding lattice electronic structure. Motivation for the electron capture part of the research comes from two studies where changes in high Z half-lives were reported. Ray et al. [2] found signiﬁcant changes in the electron capture decay half-life comparing 109In and 110Sn nuclei situated in gold versus lead lattices. They concluded that compression of the indium and tin electronic structure occurred after ion implantation of the indium and tin atoms into the gold and lead lattices, increasing slightly the electron density in the indium and tin nuclei thereby changing the electron capture decay half-lives. Bainbridge et al. [3] saw the internal conversion decay half-

99m life change signiﬁcantly with the chemical state change of Tc in KTcO4 versus Tc2S7.The ﬁrst part of this research was initiated in an attempt to determine if this e↵ect can be seen in other higher Z electron capture decay such as 51Cr in a gold lattice or in 97Ru in ruthenium

oxide, RuO2.

1 A motivation for the zinc study comes from a study by Reifarth et al. [4] where the beta- minus decay half-life of 71mZn was measured with signiﬁcant di↵erence compared to previous data. The zinc measurements of this research were performed to determine if Reifarth’s ﬁndings were correct.

1.1 Nuclear Beta Decay

Nuclear beta decay occurs when an unstable nucleus with atomic number Z and neutron number N, is transformed into a more stable nucleus with Z 1andN 1withtheemissionof ± ⌥ a particle (e⌥)andaneutrino(⌫); the mass number A = Z + N does not change (Meyerhof [5]). The decay processes are

A A Z XN Z+1YN 1 + e +¯⌫e, decay (1.1) !

A A + + Z XN Z 1WN+1 + e + ⌫e,decay (1.2) ! 1.1.1 Electron Capture Beta Decay

Electron capture (EC) is a nuclear beta decay process where an atomic electron is absorbed by a nucleus and a neutrino is emitted. The resulting Z-1 atom has the correct number of orbital electrons, but the capture process creates a vacancy in one of the electron shells. When this vacancy is ﬁlled, x-rays or Auger electrons are generated that are characteristic of the new element, and often the nucleus, in an excited state, emits a gamma ray. The decay process is

A A Z XN + e Z 1WN+1 + ⌫e, EC decay (1.3) ! The most probable electrons for capture are from the inner K shell. Electrons that surround the nucleus have wavefunctions with a non-zero probability of overlap with the nucleus and thus have a chance of being found in the nucleus. The amount of overlap depends on the distribution of the electron conﬁguration surrounding the nucleus, which in turn is a↵ected by the lattice structure and the electron anity of the surrounding material. Independently, Segr´eand Daudel proposed in 1947 that electron capture decay half-lives

2 of radioactive nuclides might change due to change in the electron density near the nuclei (Segre [6], Daudel [7]). By introducing the atoms under study into lattice locations of a di↵erent host material, the electron conﬁguration of the inner electrons can potentially be a↵ected and the electron capture half-life can be slightly altered. By performing high precision half-life measurements, this e↵ect can be quantiﬁed and compared with theoretical analysis. Observed variations in electron capture half-life have been seen on the order of 1.0%, requiring high precision half-life measurement techniques on the order of 0.1% uncertainty standard error.

1.2 Measurement Campaigns

Three measurements of high Z beta decay were performed in this research.

1. A sample of pure chromium was activated in the USGS TRIGA reactor at the Denver Federal Center creating 51Cr, by the reaction 50Cr(n,)51Cr, which decays via electron capture with a half-life of 27.7 days. Chromium was then co-sputtered with gold ⇠ onto a Grafoil substrate and, as a result, the electron conﬁguration surrounding the 51Cr was slightly altered due to the gold lattice atoms adjacent to the 51Cr atoms in the gold lattice. The change in electron capture decay half-life was determined by comparing the two 51Cr half-lives: pure chromium versus the AuCr sample. The activated gold, 198Au, which decays with a half-life of 2.7 days did not interfere with ⇠ the 51Cr measurement after a sucient cool-down period. As a check the half-life of 198Au was also measured.

2. The electron decay half-life of 97Ru in activated pure ruthenium versus ruthenium oxide

was also measured to study the nuclear electron density e↵ect and as a calibration of

the measurement methods. The electron capture decay of 97Ru has been established with high precision (Goodwin et al. [8]); this a↵ords a good standard for comparison for our half-life measurement techniques and data analysis. As a check the half-life of another ruthenium decay nuclei, 103Ru, was also measured.

3 3. A sample of zinc enriched in 70Zn was irradiated using the USGS TRIGA reactor, and the beta-minus decay half-life of 71mZn was measured. Reifarth et al. [4] recently measured the half-life of 71mZn using a natural Zn sample changing the accepted half- life value by more than 4%. This research measures the 71mZn decay half-life to provide anew,independentmeasurement.

1.3 Theoretical Descriptions

Theoretical calculations using density functional theory methods were made to explain

51 97 the change in electron capture half-life of Cr in gold and Ru in RuO2 using the WIEN2k code, as described in Chapter 7. Numerical theoretical methods have been developed which can quantify this e↵ect by calculating the electron conﬁguration and resulting wavefunction overlap at the nucleus. The required inputs to the codes are the space group number of the host lattice, dimensions of the lattice, atomic numbers and positions of the constituent host atoms in the lattice, and the electronic structure of each of these atoms. WIEN2k is a program package that performs electronic structure calculations of solids using DFT (Blaha et al. [9]). It is also based on the full-potential linearized augmented plane-wave (LAPW) method, an accurate scheme for band structure calculations. WIEN2k uses an all-electron scheme including relativistic e↵ects.

1.4 Neutron Activation Laboratory

The neutron activation and decay rate measurements were performed at the USGS

TRIGA reactor building at the Denver Federal Center near Golden. The material samples were irradiated by the TRIGA “dry-tube” reactor ﬂux of 1.2 x 1012 thermal neutrons per second per cm2. The ORTEC HPGe detectors located in the CSM half-life measurement laboratory at the reactor building are shown in Figure 1.1(a) and Figure 1.1(b).

The activity of the samples is measured using three liquid nitrogen cooled ORTEC HPGe detectors each with a multi-channel bu↵er and MAESTRO MCA emulation software running on a personal computer running Windows-XP. Counts from the 320 keV gamma line of 51Cr,

4 (a) Gamma 1 Detector (b) Loaner 4 (on ﬂoor) and Gamma 5 Detectors

Figure 1.1: HPGe Detectors the 216 keV gamma line of 97Ru, and the 386, 487, and 620 keV gamma lines of 71mZn were used to measure and compare the half-life changes.

1.5 Summary of Chapters for Part 1

First, a summary of past work into electron capture half-life changes will be presented in Chapter 2, then discussions of each of the measurement campaigns are presented in the next three chapters in the functional order: data collection, analytical techniques, and half-life measurement results. (This was done to avoid redundant discussions for each measurement campaign). Sample preparation and measurement techniques will be discussed in Chapter 3, then half-life estimation analytical methods in Chapter 4, and half-life measurements and results will be given in Chapter 5 for the electron capture cases and in Chapter 6 for the 71mZn measurement campaign. An overview of theoretical methods and theoretical analysis

will be given in Chapter 7, and ﬁnally, a wrap-up and discussion of possible future research

will be given in Chapter 8.

5 CHAPTER 2 PREVIOUS RESEARCH INTO CHANGES IN ELECTRON CAPTURE HALF-LIFE

E↵orts to observe changes in electron capture half-life by altering the physical or chemical environment of various nuclides have been made by researchers over the past six decades. The earliest studies considered the dependence of the decay constant on the chemical and physical environment of 7Be (Leininger et al. [10]) and 99mTc (Bainbridge et al. [3]). Later 90Nb (Cooper and Hollander [11]) and 64Cu (Ehrhart et al. [12]) were studied. 7Be has been studied extensively in a variety of host materials because it is the lightest nuclide that undergoes electron capture with a half-life of approximately 53 days (Liu and Huh [13]). Ohtsuki et al. [14] saw a 0.83% di↵erence in electron capture decay half-life between 7Be encapsulated in C60 cages and beryllium metal. Qualitatively, it was determined that a combination of electron anity and lattice geometry of the host medium causing a change in the density of 2s valence electrons determined the variation in decay rate of nuclei in di↵erent media.

2.1 Earliest Research

The earliest references to the possibility of altering the electron capture decay rate due to changes in electron conﬁguration around the nucleus was in 1947 by both Segre [6] and

Daudel [7] independently. To quote Segr´efrom his 1947 paper: “The radioactive decay

constant of a substance decaying by orbital electron capture is proportional to (0) of the electrons. In the case of a light element like Be it may be possible to alter this quantity by an appreciable amount by putting the Be in di↵erent chemical compounds. The magnitude of the e↵ect may be in the neighborhood of one percent.” By 1951 Segre and Wiegand [15] were able to measure a change in 7Be electron capture half-life using a di↵erential ionization chamber (shown in Figure 2.1) capable of extremely

6 Figure 2.1: Balanced Ionization Chambers

high precision measurements. Since 7Be is the lightest radioactive nucleus that decays by electron capture, it was considered the most suitable candidate for studying the change of decay rate in di↵erent environments. The cases (also studied by Kraushaar et al. [16]) included the following with the percent change observed (in the following, for example, the decay constant of Be is 0.015% less than BeO).

• 7Be decay constant changes

– Be versus BeO: -0.015 ± 0.009%

– Be versus BeF2:-0.084± 0.010%,

– BeO versus BeF2:-0.069± 0.003%

In the 1950’s, Bainbridge et al. [3] studied the inﬂuence of the chemical state on 99mTc decay in an internal conversion process, which is not electron capture decay. Internal conversion is a decay process where a nucleus directly causes one of the atom’s electrons to be ejected. However the same principal applies: the electron density at the nucleus a↵ects the internal conversion decay half-life. The 99mTc case is an occurrence of a nuclide that has a signiﬁcant change in decay half-life from a di↵erent chemical (i.e. oxide) state.

7 The measurable change of the 99mTc half-life in the oxide state suggests that a similar change in ruthenium may be observable, since ruthenium is close in atomic number to technetium. The oxide state changes the electron conﬁguration around the ruthenium nucleus which results in a change in electron density at the nucleus and therefore a change in decay half-life. These technetium results provided a motivation for the ﬁrst part of this research: to explore changes in the electron capture decay half-life of the 97Ru atom when placed in a pure ruthenium lattice versus in a oxide state with NAA measurements and supporting DFT analysis.

• 99mTc (internal conversion)

– 1953, Chemical state change, KTcO4 versus Tc2S7:0.27± 0.01%

– 1958, (Byers and Stump [17]) Lower temperature, 77 K: 0.013 ± 0.004%

∗ 0.064 ± 0.004% (Superconducting, 4.2 K)

2.2 Later Research

In 1965 Cooper and Hollander [11] studied changes in chemical state on the lifetime of the 24-second isomer of 90mNb and saw the ﬁrst large change in half-life.

• 1965, 90Mo (90mNb): Metal versus ﬂuoride complex: 3.6 ± 0.4%

In the late 1970’s and early 1980’s Ehrhart et al. [12] deduced ⇢/⇢ from / in changes

in 64Cu half-life.

• Relative changes of electron densities from changes in in varying Cu concentrations

– 1978, Cu-Au: 0.031 ± 0.004%

– 1979, Cu-Ag: 0.017 0.003% ±

– 1981, Cu(SCN)2:0.029± 0.005%

8 2.3 Recent Measurements

Recent research has included a study of the terrestrial 7Be decay rate in relation to the 8B solar neutrino ﬂux (Das and Ray [18]). The change of decay rate of 7Be in di↵erent beryllium compounds was measured and a maximum change of up to 0.2% was observed. Das and Ray found that a combination of electron anity and lattice geometry of the host medium best predicts the change in decay rate of 7Be nuclei in di↵erent media. They found that for various compounds the valence electrons of an atom can be a↵ected by the surrounding environment and the overlap of electronic wave functions at the nucleus becomes progressively smaller for outer shell electrons.

• Several studies on 7Be were done with various changes in half-life reported.

– 1999, (Ray et al. [19]), Be-Au versus Be-Al2O3:0.72± 0.07%

– 1999, (Huh [20]), Be(OH)2 versus BeO: 1.5 ± 0.01%

– 2000, (Liu and Huh [13]), Pressure at 400 kilobar: 1% ⇠ – 2001, (Norman et al. [21]), Hosts of graphite, boron nitride, tantalum, gold: max e↵ect of 0.38%

– 2004, (Ohtsuki et al. [14]), Encapsulated in C60 cages: 0.83 ± 0.10%

High precision half-life measurements at Texas A&M University of 198Au (Goodwin et al. [22]) and 97Ru (Goodwin et al. [8]) were done to test measurements of beta decay half- life change between room temperature and 12 K. Some of the measurement and analysis

techniques of this Texas A&M group were used in this research, including precise time

synchronization of the PC clock and use of the Radware gf3 code.

• 198Au and 97Ru

– 2007 to 2009: (Texas A&M, Goodwin et al. [8, 22]) No temperature dependence seen to 19 K

9 2.4 Recent High Z Research, a Motivation for this Research

Segréand Daudel originally pointed out that the electron capture decay rate of low- Zelementswouldbemostsusceptibletochangesofthesurroundingenvironment.They reasoned that only for low-Z elements do valence electrons have a measurable overlap at the nucleus, and also only s-electrons have significant overlap at the nucleus. No significant change in the decay rate of higher Z electron capture nuclides was expected because valence, s-electrons only occur in low-Z elements. Recently, however, the electron capture rates of 109In and 110Sn were observed by Ray et al. [2] and Ray et al. [23] to increase by 1.00 ± 0.17% and 0.48 ± 0.25% respectively when placed via ion implantation in a smaller gold lattice versus a larger lead lattice. Spatial confinement of the indium and tin atoms assumed to be in interstitial lattice locations was postulated for this e↵ect. The larger ions implanted into the smaller lattices occupy interstitial locations and experience greater levels of compression a↵ecting the electron density at the nucleus, thereby changing the electron capture decay rate. The e↵ect of the compression of the smaller lattice when the much bigger atom such as indium or tin was implanted in it was found to be measurable. Supporting calculations were done to explain these results using DFT codes, however the DFT results did not indicate a measurable di↵erence. Ray postulated that this was due to the way that the inner orbitals were modeled and that the way that the inner electron wave functions change under compression was not “properly taken care of.” Hence electron density computed could not explain the observed decay rate change. An explanation based on a zeroth order (Ray’s assessment) Thomas-Fermi approach was then developed that gave results of the same magnitude as the measurements.

• Ray et al. results:

– 109In implanted in gold host versus lead host: 1.00 ± 0.17%

– 110Sn implanted in gold host versus lead host: 0.48 ± 0.25%

10 • Supporting calculations using Thomas-Fermi theory:

– Predicted change in109In decay half-life in gold host versus lead host: 0.86%

– Predicted change in109Sn decay half-life in gold host versus lead host: 0.67%

• Supporting calculations using Density Functional Theory:

– The WIEN2k and TB-LMTO DFT codes were used to explain changes in electron conﬁguration electron decay half-life. The DFT results indicated very little change in electron density at the nucleus.

∗ WIEN2k results did not explain the magnitude of observed decay rate change of 7Be in di↵erent host media, Das and Ray [24].

This Ray et al. [2] study provided the chief motivation for the ﬁrst part of this research: to explore changes in the electron capture decay half-life of the relatively higher Z 51Cr atom when placed in a gold lattice versus in a pure chromium lattice with NAA measurements and supporting DFT analysis. Ion implantation was not used for this study because of the lack of availability of a facility. Co-sputtering of gold and chromium was used to create a mixture lattice.

11 CHAPTER 3 DATA COLLECTION METHODS

Chapter 3 discusses the measurement apparatus and methods for sample preparation that were used to acquire data for the decay half-life measurement campaigns.

3.1 Decay Half-life Measurement Apparatus

Decay half-life measurements were performed at the CSM lab in the USGS Reactor building at the Denver Federal Center in Lakewood Colorado using the HPGe detectors shown in Figure 1.1.

3.1.1 The USGS TRIGA Reactor

The neutron activation of the chromium, gold/chromium, ruthenium, ruthenium oxide, and zinc samples was done at the USGS TRIGA reactor. TRIGA (Training, Research, Isotopes, General Atomics) is a small research nuclear reactor manufactured by General Atomics. The USGS TRIGA design uses uranium-zirconium hydride fuel, operates at 1 ⇠ MW of power, and produces 1012 thermal neutrons per cm2 per second in the “dry tube” ⇠ location for neutron activation of small (usually less than one gram) samples. TRIGA has an installed base of over sixty-five facilities in twenty-four countries on five continents. General Atomics TRIGA reactors around the world have a variety of config- urations and capabilities, with steady state power levels ranging from 20 kilowatts to 16 megawatts. The TRIGA reactor is designed with inherent safety; from a shut-down con- dition with all control rods instantaneously removed, the reactor would settle down to a steady level of operation without melting any of its fuel. As described by General Atomics

[25], the warm neutron principle is a part of the design of an inherently safe reactor. In a water-cooled reactor, suddenly removing the control rods is a catastrophic accident, leading to a melting of the fuel as the neutrons from the ﬁssion reaction remain cold from interacting

12 with the cold water around the fuel and maintain their ability to cause further fissioning of uranium atoms in the fuel. This in turn results in the temperature of the fuel continuing to increase rapidly until it finally melts. In a TRIGA reactor the moderation of neutrons is due to the hydrogen that is mixed in with the fuel. As the fuel temperature increases when the control rods are suddenly removed, the neutrons inside the hydrogen-containing fuel rod become warmer than the neutrons outside in the cold water. The warmer neutrons inside the fuel cause less fissioning in the fuel and escape into the surrounding water. The reactor automatically reduces power within a few thousandths of a second as the fuel rods act as an automatic power regulator, shutting the reactor down.

3.1.2 ORTEC HPGe Detectors

Measurement of decay radiation was performed using HPGe detectors manufactured by the ORTEC products group of AMETEK, Inc. High purity germanium detectors have been developed to create active volumes large enough for e↵ective gamma-ray detection. Large depletion depths can be achieved with germanium impurity concentrations of approximately 1010 atoms/cm3 (Knoll [26]). Due to the small band gap (0.7 eV) of germanium these detectors must be cooled to liquid nitrogen temperature (77 K) in order to reduce thermally induced leakage current. This is done by housing the germanium detector crystal in a cryostat attached to a liquid nitrogen (LN) dewar. The dewars hold approximately 30 liters of LN and must be refilled every week. The three HPGe detectors in the lab have excellent energy resolution performance. The HPGe detector in the lab that was used for this study has the name “Loaner 4” and is a 25% relative eciency1 detector. The detectors interface to the PC using ORTEC boards as shown in Figure 3.1. The first board on the left (Ethernim) serves as the multi-channel bu↵er (MCB) and the interface to the PC via Ethernet. The next board on the right is the analog-to-digital-convertor (ADC), then on the right are the high voltage (HV) power supply and amplifier boards. A block

1Relative eciency is deﬁned as the eciency of a point Co-60 source at 25 cm from the face of a standard 3-inch x 3-inch right circular cylinder NaI(Tl) detector.

13 Figure 3.1: ORTEC HPGe Interface Boards

Figure 3.2: HPGe Detector Block Diagram

14 diagram showing how these components are functionally connected is shown in Figure 3.2.

3.1.3 MAESTRO Software

The HPGe detectors are controlled by MAESTRO software from ORTEC running under Windows XP on two PCs in the lab. MAESTRO, combined with ORTEC multichannel bu↵er hardware, emulates a multi-channel analyzer. The multi-channel bu↵er performs pulse height analysis, and the computer and operating system display the count data, perform data archiving, and interface to the hardware via drivers.

3.1.4 PC Clock Synchronization

In order to provide accurate time measurements the clock on each of the PCs is synchronized by a signal provided by the National Institute of Standards and Technology (NIST). The Meinberg2 WVB600USB is a radio clock, shown in Figure 3.3 that receives the WWVB long wave time signal and synchronizes a PC or laptop using a USB connection. WWVB is a NIST time signal radio station near Fort Collins, Colorado. NIST continuously broadcasts digital time codes on a 60 kHz carrier that serves as a stable frequency reference traceable to the national standard. The measurement accuracy goal requires PC clock synchronization because PC clocks drift signiﬁcantly and lose accuracy, especially over the periods of time of the longer measurement campaigns.

3.2 Pure Chromium Campaign

The ﬁrst data acquisition campaign of this research measured the electron capture decay half-life of 51Cr in pure chromium.

3.2.1 51Cr Decay Scheme

The decay scheme for 51Cr is shown in Figure 3.4 (Brookhaven [27]). 51Cr decays by electron capture either to the ground state of 51V(90.11%)orviathe320keVexcitedstate of 51V(9.89%).

2www.meinbergglobal.com/english/products/usb-clocks.htm

15 Figure 3.3: WWVB Receiver

Figure 3.4: 51Cr Decay Scheme

16 3.2.2 Chromium Sample Preparation

Pure chromium was obtained from Alfa Aesar, a company that provides materials for research. A small piece of the pure chromium material weighing 5mgwassealedinasmall ⇠ plastic packet for irradiation. 51Cr is formed by the neutron capture of 50Cr (4.345% in a natural distribution of chromium isotopes) in the reaction 50Cr(n, )51Cr.

3.2.3 Irradiation and Decay Count Spectrum

The sample was irradiated in the USGS TRIGA reactor for 45 minutes. After a short cool-down period, it was then placed in slot ﬁve in the Loaner 4 detector, 41.75 mm from

the detector. The eciency for slot 5 in the Loaner 4 detector for 320 keV was measured to be 0.59% ( 10%). The 320 keV line for 51Cr was measured for 210 days (7.6 half-lives) with ± 7,924 30-minute measurements. The initial decay rate of the 320 keV line of the sample was 169 decays per second, consistent with the mass of the sample and eciency of the detector. The full decay count spectrum across all 8,192 channels of data is shown in Figure 3.5. The region of the 320 keV line is expanded in Figure 3.6. The calculation for the estimate of electron decay half-life for this data is presented in Chapters 4 and 5.

3.3 Gold/Chromium Campaign

Asampleofchromiumatomsmixedinagoldlatticewaspreparedbysputteringgold and chromium together onto a Grafoil (i.e. ﬂexible graphite) substrate obtained from Alfa Aesar. The gold and chromium was co-sputtered together and then annealed (as described in the following section) to create a lattice where chromium atoms are surrounded by gold atoms. The main gold gamma line at 412 keV comes from 198Au, as shown in the decay scheme in Figure 3.7.

3.3.1 Sample Preparation for Sputtering

A set of test runs were made to determine the amount of gold and chromium that would be deposited for a given HV power on the target (MW) and time of sputter. These gold and

17 Figure 3.5: Full Pure Chromium Campaign Spectrum

18 Figure 3.6: Pure Chromium Spectrum in Region of 320 keV

19 Figure 3.7: 198Au Decay Scheme chromium target test runs were performed in order to better understand the amount of each material that was expected to be deposited. The data from these runs is in Table B.1 in the appendix. The sputter machine used to prepare the AuCr sample is shown in Figure 3.8. Fig- ure 3.8(a) shows the way the sample is held by the holder disc in the machine and Fig- ure 3.8(b) shows the main sputter chamber. A co-sputter of gold and chromium was run with the following parameters:

• Pressure before: 7.7 x 10-7 mbar

• Pressure after: 10 mTorr (Ar)

• Time: 10 minutes

• Power: 75W Au, 100W Cr

• Bayonet height: 30 units

From the target test run data approximately 2000 Angstroms of gold was deposited and approximately 700 Angstroms of chromium were deposited, 26% chromium by volume of non-annealed materials. The anneal lamps were turned on 30 seconds after the end of ⇠

20 (a) Sputter Machine (b) Main Chamber

Figure 3.8: Sputter Apparatus

the sputter session. The sample was then annealed for one hour at 300 °C(stableafter seven minutes) using the heat lamp in the sputter chamber, ﬁfteen minutes at 12 mbar (Ar) pressure before changing to vacuum (approximately 5 x 10-6 mbar) for the remainder. The temperature rose from 15 °Cover2minutesthenjumpedveryquicklyafter100°Cto330

°C in under a minute. After the anneal the sample cooled in a 100 mTorr N2 environment

to 200 °CbypartiallyclosingthemainchamberpumpandleakinginN2.Thenthesample was moved into the sample loading chamber to rest in air until it was cool enough to work with ( 30 minutes). ⇠ The mount for the sputter target is shown in Figure 3.9, the mount is shown on the left in Figure 3.9(a) and the grafoil piece is shown in Figure 3.9(b). A proﬁler was used to determine the thickness of the material that was laid down as shown in Figure 3.10 on the left is the machine in Figure 3.10(a) and on the right is the display in Figure 3.10(b) .

21 (a) Sputter Target Holder (b) Grafoil Substrate

Figure 3.9: Sputter Target Preparation

(a) Proﬁler Chamber (b) Proﬁler Display

Figure 3.10: Proﬁler Machine

22 Figure 3.11 shows the packaging of the AuCr sample for irradiation. The AuCr sputter sample was cut up into small squares as shown in Figure 3.11(a). The squares were sealed in a small packet; one of the squares (on the right) was set aside for x-ray di↵raction (XRD) analysis as shown in Figure 3.11(b). The total weight of the AuCr Grafoil sample was 0.89

(a) AuCr Sputter Sample Cut Up (b) AuCr Sample Packaging

Figure 3.11: AuCr Sample Preparation grams, the initial estimate of material laid down was 2mgofchromiumand 10 mg of ⇠ ⇠ gold.

3.3.2 Irradiation and Decay Spectrum

The AuCr sample was irradiated for one hour in the TRIGA reactor dry tube. Because of the large amount of gold in the sample the activity was very high, initially 51 mR/hr

198 , at 12 inches. After a 38 day cool-down, the Au (T1/2 =2.7days)gammaline was reduced suciently and did not interfere with the 51Cr measurement. The dead time of the measurements was solely due to the 51Cr line and was very small. After 84 days of measurement ( 3 half-lives) in slot 5 of the Loaner 4 detector a very clean spectrum ⇠ was seen. The full spectrum plot of the AuCr data is shown in Figure 3.12. The part of the spectrum near the measurements is shown in Figure 3.13. No competing gamma lines contaminated the half-life decay count measurement.

23 Figure 3.12: Full AuCr Spectrum

24 Figure 3.13: AuCr Spectrum in Measurement Region

25 3.3.3 Mass from Activity Analysis

The mass of chromium can be roughly inferred from the 51Cr activity. The Erdtmann [28] neutron activation tables have a value of 84.3 decay per sec of activity per µgram of chromium for a 1 hour irradiation of 1.2 x 1012 thermal neutrons per cm2 per second. Mass can be inferred from activity at irradiation time divided by the Erdtmann activity per unit mass. After irradiation for 1 hour and the 38 day cooling o↵ period, the activity of the 320 keV line of 51Cr was 6.45 decays per second. Accounting for the natural occurrence of 50Cr of 4.345% and the approximate eciency for the 320 keV gamma line of the Loaner 4 detector at slot 5 of 0.59% the mass of sputtered chromium from the activity of the sample is estimated to be 0.8 mg, somewhat less than the original sputter estimate of 2mg. ⇠ 3.4 Ruthenium Crystal and Ruthenium Oxide Campaigns

The change in electron decay half-life for 97Ru in a pure crystal versus in ruthenium oxide was explored in two measurement campaigns.

3.4.1 Electron Capture Decay Scheme of 97Ru

The electron capture decay scheme for 97Ru is shown in Figure 3.14 (Goodwin et al. [8]). 97Ru decays by electron capture to the ground state of 97Tc via the 216 keV level of 97Tc (87.7%).

3.4.2 Irradiation and Decay Count Spectra

The ruthenium samples in sealed packets are shown in Figure 3.15. The ruthenium crystal sample was a 99.999% chemical purity single circular disk (8 mm by 1 mm) crystal of ruthenium obtained from Goodfellow Corp. and shown in Figure 3.15(a). The ruthenium oxide sample, made from 5 mg of material obtained from Alfa Aesar, is shown in Figure 3.15(b).

26 Figure 3.14: 97Ru Decay Scheme

(a) Ruthenium Crystal (b) Ruthenium Oxide

Figure 3.15: Ruthenium Samples

27 3.4.3 Ruthenium Crystal

The ruthenium crystal was irradiated for 1 minute in the TRIGA dry tube ﬂux of 1012 ⇠ thermal neutrons per cm2 per second, and 133 six hour measurements were taken over a 33 day campaign (11.7 half-lives of 97Ru decay). A plot of the full decay count spectrum for the ruthenium crystal is shown in Figure 3.16 and the expanded plot of the measurement region

Figure 3.16: Full Ruthenium Crystal Spectrum

is displayed in Figure 3.17. The large peak at 497 keV of 103Ru, which has a long half-life of 39.27 days, is the main contributor to the dead time of the spectrum for late times.

28 Figure 3.17: Ruthenium Crystal Spectrum in Region of Measurements

29 3.4.4 Ruthenium Oxide

The ruthenium oxide sample was activated for 15 minutes in the TRIGA dry tube, and 101 six hour measurements were taken over a 25 day campaign (8.9 half-lives). A plot of the full decay count spectrum for the ruthenium oxide sample is Figure 3.18. The region of

Figure 3.18: Ruthenium Oxide Full Spectrum the 216 keV line is expanded in Figure 3.19. The purity of the ruthenium oxide sample is not as high as the ruthenium crystal and numerous gamma lines exist in the RuO2 sample spectrum.

30 Figure 3.19: Ruthenium Oxide Spectrum in Region of Measurements

31 3.5 Zinc Campaign

The beta-minus decay half-life of 71mZn was measured in the final campaign of this research. Recent high precision measurements of the decay half-life of 71mZn by Reifarth et al. [4] are significantly di↵erent than earlier measurements. A motivation for this research was to use zinc enriched in 70Zn in order to observe a cleaner 71mZn signal to check the findings of Reifarth. Zinc oxide (ZnO) enriched in 70Zn was obtained from Trace Sciences International in order to enhance 71Zn production and signal after neutron activation. The isotopic composition of the sample as certified by Trace Sciences International is shown in Table 3.1. A sample

Table 3.1: Enriched 70Zn Sample Isotopic Composition

Isotope 64 66 67 68 70 Enrichment % 0.07 0.09 0.08 5.81 93.95

was fabricated by placing the material in a sealed packet as shown in Figure 3.20.

Figure 3.20: Enriched 70Zn Sample (Powder)

32 3.5.1 Decay Scheme of 71Zn

71mZn is produced by thermal neutron activation of 70Zn with a total reaction Q value of 2810.2 keV. The beta minus decay scheme for 71Zn (Abusaleem and Singh [29]) is shown in Figure 3.21. 71Zn decays with a half-life of approximately four hours by beta minus decay

Figure 3.21: 71Zn Decay Scheme

to the ground state of 71Ga via three prominent gamma lines: 386 keV, 487 keV, and 620 keV, highlighted in the ﬁgure.

3.5.2 Irradiation and Decay Count Spectrum

The enriched 70Zn sample was activated for 1 hour in the TRIGA dry tube, and 117 half hour measurements were taken over a 2.5 day period, about 15 half-lives of 71mZn. The activity was followed until no signiﬁcant signal above background could be detected. A plot of the full decay count spectrum for the 71Zn measurement campaign is shown in Figure 3.22. The region of the 71Zn gamma lines line is expanded in Figure 3.23. The results of this data

33 Figure 3.22: Full 71mZn Sample Spectrum

34 Figure 3.23: 71mZn Spectrum in Region of Measurements

35 and the half-life measurements derived from it are presented in Chapter 6.

36 CHAPTER 4 HALF-LIFE ANALYSIS METHODS

The data collection campaigns discussed in Chapter 3 generated a large amount of data in the form of decay counts distributed in multi-channel analyzer (MCA) bins. A signiﬁcant part of this research was the development of data analysis methods to eciently process this data into high precision half-life measurements with estimates of both statistical and systematic standard error.

4.1 Radioactive Decay Equation

Radioactive nuclear decay is a quantum mechanical process described probabilistically, not because of any limitation to the physical model, but as a profound and fundamental part of the physics (Bell [30]). The equation for the nuclear rate of decay is dN = N (4.1) dt

-t with solution N = N0 e where N is the number of radioactive nuclei; is deﬁned as the decay constant, and N0 is the initial (at time = 0) value. The half-life of a radioactive decay

T1/2 is the time interval in which the original number of nuclei is reduced to one-half. ln 2 T = (4.2) 1/2

4.1.1 Linearization Method Not Adequate for High Precision

A common method used to calculate the half-life of radio-active decay data is to linearize

-t the data. Taking the natural logarithm of the both sides of N = N0 e yields the equation

ln(N) = ln(N0)-t, a linear relationship between t and ln(N) that has - as slope. When the natural logarithm function is applied the equation of a straight line in t is obtained and aﬁtismadebylinearweightedleastsquaresregression.Thismethodisadequateforpreci- sion uncertainty of 1.0% or greater, however for a precision goal of 0.1%, a strictly unbiased

37 method is required. Fraile and Garcia-Ortega [31] argue against the linearization method for calculating for the exponential distribution. They illustrate that this is equivalent to a least squares ﬁt with a weight function that assigns more importance to the higher (later) values of time. Fraile and Garcia-Ortega argue that the method of maximum likelihood should be applied for cases of high precision, because it takes into account all of the data equally.3 For this reason a full maximum likelihood solution to ﬁtting a single exponential including background calculation to the decay data is calculated for the half-life measurements, employing a Levenberg-Marquardt algorithm implemented in the R statistical language, as discussed in Subsection 4.3.3.

4.2 Protocol for Uncertainty Assessment of Half-lives

The protocol for uncertainty assessment of half-lives as given by Pomméet al. [1] describes methods for analyzing uncertainty in half-life measurements. This protocol gives arealisticerrorbudgetinwhichtheexperimentaluncertaintiesforhalf-lifemeasurements are subdivided into categories according to the time frame in which they occur. Because observations of half-life decay can be correlated over time measurements must be tested and verified for randomness. The validity and interpretation of statistical tests for half-life uncertainty estimates assumes that the data does not contain systematic non-random patterns. Error residuals are the di↵erence between the measured data points with the fit points and indicate the convergence of the fit. An exponential fit to decay data is valid only if the error residuals are stochastic and do not contain systematic deviations or patterns. As prescribed by Pommé, autocorrelation calculations and lag plots along with the Breusch-Godfrey test were used in this research to quantitatively check for randomness in nuclear decay data.

4.2.1 Uncertainty Deviation Models

Measurements of decay half-lives can fail to take into consideration the e↵ects of medium and long-term instabilities. There can be low, medium, and high frequency deviations as

3In the case of an exponential function, the maximum likelihood and the method of moments solutions are identical (Cleveland [32]).

38 shown in Figure 4.1. High frequency deviations are sources of uncertainty that occur at a rate greater than the measurement interval of one set of data. Poisson distributed stochastic counting statistics for half-life measurements are an example. Poisson processes have an exponential distribution of the interval times between successive events. High frequency instabilities such as electronic noise are also included in this category. Normal statistical techniques can be applied if the data is shown to be suciently random. Medium frequency deviations show up as a short-term trend in the residuals; these include seasonal or weekly e↵ects. This e↵ect is often underestimated by looking only at the goodness of fit statistical parameters. In addition, a fit minimizes the residuals and can cover-up these e↵ects. Examples include interference by radioactive impurities, reproducibility of the source-detector geometry, and changes in detector eciency from temperature, pressure, vibrations, and humidity. If the medium-term e↵ects are not clearly visible in the residuals an autocorrelation plot (or correlogram) can be used to check the randomness of the data. Low frequency deviations include sources of uncertainty that occur at a rate that is lower than the duration of the whole measurement campaign. They are practically invisible to the residuals and the fit will compensate for this trend and can erase it erroneously. Common problems in this range are the systematic errors in the background subtraction, dead time correction, long-term drift of the counting eciency, and source degradation (e.g. source oxidation).

4.3 Data Processing Methods

Processing the large amount of MCA data was automated as much as possible using

ORTEC MAESTRO, Radware gf3, and RStudio software scripts.

4.3.1 Half-life Data Collection using ORTEC MAESTRO Software

Data acquisition for ORTEC HPGe detectors is managed by ORTEC MAESTRO software running on Windows XP. Each of the PCs in the laboratory has MAESTRO software

39 Figure 4.1: Uncertainty Sources (from Pomm´eet al. [1]) that interfaces with the detector via ORTEC electronics over an Ethernet connection. MAE- STRO has the capability to automatically acquire count data in regular unattended time intervals by means of a scripting language. An example of a MAESTRO script is given in Listing A.1. The run data is stored by the MAESTRO script in the following three di↵erent ﬁle formats.

1. The .CHN ﬁles (CHaNnels) are the MAESTRO document ﬁles and store all of the

data from the data acquisition session. These are spectral data ﬁles in binary format.

Opening this ﬁle under MAESTRO allows the user to return the program to the state

at the end of the data acquisition period.

2. The .RPT ﬁles (RePorT) are ASCII text ﬁles that are the output of the MAESTRO

analysis engine. Data provided includes real and live times of the data acquisition session, ROI parameters, gross and net count data from MAESTRO’s count area algorithm, and nuclides identiﬁed from the MAESTRO gamma line library.

40 3. The .TXT files (Text) are general ASCII text files used by the MAESTRO File/Print facility. This file contains all of the MCA count data from each of the separate channels and as such represents the raw spectral data for each data acquisition session.

MCA bin data was taken at regular intervals after which the three files were written in sequential order, with a number between 000 and 999 (e.g. 123.CHN, etc.). After 999 the numbering sequence wraps and data is overwritten; care was taken to avoid this. The .RPT files were processed using a python script that extracts and stores in a comma separated value file the gamma line data at the energy of interest. An example report python script is shown in Listing A.3.

4.3.2 Method for Analyzing Gamma-ray Spectra Using gf3

The gf3 program, a part of RadWare4,wasusedtoanalyzethegammaspectra.RadWare is a software package for interactive graphical analysis of gamma coincidence data developed by David Radford of the Physics Division at Oak Ridge National Laboratory. Gf3 is a least- squares peak fitting program for analyzing gamma spectra from HPGe detectors that fits a portion of the spectrum using the sum of up to fifteen peaks on a quadratic background. Each peak is composed of three components: (1) a Gaussian, (2) a skewed Gaussian, and (3) a smoothed step function to increase the background on the low-energy side of the peak. Components (2) and/or (3) can be set to zero if not required. Component (1), the Gaussian, is usually the main component of the peak, and in HPGe detectors, physically arises from complete charge collection of a photoelectric event in the detector. Component (2), the skewed Gaussian, arises from incomplete charge collection, often due to “trapping” of charge at dislocations in the crystal lattice caused by impurities or neutron damage. If the detector and electronics had perfect resolution, component (1) would be a delta-function and component (2) would yield an exponential tail on the low-energy side. Component (3) arises mainly from Compton scattering of photons into the detector and from

4http://radware.phy.ornl.gov

41 escape of photoelectrons from the Ge crystal, which result in a slightly higher background on the low-energy side of the peak. Figure 4.2 taken from the gf3 documentation shows the three components of the gf3 peak ﬁtting approach.

Figure 4.2: gf3 Fit Components

The MCA data in the .TXT files was converted to a format for use with gf3 using the rwspec code written by the author in C and shown in Listing A.2. The gfinit file initiates gf3 and is shown in Listing A.4. Three other python scripts are used to manipulate the data; these are shown in Listing A.5, Listing A.6, and Listing A.7. The data is combined into an

Excel spreadsheet for checking the data and correlating the time stamps. The data is then exported in a .csv ﬁle for import into the R program.

The order of processing for the gf3 is as follows:

1. Copy rwspec, sum.py, fit.py, sto.py,andgfinit.dat to the folder with the MAESTRO .TXT files

42 2. Determine the range of ﬁles for processing. (For this example assume a range of 000 to 100.)

3. Run rwspec:“rwspec000100”.Thiswillcreateagf3.spespectrumﬁleforeachofthe .TXT ﬁles.

4. Run sum.py by clicking on the ﬁle to launch the Python Launcher and enter 1 100 for the values (the ﬁrst number is one greater than the starting number) to generate the gf3 script s001 100.cmd.

5. Run ﬁt.py is a similar fashion and enter 0 100 to generate the gf3 script f000 100.cmd.

6. Run gf3 for the ﬁrst spectrum: “gf3 000”. Inside this gf3 session run the following commands.

(a) cf s001 100 (this command file creates a new spectrum file to be read by summing up all of the .spe files into one and naming it s001 100.spe)

(b) st (stop/end the session)

7. Run gf3 for the new summed .spe ﬁle: “gf3 s001 100”. Inside this gf3 session run the following commands.

(a) ms 0.01 (or 0.001, this rescales the spectrum for a better ﬁtting)

(b) fx rw (ﬁx relative widths5)

(d) af 1 700 750 (where the numbers are the energy spread for the ﬁt)

5Fixing the relative positions and/or widths is very useful in analyzing a series of spectra for which there may be slight gain shifts, so that the peaks may move slightly in absolute position but have a constant spacing. Fixing the relative widths from the start of a fit also has the e↵ect of fitting one common width to all peaks in the fitted region. This is usually an excellent approximation, and has the additional advantage of decreasing the uncertainties on the peak areas, especially for weak peaks.

43 (e) ft (and return)

(f) cf f000 100 (this runs the command ﬁle to calculate the areas)

(g) st (stop/end the session)

(h) y (conﬁrm)

8. Move the .sto ﬁle to another name: “mv gf3.sto f000 100.sto”

9. Run sto.py and enter for the values: 000 100, this will write the ﬁle f000 100.txt, which contains the gamma line area and time data.

10. Import the f000 100.txt ﬁle into a spreadsheet for export to RStudio.

4.3.3 RStudio, a Statistical Computational Tool

Risalanguageandenvironmentforstatisticalcomputingandgraphics6.Rprovides awidevarietyofstatisticaltechniques.RStudioisanopensourceintegrateddevelopment environment (IDE) for R. RStudio scripts were used to calculate the maximum likelihood ﬁt to a single exponential using a Levenberg-Marquardt non-linear least-squares scheme. Exponential ﬁt error residuals and autocorrelation lags were also calculated and are presented for each measurement campaign in Chapter 5. RStudio scripts for calculating the half-life values using R are given in A.8 through A.11.

4.4 Data Analysis Methods

For each measurement campaign, a single exponential function using a maximum likelihood (non-linear least-squares) method was ﬁt to the decay counts corrected for dead time.

The dead time correction is done by taking the average activity (actual counts divided by live time) and multiplying it times the actual time of the measurement interval. The live time of a measurement interval is calculated as the actual time of the measurement interval

6http://www.r-project.org

44 minus the dead time, as estimated from the MAESTRO software and described in section 4.5. For each curve fit, error residuals are the di↵erence between the measured data points with the fit points, and are an indication of the goodness of the fit. An exponential fit to decay data is valid only if the residuals are randomly distributed and do not contain systematic deviations or correlated patterns.

4.4.1 Autocorrelation as a Data Acceptance Criterion

In statistics, correlation is the degree to which two random variables depend on each another; correlation analysis quantifies the strength of an underlying relationship. Autocor- relation is the cross-correlation of a time series with itself (Box and Jenkins [33]). Auto- correlation plots (also called correlograms) describe the correlation between all the pairs of points in the time series with a given time separation - or lag. Randomness can be quantified by computing autocorrelations for data values at varying time separations. If the data is random, the autocorrelations should be near zero for all time lags. If non-random, then one or more of the autocorrelations will be significantly non-zero. Autocorrelation values of a time series should be near zero all time-lag separations if the data is randomly distributed. (By definition the first autocorrelation, lag zero, always has a value of one.) In this analysis the regression fit residuals are tested for autocorrelation. Equation 4.3 gives the formula for

the autocorrelation coecient r for lag k where Y¯ is the mean of the data points Yi.

N k (Y Y¯ )(Y Y¯ ) i i r = i=1 (4.3) k X N (Y Y¯ )2 i i=1 X Because radioactive decay is a fundamentally probabilistic process, adjacent sets of count data should not correlated if the time interval of the measurement is much smaller than the half-life. The small amount of negative correlation because of exponential decay will not be seen if the time di↵erence between measurements is small. This is also true for the regression

45 ﬁt residuals.

4.4.2 The Breusch-Godfrey Autocorrelation Test

The Breusch-Godfrey (BG) test (Breusch [34], Godfrey [35]) in statistical theory is used to quantify the e↵ects of serial auto-correlation in time series. It is more general and more powerful than the Durbin-Watson (DW) test (Durbin and Watson [36]); the DW test is a special case of the BG test. The full name is Breusch–Godfrey serial correlation Lagrange multiplier test which indicates the nature of the algorithm which uses a Lagrange multiplier scheme. The BG test is general in that it can accommodate tests of order greater than 1, where the order is the distance between data points being tested for serial correlation. All BG tests in this dissertation are first-order serial tests, i.e. regression fit residuals are tested for serial correlation with adjacent residuals. The p-value of a statistical significance test is the probability that the test statistic, the Breusch-Godfrey parameter in this case, is farther out on the tail of the distribution than the observed data, assuming that the null hypothesis is true. The null hypothesis here is that the data is not autocorrelated, and it is rejected when the p-value is less than a significance level, indicating that the observed result is highly unlikely for the null hypothesis. In other words, the observation is highly unlikely to be the result of random chance. When the p- value is greater that 0.10, there is no evidence against the null hypothesis; the data appear to be consistent with the null hypothesis that there is no autocorrelation. When the p-value is between 0.05 and 0.10, there is weak evidence against the null hypothesis in favor of the alternative, i.e. the data is autocorrelated. When the p-value is between 0.01 and 0.05 there is moderate evidence against the null hypothesis in favor of the alternative, and when the p-value is less than 0.01 there is strong evidence against the null hypothesis, and there is strong evidence that the data is autocorrelated. As a criterion for data acceptance for half- life values used in this research a p-value greater than 0.001 (at the 0.1% level) was used. With this criterion only highly correlated data is rejected; this is an inclusive approach which accepts data unless there is irrefutable evidence for autocorrelation.

46 For each campaign, the activity data, exponential error ﬁt residuals, autocorrelation lags, Breusch-Godfrey test p-values, half-life measurements and uncertainty standard errors are presented and discussed.

4.4.3 Simulated Data Used as a Reference for Statistical Consistency

Ideal simulated decay data can be generated by sampling a random variable with a Poisson distribution at regular intervals. This simulated data is a near exact representation of a perfect measurement; only the approximation of the Poisson distribution for the Binomial distribution and imperfect random number generation is inexact in this description. Superior statistical outcomes than the simulated data for a given experiment cannot be expected, and in this way the simulated data represent an ideal bound on the outcome.

For a given initial count N0 at time t,aPoissondistributedrandomvariablewithexpected

- t value and variance equal to N = N0 e 4 will yield a value consistent with ideal decay counting measurements (Knoll [26]) at the next time interval t + t. New values of N 4 can be calculated at subsequent times according to the decay law using derived from the established value of half-life. This is possible to do in R using the rpois function. Data generated in this way represents stochastically near-perfect data and provides an informative comparison with the actual measurements. This is illustrated in Figure 4.3 where Figure 4.3(a), Figure 4.3(b), Figure 4.3(c), and Figure 4.3(d) are four Monte Carlo realizations7 of the Poisson sampling of data with starting activity of the AuCr campaign are shown. These ﬁgures show half-life as a function of

succeeding starting point in the data. The x-axis is the number of days into the data

that the half-life calculation was started, or the number of days of data excluded from

the beginning of the half-life calculation. Analysis of this type can uncover non-stochastic

behavior in the data as a function of time. Figure 5.13 shows the measured AuCr campaign

data for comparison. As a consistency check, data points were removed in this way from the beginning of the data set to uncover any non-stochastic behavior. Succeeding points are

7Each simulation is equally likely and is referred to as a realization of the system.

47 (a) Monte Carlo Realization 1 (b) Monte Carlo Realization 2

Figure 4.3: AuCr Monte Carlo Half-lives for Varying Starting Point

48 used as starting point for the half-life calculations that are used for comparison. For each of the campaigns, a plot of these succeeding half-lives is shown, and along with a plot of Monte Carlo data generated using the equivalent initial count.

4.4.4 Half-life Measurements and Uncertainty Analysis

Half-life measurements and systematic and statistical uncertainties were calculated using the net count values calculated by gf3 corrected for live time employing the analytical methods described in this subsection 4.4. Statistical uncertainties are the standard error values from the Levenberg-Marquardt (LM) algorithm used in the determination of the half-life value. The LM algorithm is widely used for least squares estimation of non-linear parameters (Marquardt [37]). It outperforms other conjugate gradient methods in a wide variety of minimization problems. Nonlinear least squares methods involve finding parameters in an iterative scheme to reduce the sum of the squares of the errors between the function and the measured data points. The LM curve-fitting method combines the gradient descent method and the Gauss-Newton method. In the gradient descent method, the sum of the squared errors is minimized by updating the parameters in the direction of the greatest reduction of the least squares. In the Gauss-Newton method, the sum of the squared errors is decreased by assuming the least squares function is locally quadratic, and finding the quadratic minimum. The LM approach acts more like a gradient-descent method when the parameters are far from their optimal value, and acts more like the Gauss-Newton method when the parameters are close to their optimal value. The LM method has the flexibility to switch between the gradient-search method when far from the minimum to the Gauss-Newton method close to the minimum.

The ﬁnal half-life value and systematic uncertainty were calculated in the following way.

After excluding initial data with maximum dead times greater than 1.5% (as described in subsection 4.5) or Breusch-Godfrey p-value consistently greater than 0.001, the half-life value of the first point satisfying these criteria is the ocial half-life value for the campaign. The final value quoted for the half-life in this dissertation is the half-life at the first accepted data

49 point.

4.4.5 Examining the Data for Possible Medium Term Periodic Patterns

The decay count data for chromium and ruthenium was examined for potential medium frequency deviations by calculating half-lives using data points at constant intervals. The possibility of weekly or daily correlations and periodic patterns in the data was investigated by calculating half-lives using subsets of points spaced by exactly either one week or one day apart. For example, a half-life was calculated using all data taken on Mondays at exactly same time with a subset of the data all from Tuesday at the same time, then all from Wednesday, and so forth. In doing this possible systematic errors that are dependent on weekly or daily variation can be discovered. In the case of the longer 51Cr campaigns lasting months, an examination of weekly variation was made. For the shorter ruthenium campaigns lasting a few weeks, daily correlations were also investigated. Daily correlation studies used data spaced 24 hours apart at the same time each day. Figure 4.4 is a plot of a study where data every seven days is computed and compared for the pure chromium campaign. There is no obvious non-stochastic medium term structure evident in this data, although a long term bias is evident in Figure 5.2. Likewise, Figure 4.5 is a plot of a study where data every 24 hours is computed and compared for the ruthenium crystal campaign where there is no strong daily correlation evident. Similar plots are presented and discussed in the section for each measurement campaign in Chapter 5. The overall conclusion is that there are no strong medium term periodic correlations evident in any of the campaigns.

4.4.6 Systematic Error Estimation

The constant interval approach was also used to estimate systematic error. Estimates of systematic error for a measurement system are typically derived from many sets of data in a series of repeated, controlled experiments. Because of the length of time for these measurement campaigns only one set of data of each is available. In addition, subsequent activations of the material samples used, such as the ruthenium crystal, result in residual activity that

50 Figure 4.4: Pure Chromium Week Correlation Study

Figure 4.5: Ruthenium Crystal Daily Correlation Study

51 increases the dead time of the measurement and interferes with the succeeding measure- ment8.Forthesereasonsestimatesofsystematicerrorinthisthesisaremadebycalculating the half-lives of independent subsets of periodic data and then deriving the standard error of the values. Good data should not contain a non-stochastic structure. This type of structure can indicate some sort of systematic problem with the measurement that has added a non- random error component, however even perfect data will have natural statistical variation. The approach used here for systematic error estimation attempts to quantify this. In a method similar to the analysis for medium term correlation, periodic intervals of data are formed from the set of accepted data. In this case, however, the interval is over a shorter period, all of the data is used, and no data point appears in more than one subset. In this way subsets of the data are created that are independent, and the half-lives from each subset is an estimate independent of all others. Because these are independent, they can be used to simulate the standard error of half-lives measured under varying conditions. As an example, Figure 4.6 is a plot of a study where 48 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared for the pure chromium campaign. The dashed lines are the standard error values formed by calculating the weighted standard deviation of the half-life values. The spread in the dashed lines is the systematic standard error, calculated by the weighted standard deviation of the 48 half-life values to be 0.163 days or 0.59%.

Even in ideal Monte Carlo data there is an inherent spread in the data in this analysis.

Figure 4.7 is a plot of the same study of 48 data sets of half hour measurements for the pure chromium campaign. As can be seen there is inherent variation in the data of 0.081 days or 0.29%. Because of this inherent statistical behavior the estimate for systematic error is a conservative number, representing an upper bound on systematic error. For each campaign, this method will be presented and the Monte Carlo case will be included for comparison.

8As another check of systematic error, data was taken using other detectors in the lab for the ruthenium cases; however, problems discovered with these detectors precluded their use.

52 Figure 4.6: Pure Chromium Systematic Error Study

Figure 4.7: Pure Chromium Monte Carlo Systematic Error Study

53 Finally, the results of the chromium campaigns are compared with the established half- life of 51Cr of 27.7010(11) days9 and the established half-life of 198Au of 2.6948(12) days (Audi et al. [38]). The established half-life values for 97Ru of 2.8370(14) days and 103Ru of 39.247(13) days (Audi et al. [38]) are compared with results of the ruthenium measurement campaigns to validate the estimates of systematic error, as will be discussed in Chapter 5. The systematic standard error estimate for the zinc campaigns is discussed in Chapter 6.

4.5 Dead Time Measurement Studies Using a Precision Pulse Generator

All of the early measurements in this dissertation relied on the dead time calculation done by the Ortec MAESTRO data analysis system. The later experiments with ruthenium and zinc had to be run at higher and varying dead times where the suspicion arose that the MAESTRO calculations might be erroneous. In order to quantify the e↵ects of dead time on the Loaner 4 detector measurements two studies were performed using the ORTEC precision pulse generator shown in Figure 4.8. The precision pulse generator introduces a constant signal to the detector system of 73.47 pulses per second rate. In the ﬁrst study, pulser measurements were taken without a radioactive sample present (i.e. a background measurement) and also during a second 71mZn measurement campaign. The data from this second zinc campaign was very noisy due to large dead times from high activity in the sample from a previous irradiation in the central thimble10 of the USGS reactor. The results of this campaign were only useful in determining valid dead time percentages.

The e↵ective dead time derived from counts from the precision pulser was calculated and

compared to the dead time measured by the ORTEC hardware and the MAESTRO program.

The dead time as determined by the pulser data can be established by ﬁrst calculating the

corresponding live time consistent with the rate of 73.47 pulser counts per second. The

number of pulser events detected over a measurement period divided by the actual number

9The 27.7010(11) notation signiﬁes 27.7010 0.0011 10The neutron ﬂux is considerably higher in± the central thimble than in the dry tube location.

54 Figure 4.8: ORTEC Precision Pulse Generator

of 73.47 pulses per second gives the e↵ective live time for the measurement period, as derived by the pulser data. The dead time is then simply the total (real) time minus the live time over the period. By comparing the dead time values from the pulser data and from ORTEC MAESTRO, it is possible to infer when the dead time correction displayed by MAESTRO is valid as shown in Figure 4.9. When the di↵erence of the two dead time values is not consistent the results are less valid11.Forearlymeasurementswithhighactivityandhigh dead time, the results from the two methods were somewhat inconsistent; only when the dead time displayed by MAESTRO is less than 3% is the di↵erence constant but still shows oscillation.

Therefore a second pulser study was performed using two 152Eu sources, a weak source and a strong source, which were measured at di↵erent locations in the Loaner 4 detector slots; the results are shown in Figure 4.10. As shown in the ﬁgure, the dead time values are consistent up to the 1.5% level, and after this the di↵erence between the MAESTRO and

11For half-life measurements the magnitude of the live time correction is not signiﬁcant, only the rate of change of the correction is important, a feature of the exponential decay function.

55 Figure 4.9: Zinc Pulser Study Results

Figure 4.10: Europium Pulser Study Results

56 the pulser dead times diverges. Because pulser dead time data measurement were not taken and only the MAESTRO vales are available, only MAESTRO dead time that is valid can be used. Future half-life measurement campaigns should use the precision pulser for higher dead time values. Thus a criterion of dead time equal to 1.5% or less is used for data acceptance for half-life calculations. This criterion plus the Breusch-Godfrey p-value criterion that is discussed in section 4.4 is applied to all of the data. Only data with less than 1.5% dead time and Breusch-Godfrey p-value greater than 0.001 are used in half-life calculations.

57 CHAPTER 5 RESULTS OF ELECTRON CAPTURE HALF-LIFE MEASUREMENTS

Chapter 5 will present the measured decay half-lives and the statistical uncertainty parameters that were calculated for the chromium and ruthenium electron capture half-life measurement campaigns using the samples and measurement methods of Chapter 3 and the analytical methods discussed in Chapter 4.

5.1 Pure Chromium 51Cr Results

Atotalof7,924half-hourmeasurementrunsweretakenofthe27.7dayelectroncapture decay half-life of 51Cr in a pure chromium sample over a 210-day measurement campaign. This was the ﬁrst measurement campaign of this research, and the PC clock was not synchronized for the entire campaign. The WVB600USB radio clock (described in section 3.1.4) was not acquired and installed until day 140 of the pure chromium campaign. For all later campaigns the PC clock time was synchronized for the full duration of the campaign. The data of the ﬁrst 140 days was taken using the standard PC non-synchronized clock with inadequate time accuracy, however, most of this early data was not used in the half-life calculation because of the BG correlation acceptance criterion (greater than 0.001). Only the data from day 125 until day 210 was used in the half-life calculation for the pure chromium 51Cr campaign. However, lack of PC clock synchronization may still have contributed to questions with the veracity of the data.

5.1.1 Pure Chromium 51Cr Decay Count Plot

The decay count data (beginning at 290,000) counts for the pure chromium campaign ⇠ are shown in Figure 5.1. Four gaps in the data occurred over the 210 day period. The two longest breaks in the 51Cr campaign allowed for short 97Ru decay measurements; the other breaks in the data were due to a mandatory power outage at the USGS reactor facility and

58 adataglitchintheOrtecdetectorsystem.Thegaps,whichoccurredinthemiddleofthe campaign, may have a↵ected the overall half-life measurement accuracy. The 51Cr sample was never moved from its ﬁxed position in front of the detector.

Figure 5.1: Pure Chromium 51Cr Decay Count Data

5.1.2 Half-life Values for Full Pure Chromium Campaign

Figure Figure 5.2 shows the full set of half-life values as a function of starting data point in the half-life calculation for the entire campaign. The ﬁgure shows an unmistakable trend in the data where the half-life values decrease from left to right. This problematic behavior indicates that there is a bias in the measurements in the ﬁrst half of the campaign and that these values are not statistically consistent.

5.1.3 Breusch-Godfrey Plot for Pure Chromium Data

Figure 5.3 shows the Breusch-Godfrey p-values as a function of varying starting point in the data. The plot shows that values of p-value are initially very low indicating highly

59 Figure 5.2: Pure Chromium Half-life Values for Later Starting Points

Figure 5.3: Pure Chromium Campaign Breusch-Godfrey P-Values

60 correlated data. The p-value goes above the 0.001 criterion value and then goes back below, indicating strong correlation recurring in the data. For this reason, the ﬁrst 125 days (4,000 data points) were not considered in the ﬁnal half-life calculation. The green dot in the plot indicates the starting value according to the data acceptance criteria of Breusch-Godfrey p-value greater than 0.001. All of the pure chromium campaign data had maximum dead time less than 1.5%, satisfying the dead time acceptance criterion. The maximum dead time percentage for the pure chromium data was 0.04%, the minimum was 0.02%, and the average was 0.02%.

5.1.4 Half-life Results for Pure Chromium for the Accepted Data

Figure 5.4 shows the value of the half-life at the ﬁrst point (in green) passing the acceptance criteria (starting with point 4,000 on day 125) along with the established 51Cr half-life of 27.7010(11) (Audi et al. [38]) shown as the dotted line. The dashed lines represent the total standard error of the measurement. Figure 5.5 is a plot of a Monte Carlo simulation

Figure 5.4: Pure Chromium Campaign Half-life Values data for the pure chromium case, shown for comparison. As shown, the ideal Monte Carlo data exhibits none of the bias evident in the measurement data.

61 Figure 5.5: Pure Chromium Monte Carlo Data

The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.054 days (0.20%); the Monte Carlo data has a standard error of 0.011 days (0.04%); the quadrature di↵erence is 0.053 days (0.19%). The exponential ﬁt residuals for the accepted pure chromium data are shown in Figure 5.6. These residuals of the 51Cr measurement campaign appear to be statistically consistent (other than the one outlier point at day 137) and exhibit no obvious non-stochastic structure. ⇠ Figure 5.7 is a plot of the autocorrelation lags of the pure chromium ﬁt residuals which shows that the later data satisfying the BG criterion is less correlated.

Figure 5.8 is a plot of a study where data every seven days at one day intervals is computed and compared as described in section 4.4.5. There appears to be no strong medium term structure evident in this subset of the data. The only non-stochastic structure in the data is the long term bias downward.

The pure chromium 51Cr electron-decay half-life was calculated in this way to be 27.621 days with a statistical uncertainty of 0.015 days (0.05%). The di↵erence of this measured value with the accepted 51Cr value of 27.7010(11) is -0.081 days, a di↵erence of -0.29%.

62 Figure 5.6: Pure Chromium 51Cr Exponential Fit Residuals

Figure 5.7: Pure Chromium Autocorrelation Lags

63 Figure 5.8: Pure Chromium Seven Day Correlation Study

5.1.5 Estimate of Systematic Standard Error for the Pure Chromium Measure- ment

Figure 5.9 is a plot of a study where 48 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The systematic uncertainty from this method is estimated to be 0.162 days (0.59%) from a consideration of the standard error of the half-life values in the graph above. The total uncertainty (statistical and systematic in quadrature) is 0.163 days (0.59%).

Figure 5.10 is a similar plot for Monte Carlo data. The standard error of the Monte Carlo data is 0.081 days (0.29%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate leaves 0.141 days (0.51%).

5.1.6 Pure Chromium Campaign Data Judged to be Spurious

Because of the exhibited long term bias in the half-life values, this data is deemed to be erroneous and was not used in comparison to the AuCr results. The established value for

64 Figure 5.9: Pure Chromium Systematic Error Study

Figure 5.10: Pure Chromium Systematic Error Monte Carlo Study

65 51Cr is used as the standard for comparison for the AuCr results.

5.2 51Cr in a Gold Lattice: AuCr Results

4,029 half-hour measurement sessions were taken of the electron capture decay half-life of 51Cr in the AuCr sample over a 84-day measurement, representing 3.03 half-lives. PC clock synchronization to the WWVB time signal was implemented for the entire campaign.

5.2.1 AuCr 51Cr Decay Count Plot

The decay count data (beginning at 11,500) counts for the AuCr campaign are shown ⇠ in Figure 5.11. No gaps occurred in the measurements over the period of the campaign. The

Figure 5.11: AuCr 51Cr Count Data

AuCr sample was allowed to cool after irradiation so the decay counts and therefore dead

times are low. The maximum dead time percentage for the gold chromium data was 0.38%, the minimum was 0.02%, and the average was 0.04%.

66 5.2.2 Breusch-Godfrey Plot for Gold Chromium

The Figure 5.12 shows the BG plot for the AuCr data. The data is consistently above 0.001. All of the data satisﬁes both acceptance criteria of dead time and BG p-value.

Figure 5.12: AuCr Breusch-Godfrey P-values

5.2.3 Half-life Results for AuCr for the Accepted Data

The full set of half-life values as a function of starting point are shown in Figure 5.13. The dashed lines represent the total standard error of the measurement. Simulated Monte Carlo half-life values for this case as a function of starting value are shown in Figure 5.14 for comparison. As can be seen in the plots, the measurement data compares more favorably to the simulated data than in the pure chromium case. The exponential ﬁt residuals for the

AuCr data are shown in Figure 5.15 where the data shown to be statistically well-behaved without obvious non-stochastic structure. The autocorrelation lag plot shows very clean and stochastically random data in Figure 5.16. None of the 4,029 data points were excluded in the calculation for 51Cr half-life. Figure 5.17 is a plot of a study where data every seven days at one day intervals is computed and compared. There appears to be no strong medium

67 Figure 5.13: AuCr Campaign Half-life Values for Later Starting Points

Figure 5.14: AuCr Campaign Half-life Values for Monte Carlo Simulation

68 Figure 5.15: AuCr Residuals

Figure 5.16: AuCr Autocorrelation Lags

69 Figure 5.17: AuCr Seven Day Correlation Study term structure evident in the data. The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.053 days (0.19%); the Monte Carlo data has a standard error of 0.041 days (0.15%); the quadrature di↵erence is 0.033 days (0.12%).

5.2.4 Estimate of Systematic Standard Error for the Gold Chromium Measure- ment

Figure 5.18 is a plot of a study where 48 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The systematic uncertainty from this method is estimated to be

0.148 days (0.53%) from a consideration of the standard error of the half-life values in the graph above. The total uncertainty (statistical and systematic in quadrature) is 0.149 days

(0.54%). Figure 5.19 is a similar plot for Monte Carlo data. The standard error of the Monte Carlo data is 0.104 days (0.37%). Subtracting out the Monte Carlo component in quadrature from

70 Figure 5.18: AuCr Systematic Error Study

Figure 5.19: AuCr Systematic Error Monte Carlo Study

71 the systematic error estimate leaves 0.106 days (0.38%).

5.2.5 198Au Half-life Measurement

In addition, data from the 412 keV 198Au line was processed to check against the established value of 2.6948(12) days (Audi et al. [38]). The full set of half-life values as a function of starting point are shown in Figure 5.20. Figure 5.21 is the the Breusch-Godfrey plot for

Figure 5.20: 198Au Half-life Values for Starting Point the 198Au data showing a starting point of 70, about 1.5 days into the campaign. Figure 5.22 shows the value of the half-life at the ﬁrst point (in green) passing the acceptance criteria

(starting with point 70) along with the established 198Au half-life shown as the dotted line. The dashed lines represent the total standard error of the measurement. Simulated Monte

Carlo data for this case are shown in Figure 5.23. The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.011 days (0.41%); the

Monte Carlo data has a standard error of 0.004 days (0.14%); the quadrature di↵erence is 0.010 days (0.39%).

72 Figure 5.21: 198Au Breusch-Godfrey P-values

Figure 5.22: 198Au Half-life Values for Later Starting Point

73 Figure 5.23: 198Au Data Half-life Monte Carlo Values

Figure 5.24 is a plot of a study where data in 24 hour intervals is computed and compared as described in section 4.4.5. There appears to be no obvious medium term structure evident in this subset of the data. Figure 5.25 is a plot of a study where 48 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. Figure 5.26 is a similar plot for Monte Carlo data. The standard error of the Monte Carlo data is 0.011 days (0.43%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate leaves 0.015 days (0.54%).

The half-life value for the 412 keV 198Au line from the measured data was determined to be 2.685(15) days, 0.37% lower than the accepted value. As a result of this measurement,

the systematic error of the AuCr measurement is conﬁrmed to be 0.5%. ⇠ 5.2.6 Comparison with Established Chromium Results

The 51Cr in AuCr electron capture decay half-life was 27.715 days with a statistical uncertainty of 0.016 days (0.06%) and a systematic uncertainty of 0.148 days (0.53%) for a

74 Figure 5.24: 198Au 24 Hour Correlation Study

Figure 5.25: Au Systematic Error Study

75 Figure 5.26: Au Systematic Error Monte Carlo Study total uncertainty (in quadrature) of 0.149 days (0.54%). Because of the dubious data of the pure chromium campaign, the comparison is made with the accepted 51Cr half-life value, as summarized in Table 5.1. The 51Cr half-life value

Table 5.1: Comparison of Established 51Cr Half-life versus AuCr Results

Sample Half-life (days) Stat. Uncertainty Sys. Uncertainty Total Uncertainty Established 51Cr 27.7010 – – 0.0011 (0.004%) AuCr 27.715 0.016 (0.06%) 0.148 (0.53%) 0.149 (0.54%) of 27.715 from the AuCr campaign is 0.05% greater than the accepted value of 27.7010(11)

(Audi et al. [38]) at a standard error of 0.54%.

5.2.7 Comparison to Previous 51Cr Measurements

The previously published results for 51Cr half-life measurements from Be et al. [39] are summarized in Table 5.2 and shown in Figure 5.27. Be et al. [39] found in a comprehen- sive survey of the existing half-life measurements of 51Cr that the average of the studies was 27.7010(12) days, an uncertainty of 0.01%. The 51Cr half-life result of this research,

76 Table 5.2: 51Cr Half-life Measurement Results

Half-life (days) Standard Error Year 26.0 1.0 1940 26.5 1.0 1940 27.75 0.3 1952 27.9 0.2 1956 27.8 0.1 1956 27.85 0.2 1957 28.04 0.16 1957 27.75 0.3 1957 27.82 0.2 1963 27.701 0.006 1964 27.7 0.2 1967 27.8 0.51 1968 27.704 0.003 1969 27.679 0.017 1970 27.76 0.15 1972 28.1 0.17 1973 27.721 0.026 1973 27.75 0.009 1973 27.703 0.008 1974 27.72 0.03 1975 27.69 0.005 1980 27.71 0.01 1982 27.705 0.012 1982 27.73 0.01 1982 27.704 0.003 1982 27.71 0.03 1983 27.7010 0.0012 1992 27.715 (This research) 0.149 2013

77 Figure 5.27: 51Cr Half-life Measurement History

27.715(149) days is a di↵erence of 0.05% from the accepted value, but with a standard error of 0.54%.

5.3 Ruthenium Crystal Results

133 six-hour measurement sessions were taken of the electron capture decay half-life of 97Ru in the ruthenium crystal sample over a 33-day period, representing 11.66 half-lives.

5.3.1 Ruthenium Crystal 97Ru Decay Count Plot

The decay count data for the ruthenium crystal sample are shown in Figure 5.28. No

gaps occurred in the measurements over the period of the campaign. The ruthenium crystal

sample was fairly large in mass which resulted in high activity and therefore high dead

times12.Themaximumdeadtimepercentageforacceptedrutheniumcrystaldatawas1.5%, the minimum was 1.17%, and the average was 1.33%, the highest of all of the campaigns.

12The activity of the sample was also higher because of residual activity from a previous activation.

78 Figure 5.28: Ruthenium Crystal 97Ru Activity Data

5.3.2 Ru Crystal Half-life Values

The complete half-life values for starting point are shown in Figure 5.29. The dashed line represents the established 97Ru electron decay half-life of 2.8370(14) days.

5.3.3 Breusch-Godfrey Plot for the Ruthenium Crystal

Figure 5.30 is the BG plot for the ruthenium crystal data. It shows highly correlated and stochastically non-random data for the ﬁrst 9 days (33 data points). The dead time criterion of 1.5% also excludes data up to day 19 (point 72), indicated by the green dot.

5.3.4 Half-life Results for the Ruthenium Crystal Campaign

Figure 5.31 shows the accepted data used for the ruthenium crystal half-life measurement.

Simulated Monte Carlo data for this case are shown in Figure 5.32. The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.039 days (1.39%); the Monte Carlo data has a standard error of 0.022 days (0.78%); the quadrature

79 Figure 5.29: Ruthenium Crystal Half-life Values

Figure 5.30: Ruthenium Crystal Breusch-Godfrey P-values

80 Figure 5.31: Ruthenium Crystal Half-life Values for Accepted Data

Figure 5.32: Ruthenium Crystal Campaign Half-life Monte Carlo Values

81 di↵erence is 0.032 days (1.15%). The exponential ﬁt residuals for the ruthenium crystal calculation starting at point 72 are shown in Figure 5.33. The autocorrelation lag plot in Figure 5.34 shows relatively correlated

Figure 5.33: Ruthenium Crystal Residuals data due to high residual dead time. Figure 5.35 is a plot of a study where data in 24 hour intervals is computed and compared as described in section 4.4.5. There appears to be no obvious medium term structure evident in this subset of the data.

The ruthenium crystal 97Ru electron-decay half-life was calculated to be 2.816 days with astatisticaluncertaintyof0.018days(0.63%).

5.3.5 Estimate of Systematic Standard Error: Ruthenium Crystal Measure- ment

Figure 5.36 is a plot of a study where 4 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The systematic uncertainty from this method is estimated to be

82 Figure 5.34: Ruthenium Crystal Autocorrelation Lags

Figure 5.35: Ruthenium Oxide 24 Hour Correlation Study

83 Figure 5.36: Ruthenium Crystal Systematic Error Study

2.06% from a consideration of the standard error of the half-life values in the graph. The total uncertainty (statistical and systematic in quadrature) is 0.061 days (2.15%). Figure 5.37 is a similar plot for Monte Carlo data. The standard error of the Monte Carlo data is 0.029 days (1.01%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate leaves 0.050 days (1.79%). Goodwin et al. [8] reported a half-life measurement value of 2.8370(14) days, the di↵erence between the Goodwin result and the value here of 2.816(61) is -0.73%, well within the standard error of the measurement.

5.3.6 Comparison to Previous 97Ru Measurements

The previously published results for 97Ru half-life measurements are summarized in Ta- ble 5.3 and shown in Figure 5.38 .

5.3.7 Results for 103Ru 497 keV Line

In addition, data from the 497 keV of 103Ru line was processed to check against the established for 103Ru value of 39.247(13) (Audi et al. [38]) days. Half-life values as a function

84 Figure 5.37: Ru Systematic Error Monte Carlo Study

Table 5.3: 97Ru Half-life Measurement Results

Half-life (days) Standard Error Reference Year 2.8 0.3 Sullivan [40] 1946 2.8 0.1 Mock [41] 1948 2.88 0.04 Katco↵ and Williams [42] 1958 2.9 0.1 Cretzu [43] 1966 2.839 0.006 Silvester [44] 1979 2.79 0.03 Kobayashi et al. [45] 1998 2.8370 0.0014 Goodwin et al. [8] 2009 2.816 0.061 This Research 2013

85 Figure 5.38: 97Ru Half-life Measurements

of starting point are shown in Figure 5.39. Figure 5.40 is the the Breusch-Godfrey plot for the 103Ru data showing a starting point of 70, about 1.5 days into the campaign. Figure 5.41 shows the accepted data used for the ruthenium crystal half-life measurement. Figure 5.42 shows the equivalent Monte Carlo data. The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.860 days (2.14%); the equivalent Monte Carlo data has a standard error of 0.075 days (0.19%); the quadrature di↵erence is

0.857 days (2.14%).

Figure 5.43 is a plot of a study where 48 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The half-life value from the data is 39.113 days with a statistical uncertainty of 0.234 days (0.60%). The systematic uncertainty is estimated to be 0.46% or 0.180 days for a total uncertainty of 0.295 days (0.76%). This is 0.34% lower than the accepted value at a 0.76% standard error. Figure 5.44 is a similar plot for Monte Carlo

86 Figure 5.39: 103Ru Half-life Values

Figure 5.40: 103Ru Breusch-Godfrey P-values

87 Figure 5.41: 103Ru Half-life Values for Accepted Data

Figure 5.42: 103Ru Half-life Monte Carlo Values

88 Figure 5.43: 103Ru Systematic Error Study data. The standard error of the Monte Carlo data is 0.096 days (0.25%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate leaves 0.152 days (0.39%).

5.4 Ruthenium Oxide Results

101 six-hour measurement sessions were taken of the electron capture decay half-life of 97Ru in the ruthenium oxide sample over a 25-day measurement campaign, 8.9 half-lives.

5.4.1 Ruthenium Oxide 97Ru Decay Count Plot

The decay count data for the ruthenium oxide sample are shown in Figure 5.45. There

are two small gaps in the middle of the data where spurious data was excluded. The energy

of the excluded data was identiﬁed as 210 keV, signiﬁcantly di↵erent than the 216 keV energy

of the 97Ru line. For this reason the data was deemed questionable and was excluded. The small amount of data excluded in the middle of the measurement campaign had little e↵ect on the extracted half-life value.

89 Figure 5.44: 103Ru Systematic Error Monte Carlo Study

Figure 5.45: Ruthenium Oxide 97Ru Activity Data

90 5.4.2 Ru Oxide Half-life Values

The complete half-life values for starting point are shown in Figure 5.46. Initially the

Figure 5.46: Ruthenium Oxide Half-life Values values have a downward trend, however the data converges on the established value.

5.4.3 Breusch-Godfrey Plot for Ruthenium Oxide

Figure 5.47 is the BG plot for the ruthenium oxide data. The dead time criterion of 1.5% would exclude data up to day 1.25 (point 5) however the Breusch-Godfrey parameter criterion in this case takes e↵ect and the ﬁrst data point with BG p-value greater than 0.001 is on day 5 (point 20), as indicated by the green dot. The maximum dead time percentage for the ruthenium oxide data was 0.49%, the minimum was 0.29%, and the average was 0.35%.

5.4.4 Half-life Results for the Ruthenium Oxide Campaign

Figure 5.48 shows the accepted data used for the ruthenium oxide half-life measurement. Simulated Monte Carlo data for this case are shown in Figure 5.49 for comparison. The comparison is favorable with the Monte Carlo data without any obvious long term trends in the

91 Figure 5.47: Ruthenium Oxide Breusch-Godfrey P-values

Figure 5.48: Ruthenium Oxide Half-lives

92 Figure 5.49: Ruthenium Oxide Campaign Half-life Monte Carlo Values measured data. The set of half-life values for succeeding starting points of the measurement data has a standard error of 0.014 days (0.48%); the Monte Carlo data has a standard error of 0.009 days (0.31%); the quadrature di↵erence is 0.010 days (0.36%). Figure 5.50 is a plot of a study where data in 24 hour intervals is computed and compared as described in section 4.4.5. There appears to be no obvious medium term structure evident in this subset of the data. The exponential fit residuals for the ruthenium oxide data fit starting at point 20 are shown in Figure 5.51. The autocorrelation lag plot shows very stochastically random data in Figure 5.52 after the first 20 points, which were excluded from the half-life calculation.

The ruthenium oxide 97Ru electron-decay half-life starting at point 20 was calculated to be 2.824 days with a statistical uncertainty of 0.006 days (0.22%) This value with the

standard error bars is shown as the green dot on Figure 5.47.

93 Figure 5.50: Ruthenium Oxide 24 Hour Correlation Study

Figure 5.51: Ruthenium Oxide Residuals

94 Figure 5.52: Ruthenium Oxide Autocorrelation Lags

5.4.5 Estimate of Systematic Standard Error for the Ruthenium Oxide Mea- surement

Figure 5.53 is a plot of a study where 4 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The systematic uncertainty from this method is estimated to be 0.026 days (0.91%) from a consideration of the standard error of the half-life values in the graph. The total uncertainty (statistical and systematic in quadrature) is 0.026 days

(0.94%). Figure 5.54 is a similar plot for Monte Carlo data. The standard error of the

Monte Carlo data is 0.008 days (0.29%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate leaves 0.025 days (0.86%).

5.4.6 Comparison with Ruthenium Crystal Results

The comparison with the ruthenium crystal run is summarized in Table 5.4. The dif- ference between the ruthenium crystal and the ruthenium oxide half-life values is 0.29%,

95 Figure 5.53: Ruthenium Oxide Systematic Error Study

Figure 5.54: Ruthenium Oxide Systematic Error Monte Carlo Study

Table 5.4: Comparison of Ruthenium Crystal versus Ruthenium Oxide

Sample Half-life (days) Stat. Uncertainty Sys. Uncertainty Total Uncertainty Ru Crystal 2.816 0.018 (0.63%) 0.058 (2.06%) 0.061 (2.15%) Ru Oxide 2.824 0.006 (0.22%) 0.026 (0.91%) 0.026 (0.94%)

96 well within the standard error of both measurements. There is a null result for a di↵erence between the half-life values of pure ruthenium and ruthenium oxide.

97 CHAPTER 6 RESULTS OF ZINC MEASUREMENTS

Recent high precision measurements of the -decay half-life of 71mZn made by Reifarth et al. [4] are significantly di↵erent than the previous 71mZn measurements made 50 years ago (Levkovskii [46], Thwaites and Pratt [47], Sonnino et al. [48]). Reifarth measured the three 71mZn gamma lines 386 keV, 487 keV, and 620 keV with a linear-fit and derived a weightedaverage half-life value of 4.125(7) hours, a 4.2% increase to the weighted average of the previous measurements 3.96(5) hours, with a significantly improved uncertainty compared to the previous value. The recent 71mZn measurements were part of a study where the neutron-capture cross sections of 64Zn, 68Zn, and 70Zn were measured with the activation technique in a quasi-stellar neutron spectrum corresponding to a thermal energy of kT = 25 keV. These results have been used in calculations for convective core He burning and convective shell C burning in massive stars. Reifarth used naturally occurring zinc with relative isotope abundance ratios of 48% for 64Zn, 19% for 68Zn, and 0.6% for 70Zn. Zinc enriched in 70Zn was used in this research to attempt to observe a cleaner 71mZn signal in order to corroborate the new 71mZn half-life value. As previously discussed in Section 3.5, Zinc oxide (ZnO) enriched in 70Zn was obtained from Trace Sciences International in order to enhance 71Zn production and signal after neutron activation. The isotopic composition of the sample as certified by Trace Sciences

International (previously shown in Table 3.1) is 93.95% for 70Zn. 117 half-hour measurement sessions were taken of the electron capture decay half-life of 71mZn in the enriched zinc sample over a 2.5 day period ( 15 half-lives) for the three 71mZn decay gamma lines. Plots ⇠ of the decay count spectrum for the 71Zn measurement campaign were shown previously in Figure 3.22 and in Figure 3.23 in the sample preparation and data collection chapter.

98 6.1 Enriched 71mZn Decay Count Plots

The decay count data plots for the three gamma lines of the 71mZn sample are shown in Figure 6.1, Figure 6.2, and Figure 6.3. The count rate for these lines decreases for increasing

Figure 6.1: 71mZn 386 keV Decay Counts

energy due to the decreasing eciency of the germanium detector. The quality of the ﬁts follow this trend with the 386 keV and 487 keV lines having the best ﬁt statistical values and the lowest overall uncertainty standard error. Because of the short half-life of 71mZn the drop in counts occurs quickly, and the counts become small quickly; this adversely a↵ects the uncertainty values.

6.2 Half-life Plots for 71mZn Lines

The full set of half-life values as a function of starting point are shown in Figure 6.4, Figure 6.5, and Figure 6.6. For the 386 keV and 487 keV lines the data quickly converges to a value close to the established value; for the 620 keV line the data diverges away. A

99 Figure 6.2: 71mZn 487 keV Decay Counts

Figure 6.3: 71mZn 620 keV Decay Counts

100 Figure 6.4: 71mZn 386 keV Line Half-life Values for Later Starting Points

Figure 6.5: 71mZn 487 keV Line Half-life Values for Later Starting Points

101 Figure 6.6: 71mZn 620 keV Line Half-life Values for Later Starting Points possible reason for this e↵ect is another longer-lived nuclear specie with a gamma line close to the 620 keV 71mZn line that inﬂuences the count rate as the 71mZn 620 keV line decays.

6.3 Breusch-Godfrey 71mZn Plots

Figure 6.7, Figure 6.8, and Figure 6.9 are the BG plots for the 386 keV line, the 487 keV line, and the 620 keV line. The ﬁrst two lines have p-values consistently above 0.001 after the ﬁrst 8 hours. The 620 keV line has the troubling behavior where the p-value is above the threshold and then goes below again; this inconsistency is a sign of problems with the data.

The criteria for acceptance of the data is not the BG p-value in this case, but rather the 1.5% dead time criterion which occurs at the 27.5 hour point (point 56 in the data) as indicated by the green dots on the plots for the 386 keV line and the 487 keV line. For the

620 keV line the green dot represents a point later where the BG parameter is consistently above 0.001. The data starting at 1.5% dead time point at 27.5 hours is used to calculate the half-life value for each of the three gamma lines.

102 Figure 6.7: 71mZn 386 keV Line Breusch-Godfrey P-values

Figure 6.8: 71mZn 487 keV Line Breusch-Godfrey P-values

103 Figure 6.9: 71mZn 620 keV Line Breusch-Godfrey P-value

6.4 Half-life Results for the Zinc Campaign

The half-life values as a function of starting point for the accepted data of the 386 keV line are shown in Figure 6.10. The half-life for 386 keV (shown as the green dot) has a value of 4.171 hours with a statistical standard error of 0.021 hours (0.50%). Simulated Monte Carlo data for this case are shown in Figure 6.11. The set of half- life values for succeeding starting points of the measurement data has a standard error of 0.079 hours (1.88%); the Monte Carlo data has a standard error of 0.068 hours (1.64%); the

quadrature di↵erence is 0.040 hours (0.96%).

The accepted data half-life values for the 487 keV line are shown in Figure 6.12 with a value (shown as the green dot) of 4.075 hours and a statistical standard error of 0.022 hours

(0.54%).

Simulated Monte Carlo data for this case are shown in Figure 6.13. The set of half- life values for succeeding starting points of the measurement data has a standard error of 0.082 hours (2.01%); the Monte Carlo data has a standard error of 0.175 hours (4.22%); the

104 Figure 6.10: 71mZn 386 keV Line Half-life Values

Figure 6.11: 71mZn 386 keV Line Half-life Monte Carlo Values

105 Figure 6.12: 71mZn 487 keV Line Half-life Values

Figure 6.13: 71mZn 487 keV Line Half-life Monte Carlo Values

106 quadrature di↵erence is not deﬁned because the Monte Carlo result is larger. The accepted data half-life values for the 620 keV line are shown in Figure 6.14. The

Figure 6.14: 71mZn 620 keV Line Half-life Values half-life values begin very close to the expected value of 71mZn and then diverge upward for later data, possibly from an other nearby gamma line. Because of this inconsistency the 620 keV data was not used in the weighted ﬁnal average.

6.4.1 Residual and Autocorrelation Plots

The exponential ﬁt error residuals for the three gamma lines of the 71mZn sample are shown in Figure 6.15, Figure 6.16, and Figure 6.17. The error residuals for the 620 keV line have an obvious trend upward for later data, further conﬁrmation of problem with the data.

The correlograms for the three gamma lines of the 71mZn sample are shown in Figure 6.18, Figure 6.19, and Figure 6.20. The 620 keV line demonstrates more structure in the later

time lags than the 386 keV and 487 keV lines, as expected.

107 Figure 6.15: 71mZn 386 keV Residuals

Figure 6.16: 71mZn 487 keV Residuals

108 Figure 6.17: 71mZn 620 keV Residuals

Figure 6.18: 71mZn 386 keV Autocorrelation Lags

109 Figure 6.19: 71mZn 487 keV Autocorrelation Lags

Figure 6.20: 71mZn 620 keV Autocorrelation Lags

110 6.4.2 Estimate of Systematic Error for the Zinc Data

Because of the high initial activity of the sample and the short half-life of 71mZn, the dead time of the measurements was considerably higher than previous measurement campaigns. The maximum dead time percentage for the zinc data was 1.5%, the minimum was 0.16%, and the average was 0.77%. Data from the 620 keV line proved to be usable above the 1.5% dead time threshold. The di↵erence in the half-life values of the 386 keV line and the 487 keV line is 2.3%. Figure 6.21 is a plot for the 386 keV line of a study where 4 data sets of half hour measurements at the same time every day for the accepted data (one day intervals) is computed and compared as described in section 4.4.6. The systematic uncertainty from this method is

Figure 6.21: Zinc 386 keV Line Systematic Error Study estimated to be 0.042 days (1.00%) from a consideration of the standard error of the half-life values in the graph. The total uncertainty (statistical and systematic in quadrature) is 0.047 days 1.12%). Figure 6.22 is a similar plot for Monte Carlo data for the 386 keV line. The standard error of the Monte Carlo data is 0.052 days (1.27%). Subtracting out the Monte Carlo component

111 Figure 6.22: Zinc 386 keV Systematic Error Monte Carlo Study in quadrature is not possible in this case. Because of the short half-life of this case and the low initial decay count, the Monte Carlo data is very noisy. Figure 6.23 is a similar plot for the 487 keV line of the systematic error study and The systematic uncertainty from this method is estimated to be 0.047 days (1.14%) from a consideration of the standard error of the half-life values in the graph. The total uncertainty (statistical and systematic in quadrature) is 0.051 days 1.26%). Figure 6.24 is a similar plot for Monte Carlo data. The standard error of the Monte Carlo data is 0.131 days (3.23%). Subtracting out the Monte Carlo component in quadrature from the systematic error estimate is again not possible in this case.

6.4.3 Weighted Average

The half-life and standard error values of the ﬁrst two 71mZn gamma lines were used to derive a weighted average for a ﬁnal result. Inverse variance weighting was used; the relative

weights for the calculation are the inverse square of the total standard error of each of the measurements. The weighted 71mZn electron-decay half-life for the ﬁrst two gamma lines was calculated to be 4.128 hours with a statistical uncertainty of 0.015 hours (0.37%) and

112 Figure 6.23: Zinc 487 keV Line Systematic Error Study

Figure 6.24: Zinc 487 keV Systematic Error Monte Carlo Study

113 a systematic uncertainty of 0.031 hours (0.75%) for a total standard error of 0.035 hours (0.84%). The results for the gamma lines are summarized in Table 6.1.

Table 6.1: Results for 71mZn

Sample Half-life (hrs) Stat. Uncertainty Sys. Uncertainty Total 386 keV 4.171 0.021 (0.50%) 0.042 (1.00%) 0.047 (1.12%) 487 keV 4.075 0.022 (0.54%) 0.047 (1.14%) 0.051 (1.26%) 620 keV - - - - Weighted Average 4.128 0.015 (0.37%) 0.031 (0.75%) 0.035 (0.84%)

6.5 Comparison to Previous 71mZn Measurements

The previously published results for 71mZn half-life measurements are summarized in Table 6.2 and shown in Figure 6.25. The weighted result for this research is 0.07% less

Table 6.2: 71mZn Half-life Measurement Results

Half-life (hours) Standard Error Reference Year 3.92 0.05 Levkovskii [46] 1958 4.0 0.1 Thwaites and Pratt [47] 1961 4.1 0.1 Sonnino et al. [48] 1964 4.125 0.007 Reifarth et al. [4] 2012 4.128 0.035 This Research 2013 than the Reifarth weighted result, but within a standard error of 0.84%. This research corroborates the ﬁndings of Reifarth et. al however at a much larger standard error.

114 Figure 6.25: 71mZn Half-life Measurements

115 CHAPTER 7 THEORETICAL ANALYSIS OF CHANGES IN ELECTRON CAPTURE DECAY HALF-LIFE

Due to the fact that the experimental research presented here did not ﬁnd measurable half-life di↵erences due to lattice surrounding or chemical composition, an attempt was made to ﬁnd a theoretical explanation. Relative changes in electron capture half-life of nuclear species in di↵erent host material have been analyzed using numerical density functional theory methods. These computational techniques calculate changes in electron structure and, in particular, change in electron density at the nucleus due to di↵erences in host medium.

7.1 Theoretical Approaches

Since the Schrödinger equation was formulated in the 1920’s, a progression of approximate methods to solve for the electron configuration of lattice structures has been developed after a full solution of the many body problem for lattice nuclei and atomic electrons was quickly understood to be infeasible. Analytical and computational approaches to this problem have been developed and, with varying degrees of simplification, agree reasonably well with measurements.

7.1.1 Thomas-Fermi Theory

Thomas-Fermi theory (Thomas [49], Fermi [50]) was the ﬁrst attempt to approximate the distribution of electrons in an atom using a straightforward statistical energy model.

The Thomas-Fermi model assumes that a spherically symmetric Fermi degenerate electron gas surrounds the nucleus (Wieder [51]). The electron density is assumed to vary slowly with distance from the nucleus. As a result, each volume element contains a homogeneous electron gas with a local density consistent with the local Fermi level. This model gives no insight into the details of atomic structure; valence and shell structure do not appear in

116 this approach, however it gives a kinematic result that remains valid even in less simpliﬁed treatments. Ray and Das ( Ray et al. [2]; Ray et al. [23]) used Thomas-Fermi theory to calculate changes in inner orbital electron density from volume changes due to electron compression. As discussed in Chapter 2, Ray and Das recently observed the electron capture rates of 109In increased by 1.00 0.17% and 110Sn increased by 0.48 0.25% when implanted in the ± ± smaller gold lattice versus the larger lead lattice . Using a procedure based on a Thomas- Fermi model they calculated an increase in decay rate of indium implanted in gold versus lead of 0.86% and for tin of 0.67%, in reasonable agreement. A study by Aquino et al. [52] gives some justiﬁcation of this; they studied compressed helium atoms by placing a helium atom in an impenetrable spherical box and found that the ground state energy of the atom increases as the radius of the box is reduced. Ray and Das used the Aquino theoretical result to calculate that the increase of electron density at the nucleus due to the compression of the inner orbitals of the implanted ion in the zeroth order.

7.1.2 Hartree-Fock-Slater Method

A more accurate quantum treatment of electronic structure was developed next as the Hartree–Fock-Slater approximation. This approximation treats the Schrödinger equation as an eigenvalue equation of the electronic Hamiltonian, with a discrete set of solutions of the ground-state wave function and ground-state energy of a quantum many-body system. The Hartree–Fock method assumes that the exact, N-body wave function of the system can be approximated by a single Slater determinant of N spin-orbitals. Using a variational method, a set of N-coupled equations for the N spin orbitals yields solutions of these equations giving the Hartree–Fock wave function and energy of the system, which are approximations. Other types of calculations begin with a Hartree–Fock calculation and then correct for electron- electron repulsion and electronic correlation (Wieder [51]). A self-consistent field (SCF) method is used to find a solution that is convergent, i.e. the e↵ects that the fields of each of the electrons have on each other are successively taken into account in a iterative fashion.

117 The SCF method remains a main part of the Density Functional Theory approach.

7.1.3 Density Functional Theory

In 1964 Walter Kohn (Hohenberg and Kohn [53]) developed two remarkably simple the- orems:

Theorem I : For any system of interacting particles in an external potential Vext(˜r), the density is uniquely determined (in other words, the external potential is a unique functional of the density). Theorem II : A universal functional for the energy E[n] can be deﬁned in terms of the density. The exact ground state is the global minimum value of this functional. One year later Kohn published the equations, developed using the variational principle, that are solved to obtain the ground state electron densities (Kohn and Sham [54]). The Kohn–Sham wavefunction is a single Slater determinant of non-interacting fermions constructed from a set of orbitals that are the lowest energy solutions to the typical representation of the Kohn–Sham equations

~2 ( 2 + ) (r)=" (r)(7.1) 2mr eff i i i

Here, eff is the Kohn-Sham potential, "i is the orbital energy of the corresponding

Kohn–Sham orbital, i, and the density for an N-particle system is

N ⇢(r)= (r) 2 (7.2) | i | i X The form of the Kohn-Sham equations is similar to the Schr¨odinger equation, and indeed the Schr¨odinger equation, in the general form Hˆ = E ,canbeobtainedfromthevariational principle (Landau and Lifshitz [55]). The Kohn-Sham formulation is exact except for the

Born-Oppenheimer approximation in which the kinetic energy of the nuclei is neglected, i.e. the nuclei are “clamped” in space at their lattice locations. The Hohenberg-Kohn energy functional and the Kohn-Sham equations are the basis for Density Functional Theory (DFT), a primary method for calculations of the structure of

118 atoms, molecules, crystals, surfaces and their interactions. This theory uses functionals (i.e. functions of another function) of spatially dependent electron density. DFT can also be readily developed as a generalization of the Legendre transform from the chemical potential to the number of particles N (Argaman and Makov [56]).

7.2 Density Functional Theory Calculations

Density Functional Theory was used to analyze the change in electron capture decay half-life of 51Cr and 97Ru from changes in the host medium. Calculations were performed using the DFT program WIEN2k (Blaha et al. [9]). The required input to the code are the space group number of the host lattice, dimensions of the lattice, atomic numbers and positions of the constituent host atoms in the lattice, and the electronic structure of each of these atoms. Lee and Steinleneumann [57] used the WIEN2k code to predict changes in the electron capture decay rates of 7Be, 22Na, and 40K.

7.2.1 The WIEN2k Program Package for DFT Calculations of Solids

WIEN2k performs electronic structure calculations of solids using DFT in an all-electron scheme including relativistic e↵ects; it has been licensed by more than 2,000 user groups. It is based on the full-potential linearized augmented plane-wave (LAPW) plus local orbitals (lo) method, an accurate scheme for band structure calculations. An ecient and accurate scheme for solving the many-electron problem of a crystal (with nuclei at ﬁxed positions) is the local spin density approximation (LSDA) within density functional theory (Hohenberg

and Kohn [53], Kohn and Sham [54]). The key quantities are the spin densities ⇢ (r)in terms of which the total energy is

Etot(⇢↑,⇢↓)=Ts(⇢↑,⇢↓)+Eee(⇢↑,⇢↓)+ENe(⇢↑,⇢↓)+Exc(⇢↑,⇢↓)+ENN (7.3)

with ENN the repulsive Coulomb energy of the ﬁxed nuclei and the electronic contributions, labelled conventionally as, respectively, the kinetic energy (of the non-interacting particles), the electron-electron repulsion, nuclear-electron attraction, and exchange-correlation ener-

119 gies. WIEN2k 12.1 (Release 22/7/2012) was compiled with Intel Fortran composer xe 2011 sp1.9.289 and run on mac OSX 10.8.2.

7.2.2 Linear Relationship Between Nuclear Electron Density and Half-life

Alinearrelationshipbetweenelectrondensityatthenucleus⇢ and decay constant is developed to first order by Bukowinski [58] by relating the electron density at the nucleus change to half-life change based on proportionality to the square of the matrix element of the interaction Hamiltonian between the initial and final states. The probability of the electron capture decay reaction is proportional to the square of the matrix Hint, between the initial and final states of the atom. To a good approximation the process may be treated as a two-body interaction

p + e n + ⌫ (7.4) !

where p is a proton, e is an electron, n is a neutron, and ⌫ is an electron neutrino. It then follows that the decay constant for electron capture, e is given by

2 = ↵ ⇤ ⇤ H d⌧ (7.5) e ˆ n ⌫ int p e where , , ,and , are the wavefunctions of the neutron, neutrino, proton, and n ⌫ p e electron, respectively, and ↵ is a constant of proportionality. Because of the small size of the nucleus equation 7.5 may be approximated by

2 2 = ↵ (0) ⇤ ⇤ H d⌧ (7.6) e | e | ˆ n ⌫ int p and the change in can be written e 2 = ↵ (⇢0 ⇢ ) ⇤ ⇤ H d⌧ (7.7) e 0 ˆ n ⌫ int p The derived proportionality in equation 7.8 is between the total electron density at the nucleus ⇢,thedecayconstant,andthehalf-lifeT1/2 (the primed values are for altered electronic conﬁgurations).

120 0 ⇢0 ⇢ 0 T1/2 T1/2 0 = 0 = (7.8) ⇢0 0 T1/2 As an example, a -0.02% change in the electron density at the nucleus of a 51Cr atom would result in a 0.02% longer half-life.

7.2.3 The Location of the Chromium Atoms in the Gold Lattice

The possible locations of the chromium atoms in the gold lattice are either interstitial (i.e. occupying a site in the crystal structure where there is not usually an atom, generally a high energy configuration) or substitutional sites in a solid solution of gold and chromium. In the research of Ray et al. [23], the larger tin and indium atoms are believed to be located in interstitial sites in the gold lattice as a result of ion-implantation, and experience compression of the inner electron orbitals, resulting in a change in electron capture decay half-lives. In the case of chromium and gold, the smaller chromium atoms easily assume substitutional sites due to the solubility of chromium in gold. Moody et al. [59] researched the solubility of chromium in gold by fabricating thin gold and gold-chromium films that were sputter deposited onto polished single crystal sapphire substrates, then heated at 400 °Cfor8hoursinair.Chromiumwasfirstdepositedonthree substrates to a thickness of 6 nm (60 Angstroms); this was followed by gold deposition to a thickness of 200 nm (2,000 Angstroms), Moody et al. [60]. They determined that the continuous chromium layer had been completely reduced to a solid solution of gold and chromium.

The AuCr phase diagram in Figure 7.1 indicates that at 26% chromium by weight AuCr phases exist near 300 to 400 °C, and as a result of the co-sputtering of the gold and chromium and subsequent annealing, the gold and chromium have formed a solid solution and the chromium atoms are located in substitutional sites in the gold lattice.

121 Figure 7.1: AuCr Phase Diagram

7.2.4 Chromium in Gold Lattice Calculation

The WIEN2k code was used to calculate the potential change in the 51Cr electron capture decay half-life from changes in the host medium from chromium metal to gold. The host gold was modeled as an fcc (face centered cubic) lattice with a lattice constant of 4.080 A and electron anity 2.30861 eV; the space group for gold is fm-3m, number 225 (Winter [61]). The 51Cr atoms were modeled as occupying gold lattice substitutional sites. The electronic structure of gold is [Xe] 6s1 4f14 5d10, and for chromium it is [Ar] 4s1 3d5. The chromium

lattice space group used was 229 lm-3m, where a = b = c = 2.88 Angstroms, with a bcc (body centered cubic) lattice. A value of RKMAX = 8 was used with 10,000 k-points of

SCF cycles.

The total calculated pure chromium electron density at the nucleus was 11568.14 ARU

(Atomic Rydberg Units); the valence electron density at the nucleus was calculated as 141.45 ARU. A supercell of gold atoms was created, then a chromium atom was introduced, surrounded by gold atoms, as shown in Figure 7.2. The gold lattice space group was modeled as

122 Figure 7.2: AuCr Lattice Structure

225 fm-3m with a = b = c = 4.0782 Angstroms, the fcc model included with a 5% reduction for chromium sites. A value of RKMAX = 8 was used with 5,000 k-points of SCF cycles. The valence electron density at the nucleus was calculated to be 138.53 ARU for a -2.07% di↵erence. The total calculated electron density at the nucleus for chromium atoms in gold was calculated to be 11565.58 ARU for a -0.0221% di↵erence with the pure chromium case.

7.2.5 AuCr Comparison to Theoretical Analysis

The DFT WIEN2k code calculated an increase of 0.02% in the half-life of the 51Cr in the AuCr sample. The measured increase between 27.7010(11) days (established 51Cr value) and 27.715(149) days (AuCr) is 0.05%. The di↵erence is well within the total uncertainty of the

measurements, and not proof for the e↵ect to occur. It is It is unlikely that the experiment

can be improved to the point where a 0.02% becomes discernible.

123 7.2.6 Ruthenium Oxide Calculation

In addition the WIEN2k code was used to analyze the change in electron capture decay half-life from pure ruthenium and ruthenium oxide. The ruthenium was modeled with lattice parameters = 2.7059 Angstroms, with a space group 191 P6/mmm by WIEN2k code. A value of RKMAX = 9 was used with 10,000 k-points of SCF cycles. The total calculated pure ruthenium electron density at the nucleus was 139662.01 ARU; the valence electron density at the nucleus was calculated as 471.12 ARU. Ruthenium oxide was modeled in a rutile lattice structure with a = 8.4885 Bohr, c =

5.8706 Bohr, u = 0.306 from Calculated Optical Properties of RuO2 (Williams et al. [62] and Xu et al. [63]), as shown in Figure 7.3. A value of RKMAX = 9 was used with 10,000

Figure 7.3: RuO2 Rutile Lattice Structure k-points of SCF cycles.

The valence electron density at the nucleus was calculated to be 467.63 ARU for a - 0.74% di↵erence. The total calculated electron density at the nucleus for ruthenium oxide was calculated to be 139658.44 ARU for a -0.0026% di↵erence with the pure ruthenium case.

124 7.2.7 Ruthenium Comparison to Theoretical Analysis

The WIEN2k code calculated an increase of 0.002% in the half-life of the 97Ru in the ruthenium oxide sample, clearly not measurable. The di↵erence between the measured ruthenium crystal 97Ru half-life 2.816(61) and ruthenium oxide 97Ru half-lives of 2.824(26) days, a di↵erence of 0.29%, is within the total uncertainty of the measurements and cannot show an e↵ect of the order of magnitude calculated.

7.2.8 WIEN2k Results

The results of the WIEN2k theoretical calculations are summarized in Table 7.1.

Table 7.1: Theoretical Calculations of Half-life Change

Case Change in Half-life 51Cr in gold lattice 0.0221% 97 Ru in RuO2 0.0026%

Das and Ray [24] reported results of calculations using WIEN2k for electron capture decay in di↵erent host media, and were unable to explain observed decay rate change in di↵erent host media. Das and Ray speculated that the change of inner core wave functions under compression has not been properly modeled in WIEN2k.

125 CHAPTER 8 PART 1 SUMMARY AND CONCLUSIONS HIGH PRECISION HALF-LIFE MEASUREMENTS

Part one of this research on applications of neutron activation analysis focused on the development of methods for making high precision nuclear beta decay half-life measurements with a challenging accuracy goal of 0.1% uncertainty standard error. HPGe detectors with excellent energy resolution operating at LN temperature were used to count characteristic gamma photons from nuclear beta decays produced by materials irradiated with thermal neutrons at the USGS TRIGA reactor. Statistical methods that give un-biased maximum likelihood single exponential estimates were used because linearization of the decay data overly biases later measurements. MAESTRO job control scripts, python scripts, gf3 area calculation software and R statistical software were necessary to approach the accuracy goal. The protocol for half-life estimation of Pomm´einformed this research, and synchronization of the PC clock to the NIST WWVB signal was done to stabilize the time base.

8.1 Research Motivation

Motivation for this research came primarily from three studies. This ﬁrst study by Ray et al. [2] saw changes in the electron capture half-lives of 109In and 110Sn when indium and tin nuclides were introduced into gold and lead lattices by ion implantation. They observed that the orbital electron capture rates of 109In and 110Sn increased by 1.00 0.17% and 0.48 ± 0.25% respectively when implanted in the small gold lattice versus the larger lead lattice ± due to the higher compression experienced by the larger radioactive atoms and the spatial

conﬁnement in the smaller gold lattice. The Ray research showed that changes in electron

capture half-life could be observed by placing a high Z nucleus in di↵erent host lattices in interstitial sites, and they developed a zeroth order Thomas-Fermi theory to explain these results and calculated changes in the inner core orbital eigenstate energies. The Ray

126 results appear to be valid even though the precision of the measurements and the simplifying assumptions in the theory were very close to the limit of the accuracy of the analysis. The second study by Bainbridge et al. [3] measured the internal conversion decay half-

99m life of Tc in KTcO4 versus Tc2S7and saw a signiﬁcant di↵erence due to a chemical state change. A ﬁrst piece of this research was, in part, initiated in an attempt to determine if this e↵ect can be seen in other higher Z electron capture decay such as 51Cr in a gold lattice

97 or in Ru in ruthenium oxide, RuO2. The third was a recent study by Reifarth et al. [4] where the beta-minus decay half-life of 71mZn was measured with signiﬁcant di↵erence to previous data.

8.2 Detector Dead Time

Achieving the accuracy goal of 0.1% uncertainty standard error proved to be dicult due mostly to detector dead time issues. Counts that are lost while a detector is busy processing previous events are a main contributor to half-life uncertainty. The period of time over which the detector is not able to process new counts is deﬁned to be the dead time of the detector. Long-lived gamma lines in the spectrum from nuclear species that are not of interest (e.g. the 497 keV 103Ru line in a 97Ru measurement) compete with the measurement, increase the dead time, and are an obstacle to the accuracy goal. The best achieved accuracies were 0.06% statistical uncertainty and 0.5% systematic uncertainty for the lowest dead time ⇠ ⇠ cases. Runs with greater dead time resulted in greater uncertainty, up to 2%. Figure 8.1 shows the variation of dead time percent with statistical standard error, Figure 8.2 shows the variation of dead time percent with systematic standard error, Figure 8.3 shows the variation of dead time percent with total standard error. Total uncertainty values are in quadrature: the square root of the sum of the squares of the statistical and systematic standard uncertainty values.

An ORTEC precision pulse generator was used to compare dead time values from two di↵erent methods. An e↵ective dead time calculated using the pulser counts was compared with the value from the ORTEC hardware and MAESTRO software. By comparing values

127 Figure 8.1: Dead time versus Statistical Error

Figure 8.2: Dead time versus Systematic Error

128 Figure 8.3: Dead time versus Total Standard Error

from these two methods it was determined that a maximum of 1.5% dead time in the MAE- STRO system was allowable; data with greater dead time percentages had inconsistent dead time values. For the most part the maximum dead times of the data used were less than 1.5%; maximum dead times were 0.38% for the gold chromium case, 1.5% for the ruthenium crystal, and 0.49% for the ruthenium oxide samples and 1.5% for the zinc campaigns.

8.3 51Cr in Gold Lattice

The objective of the ﬁrst two measurement campaigns was to see if changes in electron capture decay half-life could be observed in 51Cr by comparing the decay half-life of 51Cr nuclei in interstitial sites in a gold lattice versus 51Cr nuclei in a pure chromium lattice. An AuCr sample was created by co-sputtering gold and chromium onto a Grafoil substrate and then annealing the target in the sputtering chamber at 300 .Thissamplewasthen activated by irradiating it at the USGS TRIGA reactor. A measurement of electron capture decay half-life was then made and compared to the well-known electron decay half-life of

129 51Cr. As the expected e↵ect was not observed, Density Functional Theory was used to analyze changes in electron density at the nucleus due to changes in atomic electron conﬁguration for pure chromium versus chromium atoms in a gold lattice. The WIEN2k code was used to estimate electron density at the nucleus. These calculations proved to be consistent with the measured data. The calculated e↵ect was smaller than the measurement uncertainty. In the analysis, publications were found that show that the chromium atoms are very soluble in the gold lattice. The chromium lattice of 2.88 Angstroms is smaller than the gold lattice constant of 4.08 Angstroms. In addition the electron anity of gold is very high. As a result it is believed that the chromium atoms mainly occupy substitutional sites in the gold lattice and not interstitial sites as hypothesized to explain the results by Das et. al. This combined with the high electron anity of the gold lattice results in a lack of compression of the inner chromium electron orbitals, indeed the valence electrons are drawn away from the nucleus and the electron density at the nucleus of the chromium atom is lower in the gold lattice compared to the pure chromium lattice case. This e↵ect was corroborated with the calculations using the WIEN2k code. The DFT calculations, done after the data was taken, conﬁrmed the measurements within the accuracy of the data. The DFT WIEN2k code calculated an increase of 0.02% in the half-life of the 51Cr in the AuCr sample. The measured increase between 27.7010(11) days (established value) and 27.715(149) days (AuCr) is 0.05%. The di↵erence of 0.02% is within the total uncertainty

budget of the measurements, 0.5%. The chromium campaign results are summarized in ⇠ Table 8.1.

Table 8.1: Comparison of Established 51Cr Half-life versus AuCr Results

Sample Half-life (days) Stat. Uncertainty Sys. Uncertainty Total Uncertainty 51Cr 27.7010 – – 0.0011 (0.004%) AuCr 27.715 0.016 (0.06%) 0.148 (0.53%) 0.149 (0.54%)

130 8.4 97Ru in Ruthenium Oxide

Electron capture half-life changes for 97Ru in a pure ruthenium crystal versus ruthenium

99m oxide, RuO2 were investigated next. The results of Bainbridge et al. [3] for Tc suggested that a similar result might be seen in 97Ru. Activation and measurement for a pure ruthenium

crystal and RuO2 powder was done in a similar way to the chromium study. In addition, the results for the ruthenium crystal were used as a standard for the measurement and were compared with a high precision Texas A&M (Goodwin et al. [8]) half-life measurement for an independent accuracy uncertainty conﬁrmation.

In the ruthenium case, the RuO2 oxide is already in a minimum energy conﬁguration and no compression was seen. No appreciable change in the electron capture half-life was calculated by WIEN2k or measured between pure ruthenium and ruthenium oxide. Because of the longer half-life of 103Ru ( 39 days), the dead time from the ruthenium measurements ⇠ stayed relatively high throughout the measurement campaign. As a result the systematic standard error of the ruthenium data was higher. The WIEN2k code calculated an increase of 0.002% in the half-life of the 97Ru in the ruthenium oxide sample, too small to be observable. The di↵erence seen between the ruthenium crystal 2.816(33) and ruthenium oxide half-lives of 2.824(29) days is 0.28%, well within the total uncertainty of the measurements. The ruthenium results are summarized in Ta- ble 8.2.

Table 8.2: Comparison of Ruthenium Crystal versus Ruthenium Oxide

Sample Half-life (days) Stat. Uncertainty Sys. Uncertainty Total Uncertainty Ru Crystal 2.816 0.018 (0.63%) 0.058 (2.06%) 0.061 (2.15%) Ru Oxide 2.824 0.006 (0.22%) 0.026 (0.91%) 0.026 (0.94%)

8.5 71mZn Beta-minus Decay Half-life Measurement

Ameasurementoftheelectroncapturedecayhalf-lifeof71mZn was performed to compare with a recent study by Reifarth et al. [4] which is signiﬁcantly di↵erent than the previous

131 71mZn measurements made 50 years ago, summarized in Table 6.2 and Figure 6.25. Reifarth measured the three 71mZn gamma lines 386, 487, and 620 keV with a linear-fit and derived aweighted-averagehalf-lifevalueof4.125(7)hours,a4.2%increasetotheweightedaver- age of the previous measurements 3.96(5) hours, with a significantly improved uncertainty compared to the previous value. Reifarth used naturally occurring zinc with relative isotope abundance ratios of 48% for 64Zn, 19% for 68Zn, and 0.6% for 70Zn. Zinc enriched in 70Zn (isotopic composition = 93.95% for 70Zn) was used in this research to observe a cleaner 71mZn signal in order to corroborate the new 71mZn half-life value. Half-life and standard error values were calculated from the decay data from each of the three 71mZn gamma lines and a weighted average of the first two lines was derived using relative uncertainties. Because of the high initial activity of the sample and the short half- life of 71mZn, the dead time of the measurements was higher than previous measurement campaigns. The maximum dead time percentage for the zinc lines was 1.5%, the minimum was 0.38%, and the average was 0.77%. The zinc results are summarized in Table 8.3. The weighted result for this research is 0.07% less than the Reifarth weighted result, but within astandarderrorof0.84%.ThisresearchisconsistentwiththefindingsofReifarthet.al however at a much larger standard error.

Table 8.3: Results for 71mZn

8.6 Overall Conclusions, Part 1

Part one of this research developed the capability to make high precision measurements of radioactive decay half-life. The precision goal for a combination of statistical and systematic

132 standard uncertainty was 0.1%. Detector dead time proved to be an important factor in limiting measurement uncertainty. However, even for cases such as 51Cr where there was a single gamma line without other competing lines to increase the dead time, the precision goal was not achieved. For cases such as 97Ru, the long lived gamma line of 103Ru at 497 keV (half-life of 39 days) increased the dead time enough so that the achievable precision was ⇠ 1%. For the 71mZn measurement with three active lines and other zinc lines, the achieved ⇠ precision for the weighted average of the ﬁrst two lines was 0.84%. Measurements to observe changes in electron capture half-lives due to changes in surrounding electronic structure were done for 51Cr in a gold lattice and for 97Ru in an oxide. In the case of chromium being mixed into a gold lattice, compression of the chromium core electron orbitals, it was found, does not occur as is postulated for the indium and tin atoms of the Ray et al. study. It was anticipated that the chromium nuclei would experience compression from being in interstitial sites, however, because the chromium atoms are in substitutional sites this e↵ect was not seen. The electron anity of the gold lattice and the smaller lattice constant of the chromium lattice does not allow for compression. Because the gold lattice does not create a compression of the interior electron orbitals no signiﬁcant change in electron capture half-life was seen.

8.7 Areas of Continuing Research

Research utilizing the capability of making high precision half-life measurements can be envisioned in the following areas.

8.7.1 Changes in Electron Capture Half-life from Electronic Structure Com- pression

Follow-on research would explore electronic structure compression of high Z nuclides to

see if a change of electron capture half-life is observable. Electronic structure compression could be achieved either by mechanical means or by placement of the nuclei in interstitial locations in a smaller lattice.

133 Diamond anvil cells are able to create mechanical pressures that are potentially high enough to produce a measurable electron capture decay half-life e↵ect. A diamond anvil cell can compress a sub-millimeter sized material sample to extreme pressures which can exceed 300 giga-pascals. Compression of 51Cr, 97Ru, or one of the candidates listed below could be investigated using a mechanical method. Changes in electron capture half-life from interstitial electronic structure compression could also be explored, creating a case to check Ray’s theoretical approach. A host with a lattice constant that is smaller than the nuclide under study would have to be used. Metals with small lattice constants include titanium, vanadium, and iron.

Nuclides that would be ideal candidates for electron capture studies would have half-lives of a few days to weeks without any long lived gamma lines to compete with the measurement. Possible high Z candidates for electron capture decay half-life alteration studies with varying degrees of suitability are:

• 103Pd, 100% electron capture decay, 17 day half-life, 357.45 keV gamma line

– For NAA 102Pd has 1% natural occurrence.

– Other palladium nuclides have short half-lives.

• 186Re, 7.5% electron capture decay, 3.7 day half-life, 122.64 keV gamma line

– For NAA185Re has a 37% natural occurrence.

– Beta-minus decay gamma lines could compete.

• 191Pt, 100% electron capture decay, 2.88 day half-life, 538.9 keV gamma line

– For NAA 190Pt has only a 0.014% natural occurrence.

– Other platinum decays could compete.

• 197Hg, 100% electron capture decay, 2.672 day half-life, 77.3 keV gamma line

134 – For NAA 196Hg has 0.15% natural occurrence.

– Other mercury decays could compete.

135 CHAPTER 9 DEBRIS COLLECTION NUCLEAR DIAGNOSTIC AT THE NATIONAL IGNITION FACILITY

Part two of this research describes work toward the design and development of a solid debris collector for use as a nuclear diagnostic tool at the National Ignition Facility (NIF). Initially, this topic was the motivation to build up the Neutron Activation Analysis (NAA) capability at the USGS TRIGA. However, interaction, like sample acquisition or sample holder deployment, with NIF was not in a way compatible with the time scale of a PhD thesis. Presented here are the NIF/NAA related developments performed in the ﬁrst year of this thesis. In this application neutron activation analysis was used to detect and quantify the amount of trace amounts of gold from the hohlraum and germanium from the pellet present in the debris collected after a NIF inertial conﬁnement fusion (ICF) shot. Design considerations for the solid debris collector will be presented in this part as well as calculations to predict performance and results for the collection and measurements of trace amounts of gold and germanium from dissociated hohlraum debris. This is not just design e↵ort, however, but data was taken also, as will be discussed.

9.1 Introduction

The National Ignition Facility is a 192-beam ICF research facility at the Lawrence Liv- ermore National Laboratory (LLNL) capable of delivering up to 1.8 MJ of laser energy to millimeter size target pellets at the center of a ten-meter diameter target chamber. The mission of NIF is to demonstrate nuclear fusion ignition, a self-sustaining reaction where a highly compressed fuel mixture at the center of the target pellet ignites with sucient temperature and density to maintain thermonuclear burn throughout the remaining fuel. Direct drive and indirect drive are two approaches to ICF. In direct drive, the laser energy

136 ablates the pellet surface directly causing an implosive force. In indirect drive, the pellet is held inside of a small cylindrical hohlraum where entering UV laser light is absorbed and re-radiated as x-rays, achieving a more uniform implosion. As the laser energy is absorbed, disassociated hohlraum and pellet debris moves out from the NIF target chamber center at high velocity. Figure 9.1 below is the functional diagram of NIF.

Figure 9.1: The National Ignition Facility

AmethodtocollectandradiochemicallycharacterizesoliddebrisproducedfromICF experiments would be a signiﬁcant nuclear diagnostic capability at NIF. An improved understanding of fusion ignition physics can be gained by collecting and analyzing the residue produced from NIF indirect drive shots. The details of the thermonuclear burn in the target can be explored by examining the by-products and isotopes found in the reaction debris.

Collection and subsequent thermal neutron activation of NIF debris products will give diagnostic information about charged particle reactions within the imploded target and hohlraum leading to a better understanding of the nuclear fusion reaction eciency of ICF targets. Radiochemical analysis of neutron-activated debris from indirect drive shots will provide insight into indirect drive ICF processes, (Grim et al. [64]). Developing a NIF solid debris

137 collection method involves three considerations:

1. Devising an ecient geometry for debris collection,

2. Selecting the most appropriate materials to withstand the radiation and debris environments while maximizing collection eciency,

3. Demonstrating a viable method for neutron activation analysis of collected debris.

The collection geometry described in this research is a foil lined truncated cone vessel. This approach provides a cavity in which the debris can collect and also allows for oblique angles of x-ray incidence and ablation. This should minimize the amount of ablated material released into the target chamber and improve overall collection eciency. The foil provides acollectionsurfaceintowhichthedebrisimbeds.Thefoilcanthenbesectionedintosmall material coupons for subsequent neutron activation analysis. The materials selected for use in the collection vessel must survive the radiation and debris environments, produce a minimum amount of additional ablated debris, eciently collect the pellet solid debris, and produce no nuclear species that interfere with subsequent neutron activation analysis. Indirect drive NIF experiments employ a hohlraum to convert the UV laser light to x-rays for a more uniform inertial implosion. Use of a hohlraum, however, results in an x-ray wavefront that ablates the surfaces of the collection system, and the vaporization of the hohlraum creates a “debris wind” that can interact with the ablated material. The material mechanical response of the collector is driven from a stress shock wave from x-rays and the debris impulse imparted to the foil and the vessel wall. The structural integrity of the vessel must be preserved for use in the NIF target chamber.

The amount and composition of the collected solid debris was studied using neutron activation analysis (NAA). This method measures gamma radiation emitted from trace amounts of pellet and hohlraum debris activated from thermal neutron irradiation. By comparing the activity of a known mass of pure material irradiated along with the test samples, the mass of collected material can be estimated. In order to analyze pellet debris material, this tech-

138 nique must be able to di↵erentiate between the signal (ultimately from the germanium pellet debris) and the background (from the aluminum impurities and ultimately hohlraum gold debris) accounting for the half-lives of the nuclear species involved. Details of the shot, such as shot energy and distance from the chamber center, have an e↵ect on the amount of debris material collected. Selecting the potential reactions to be studied and understanding the rationale for using them are part of the development of this method. As an example, one approach is to seed the pellet with a material whose post-shot isotopic abundance is an indication of the neutron environment seen in the pellet.

139 CHAPTER 10 COLLECTOR DESIGN CONSIDERATIONS

A solid debris collecting structure must be designed to withstand the radiation and debris environment inside the NIF test chamber, eciently collect the reaction debris produced in the experiment, and survive structurally intact.

10.1 Geometry and Scale

The purpose of this aspect of this research is to explore the x-ray ablation properties of candidate materials for a fusion reaction debris collector design to provide diagnostic information about ICF reaction eciency. In addition, the knowledge gained from this analysis will help to plan for future experiments at NIF by obtaining data on x-ray spectra and materials response to it. The geometry of the solid debris collection surfaces plays a signiﬁcant role in the collection eciency. Various geometries have been proposed including ﬂat plates, parabolic focusing surfaces, and an open conical frustum vessel.

10.2 Preliminary Vessel Design

A notional diagram of a debris collection vessel concept is shown in Figure 10.1. This proposed design is a truncated cone shape with the front-end open and the back-end closed. The interior of the vessel will be lined with ﬂexible graphite (Grafoil) or titanium foil that will collect the reaction debris. The titanium foil will then be removed post-shot for radiochemical analysis. The size and location of the vessel as shown subtends roughly 1% of the solid angle of the target.

10.3 X-ray/Debris Source Characterization

Use of a hohlraum in indirect drive NIF experiments results in an x-ray wavefront that ablates the surfaces of the collection system. In addition, the vaporization of the hohlraum

140 Figure 10.1: Debris Collection Vessel Design

creates a debris wind that interacts with the ablated material. In order to predict the x-ray response, the x-ray output characterization parameters that are required are fluence, pulse width, and a detailed x-ray energy spectrum. A radiation hydrodynamic calculation for the anticipated x-ray emission and debris for the specific shot conditions (total energy, target / hohlraum composition, etc.) was performed by researchers at LLNL. These calculations were done by Eder et al. [65]. Typically x-ray sources can be well approximated as spectra from black body radiators of a given temperature. From the results of the Eder calculations, a 250 eV (2.90 x 106 degrees Kelvin) temperature blackbody x-ray spectrum and x-ray fluence of 22.1 J/cm2 values are used as representative values for a NIF shot at full power shot; an excursion to 300 eV (3.48 x 106 degrees Kelvin) was also done. An x-ray pulse width of 4 nano seconds is used for the hydrocode calculations given below, and

a material mass and velocity estimate of approximately 323 dyne-sec/cm2 from the debris wavefront of the disassociated hohlraum was calculated from ﬁgures in the paper Eder et al.

[65].

10.4 Candidate Material Analysis

Candidate materials for use in the debris collector are evaluated for their material and thermo-structural response to the NIF x-ray and neutron radiation. In addition, the materi-

141 als are evaluated for debris adhesive properties as well as the potential to become radioactive. Once a subset of materials is selected and the size and shape of the structure can be initially designed, the structural response and integrity of the debris collector can be predicted ana- lytically using computer models and eventually will be compared to experimentally measured stress and impulse response data.

10.4.1 Original Material Candidates

The following set of candidate materials were initially considered for use in the solid collector vessel design:

1. Silver

2. Aluminum

3. Grafoil (carbon foil)

4. Molybdenum

5. Niobium

6. Tantalum

7. Titanium

8. Vanadium

For each of these materials x-ray ablation predictions were done, as presented in the following sections. The original criteria for evaluation were ablation performance, structural integrity, and potential for activation (that would compete with the pellet signal). All of these materials will necessarily be of high purity to reduce the amount of activation.

Possible activation problems may come from isotopes of titanium, and from impurities in aluminum such as chromium, manganese, and iron. For example, certain aluminum alloys

142 were eliminated because of the amount of manganese that made the samples too radioactive after neutron irradiation. Of these materials, four were chosen for further analysis: two foil (Grafoil and titanium) and two vessel wall candidates (aluminum and tantalum). Carbon is a lower Z (or atomic number) material and would result in less ablated material. The titanium can be obtained in high purity. The potential layups of materials would be:

1. Titanium foil over aluminum

2. Carbon foil over aluminum

3. Titanium foil over tantalum

4. Carbon foil over tantalum

Other issues for material selection include amount of material ablated, the particle velocity proﬁle, and the structural integrity of the material under the radiation and debris environment stresses.

10.4.2 Proposed Ablation E↵ects Experiments

This research also supported experiments that were done at NIF by providing x-ray ablation predictions for candidate materials for NIF shots. In order to evaluate candidates for the solid collector design, future experiments will have to be performed as well. The purpose of these experiments will be to explore the x-ray ablation properties of a range of candidate materials. The data obtained from these experiments will be used to design the solid collection vessel and foil.

Each material is made into a thin coupon of approximately 1 square inch in area and

0.25 inches thick. A shadow bar covers half of the area of the sample. The shadow bar will be made of anodized tungsten (or another appropriate material approved for use in the NIF chamber). Each sample is carefully measured in thickness and weight before the shot so that

143 the amount of material that was ablated can be determined. The samples along with the shadow bar will be mounted on the end of a diagnostic instrument manipulator (or DIM) in the target chamber at a distance of from 25 to 50 cm away from the hohlraum (depending on the final determination of the anticipated x-ray fluence). The samples will be retrieved after the shot, inspected and measured for material ablated (profilometer and/or electron microscopy) and other reaction/debris e↵ects.

10.4.3 Material X-ray Response Analysis and X-ray Ablation Predictions

Predictions of the amount of material that will ablate from surface of the materials were made using an exponential deposition calculation which gives the amount of energy deposition as a function of distance into a material for a given x-ray spectrum. The phases of a material exposed to x-ray radiation are shown in Figure 10.2. As the radiation interacts with the material, there are layers of vaporization, decomposition, melt and transition. The assumption made for these predictions was that the material ablates down to the depth half way between incipient melt and incipient vaporization.

Figure 10.2: X-ray Deposition Proﬁle

Material properties were compiled from the NIST-JANAF Thermo-chemical Tables 4th Edition (Chase [66]); values for incipient vaporization and melt were derived as presented

144 in Table C.1. Estimates of material ablation were made as shown in the following plots for aluminum (Figure 10.3), Grafoil (Figure 10.4), titanium (Figure 10.5), and tantalum (Figure 10.6). Ablation predictions for the four materials are summarized in Table 10.1.

Figure 10.3: X-ray Energy Deposition Proﬁle for Aluminum 6061

Aluminum ablates the greatest amount of material according to these predictions, with tan-

Table 10.1: X-ray Ablation Predictions

Lower Bound (microns) Upper Bound (microns) Average (microns) Al6061 4.5 8.0 6.2 Grafoil 0.4 3.3 1.8 Tantalum 0.8 0.9 0.8 Titanium 1.7 2.4 2.1

talum producing the least amount of material. Grafoil would appear to be a good candidate

for a low Z material. These results are consistent with the Z and the density of the material,

with higher Z elements absorbing more of the energy in front layers. It is a complex interplay between the energy absorbing properties of the materials which is dependent upon Z and the thermodynamic properties which determine how the energy is dissipated.

145 Figure 10.4: X-ray Energy Deposition Proﬁle for Aluminum Grafoil

Figure 10.5: X-ray Energy Deposition Proﬁle for Aluminum Titanium

146 Figure 10.6: X-ray Energy Deposition Proﬁle for Aluminum Tantalum

10.4.4 Grazing Incidence Predictions

The values given above assume normal incidence of the x-ray radiation on the front surface of the material, which results in the worst-case (i.e. greatest) ablation e↵ects. Calculations for grazing incidence of the x-rays were also done. At grazing incidence the deposition into the material is dramatically reduced. As a result, only a negligible amount of material is ablated at grazing incidence. For this reason the sides of the vessel should not produce much ablated material. If the front lip of the vessel were fabricated as a sharp knife-edge then the ablated material would come only from the back surface, well within the conﬁnes of the vessel. This e↵ect should help to contain the ablated material, as will be discussed in the

next section.

10.4.5 Hydrodynamic Analysis

Hydrodynamic calculations were used to predict time proﬁles of stress in the material and particle velocities of the ablated material response to x-ray deposition. Bounding values for the maximum particle velocity throughout the ablated material are displayed in the next

147 set of plots (Figure 10.7, Figure 10.8, and Figure 10.9), showing maximum velocity envelopes as a function of fractional distance into the ablated material.

Figure 10.7: Al Max Particle Velocity

10.4.6 Material Transport Process

The interaction of the opposing x-ray wave fronts and the ablation and debris wind is a complex process. This “transport” problem involves the interaction of the source radiation, foil ablation, debris and ablation impulse, and stress wave timings all of which a↵ect collection eciency. As stated previously, use of a hohlraum in indirect drive NIF experiments creates an x-ray wavefront that ablates the surfaces of the NIF chamber, and vaporization of the

hohlraum creates a debris wind that interacts with the ablated material. The material

response, which involves x-ray ablation, also creates a stress response to x-rays, debris, foil

and the housing wall.

The estimate for hohlraum debris velocity taken from the Eder paper (Eder et al. [65]) is

2.56 x 106 cm/sec. By comparing this to the values for maximum particle velocity, a picture of the debris ablation interaction can be formed. The time required for the hohlraum debris to travel 50 cm to the back of the collection vessel is 19.5 µs. In that time the ablation

148 Figure 10.8: Ti Max Particle Velocity

Figure 10.9: Grafoil Max Particle Velocity

149 debris would have to be traveling in excess of 1.5 x 106 cm/sec in order to travel 30 cm and exit the vessel before the debris reached the back wall of the collection vessel. This is only aproblemforthefrontlayermaterial;mostofthematerialablateswithasucientlylow velocity to interact inside of the vessel. The ﬁgures below depict the transport process timeline. At t = 0 as shown in Figure 10.10, UV laser light enters the hohlraum and is converted to x-rays. The hohlraum heats up,

Figure 10.10: Hohlraum and Debris Collector begins to disassociate and radiate x-rays. After approximately 2 nano-seconds, the x-rays have travelled 50 cm to the end of the vessel. The x-rays are absorbed and ablate the catcher material as shown in Figure 10.11. On the order of 12 microseconds later, the hohlraum debris (moving to the right with velocity = 1.6 x 106 cm/s) meets the most energetic ablation material (traveling in the opposite direction at 1.6 x 106 cm/s) around 30 cm from the target chamber center and inside of the vessel as shown in Figure 10.12.

The velocities and distances given here are for estimates assuming maximum laser power.

Lower energy shots would change the relative velocities and distances. This analysis indicates that from a kinematic perspective the basic concept of the debris catcher is viable.

150 Figure 10.11: Disassociated Hohlraum

Figure 10.12: Hohlraum Debris and Ablated Material Interaction

151 CHAPTER 11 NIF NEUTRON ACTIVATION ANALYSIS RESULTS

The debris for some test collections on ﬂat collectors was analyzed using thermal neutron activation analysis by measuring the activity of gamma lines from micrograms of neutron- activated collected pellet and hohlraum debris. This involves characterizing background and signal levels from thermal neutron activation factoring in the half-lives of the nuclear species involved. This method must be able to di↵erentiate the aluminum background impurities and the hohlraum gold debris from the signal activity levels of the germanium in the pellet.

11.1 Neutron Activation Analysis Procedure

Eleven sets of samples from NIF shots, including one set from the polar DIMM, were analyzed as summarized in Table 11.1. The sample coupons were ﬁrst removed from the

Table 11.1: Test Descriptions for NIF Shots

Sample ID, Shot Description Laser Energy (kJ) TCC (cm) Au Original Mass (g) 22, Au Hohlraum, D-D cryogenic 568 50 0.11848 00, Au Hohlraum, D-D cryogenic 516 50 0.11848 31, Exploding Pusher No Hohlraum 46 25 0 28, Au Hohlraum, D-D cryogenic 689 25 0.11848 30, Au Hohlraum, D-D cryogenic 729 25 0.11848 35, Au Hohlraum, D-D cryogenic 831 25 0.167 33, Au Hohlraum, D-D cryogenic 836 25 0.167 Polar DIMM, Au Hohlraum, D-D cryogenic 567 50 0.11848 21, Au Hohlraum, D-D cryogenic 574 50 0.11848 23, Au Hohlraum, D-D cryogenic 668 50 0.11848 24, Au Hohlraum, D-D cryogenic 837 50 0.167

NIF packaging and photographed with their sample set number and location, as shown in Figure 11.1 for the example sample 21 set. The coupons were then weighed to one-milligram accuracy. They were handled to avoid touching the front surface by tweezers and pushed

152 Figure 11.1: Example Coupon Sample 21 on the side when moved. They were then placed inside small plastic sacks, heat-sealed on the edges. The plastic sacks protected the sample coupons during irradiation and provided a holder during measurement in the detector setup. The material sample sets (along with the gold sample of known weight) were irradiated by the TRIGA reactor ﬂux of 1012 thermal neutrons per second per cm2 for approximately ⇠ 6 minutes. After this there was a cooling o↵ period of 1-2 hours before the samples were handled. The activity of the samples was measured using the Loaner 4 liquid nitrogen cooled HPGE

detector setup with a multi-channel bu↵er and MAESTRO MCA emulation software. Count

measurements were taken for roughly 300 seconds. The net count area at the 412 keV 198Au gamma line divided by the measurement time (gold counts/sec) was calculated for each

sample.

A sample of pure gold of known weight irradiated with the NIF coupons was used to determine the gold activity as a function of mass for the irradiation period. The activity of the pure gold was calculated in the same way by dividing the net count area by the

153 measurement time period. The gold count rate was measured before and after the coupon measurements to assure that it had not signiﬁcantly changed. The count rate of a known mass of gold can be used to infer the mass of gold in a sample coupon from the coupon’s gold count rate. In this way, the mass of gold in each of the samples was estimated. Finally, the gold mass calculated for each coupon was divided by the total coupon mass to give grams of gold per gram of coupon material.

11.2 Detector Setup

This shows the Loaner 4 detector at the USGS TRIGA reactor at the Denver Federal Center Figure 11.2.

Figure 11.2: Loaner 4 Detector Setup

11.3 Tests and Analysis

The sample sets were irradiated in the USGS TRIGA reactor dry tube for 6 minutes at approximately 1012 thermal neutrons per sec per cm2.Foreachsampleset,theanalysis procedure described above was performed. The ratio of grams of gold to total grams of sample material was calculated. For each of the samples the amount of gold measured was

154 compared to the gold that would be expected if it were distributed isotropically in angle over 4⇡ steradian. The ratio of measured over expected (isotropic) gold per cm2 was calculated. The plot in Figure 11.3 shows this ratio of the gold ratio measured versus an assumed isotropic distribution as a function of shot energy.

Figure 11.3: Gold Versus Shot Energy

11.4 Summary and Conclusions, Part 2

The ﬁrst sets of data at 50 cm collection distance indicate stable Au collection independent of laser energy while collection at 25 cm indicates that with increasing NIF shot energy less material is collected. This is possibly due to ablation debris interacting with the hohlraum debris. The 50 cm distance appears to be relatively more ecient in collection compared to the 25 cm distance, which could be from a combination of ablation and/or anisotropy e↵ects. A sample from a test shot without a gold Hohlraum consistently showed alowgoldcontent,howeversomesmallgoldresidualwasstillseen.Shotsatthe50cm distance show gold amounts signiﬁcantly above what is expected from an assumed isotropic distribution, however there is no clear relationship with shot energy. Shots at the 25 cm distance still show some increase of gold collected compared to an isotropic expectation,

155 but not as much as at 50 cm. This is a possible indication of debris material loss at shot distances. Material collected at the polar angle shows only trace amounts of gold; this appears to be consistent with the postulated geometry of the hohlraum disassociation in the Eder paper. A NIF pellet with 2.6 x 1016 atoms of germanium doping was irradiated for 1 hour resulting in a very clean 264 keV spectrum line. If no impurities or gold were present in asamplethedetectionsensitivityisestimatedtobegreaterthan4x1013 atoms. The gold present on equatorial samples (as well as the signiﬁcant amount of impurities in the aluminum samples tested thus far with varying amounts of copper and manganese) will not allow for germanium detection at this sensitivity. The Polar DIM appears to be the prime candidate to attempt germanium detection if a clean collector material can be used. The collector has to be located in the polar position where signiﬁcant gold deposit can possibly be avoided. Clean graphite, aluminum, titanium or vanadium backings will need to be used, allowing for germanium measurement within 1 hour of activation. Alternatively, germanium would need to be separated chemically with a high (and known) eciency.

11.5 Ideas for Continuing Research

Improvements in gamma detector eciency, geometry, and shielding could increase the NAA sensitivity by approximately a factor of two. Low levels of gold and contaminants in the collector would allow increase in the sensitivity by a factor of between two to ten for germanium through lengthened irradiation time and ﬂux. Further investigation of the inﬂuence of collector geometry and position and catcher material on collection eciency

(equatorial and polar) is needed. Ways to increase germanium detectability need to be explored (as described above) and the limits of NAA sensitivity for germanium discovery quantiﬁed further.

156 REFERENCES CITED

[1] S. Pomm´e,J. Camps, R. Van Ammel, and J. Paepen. Protocol for uncertainty assessment of half-lives. Journal of Radioanalytical and Nuclear Chemistry,276(2):335–339, May 2008. ISSN 0236-5731. doi: 10.1007/s10967-008-0508-y.

[2] A. Ray, P. Das, S.K. Saha, A. Goswami, and A. De. Observation of enhanced orbital electron-capture nuclear decay rate in a compact medium. Physics Letters B,679(2): 106–110, August 2009. ISSN 03702693. doi: 10.1016/j.physletb.2009.07.036.

[3] Kenneth Bainbridge, M. Goldhaber, and Elizabeth Wilson. Inﬂuence of the Chemical State on the Lifetime of a Nuclear Isomer, Tc99m. Physical Review, 90(3):430–439, May 1953. ISSN 0031-899X. doi: 10.1103/PhysRev.90.430.

[4] R. Reifarth, S. Dababneh, M. Heil, F. K¨appeler, R. Plag, K. Sonnabend, and E. Uberseder. Neutron activation of natural zinc samples at kT=25 keV. Physical Re- view C,85(3):035802,March2012.ISSN0556-2813.doi:10.1103/PhysRevC.85.035802.

[5] Walter E. Meyerhof. Elements of Nuclear Physics. Mcgraw-Hill (Tx), 1967. ISBN 0070417458.

[6] E. Segre. Possibility of altering decay rate of a radioactive substance. Physical Review, 71:274–275, 1947.

[7] R. Daudel. Alteration of radioactive periods of elements with the aid of chemical methods. Revue Scientiﬁque,85:162,1947.

[8] J. R. Goodwin, V. V. Golovko, V. E. Iacob, and J. C. Hardy. Half-life of the electron- capture decay of 97 Ru: Precision measurement shows no temperature dependence. arXiv:0910.4338v1 [nucl-ex],pages1–7,2009.

[9] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz. WIEN2k: An Augmented Plane Wave Local Orbitals Program for Calculating Crystal Properties. 2001.

[10] R. Leininger, E. Segr`e,and C. Wiegand. Erratum: Experiments on the E↵ect of Atomic Electrons on the Decay Constant of Be7. II. Physical Review, 81(2):280–280, January 1951. ISSN 0031-899X. doi: 10.1103/PhysRev.81.280.

[11] JA Cooper and JM Hollander. E↵ect of the Chemical State on the Lifetime of the 24-second isomer of Nb90. Physical Review Letters,15(16):680–683,1965.

157 [12] P. Ehrhart, P. Koran, and W. Gnettner. Relative change of the electron density at the Cu nucleus in Cu-Ag alloys. Hyperﬁne Interactions,7(1):207–210,1979.ISSN 0304-3843. doi: 10.1007/BF01021503.

[13] L. Liu and C. Huh. E↵ect of pressure on the decay of 7Be. Earth and Planetary Science Letters,180(1-2):163–167,2000.

[14] T. Ohtsuki, H. Yuki, M. Muto, J. Kasagi, and K. Ohno. Enhanced Electron-Capture Decay Rate of B7e Encapsulated in C60 Cages. Physical Review Letters,93(11):2–5, September 2004. ISSN 0031-9007. doi: 10.1103/PhysRevLett.93.112501.

[15] E. Segre and C. Wiegand. Experiments on the E↵ect of Atomic Electrons on the Decay Constant of Be7. Physical Review,75(1):39–43,1949.

[16] J. Kraushaar, Elizabeth Wilson, and Kenneth Bainbridge. Comparison of the Values of the Disintegration Constant of Be7 in Be, BeO, and BeF2. Physical Review,90(4): 610–614, May 1953. ISSN 0031-899X. doi: 10.1103/PhysRev.90.610.

[17] Don Byers and Robert Stump. Low-Temperature Inﬂuence on the Technetium-99m Lifetime. Physical Review, 112(1):77–79, October 1958. ISSN 0031-899X. doi: 10.1103/ PhysRev.112.77.

[18] P. Das and A. Ray. Terrestrial Be7 decay rate and B8 solar neutrino ﬂux. Physical Review C,71(2):1–7,February2005.ISSN0556-2813.doi:10.1103/PhysRevC.71. 025801.

[19] A. Ray, P. Das, S. K. Saha, S. K. Das, and B. Sethi. Observation of large change of 7Be decay rate in Au and Al2O3 and its implications. Physics Letters B,(May):69–76, 1999.

[20] C. Huh. Dependence of the decay rate of 7Be on chemical forms. Earth and Planetary Science Letters,171:325–328,1999.

[21] E.B Norman, B Sur, KT Lesko, and RM Larimer. An improved test of the exponential decay law. Physics Letters B,1995.

[22] J. R. Goodwin, V. V. Golovko, V. E. Iacob, and J. C. Hardy. The half-life of 198Au : High-precision measurement shows no temperature dependence. The Eu- ropean Physical Journal A, 34(3):271–274, January 2008. ISSN 1434-6001. doi: 10.1140/epja/i2007-10509-0.

[23] A. Ray, P. Das, S. K. Saha, A. Goswami, and A. De. Enhanced orbital electron- capture nuclear decay rate in compact medium. page 30, April 2009. URL http: //arxiv.org/abs/0904.0326.

158 [24] P. Das and A. Ray. Electron capture decay rate change and Ab initio calculation of electron density at the nucleus. Proceedings of the DAE Symp. on Nucl. Phys.,55: 470–471, 2010. URL www.sympnp.org/proceedings.

[25] General Atomics. TRIGA Research Reactors. URL http://www.ga-esi.com/triga/ about.

[26] Glenn F. Knoll. Radiation Detection and Measurement. Wiley, 2010. ISBN 0470131489.

[27] Brookhaven. Evaluated Nuclear Structure Data File maintained by the National Nuclear Data Center, 2013. URL http://www.nndc.bnl.gov.

[28] Gerhard Erdtmann. Neutron Activation Tables. Verlag Chemie, Weinheim, New York, kernchemie edition, 1976. ISBN 3-527-25693-8.

[29] Khalifeh Abusaleem and Balraj Singh. Nuclear Data Sheets for A = 71*. Nuclear Data Sheets,112:133–273,2011.

[30] J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics,1:195–200,1964.

[31] Roberto Fraile and Eduardo Garcia-Ortega. Fitting an Exponential Distribution. Jour- nal of Applied Meterology,44:1620–1625,2005.

[32] Bruce Cleveland. The analysis of radioactive decay with a small number of counts by the method of maximum likelihood. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 214:451–458, 1983.

[33] G. E. P. Box and G. Jenkins. Time Series Analysis: Forecasting and Control. Holden- Day, 1976.

[34] T. S. Breusch. Testing for Autocorrelation in Dynamic Linear Models. Australian Economic Papers,17:334–355,1979.

[35] L. G. Godfrey. Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables. Econometrica,46 (6):1293–1301, 1978.

[36] J. Durbin and G. S. Watson. TESTING FOR SERIAL CORRELATION SQUARES REGRESSION . I. Biometrika,37(3):409–428,1950.

[37] Donald W. Marquardt. An Algorithm for Least-Squares Estimation of Nonlinear Pa- rameters. Journal of the Society for Industrial & Applied Mathematics,11(2):431–441, 1963.

159 [38] G. Audi, F. G. Kondev, M. Wang, B. Pfei↵er, X. Sun, J. Blachot, and M. MacCormick. The Nubase2012 evaluation of nuclear properties. Chinese Physics C,36(12):1157–2014, 2012. URL http://cpc-hepnp.ihep.ac.cn.

[39] M. Be, V. Chiste, and C. Dulieu. Table of Radionuclides (Comments on evaluation). Technical report, Bureau International des Poids et Mesures, Sevres, France, 2004.

[40] W.H. Sullivan. Discovery, Identiﬁcation, and Characterization of 2.8d Ru97. Physical Review,70:778,1946.

[41] D. L. Mock. Photo-Induced Reactions at 20 Mev. Physical Review,74:1536,1948.

[42] S Katco↵ and D. C. Williams. Branching in the Decay of 97Ru to 97mTc and 97Tc. Journal of Inorganic and Nuclear Chemistry,7(1955):189–193,1958.

[43] V. T. Cretzu. Neue Niveaus im Tc97. Annalen der Physik,472:1,1966.

[44] D. J. Silvester. Abstracts. Second international symposium on radiopharmaceuticals chemistry. Part II. Journal of Labelled Compounds and Radiopharmaceuticals,16:226, 1979.

[45] T. Kobayashi, K. Sueki, M. Ebihara, M. Imamura, and H. Nakahara. Decay properties of 97m,gTc. Nuclear Physics A, 636(4):367–378, July 1998. ISSN 03759474. doi: 10.1016/S0375-9474(98)00209-7.

[46] V. N. Levkovskii. The (n, p) reaction in gallium and germanium and the (n, g) reaction in germanium at neutron energies of 14 Mev. The Soviet Journal of Atomic Energy,4 (1):97–99, January 1958. ISSN 1063-4258. doi: 10.1007/BF01514566.

[47] T. Thwaites and W. Pratt. Decay of the Zn71 Isomers. Physical Review,124(5):1526– 1531, December 1961. ISSN 0031-899X. doi: 10.1103/PhysRev.124.1526.

[48] T. Sonnino, E. Eichler, and S. Amiel. The Decay of 4.1 Hour Zn71. Nuclear Physics, 54:568, 1964.

[49] L. H. Thomas. The calculation of atomic ﬁelds. Proc. Cambridge Phil. Soc.,23(5): 542–548, 1927.

[50] Enrico Fermi. Un Metodo Statistico per la Determinazione di alcune Priopriet`a dell’Atomo. Rend. Accad. Naz. Lincei,6:602–607,1927.

[51] Sol Wieder. The Foundations of Quantum Theory. Academic Press, New York, New York, 1973.

160 [52] N. Aquino, A. Flores-Riveros, and J.F. Rivas-Silva. The compressed helium atom vari- ationally treated via a correlated Hylleraas wave function. Physics Letters A,307(5-6): 326–336, February 2003. ISSN 03759601. doi: 10.1016/S0375-9601(02)01767-X. URL http://dx.doi.org/10.1016/S0375-9601(02)01767-X.

[53] P. Hohenberg and W. Kohn. Inhomogeneous Electron Gas. Physical Review,136(3B): B864–B871, November 1964. ISSN 0031-899X. doi: 10.1103/PhysRev.136.B864.

[54] W. Kohn and L. J. Sham. Self-Consistent Equations Including Exchange and Correlation E↵ects. Physical Review, 140(4A):A1133–A1138, November 1965. ISSN 0031-899X. doi: 10.1103/PhysRev.140.A1133.

[55] L. D. Landau and E. M. Lifshitz. Quantum Mechanics: Non-Relativistic Theory.Perg- amon Press, Ltd., London, second edi edition, 1965.

[56] Nathan Argaman and Guy Makov. Density Functional Theory — an introduction. American Journal of Physics,68:69–79,2000.

[57] K Lee and G Steinleneumann. Ab-initio study of the e↵ects of pressure and chemistry on the electron-capture radioactive decay constants of 7Be, 22Na and 40K. Earth and Planetary Science Letters, 267(3-4):628–636, March 2008. ISSN 0012821X. doi: 10. 1016/j.epsl.2007.12.014.

[58] M. Bukowinski. Theoretical estimate of compressional changes of decay constant of 40K. Geophysical Research Letters,6(9):697–699,1979.

[59] N. R. Moody, D. P. Adams, D. Medlin, and T. Headley. E↵ects of di↵usion on interfacial fracture of gold-chromium hybrid microcircuit ﬁlms. International Journal of Fracture, (119/120):407–419, 2003.

[60] N. R. Moody, D. P. Adams, M. D. Volinsky, M. D. Kriese, and W. W. Gerberich. An- nealing E↵ects on Interfacial Fracture of Gold-Chromium Films in Hybrid Microcircuits. Materials Research Society Symp.,586,2003.

[61] M. Winter. Web Elements. URL http://www.webelements.com.

[62] T.D. Williams, Bagayoko D., and G. L. Zhao. Calculated Optical Properties of RuO2. Technical report, 2010.

[63] J. H. Xu, T. Jarlborg, and A. J. Freeman. Self-consistent band structure of the rutile dioxides Nbo2, RuO2, and Iro2. Physical Review B,40(11):7939–7947,1989.

161 [64] G P Grim, P Bradley, T Bredeweg, L Keksis, M M Fowler, C Hayes, G Jungman, W Obst, R S Rundberg, D J Vieira, J B Wilhelmy, L Bernstein, C J Cerjan, R J Fortner, K J Moody, D H Schneider, D a Shaughnessy, W Stoe✏, and M Stoyer. Prompt radiochemistry at the National Ignition Facility (invited). The Review of scientiﬁc instruments,79(10):10E503,October2008.ISSN1089-7623.doi:10.1063/1.2972174. URL http://www.ncbi.nlm.nih.gov/pubmed/19044489.

[65] D. C. Eder, A. E. Koniges, O. S. Jones, M. M. Marinak, M. T. Tobin, and B. J. MacGowan. Late-time simulation of National Ignition Facility hohlraums. Nuclear Fusion, 44(7):709–719, July 2004. ISSN 0029-5515. doi: 10.1088/0029-5515/44/7/003.

[66] Malcom Chase, editor. NIST-JANAF Thermochemical Tables. American Chemical Society and the American Institute of Physics, New York, New York, 1998.

162 APPENDIX A - COMPUTER PROGRAM LISTINGS

This appendix lists all of the computer programs used for data analysis.

A.1 MAESTRO data acquisition script

This is a listing of a ORTEC MAESTRO software script that controls data acquisition.

Listing A.1: MAESTRO Job Control Script

SET DETECTOR 1 SET PRESET CLEAR SET PRESET REAL 1800 LOOP 5 0 0 0 CLEAR START WAIT FILL BUFFER SET DETECTOR 0 DESCRIBE SAMPLE ” T h i s i s s p e c t r u m ? ? ? ” SAVE ”C : Documents and Settings All Users Documents USGS Measurements \ \ \ \ \ AuCr2F Spectrum ???.CHN” \ EXPORT ”C : Documents and Settings All Users Documents USGS Measurements \ \ \ \ AuCr2F Spectrum ???.CHN” \ \ MARK PEAKS REPORT ”C : Documents and Settings All Users Documents USGS Measurements \ \ \ \ AuCr2F Spectrum ???.RPT” \ \ SET DETECTOR 1 END LOOP

A.2 The rwspec code

The rwspec code translates MCA data to gf3 .spe ﬁle format.

Listing A.2: rwspec program

// // main . c // rwspec // // Created by Robert Larson on 9/4/12.

#include #include ” u t i l . h” #include #include const int DIM = 8190; float sp[DIM]; // 8192 55 int idimsp=DIM, ret ; //numch, 8192 55

FILE ∗ f1 ; char string [100]; int main(int argc , const char ∗ argv []) { int ifileMin=0, ifileMax=0;

ifileMin = atoi(argv[1]) ; ifileMax = atoi(argv [2]) ;

// loop over f i l e names for ( int ifileNum = ifileMin ; ifileNum <=ifileMax;ifileNum++) { char outFileName [8] = ”nnn. spe ”; char inFileName [16] = ”Spectrum”; // char inFileName[17] = ”Spectrum1”; //use this line for rwspec1000 char fileStr [4] = ”000”;

sprintf(fileStr , ”%03d”, ifileNum);

// make the output file name strncpy(outFileName , fileStr , 3) ; printf(”outfileNum = %s n”, outFileName) ; \ // make the input file name strcat(inFileName , fileStr ); strcat(inFileName , ”.txt”); printf(”infileNum = %s n”, inFileName) ; \ // open the output f i l e f1 = fopen(inFileName , ”r”) ;

if (f1==NULL)

164 { printf(”Could not open file %s n”, inFileName) ; \ return 1; } int i = 0; float fl [5];

while(++i<=26) // 26 166, skip over initial lines { fgets(string , sizeof(string) , f1); } i=0; int j = 0;

while (fscanf(f1, ”%s %f %f %f %f %f”, string , &fl[0], &fl[1], &fl [2] , &fl [3] , &fl [4]) != EOF &&++j <=1638) { for(int k = 0; k < 5; k++) { sp [ i++] = fl [k ] ; } // printf(”%s %f %f %f %f %f n”, string, fl[0], fl[1], fl \ [2] , fl [3] , fl [4]) ; } // printf (”50 = %f n”, sp [50]) ; \ fclose(f1);

ret = wspec(outFileName , sp, idimsp); // printf (” ret = %d n”, ret) ; \

} return 0; }

A.3 The rpt python code

Listing A.3: Copies the correct line from the MAESTRO rpt ﬁle. import numpy as np import csv import re import sys

165 list1 = [] line1 = [] header = [ ’ File ’ , ’Date ’ , ’Time’ , ’RT’ , ’LT’ , ’ROI#’,’RANGE’ , ’(keV) ’ , ’GROSS ’,’NET’,’+/ ’,’CENTROID’,’FWHM’,’FW(1/5)M’,’LIBRARY’,’(keV) ’,’cA ’,’+/ ’] outfile1 = ’Cr51.csv ’ f1 = open(outfile1 , ’w’) data writerCr51 = csv . writer(f1 , dialect = ’excel ’ , lineterminator = ’ \ n’) data writerCr51 . writerow(header) outfile2 = ’Eu152.csv ’ f2 = open(outfile2 , ’w’) data writerEu152 = csv . writer (f2 , dialect = ’excel ’ , lineterminator = ’ n’) \ data writerEu152 . writerow(header) rptfile0 = ’Spectrum’ rptlow = int (raw input(”Enter first RPT index (negative to quit): ”)) if rptlow < 0: sys . exit () rpthigh = int(raw input(”Enter first RPT index (negative to quit): ”)) if rpthigh < 0: sys . exit () print rptlow , rpthigh rptlist = range(rptlow, rpthigh+1) print rptlist for rptcounter in rptlist :

rptnumber = ’%03d’ % ( rptcounter ) rptfile = rptfile0 + rptnumber + ’.rpt’ print rptfile fr = open(rptfile , ’r ’)

csvrowdt = [ rptnumber ] csvrow = []

#readfirstblankline line1 = fr . readline ()

#readsecondlinefordate,time,rt, lt line1 = fr . readline () list1 = line1. split () csvrowdt .append( list1 [3])

166 csvrowdt .append( list1 [5]) csvrowdt .append( list1 [8]) csvrowdt .append( list1 [11]) #printcsvrow

#skipthenextthreelines line1 = fr . readline () line1 = fr . readline () line1 = fr . readline ()

while True: line1 = fr . readline () if len(line1) == 0: break list1 = line1. split () if list1 [9] == ’Cr 51’: #printlist1[9] csvrow = csvrowdt + list1 data writerCr51 . writerow(csvrow) #elif list1 [9] == ’Np 237’: #print l i s t 1 [ 9 ] #csvrow = csvrowdt + list1 #data writerEu152 . writerow(csvrow) elif list1 [10] == ’344.30’: #printlist1[9] csvrow = csvrowdt + list1 data writerEu152 . writerow(csvrow)

fr . close() f1 . close () f2 . close () A.4 The gﬁnit.dat ﬁle

Listing A.4: gf3 Initiation File

0.0 ,0.0 ,0.0 ,0.0 ,0.0 ; < A,B,C,D,E for gf3 initialization. 0,0,0 ; < 0/1 for R,BETA,STEP fixed/ free . 3.0 ,2.0 ,0.0 ; < F,G,H for gf3 initialization (starting widths ). 1,0 ; < 0/1 for absolute widths, relative widths fixed/free . ;Filegfinit.dattoinitializeprogramgf3. ;Thisversionwillsettheinitialestimatestofitnonskew gaussians ;only.TheparameterSTEPisalsobydefaultfixedtozero.

167 ;Forgf3,andgf2versions6.1andabove. ;D.C.RadfordJune1989. A.5 The sum.py python code

Listing A.5: Python Script for Summing .spe Files import os rptlow = int (raw input(”Enter first TXT index (negative to quit): ”)) if rptlow < 0: sys . exit () rpthigh = int(raw input(”Enter last TXT index (negative to quit): ”)) if rpthigh < 0: sys . exit () #printrptlow,rpthigh rptlist = range(rptlow, rpthigh+1) #printrptlist rptlowStr = ’%03d’ % (rptlow) rpthighStr = ’%03d’ % (rpthigh) cmdStr = ”s” + rptlowStr + ” ”+rpthighStr+”.cmd” fileStr = os.getcwd() + ”/” + cmdStr print fileStr f=open(fileStr, ’w’) for rptcounter in rptlist :

f.write(”as 1 n”) \ rptnumber = ’%03d’ % ( rptcounter ) f.write(rptnumber+ ” n”) \ #f.write(”n”) \ f.write(”ws n”) \ f.write(”s” + rptlowStr + ” ”+rpthighStr+”.spe n”) \ f.write(” n”) \ f.write(”cf end n”) \ f.close() A.6 The ﬁt.py python code

Listing A.6: Python Script for Fitting .spe Data

168 import os rptlow = int (raw input(”Enter first TXT index (negative to quit): ”)) if rptlow < 0: sys . exit () rpthigh = int(raw input(”Enter last TXT index (negative to quit): ”)) if rpthigh < 0: sys . exit () #printrptlow,rpthigh rptlist = range(rptlow, rpthigh+1) #printrptlist rptlowStr = ’%03d’ % (rptlow) rpthighStr = ’%03d’ % (rpthigh) cmdStr = ” f ” + rptlowStr + ” ”+rpthighStr+”.cmd” fileStr = os.getcwd() + ”/” + cmdStr print fileStr f=open(fileStr, ’w’)

#f.write(”af12001200n”) \ #f.write(”fxrwn”) \ #f.write(”fxrpn”) \ #f.write(”ft n”) \ #f.write(” n”) \ for rptcounter in rptlist :

rptnumber = ’%03d’ % ( rptcounter ) f.write(”sp ” + rptnumber+ ” n”) \ f.write(”ft n”) \ f.write(” n”) \ f.write(”sa 1 n”) \ f.write(”sa 1 n”) \ dmpStr = ”d” + rptlowStr + ” ”+rpthighStr+”.dmp” f.write(”du ” + dmpStr+ ” n”) \ f.write(”cf end n”) \ f.close() A.7 The sto.py python code

Listing A.7: Python Script for Storing gf3 Results import os

169 rptlow = int (raw input(”Enter first TXT index (negative to quit): ”)) if rptlow < 0: sys . exit () rpthigh = int(raw input(”Enter last TXT index (negative to quit): ”)) if rpthigh < 0: sys . exit () #printrptlow,rpthigh rptlist = range(rptlow, rpthigh+1) #printrptlist rptlowStr = ’%03d’ % (rptlow) rpthighStr = ’%03d’ % (rpthigh) inStr = ”f” + rptlowStr + ” ”+rpthighStr+”.sto” outStr = ”f” + rptlowStr + ” ”+rpthighStr+”.txt” inFileStr = os.getcwd() + ”/” + inStr outFileStr = os.getcwd() + ”/” + outStr print inFileStr

#f=open(fileStr, ’w’) #forlineinf: lines = open( inFileStr , ”r” ). readlines() [1::2]

#readthedatafileinasa list #fin = open( fileStr , ”r” ) #data list = fin . readlines() #fin . close () #testfirst5 listitems... #printdatalist [:5]

#print’ ’∗60 #for i in enumerate(data list): #ifi%2==0: #deldatalist [ i ]

#removelistitemsfromindex2,4,6,8 to24(inclusive) #deldatalist[0+1] #testfirst5 listitems... #printdatalist [:5]

#writethechangeddata(list)toa file fout = open(outFileStr , ”w”) fout . writelines ( lines ) fout . close ()

170 #printlines

#f.close() A.8 R Script for Plotting

Listing A.8: Script for Using R to Calculate Half-life PLots

######L o a d L i b r a r i e s ###### library(e1071) library(ggplot2) library(plyr) library(sm) library(minpack.lm)

#df < data . frame(Cr campaign1) #df < data . frame(MCCr) #df < data . frame(AuCr2) #df < data . frame(Au2A) #df < data . frame(MCRuCrystal) #df < data . frame(RuCrystal2A) #df < data . frame(RuOxide2A) #df < data . frame(Ru103) #df < data . frame(Zn1a) #df < data . frame(Zn1b) #df < data . frame(Zn1c) df < data . frame(MCZnA1) #####R e n a m e V a r i a b l e s###### df$time< df$V1 df$activity< df$V2 df$counts< df$V3 df$dt< df$V5 #df$wgts < 1/d f $ d t #df$wgts< df$counts #df$wgts< df$counts/df$dt #df$wgts < 1/df$V4 df$countsDT< df$activity∗1800 # cr au zn ; 21600 # ru ; df$wgts< df$countsDT #setlowerandupperbounds low < 56 # zn; 76 # ru & ru103; 20 # ru oxide; 70 # au; 4000 # 100 # cr ; 1 # aucr ; high < nrow( df ) upper < high 0 spread < upper low+1

171 skip < 1 #print ( spread )

A0start < df$countsDT [ low ] #print ( A0start )

Nls .1 < nlsLM(countsDT ˜ A0 ∗ exp(lambda ∗ time) , start = list (A0 = A0start , lambda = 4.0329) , # zn ; 0.244324) , # ru ; 0.01765) , # ru103 ; 0.257207) , # au; 0.025) , # cr ; data = df [ seq(low , upper , skip ) , ] , weights = wgts) sum< summary( Nls .1 , d i g i t s =10) sum #A0LM < coef(Nls.1 , digits=10)[1] #A0LM #lambdaLM < coef(Nls.1 , digits=10)[2] #lambdaLM log(2)/ coef(Nls.1) [2] HL< ( log(2)/coef(Nls.1) [2]) HLsigma< ( sqrt(vcov(Nls.1) [4])/coef(Nls.1) [2])∗HL r1< c(df$time[low] , low, high) r1 r2< c(coef(Nls.1) [2] , sqrt(vcov(Nls.1) [4])) r2 r3< c(HL, HLsigma) r3 HLratio< HLsigma/HL HLratio

#str (m) sum$sigma

#Autocorrelationplots #computeacfwithoutplotting acz < acf(resid(Nls.1) , lag .max = upper , plot=F) #converttodataframe acd < data.frame(lag=acz$lag , acf=acz$acf) #usedataframeforggplot ggplot(acd , aes(lag , acf)) + geom area( f i l l =”grey”) + #geomhline( yintercept=c(0.05 , 0.05) , linetype=”dashed”) +

172 theme bw () + xlab(”Lag”) + ylab(”Autocorrelation Function”)

#Residualplot ggplot(data = df [ seq(low , upper , skip) , ] , aes(x = time , y = resid (Nls .1))) + #geomarea( f i l l =”grey”) + geom point( size = 2.0) + # 0.5) + #geomhline( yintercept = 0) + geom hline( yintercept = 1.0, lty = ”dashed”) + geom hline( yintercept = 1.0 , lty = ”dashed”) + theme bw () + xlab(”Time (Days)”) + ylab(”Exponential Fit Residuals (counts)”)

#countsvs.timeplot ggplot(df[seq(low, upper, skip), ], aes(x = time , y = counts)) + geom point( size = 1.0) + # 0.5) + theme bw () + xlab(”Time (Days)”) + ylab(”Decay Counts”) A.9 R Script for Looping over Contiguous Points

Listing A.9: This is an R script that calculates half-life values and uncertainties.

######L o a d L i b r a r i e s ###### library(e1071) library(ggplot2) library(plyr) library(sm) library(minpack.lm) library(lmtest)

#df < data . frame(Cr campaign1) #df < data . frame(MCCr1) #df < data . frame(AuCr2) #df < data . frame(MCAuCr1) #df < data . frame(RuCrystal) #df < data . frame(Au2A) #df < data . frame(MCAu198 1) #df < data . frame(RuCrystal2A) #df < data . frame(MCRu1) #df < data . frame(RuOxide2A) #df < data . frame(MCRuOxide1)

173 #df < data . frame(Ru103) #df < data . frame(MCRu103 1) #df < data . frame(MCZnA1) #df < data . frame(MCZnB2) #df < data . frame(Zn1a) df < data . frame(Zn1b) #df < data . frame(Zn1c) str < ”ZnBResults” #####R e n a m e V a r i a b l e s###### df$time< df$V1 df$activity< df$V2 df$counts< df$V3 #df$dt< df$V5 df$wgts< df$counts df$countsDT< df$activity∗1800 # cr au zn ; 21600 # ru ; df$wgts< df$countsDT #Set the working d i r setwd(”˜/Documents/HalfLife/Data/GF3”)

#remove file if it exists if (file .exists(str)) file .remove(str)

#setlowerandupperbounds low < 18 # 56 #znA &B; 32 # ru; 19 # ruoxide; 70 # au; 100 # aucr; 4000 # cr ; high < nrow( df ) upper < high 10# ru; 5# ru oxide; 10 #znA; 80 #au; 1450 # cr; 80 # aucr ;

spread < upper low+1 #print ( spread )

sq < seq(low , upper , by = 1) # ru ; 10) # au; 100) # cr ; 100) # aucr ; #print ( sq )

lambdaArray < numeric (0) lambdaWgtsArray < numeric (0) for ( ii in sq) { A0start < df$countsDT [ i i ] #print ( A0start )

#week < ii+198 # 4.2 days, like au, 336 one week = 336 half hours

174 Nls .1 < nlsLM(countsDT ˜ A0 ∗ exp(lambda ∗ time) , start = list (A0 = A0start , lambda = 4.0329) , # zn ; 0.244324) , # ru ; 0.01765) , # ru103 ; 0.257207) , # au ; 0.025) , # cr ; data = df [ ii : high , ] , # ii :week weights = wgts) sum< summary( Nls .1 , d i g i t s =10) #Storelambdavalues lambdaArray < c(lambdaArray, coef(Nls.1) [2]) lambdaWgtsArray < c(lambdaWgtsArray, 1/vcov(Nls.1) [4]) xdw < df [ ii : high , ] $time # ii :week ydw < resid(Nls.1) #Durbin Watson test #dw < dwtest(ydw ˜ xdw) #dwResult < c(ii , high, dw$statistic , dw$p.value) #dw #write (dwResult ,”dfDW”, append=TRUE)

#Breusch Godfrey test bg < bgtest(ydw ˜ xdw) #bgResult < c(ii , high, bg$statistic , bg$p.value) #bg #write(bgResult , ”strBG”, append=TRUE)

DegFreedom< high ii 1 HL< ( log(2)/coef(Nls.1) [2]) HLsigma< ( sqrt(vcov(Nls.1) [4])/coef(Nls.1) [2])∗HL result < c(df$time[ ii ] , ii , high, coef(Nls.1) [2] , sqrt(vcov(Nls.1) [4]) ,HL,HLsigma,bg$p.value,sum$sigma,DegFreedom) write(result , str , append=TRUE, ncol=10) #print ( r e s u l t ) } #print ( lambdaArray ) #print (lambdaWgtsArray)

#Calculatemeanandstdofthelambdas lambdaMean < wt.mean(lambdaArray , lambdaWgtsArray) lambdaSD < wt.sd(lambdaArray , lambdaWgtsArray) sdResult < c(lambdaMean, lambdaSD) write(sdResult , str , append=TRUE, ncol=2) print (sdResult)

175 A.10 R Script for Generating Monte Carlo Data

Listing A.10: This R script generates Monte Carlo simulation data.

######L o a d L i b r a r i e s ###### library(e1071) library(ggplot2) library(plyr) library(sm) library(minpack.lm) library(lmtest)

#set the working dir setwd(”˜/Documents/HalfLife/Data/GF3”)

#set f i l e name #str < ”MCAuCr3” #str < ”MCRu4” #str < ”MCCr” #str < ”MCAuCr4” #str < ”MCAu198 4” #str < ”MCRuOxide1” #str < ”MCRu103 4” str < ”MCZnB1” #remove file if it exists if (file .exists(str)) file .remove(str)

lambda < 4.0329 # zn ; 0.244324 # ru ; 0.01765 # ru103 ; 0.257207 # au ; 0.02502111 # cr ; #N0 = 5101335 # ru103; 4109792 # ru crystal; 100141 # au; N0 = 344323 # ZnB; 632666 # ZnA; 245000 # ZnC; #N0 = 757214 # ru oxide; 11543 # aucr; 290133 # cr; dtSecs < 30 ∗ 60 # cr , zn & au ; 6 ∗ 60 ∗ 60 # ru ; #setlowerandupperbounds low < 1 high < 115 # znB; 98 # ru oxide ; 116 # znA; 129 # ru crystal & ru103 ; 672 # au ; 4029 # aucr ; 7826 # cr ; step < 1 points < seq(low, high, by = step) time < points/48 # cr , zn & au; 4 # ru; #print ( time )

counts < N0 ∗ exp(lambda ∗ time)

176 #print ( counts )

activity < counts / dtSecs #print ( a c t i v i t y )

countsRan < counts activityRan < counts / dtSecs sq1 < seq(low, high, by = step) for (i in sq1) { countsRan [ i ] < rpois(1, counts[ i ]) activityRan [ i ] < countsRan [ i ] / dtSecs #result< c(i , high, time[ i ] , activityRan[ i ] , countsRan[ i ]) result < c(time[ i ] , activityRan[ i ] , countsRan[ i ]) write(result , str , append=TRUE) } A.11 R Script for Generating Results at Regular Intervals

Listing A.11: This R script calculates week spaced half-life values.

######L o a d L i b r a r i e s ###### library(e1071) library(ggplot2) library(plyr) library(sm) library(minpack.lm) library(lmtest)

#df < data . frame(Cr campaign1) df < data . frame(AuCr2) #df < data . frame(MCAuCr) #df < data . frame(RuCrystal2A) #df < data . frame(MCRuCrystal) str < ”AuCrSkip” #####R e n a m e V a r i a b l e s###### df$time< df$V1 df$activity< df$V2 df$counts< df$V3 #df$dt< df$V5 df$wgts< df$counts df$countsDT< df$activity∗1800 # cr au; 21600 # ru ; df$wgts< df$countsDT

177 #Set the working d i r setwd(”˜/Documents/HalfLife/Data/GF3”)

#remove file if it exists if (file .exists(str)) file .remove(str)

#setlowerandupperbounds low < 1#aucr;4240#cr(nogaps); high < nrow( df ) upper < high 336# 28 # 16 # 529 # low + 336 # spread < upper low+1 skip < 336 # 28 # 4 # #print ( spread ) sq < seq(low , upper , by = 8) # 48) # 28) # #print ( sq ) lambdaArray < numeric (0) lambdaWgtsArray < numeric (0) for ( ii in sq) { #print(df[seq(ii , high, skip), ])

A0start < df$countsDT [ i i ] #print ( A0start )

#week < ii+198 # 4.2 days, like au, 336 one week = 336 half hours Nls .1 < nlsLM( activity ˜ A0 ∗ exp(lambda ∗ time) , start = list (A0 = A0start , lambda = 0.025) , # cr ; 0.244324) , # ru ; data = df [ seq( ii , high , skip ) , ] , weights = wgts) sum< summary( Nls .1 , d i g i t s =10) #Storelambdavalues lambdaArray < c(lambdaArray, coef(Nls.1) [2]) lambdaWgtsArray < c(lambdaWgtsArray, 1/vcov(Nls.1) [4]) xdw < df [ seq( ii , high , skip) , ] $time ydw < resid(Nls.1) #Durbin Watson test #dw < dwtest(ydw ˜ xdw) #dwResult < c(ii , week, dw$statistic , dw$p.value)

178 #dw #write (dwResult ,”dfDW”, append=TRUE)

#Breusch Godfrey test #bg < bgtest(ydw ˜ xdw) #bgResult < c(ii , week, bg$statistic , bg$p.value) #bg #write(bgResult , ”strBG”, append=TRUE)

179 APPENDIX B - AUCR SPUTTER SAMPLE DATA

A set of test runs were made to determine the amount of gold and chromium that would be deposited for a given HV power on the target (MW) and time of sputter. These gold and chromium target test runs were performed in order to better understand the amount of each material that was expected to be deposited. The data from these runs is in Table B.1.

180 Table B.1: Sputter Data

Sample # Material Bayonet Position Ar Pressure (mTorr) HV Power (W) Time (min) Material Depth (Angstroms) 1 Cr 30 10 150 10 1099.25 2 NA NA NA NA NA NA 3 Cr 30 10 100 10 645.3 4 Cr 30 10 75 10 473.8 5 Au 30 10 75 5 969 6 Au 30 10 100 5 1308.7 7 Cr 30 10 50 10 295.7 8 Cr 30 10 25 10 125.7 9 Cr 30 10 10 15 73

181 APPENDIX C - PROPERTIES OF MATERIALS ANALYZED SOURCE: NIST-JANAF THERMOCHEMICAL TABLES 4TH EDITION

Material properties were compiled from the NIST-JANAF Thermo-chemical Tables 4th Edition (Chase [66]); values for incipient vaporization and melt were derived as presented in Table C.1. Note: Units of H are Joules / gram

Hmelt =HRT-melt +Hfusion =energytomeltmaterialfromroomtemperature

Hincipient vap =Hmelt +Hmelt-vap =energytobringmaterialtoincipientvaporization

*No melt temperature for graphite, Hvap used

182 Table C.1: Janaf Table

0 0 Tmelt ( K) Tvap ( K) HRT-melt Hfusion Hmelt Hmelt-vap Hincipient vap Hvap Henergy to vap Silver 1,235 2,435 220 105 324 501 825 2,323 3,148 Al6061 933 2,791 666 397 1,063 2,186 3,249 10,896 12,219 Grafoil* - 3915 - - - - - 7,184 59,670 Molybdenum 2,896 4,952 879 375 1,254 432 1,686 6,435 6,869 Niobium 2,750 5,131 829 290 1,118 858 1,976 7,432 7,890 Tantalum 3,258 5,778 517 202 719 413 1,132 4,082 4,322 Titanium 1,939 3,631 1,157 295 1,452 1,669 3,122 8,563 9,892 Vanadium 2,190 3,690 1,228 448 1,676 1,360 3,036 8,773 10,117

183