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ABSTRACT

SCHELHAMMER, KARL WILLIAM. Measurement of the Beta-Decay Lifetime of Magnetically Trapped Ultracold Neutrons. (Under the direction of Paul Huffman.)

In this dissertation, the progress towards the measurement of the lifetime of magnetically

trapped ultracold neutrons is discussed. Neutrons are trapped in a conservative potential using

a series of superconducting magnets arranged in an Ioffe-type field geometry. Neutron energy

is dissipated inside the trapping region by undergoing superthermal inelastic downscattering in

isotopically purified superfluid4He that also acts as a scintillator for decay events. Light from the decays are detected using a pair of photomultiplier tubes (PMTs) and decay events are

logged using high-speed digitizers. To remove the large amounts of background events present

in the data set, a set of software cuts was developed that greatly reduces the background

ob-served for a typical data series. In addition, background measurement runs are subtracted from

the trapping data to further reduce background events that are common to both

configura-tions. Preliminary results of the trap lifetime are reported, and the systematic uncertainty is

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©Copyright 2013 by Karl William Schelhammer

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Measurement of the Beta-Decay Lifetime of Magnetically Trapped Ultracold Neutrons

by

Karl William Schelhammer

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy

Physics

Raleigh, North Carolina

2013

APPROVED BY:

Chueng Ji Albert Young

David Haase Paul Huffman

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DEDICATION

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BIOGRAPHY

Karl Schelhammer was born November 9, 1981 in a small town in Minnesota. A series of

career moves for his father brought him to Lincoln, NE and then Greensboro, NC in 1988

where he would grow up playing music and sports, and make a number of lifelong friendships.

His love of science and mathematics would take hold in a beautiful mountain town in Boone,

NC at Appalachian State University. Following graduation from college, a year’s worth of

soul-searching would lead to a graduate career in physics at North Carolina State University

starting in 2006. This life-changing experience brought with it the opportunity to work at a

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ACKNOWLEDGEMENTS

During my time as a graduate student I have had effectively two advisors, my thesis advisor

Paul Huffman and the co-PI of this project Pieter Mumm. It is impossible to overstate the

extent to which I have benefitted from the lessons learned from these two mentors, both directly

and indirectly.

From the beginning, Paul afforded me a great deal of academic freedom to pursue my thesis

project at NIST. This allowed me the flexibility to investigate creative solutions (often at my

own peril!) to the difficult research problems that were a staple of my graduate career. As a

result, so much has been added to my professional skill set and my life in general. In addition,

it was his honest and patient assessment of the many revisions of this dissertation that helped

me to produce the document that I am proud to stand behind today.

To Pieter, I never could have asked for a better de-facto mentor. Through all the setbacks

preparing the apparatus, the long hours working graveyard shifts in the lab week after week,

the data sets that did not easily give up their secrets – you never lost your focus or drive and

you helped me to hold on to mine. You taught me everything I know about research and data

analysis and to that I owe you a debt of gratitude and much respect.

As I add the final edits and corrections to this thesis I am reminded of all the hard work that

went on at the NCNR. The tireless dedication of the scientists and engineers to their respective

projects – that often took many months or years to bear fruit – was a daily motivation to

continue to push hard at my own research efforts. My relationships with the people of the

NCNR made my time there that much more worthwhile in the end.

My gratitude and thanks: To my colleague Craig Huffer, it was a pleasure to work with

you on this project and I wish you all the best as you continue forward in your graduate

career. To my predecessor and former roommate Chris O’Shaughnessy, thank you for showing

me the ropes at NIST and also for your contributions to the design and construction of the

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collection effort is respected and appreciated. To Alan Thompson and Scott Dewey for their

contributions to the data acquisition and experimental control systems and for helping to keep

our morale high. To Andrew Yue, your knowledgeability and hunger for pho made for many

delicious and engaging afternoons. In addition, your writing advice was an invaluable asset

during the preparation of this dissertation. To Guillaume Darius, who reintroduced me to rock

climbing and whose equally hectic schedule made for many interesting midnight discussions

about life, physics, and the latest set of challenges to our respective projects. To George Noid,

I have many fond memories of your good humor during our weekend (and weeknight) excursions

around Gaithersburg. To Mike Rowe, thank you for your constant interest and encouragement

that kept me moving forward long after I would have liked to throw in the towel.

To the many others who lent me their time and expertise over the time I spent at NIST,

including but not limited to Jeff Nico, Tom Gentile, Dimitri Putin, Herbert Brewer, Tom

Lang-ford, Mohamed Abutaleb; thank you, all of you. Last but not least, thank you to Muhammad

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TABLE OF CONTENTS

LIST OF TABLES . . . ix

LIST OF FIGURES . . . xi

Chapter 1 Introduction . . . 1

1.1 Discovery of the Neutron . . . 2

1.2 Standard Model . . . 3

1.3 Weak Interaction . . . 6

1.4 Neutron Beta-Decay . . . 8

1.5 CKM Unitarity . . . 11

1.6 Big Bang Nucleosynthesis . . . 13

1.7 Summary . . . 16

Chapter 2 Present Status of the Neutron Lifetime . . . 17

2.1 Beam Measurements . . . 18

2.2 Material Bottle Measurements . . . 23

2.3 Magnetic Bottle Measurements . . . 28

2.3.1 Gravitomagnetic . . . 29

2.3.2 Three Dimensional Magnetic Confinement . . . 32

2.4 Summary of Results . . . 37

2.5 Conclusion . . . 40

Chapter 3 Experimental Overview . . . 42

3.1 Ultracold Neutrons . . . 43

3.2 Neutron Magnetic Properties . . . 46

3.2.1 Confinement in a Conservative Potential . . . 47

3.2.2 Spin Flipping . . . 48

3.2.3 Chaotic Trajectories in a Neutron Trap . . . 50

3.3 Superthermal Effect in Liquid Helium . . . 52

3.4 UCN Density . . . 55

3.5 Helium Purification . . . 59

3.6 Light Collection in Helium . . . 62

3.7 Summary . . . 63

Chapter 4 Experimental Apparatus . . . 66

4.1 Reactor and Beamline . . . 67

4.1.1 0.89 nm Neutron Beam . . . 68

4.1.2 Neutron Entrance Window . . . 71

4.2 Cryostat . . . 73

4.2.1 Magnet Tower and Horizontal Dewar . . . 75

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4.2.3 Cooling to<350 mK Using a Dilution Refrigerator . . . 78

4.2.4 Dilution Refrigerator Operations . . . 80

4.2.5 Experimental Cell . . . 81

4.2.6 Isotopically Pure Helium Gas Handling System . . . 84

4.3 Magnets . . . 85

4.3.1 Trapping Magnets . . . 86

4.3.2 Quench Detection and Protection . . . 87

4.3.3 Compensation Coils . . . 90

4.4 Detection System . . . 93

4.4.1 Low Intensity Light Detection Using Photomultiplier Tubes . . . 93

4.4.2 Light Extraction System . . . 95

4.5 PMT Stabilization . . . 99

4.5.1 Magnetic Shielding and Compensation Coils . . . 100

4.5.2 Gain Drift Mitigation . . . 102

4.5.3 Temperature Stability of PMT Sockets . . . 102

4.5.4 PMT Afterpulsing . . . 104

4.6 Shielding . . . 105

4.6.1 Passive Shielding . . . 106

4.6.2 Active Shielding . . . 108

4.7 Operations . . . 109

Chapter 5 Data Acquisition . . . .112

5.1 Pulse Digitization System . . . 113

5.1.1 Hardware Trigger . . . 114

5.2 Slow Controls System . . . 117

5.2.1 Trapping Magnet Controls . . . 119

5.2.2 Run Scripts . . . 121

5.3 Example Events . . . 125

5.4 Summary . . . 130

Chapter 6 Data Analysis . . . .132

6.1 Data Sets . . . 134

6.1.1 Static Configuration . . . 134

6.1.2 Flushing Configuration . . . 135

6.1.3 Above Threshold Configuration . . . 136

6.1.4 High Temperature Data Sets . . . 137

6.2 Low Level Data Analysis . . . 138

6.2.1 Timestamps . . . 139

6.2.2 Baseline Subtraction . . . 140

6.2.3 Pulse Area Calculation . . . 142

6.2.4 Kurtosis Calculation . . . 143

6.3 Software Corrections to the Data . . . 145

6.3.1 Dead Time Corrections . . . 147

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6.4 Background Reduction . . . 153

6.4.1 Reference Events Cut . . . 154

6.4.2 Muon Cut . . . 155

6.4.3 Upper Level Threshold . . . 158

6.4.4 Lower Level Threshold . . . 161

6.4.5 Kurtosis Cut . . . 163

6.4.6 Pulse Height Cut . . . 166

6.5 Extracting the Trap Lifetime . . . 168

6.5.1 Background Subtraction . . . 170

6.5.2 Statistical Sensitivity . . . 178

6.6 Summary . . . 178

Chapter 7 Systematic Effects . . . .181

7.1 UCN Upscattering Losses . . . 182

7.2 Losses due to 3He Absorption . . . 184

7.2.1 Reference Sample Preparation . . . 184

7.2.2 Loss Rate due to3He . . . 188

7.2.3 Systematic Correction to the UCN Lifetime Measurement . . . 189

7.3 Above Threshold Neutrons . . . 192

7.4 Neutron Trapping in Nontrapping Runs . . . 194

7.4.1 Phase Space Asymmetry . . . 194

7.4.2 Calculated UCN Density In Nontrapping Runs . . . 197

7.4.3 Order of Magnitude of Effect . . . 200

7.4.4 Conclusion . . . 202

7.5 Spin Flips . . . 203

7.6 Gain Drift . . . 205

7.7 Background Subtraction Imperfections . . . 206

7.7.1 Changes in the Constant Background . . . 207

7.8 Neutron Decay in Superfluid Helium Medium . . . 211

7.9 Summary of Systematic Effects . . . 211

Chapter 8 Summary . . . .213

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LIST OF TABLES

Table 1.1 Lepton properties showing the lepton number and electric charge for the three generations of known leptons. Not shown are the antimatter com-panion particles for which corresponding entries in this table would differ by a minus sign [36]. . . 4 Table 1.2 Quark properties showing the electric charge as well as the quark flavors

(‘upness’ U, ‘downness’ D, ‘charmness’ C, ‘strangeness’ S, ‘topness’ T, and ‘bottomness’ B). For the antimatter quarks, each of the entries in this table differ by a minus sign [36]. . . 5 Table 1.3 Basic properties of the four fundamental interactions. The relative strength

of the coupling constants are also shown. [36] . . . 7 Table 1.4 Typical final states for Fermi and Gamow-Teller type decays. For the

initial case |−1/2in, multiply each of the quantum numbers of the final states by a minus sign. . . 10

Table 2.1 In the upper portion of this table the seven measurements included in the 2012 Particle Data Group world average are shown. Shown below are older measurements not included in the average. . . 39

Table 3.1 Typical definitions of neutron energy ranges. . . 45

Table 5.1 Table of delay times relative to beam ‘off’ for each running configuration. (tTdelay is the delay time of the trapping run, andtN Tdelay) is the delay time of the corresponding nontrapping run. Delay times varied from configuration to configuration depending on the magnet ramp speeds, flushing of above threshold neutrons, and other optimizations. . . 125

Table 6.1 Run breakdown by experimental configuration. . . 133 Table 6.2 Total number of runs taken in static field configuration, by trap depth. . . 134 Table 6.3 Total number of runs taken in the flushing configuration, by trap and flush

depth. . . 136 Table 6.4 Total number of runs taken in the above threshold configuration. . . 137 Table 6.5 Total number of runs taken while the experimental cell was warm. . . 138 Table 6.6 Summary of the number of neutrons per run counted in the trap once data

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Table 6.7 Run Breakdown by Series Number. The † indicates data series included in the analysis that is the subject of this dissertation and presented in Table 6.6. Over half of the net data is not utilized due to gain instability, inconsistent reporting of delay times, cell temperatures above 350 mK, and problems with the low level files. Once these problems are solved, up to 302 additional static and flushing runs are potential available for reanalysis.177

Table 7.1 Helium Samples Measured Using ATLAS Apparatus. . . 185 Table 7.2 Calculated isotopic ratio of the samples mixed at NIST usingRi.p.34 = 3.3±

0.3×10−12. These number are provided for reference, the actual isotopic ratios of these samples are less than this due to the insufficient diffusion time. . . 188 Table 7.3 Systematic correction to the observed trap lifetime extracted using a single

exponential model. Two possible wall loss and wall reflection models are considered. In addition, two trap lifetimes are considered corresponding to large3He absorption (τtrap= 686 s) and no absorption (τtrap= 886 s). . 194

Table 7.4 Wall loss probability Pw estimated over an energy range using Figure 7.7. . 201

Table 7.5 Estimated values ofEcand number of trapped neutrons for various running

configurations. In this table the interaction energy due to the solenoids has been subtracted out because the field changes slowly in the central region of the trap. Vwall is the effective wall potential, andB(ρwall) is the

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LIST OF FIGURES

Figure 1.1 Examples of the lowest order weak vertices. (a) shows charged lepton - neutrino interactions, (b) shows quark interactions , and (c) shows charged lepton -charged lepton, neutrino - neutrino scattering. . . 6 Figure 1.2 Feynman diagram depicting the decay of a free neutron. The conversion

of a down to up quark inside the nucleon occurs by emission of a virtual

W− boson, which promptly decays into an electron and antineutrino. . . 11

Figure 2.1 Early apparatus used by Robsonet al. to measure the neutron lifetime [69].. . . 19 Figure 2.2 Neutron bottle used by Nicoet al. for measurement of the neutron lifetime [63]. 21 Figure 2.3 Neutron bottle used by Mampe et al. for measurement of the neutron lifetime

[53]. . . 24 Figure 2.4 Schematic of the ”Gravitrap” used by Serebrov et al. [73]. 1, neutron guide

from UCN Turbine; 2, inlet valve; 3, beam distribution flap valve (shown in the filling position); 4, connection unit; 5, ”high” vacuum volume; 6, ”rough” vacuum volume; 7, cooling coils; 8, UCN storage trap; 9, cryostat; 10, mechanics for trap rotation; 11, stepping motor; 12, UCN detector; 13, detector shielding; 14, evaporator. . . 26 Figure 2.5 Scheme of experimental setup used by Arzumanov et. al. 1, UCN guide; 2,

shutters; 3, UCN detector; 4, polyethylene shielding; 5, cadmium housing; 6, entrance shutter of inner vessel; 7 inner storage vessel; 8, outer storage vessel; 9 cooling coil; 10, thermal neutron detector; 11, vacuum housing; 12, oil puddle; 13, entrance shutter of gap vessel; 1a, oil puddle; 2a, slit. [5] . . . 27 Figure 2.6 A sketch of the magnetic walled bottle used by Ezhovet al. [24] . . . 30 Figure 2.7 A sketch of the Halbach array bottle used by Bowmanet al. [80] . . . 31 Figure 2.8 Cross section of toroid used by Kugelet al. (a) shows lines of constant magnetic

inductanceH˜. (b) shows the magnetic field linesB˜. [48]. . . 32 Figure 2.9 Drawing of the PENeLOPE design. 1, vacuum tank; 2, liquid N2 radiation

shield; 3, liquid He cryostat; 4, UCN entrance slit; 5, storage coils; 6, racetrack coils; 7, proton detector; 8, absorber; 9, supply line. [55] . . . 34 Figure 2.10 Schematic of the HOPE apparatus. [51] . . . 36 Figure 2.11 Over 17 measurements of the neutron lifetime have been published since 1986.

Only 7 are presently included in the PDG world average [6]. . . 38 Figure 2.12 Dependence of the CKM matrix element |Vud| on the values of the neutron

lifetime and the ratio of the coupling constants λ. The PDG values come from the 2012 report. [6] . . . 41 Figure 3.1 A schematic drawing of the coil arrangement for the type of field geometry used

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Figure 3.3 Neutron kinetic energy and dispersion curve for phonons and rotons in superfluid helium [21]. The intersection of the two corresponds to the energy and momen-tum of a neutron that will undergo superthermal down scattering to ultracold energies. . . 53 Figure 3.4 The3He concentration gradient as a function of position for the heat flush

tech-nique. (a) A semi-infinite tube, open at one end, contains a small amount of

3He, shown by black dots. v

n is the average velocity of the normal fluid flow.

(b) Shows the3He concentration,u(x) in the tube as a function of position when

heat is applied to the tube from the right. [38]. . . 61 Figure 3.5 Simulated detection efficiencies for various potential running modes. In the

present setup there is no reflective window. A comparison of the simulations to experimental data taken with a smaller test geometry is shown for reference [65]. . . 64 Figure 4.1 Beamline, biological shield walls, and apparatus. With the slider table in the

‘beam on’ position neutrons pass through a boroflex tube before entering the apparatus. In the ‘beam off’ position a lead stack is moved into place to block backgrounds originating from the neutron beam [83]. . . 69 Figure 4.2 A series of interlocking BN ceramic shields prevent neutrons from activating the

aluminum and stainless steel on the interior of the apparatus [65]. . . 72 Figure 4.3 Assembled apparatus in place at the NG-6 UCN station in the C-wing of the

NIST Center for Neutron Research. The white tower houses the dilution refrig-erator and the second tower houses the superconducting magnet’s HTS leads and infrastructure. Two magnetic field compensation coils are visible at either end of the apparatus. Also, large black scintillator paddles surround the exterior of the horizontal portion of the dewar, allowing rejection of muon related backgrounds.1 74 Figure 4.4 A schematic drawing of the entire apparatus is shown. The dilution refrigerator

tower is on the left side of the figure, and the magnet leads tower is on the right. The horizontal section of the apparatus houses the superconducting magnets that are used to trap neutrons [65]. . . 76 Figure 4.5 A cutaway view of the cryogenic support post used to mechanically support the

magnet bath and LN2 jacket [83]. . . 77

Figure 4.6 A schematic drawing of the dilution refrigerator and its coupling to the experi-mental cell. When condensing, isotopically pure helium is precooled using heat exchangers in the 1K pot and on the still. . . 79 Figure 4.7 Schematic of the circuit used to detect quench in the quadrupole magnet and

initiate the quench protection circuit [83]. . . 88 Figure 4.8 Schematic of circuit used to disengage the quadrupole magnet after a quench is

detected [83]. . . 91 Figure 4.9 A cross sectional view of the lightguide system used to extract scintillation light

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Figure 4.10 View of the experimental cell as seen from the left arm of the light splitter. The Winston cone allows each detector to view light originating at any point along the axis of the cell. . . 98 Figure 4.11 Data showing the change in PMT gain from temperature changes in the voltage

divider circuit as the PMT bias voltage is changes. Channel 1 data was taken using a temperature stable socket, while channel 2 used a standard PMT socket. The temperature stable socket minimizes the component of the gain drift that occurs after a PMT voltage bias change. . . 103 Figure 5.1 Schematic of main detection, reference, and muon detection PMT interface to

the digitization cards. A light pulser also connects to both main detectors and the reference PMT for gain monitoring. . . 115 Figure 5.2 Schematic of the trigger system used to control the GaGe digitizers.. . . 117 Figure 5.3 Diagram of the slow control system. . . 119 Figure 5.4 Typical sequence of operations for example data taking configurations. Some of

the running configurations used modified scripts which deviated from the depic-tion above in minor ways. A detailed discussion of the data taking configuradepic-tions is found in Section 6.1. . . 122 Figure 5.5 Example of an event caused by a muon. . . 127 Figure 5.6 Example of an event caused by the light pulser system that is used to

calibrate the main detector gain. . . 128 Figure 5.7 Example of a candidate neutron decay event. . . 129

Figure 6.1 An example of a baseline subtracted and inverted voltage pulse in the main detector. The peak of the trace is used to set the integration window shown by the dotted lines. The pulse shape metrics are computed from the segment of the trace in the window. . . 141 Figure 6.2 A histogram of the baseline calculated for a typical run. . . 142 Figure 6.3 Spectrum of events in the main detector (channel 1), showing the raw,

reference, and muon spectra. Inset shows the individually distinguishable 1, 2 and 3 PE peaks that are used to set the upper and lower PE thresholds.144 Figure 6.4 An example of a typical kurtosis histogram. The raw histogram shows the

event distribution for one run using no cuts. The other histogram shows the distribution of events that pass all of the software cuts described in Section 6.4. The kurtosis threshold of K = 15 is also shown. . . 146 Figure 6.5 Fractional live time correction due to 4µs veto window (on right) and total live

time correction due to combination of veto window and digitizer readout (on left). The total live time correction is dominated by the effect of the digitizer read out. . . 147 Figure 6.6 Observed pulser rate before and after a dead time correction. The light pulser

was nominally set at a trigger rate of 100s−1. . . . 150

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Figure 6.8 The Spectrum of Pulser Events in the Reference PMT . . . 155 Figure 6.9 Rate of muon-tagged events as a function of time for a typical run. . . 156 Figure 6.10 An example spectrum of muon events as seen by the muon veto system. . . 157 Figure 6.11 Location of noise peak, threshold used to assign muon cut, and the average rate

of muon events extracted from the data is shown here as a function of run number for a typical data series. . . 159 Figure 6.12 Two example spectra of main detector PE histograms, before and after the

background subtraction is applied. In this figure, a PE cut of 2 was used to show the low PE portion of this distribution. The events remaining after the subtraction are correlated to neutrons. . . 160 Figure 6.13 Example integrated background subtracted and trapping spectra in PE space

used to perform co-optimization of the lower and kurtosis thresholds. Minimum of the background to signal ratio is also shown. . . 162 Figure 6.14 Optimal value of the lower PE threshold as determined by minimizing a

back-ground vs. signal curve for a given kurtosis threshold. . . 163 Figure 6.15 An example of the 1D background-subtracted neutron spectra as seen in

PE and kurtosis space. . . 164 Figure 6.16 Background event rate before and after the DCS turns on the ‘white

beam’. In this mode the beam is not filtered and many more neutrons enter the DCS, causing an increase in the background observed with our instrument. A kurtosis cut removes these events. . . 165 Figure 6.17 Two dimensional histogram of the background subtracted signal showing

the neutron signal as well as asymmetries on the boundary of the Kurtosis vs. PE space. While the cuts remove the features along the upper bound-ary and low PE, slight asymmetries may persist in the region accepted by the cuts. . . 166 Figure 6.18 Example pulse height spectrum as seen by the two main detectors. . . 167 Figure 6.19 Left plot shows a background subtracted spectrum of muon events

show-ing a peak on the boundary of the Kurtosis vs. PE space. The right is the same subtracted spectrum after a pulse height cut is applied. The pulse height cut removes a large portion of the asymmetry along the upper boundary of the distribution. . . 169 Figure 6.20 Example of single exponential fits to background subtracted data sets in

the static running configuration. . . 170 Figure 6.21 Example of single exponential fits to background subtracted data sets in

the flushing running configuration. . . 173 Figure 6.22 Projected statistical sensitivity based on the analysis shown in Table 6.6.

The solid lines terminate at the number total number of runs currently available in a given running configuration. The dotted lines are projec-tions of the statistical sensitivity if additional data is taken. . . 179

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Figure 7.2 Schematic of Gas Mixing Manifold. . . 186 Figure 7.3 The calculated trap lifetime for a given 3He concentration. Preliminary

results from the ATLAS and CalTech measurements are also presented. . 190 Figure 7.4 Summary of3He/4He measurements made by groups at Oregon, CalTech,

and the measurement made by this group in collaboration with ANL. . . 191 Figure 7.5 Quadrupole field configuration as a function of time for a typical trapping

and nontrapping run. . . 196 Figure 7.6 Phase space occupation of neutron trapping for typical trapping and

non-trapping running configurations, for each phase of a run. Radial compo-nent of the trapping potential is shown. In the trapping runs, neutrons exist in both the fully trapped and marginally trapped energy regimes. In the nontrapping runs, only the fully trapped component exists. . . 197 Figure 7.7 Wall loss probability per bounce as a function of perpendicular energy [39].199 Figure 7.8 Wall collision rate as a function of neutron velocity. . . 200 Figure 7.9 Background subtracted signal using static cold 60 % nontrapping data and

static warm 70 % nontrapping data. The lack of time dependence of this plot demonstrates that there are no neutrons confined in the nontrapping runs, and calls into question the validity of the current wall loss model. . 204 Figure 7.10 Example of fluctuations in the background, presumably due to a

configu-ration change in a nearby experiment. The set of software cuts described in Chapter 6 removes these fluctuations. . . 208 Figure 7.11 Reactor startup run showing the changes in the background as the NG-6

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Chapter 1

Introduction

This dissertation will discuss the principles of operation, experimental apparatus, data analysis

and present preliminary results from the ultracold neutron (UCN) lifetime experiment operated

at the National Institute for Standards and Technology (NIST). Neutron beta-decay

measure-ments in general contribute to tests of the unitarity of the Cabbibo-Kobayashi-Maskawa matrix

as well as the ratio of the vector and axial-vector coupling constants λ = GA/GV. These

measurements test the Standard Model (SM), and constrain the number of possible quark

generations [30]. In addition, the neutron lifetime τn is the most important experimentally

determined input parameter to theoretical predictions of the primordial elemental abundances

in the early universe [26].

Recent precision measurements of τn continue to show significant discrepancy in their

re-ported results [81, 75, 6]. The seven neutron lifetime measurements included by the Particle

Data Group in the world average were performed using two fundamentally different techniques:

UCN confined using material bottles and neutron beams passing through a well defined

fidu-cial volume. The source of the discrepancy between these measurements is presumably related

to an imperfect understanding of the systematic effects of these techniques. As a result, new

measurements using techniques that are not subject to the same systematic effects are needed

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is an example of one such technique.

In this experiment, a set of superconducting magnets was used to magnetically trap neutrons

inside an isotopically pure superfluid4He filled cell. A free neutron is an unstable particle, and decays with an average lifetimeτninto a proton, electron and antineutrino. Neutron decays are

detected when the decay electron scintillates in the helium. The light produced as a result is

observed using photo-multiplier tubes (PMTs). These observations are performed in situ, and

used to make a measurement of the neutron beta-decay lifetime. In the following chapter, the

physical principles that describe neutron decay and the relevance of the lifetime measurement

to the theory of the Standard Model are discussed.

1.1

Discovery of the Neutron

As early as 1911, Ernest Rutherford had discovered evidence for the existence of a neutral

particle inside the atomic nucleus that would explain the experimentally observed discrepancy

between the mass and charge number of the known elements of the day [70, 71]. In Rutherford’s

experiments, alpha particles produced by a polonium source were elastically scattered from a

gold target. The observance of back-scattered alpha particles provided proof that the mass was

concentrated in the nucleus of the atom. The work done by Rutherford was instrumental in

developing the understanding of matter as atomic nuclei separated by mostly empty space.

Following Rutherford’s work, Walther Bothe and Herbert Becker in 1930 performed alpha

scattering from a metal beryllium target, producing a then unknown particle radiation. These

particles had the property that they could easily penetrate through matter [59]. Though not

fully known, this experiment by Bothe and Becker made use of theα+9Be→12C +n reaction to produce one of the first neutron sources.

Two years later, the neutron was discovered by James Chadwick [16]. Chadwick’s work

sought the identity of the unknown particle radiation discovered by Bothe and Becker by

bom-barding light elements and measuring the resultant products. In his experiment, hydrogen,

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producing recoil protons that were observed using an ionization chamber. Theories at the time

attempted to explain the recoil protons by invoking a physical mechanism analogous to

Comp-ton scattering. Chadwick’s results refuted this position on the grounds of simple energy and

momentum conservation arguments by explaining the observations in terms of a new neutral

particle having mass near the proton mass. This particle was thus named the neutron and the

puzzle of explaining the building blocks of ordinary matter was complete for a time. Chadwick’s

discovery of the neutron opened the door to a new field of research probing the nature of this

particle, and using them to study the structure of materials.

1.2

Standard Model

The Standard Model (SM) of particle physics and interactions is the quantum theory describing

three of the four known fundamental interactions. This theory includes the strong interaction

and the unified weak and electromagnetic interactions. The early pioneers of atomic and

nu-clear physics painted a convenient picture of the universe as consisting of protons, neutrons

and electrons, however we now know that the true explanation is much deeper. At the most

fundamental level, matter is made up of three generations of quarks and leptons as shown in

Tables 1.1 and 1.2. In addition, each of these particles, with the possible exception of a class of

neutrinos, has an antimatter companion particle, having the same mass and opposite electrical

charge.

The Standard Model is represented mathematically using the SU(3) ×SU(2) ×U(1)

sym-metry group. In this picture, interactions between the particles occur by exchange of virtual

force mediating particles, called bosons. A broad comparison of the fundamental interactions

is shown in Table 1.3.

In the Standard Model, a total of 12 bosons are needed to explain the known interactions

of the quarks and leptons. The strong interaction occurs between quarks due to the color

charge by exchanging force mediating particles called gluons. Eight types of gluons carry linear

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Table 1.1: Lepton properties showing the lepton number and electric charge for the three generations of known leptons. Not shown are the antimatter companion particles for which corresponding entries in this table would differ by a minus sign [36].

Generation Lepton Charge Lepton Number

Le Lµ Lτ

1 e− -1 1 0 0

νe− 0 1 0 0

2 µ− -1 0 1 0

νµ− 0 0 1 0

3 τ− -1 0 0 1

ντ− 0 0 0 1

states of the strong interaction occur in color charge triplets and color-anti-color pairs, forming

the color-neutral particles described below. The residual interactions of this force between the

color-neutral nucleons cause the bound states that give rise to nuclei.

The electromagnetic interaction explains the nature of electromagnetic fields as well as

atomic systems, and occurs due to the exchange of photons. Only one type of photon is

necessary to explain the electric and magnetic forces that arise due to electric charge.

Gravitational interactions occur between all particles with mass by exchange of the graviton,

which has not yet been experimentally observed. Current models expect that there is only one

type of graviton.

In weak interactions, virtual W±are emitted and/or absorbed by quarks and leptons,

chang-ing quark flavor and givchang-ing rise to phenomenon such as beta-decay. In addition, interactions

such as quark-lepton scattering occur by exchanging the charge neutralZ0 boson. In the energy range above the so called ‘unification energy’, the electromagnetic and weak interactions merge

and are described by a single electro-weak interaction.

Bound states exist for combinations of quarks and antiquarks and are called the hadrons.

Hadrons consisting of quark-antiquark pairs are called mesons, of which none are stable

par-ticles. Hadrons consisting of three quarks are called the baryons, of which only the proton is

(22)

Table 1.2: Quark properties showing the electric charge as well as the quark flavors (‘upness’

U, ‘downness’ D, ‘charmness’ C, ‘strangeness’ S, ‘topness’ T, and ‘bottomness’ B). For the antimatter quarks, each of the entries in this table differ by a minus sign [36].

Generation Quarks Charge Flavor

U D C S T B

1 u 2/3 1 0 0 0 0 0

d -1/3 0 -1 0 0 0 0

2 c 2/3 0 0 1 0 0 0

s -1/3 0 0 0 -1 0 0

3 t 2/3 0 0 0 0 1 0

b -1/3 0 0 0 0 0 -1

The hadrons were first organized by Murray Gell-Mann in 1961 according to the quantum

numbers shown in Table 1.2 [29]. In this representation, bound states between the u,d,c and

squarks form multiplets and supermultiplets according to particle properties of isospin, charge

and strangeness. Using this classification scheme called the Eightfold Way, Gell-Mann was able

to famously predict the properties of the Ω−particle. While in principle bound states involving

top and bottom quarks also exist, the t and b quarks are so short lived that they are not

observed. The Eightfold Way gives a geometric method for arranging the known fundamental

particles.

The leptons consist of the electron, mu, and tau particles (antiparticles) and their

corre-sponding neutrinos (antineutrinos). The charged leptons carry electric charge ql = −1, while

the anti-leptons carry charge ¯ql = +1. Neutrinos and antineutrinos are produced as a result

of weak interactions by emission of W± and Z0 bosons. In a typical weak interaction vertex, shown in Figure 1.1, the W± particle is virtual and said to be off the mass-shell, meaning

that the classical equations of motion are not satisfied. Therefore, the W± particle has a very

short range. The neutrino/antineutrino have electrical chargeqν = 0, and do not participate in

the strong or electromagnetic interactions. The neutrino therefore interacts very weakly with

matter.

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Figure 1.1: Examples of the lowest order weak vertices. (a) shows charged lepton - neutrino interac-tions, (b) shows quark interactions , and (c) shows charged lepton - charged lepton, neutrino - neutrino scattering.

to have massmνl = 0. However, recent experimental evidence suggests that the neutrino species

have a small mass [43]. This arises from measurements of neutrino oscillations that cause a

neutrino’s flavor eigenstate to transition to another flavor eigenstate. In addition, the possible

existence of sterile neutrinos that participate in flavor oscillations, but do not participate in the

weak interaction, remains an open subject of study. These two interesting topics are outside

the scope of this dissertation.

1.3

Weak Interaction

The weak interaction is unique in that it incorporates both ‘charged current’ and ‘neutral

current’ interactions. In the neutral current interaction, the exchange of the Z0 neutral boson causes scattering between leptons and/or quarks. In a charged current interaction, ±1 unit

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Table 1.3: Basic properties of the four fundamental interactions. The relative strength of the coupling constants are also shown. [36]

Theory Interaction Mediating Spin Number Relative Strength

Particle of Bosons

General Relativity Gravity graviton 2 1 10−42

Standard Model

Weak Z0, W± 1 3 10−13

Strong gluon 1 8 10

Electromagnetic photon 1 1 10−2

accordingly, the particle flavor is changed.

In addition, unlike the strong and electromagnetic interactions, the weak interaction does

not conserve parity. Parity is the operation of space inversion, and converts right-handed

particles into their left-handed counterparts. In order to understand this, we consider the

correlation between the neutrino’s spin and momentum. When a particle’s spin is aligned with

its direction of motion, we say that it is right-handed. When the spin is anti-aligned, we say

that it is left-handed. The parity of a system can thus be expressed in terms of the right or left

handedness of the particle system.

In charged current weak interactions, it is experimentally evident that the parity violation

is maximal. This is realized as the non-existence of right(left)-handed neutrino(antineutrino)

species. Because of this asymmetry we say that the theory of the weak interaction is a chiral

theory.

In charged current weak interactions, the Hamiltonian H takes the form

H= G√F 2J

Jc†

µ , (1.1)

where GF is the Fermi coupling constant. The weak interaction current Jµc for neutron decay

can be expressed as

(25)

where

hcµ=ψ†d¯γµ(1−γ5)ψu

lcµ=ψ†νγµ(1−γ5)ψe.

(1.3)

Here, hcµ and lcµ are the hadronic and leptonic currents, {γ} are the Dirac matrices, and

ψd¯, ψu, ψe, and ψν are the down quark, up quark, electron and antineutrino spin states,

re-spectively. The presence of the (1−γ5) factor in Equation 1.3 couples the weak currents exclusively to left (right) handed fermions (antifermions).

1.4

Neutron Beta-Decay

Neutrons undergo beta-decay due to a mass difference that exists between the neutron and its

decay products, ∆ = 782 keV. In this process, a down quark transitions to an up quark as

shown in Figure 1.2. The neutron is thus converted to a proton by emission of a virtual W−

boson, which promptly decays into an electron and antineutrino. The energy from the decay is

shared between the decay products, of which the electron and antineutrino receive the majority.

Beta decays can be classified as either Fermi or Gamow-Teller according to the spin states

of the decay products. In a Fermi decay, the antineutrino spin is antiparallel to the electron

spin, while the proton spin assumes the neutron’s spin state. For these transitions, the total

spin of the leptons is 0. In Gamow-Teller decays, the leptons are produced in the triplet state,

with total spin 0 or 1. When the leptons carry 0 spin, the proton assumes the neutron’s spin

state. When the lepton’s spin is 1 the proton’s spin is flipped.

Because there is no transfer of spin from the hadronic component of the decay to the leptons

in Fermi type decays, the operator that describes this transition is unitary (1). In the

Gamow-Teller type decays, the operators that describe these types of transitions are the set of spin

matrices~σ= (σ1, σ2, σ3), corresponding to the three spin degrees of freedom.

(26)

com-ponent of the hadronic currents shown in Equation 1.3. For the neutron system, the hadronic

term can be written as

hcµp¯γµ(GV +GAγ5)ψn, (1.4)

whereψpandψnare the proton and neutron spin state respectively. The vector and axial vector

coupling constants are given by GV =GFVudCV and GA=GFVudCA, where GF is the Fermi

coupling constant,Vudis the CKM matrix element giving the transition amplitude for anu→d

quark transition, and the constants CA and CV relate the interference of the spectator quarks

to the Fermi/Gamow-Teller transition probabilities. In the Standard Model, CV = 1 and CA

must be determined experimentally. These coupling constants give the relative strength of the

vector (Fermi) and axial-vector (Gamow-Teller) type decays.

Using the hadronic current in Equation 1.4 and leptonic current in Equation 1.3, the neutron

beta-decay hamiltonian can be written [41]

H=ψ†p¯γµ(GV +GAγ5)ψn ψν†γµ(1−γ5)ψe

. (1.5)

In order to determine the decay rate Γ, we use Fermi’s Golden Rule

dΓ = 1 (2π)5|H|

2δ(E

e+Eν¯−∆) 1 2Ee

1 2Eν¯

dp3edp3ν¯, (1.6)

whereEe and pe are the electron energy and momentum, and E¯ν and pν¯ are the antineutrino energy and momentum. The matrix element |H|2 is evaluated between the spin states of the neutron and decay products as depicted in Table 1.4, the result of which is

|H|2 =G2V| hpe−ν¯|1|ni |2+G2A| hpe−ν¯|σ|ni |2

=G2V + 3G2A.

(1.7)

Using the result of Equation 1.7 and integrating Equation 1.6 over dp3

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Table 1.4: Typical final states for Fermi and Gamow-Teller type decays. For the initial case |−1/2in, multiply each of the quantum numbers of the final states by a minus sign.

Decay Type Transition Lepton final state

Fermi |1/2in→ |1/2ip+|0iν¯+e− √1

2(|1/2iν¯|−1/2ie−− |−1/2iν¯|1/2ie−)

|1/2in→ |−1/2ip+|1iν¯+e− |1/2iν¯|1/2ie

Gamow-Teller |1/2in→ |1/2ip+|0iν¯+e− √1

2(|1/2iν¯|−1/2ie−+|−1/2iν¯|1/2ie−)

|1/2in→ |−1/2ip+|1iν¯+e− |−1/2iν¯|−1/2ie

the decay rate as

dΓ = 1 (2π)5(G

2

V + 3G2A)Eepe(∆−Ee)2dEe. (1.8)

The final integration over the electron energy Ee is complicated by three QED corrections

accounting for the proton recoil, the Coulomb interaction of participating charged particles,

and radiative corrections [81]. These effects are accounted for by f, the phase space factor,δR

the radiative correction term, and ∆VR which accounts for recoil. Finally, the neutron lifetime

is given as the inverse of the decay rate

τn=

2π3

(G2

V + 3G2A)f

= 2π

3

Vud2G2F(1 +λ2)f(1 +δ

R)(1 + ∆VR)

. (1.9)

It is evident from Equation 1.9 that the neutron lifetime can play an important role in

deter-mining the experimentally measured parameters of the weak interaction.

Measurements using neutrons yield the lifetime and the coupling constants GA, GV, and

provide a way to extract the parameterVud. At present, the most precise measurements ofGV

are obtained from the nuclear 0+ → 0+ superallowed transitions. In these types of processes, only Fermi processes are allowed, therefore only GV is determined [74]. Conversely, neutron

decays are mixed Fermi/Gamow Teller processes and thus one can determined both GV and

GA. Comparisons of the value ofVud∝GV between these two types of processes test the V-A

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Figure 1.2: Feynman diagram depicting the decay of a free neutron. The conversion of a down to up quark inside the nucleon occurs by emission of a virtual W− boson, which promptly decays into an electron and antineutrino.

1.5

CKM Unitarity

In the Standard Model, the quark mass eigenstates (also the eigenstates of the strong and

electromagnetic interactions) are not the same as the eigenstates of the weak interaction. This

leads to mixing of the states. Cabbibo, Kobayashi, and Maskawa (CKM) described this mixing

using a 3×3 matrix given as

      d s b       =      

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

            d0 s0 b0       , (1.10)

whered0,s0 andb0 represent the strong interaction or mass eigenstates, andd,sandbrepresent

the weak eigenstates [15, 44]. In this representation, the mixing is described in terms of the

down-type quarks, but it is also possible to formulate an equivalent representation using an

up-type quark mixing 3 × 3 matrix. In weak interactions, a transition between quark states

(29)

quarks and thus altering the particle’s flavor. The CKM matrix elements describe the relative

strength of these types of transitions.

The test of CKM unitarity addresses the question of how many quark generations exist in

nature. If the matrix is unitary, then for each row of the matrix, P

j

Vi,j∗Vi,j = 1 and there are

three generations of quarks. The neutron lifetime contributes to the unitarity test of the top

row

|Vud|2+|Vus|2+|Vub|2 = 1 (1.11)

by constraining|Vud|2according to Equation 1.9. In the Standard Model, this matrix is expected

to be unitary. However, a deviation from this would provide evidence for an extension to the

standard model, and possibly a fourth generation of quarks [30].

The CKM matrix element obtained using neutron decay nVud can be given in terms of the

neutron lifetime τn, and the constantλ, the ratio of the coupling constants [6, 75, 81]

|nVud|2 =

4908.7(1.9)s

τn(1 + 3λ2)

. (1.12)

The most up to date values of these parameters published by the PDG are λ=−1.2701(25),

τn= 880.1(1.1) s, giving the result nVud= 0.9773(17).

An independent determination of Vud also comes from measurements of 0+ → 0+ nuclear

transitions [18]. At present, these measurements provide the most precise determination ofVud.

The 0+→0+ beta decay is a purely Fermi-type process. As a result, these types of transitions do not depend on the axial-vector coupling constantGA. In order to determineVud from these

processes, the decay half-life is divided by the branching ratiot, and the statistical rate factorf

are measured. Radiative corrections (RC) are calculated nucleus-dependent correction factor.

Vud is given by

|0+Vud|2=

2984.48(5)s

f t(1 +RC). (1.13)

(30)

The values of the top row of the CKM matrix are [6]

Vud= 0.97425(22)

Vus = 0.2246(12)

Vub= 3.26(30)×10−3.

(1.14)

Of these three parameters, Vub is the least precisely known, but is also the smallest and

con-tributes little to Equation 1.11. Because Vud and Vus are known with high precision, the

top row of the CKM matrix gives a precise test of unitarity. The results of this test gives

Vud2 +Vus2 +Vub2 = 0.99962±0.00073, which is statistically consistent with 1.

Comparison of the value ofVudextracted from 0+→0+and neutron decays also provide an

interesting test of the V-A nature of the weak interaction. The difference between the values

of this parameter extracted from neutron decays and 0+→0+ nuclear decays is

∆ =0+ Vud−nVud= 0.003(93) (1.15)

This result is also statistically consistent with 0.

The neutron lifetime is currently the least precisely known input to Vud from neutron decay

data. Therefore, further improvements to the precision of the neutron lifetime measurement

are needed in order to improve the precision of Vud extracted from neutron decays. Chapter

2 will describe the regimen of experimental techniques that are under development to improve

this situation.

1.6

Big Bang Nucleosynthesis

Big Bang Nucleosynthesis (BBN) is the theory that predicts the primordial abundance of light

elements (H, D,3He, 4He, and7Li) by propagating the result of the known nuclear interactions as the early universe expands and cools. Experimental measurements of the neutron lifetime

(31)

decay rate of the neutron, as well as the rate of weak interactions, set the timescales for many

of these processes.

In the hot big bang models, the initial condition of the universe is assumed to be a high

temperature (T >1 GeV), high density state consisting of unbound particles and energy, called

the quark-gluon plasma. As the universe expands, the temperature decreases as a function of

time. AtT ≈1 GeV, the quarks and gluons combined to form hadronic matter. Since protons

and neutrons are the most stable hadrons, these two particle species are created in great number

and dominate the mass fraction of the universe at this time.

The rate of interactions that describe the creation and annihilation of the light nuclei at

this time is called Nuclear Statistical Equilibrium (NSE). When the effective temperature drops

below the binding energy of a species, it is energetically possible for the formation of this species

of particle to occur. Thus, this process essentially explores the tradeoff that occurs between

the expansion rate of the universe and the particle creation/annihilation rates Γ that determine

equilibrium.

The formation of light elements in the early universe proceeds in essentially 3 phases. The

first phase takes place at time scales of up to t = 10−2 s at temperatures of approximately

T = 10 MeV. In this phase the energy density of the universe is dominated by radiation and

light elements do not form in great abundance. During the first phase, the weak interactions take

place at a rate that is much faster than the expansion of the universe so thatn/p= (n/p)EQ'1.

Above temperatures T &1 MeV, the following particle reactions occur between neutrons and

protons in equilibrium:

n↔ p+e−+ ¯ν

n+ν ↔ p+e−

n+e+↔ p+ ¯ν.

(1.16)

The second phase takes place from approximately t ∼ 1s to t ∼ 60 s at temperatures

(32)

increasing the average temperature of the phonons. In addition, the rate of weak interactions

becomes smaller than the rate of expansion of the universe, therefore the weak interactions are

said to ‘freeze-out’. At the freeze-out, the ratio of neutrons to protons is given by

n/p= exp(−Q/TF)∼1/6, (1.17)

where Q = mn−mp = 1.293 MeV is the neutron-proton mass difference. The rate of weak

interactions Γ that occur by the processes shown in Equation 1.16 are proportional toG2F(1 + 3λ2). In terms of the neutron lifetime, this is Γ ∝ T5/τn [37]. This gives the freeze-out

temperatureTF ∝τn1/3. Therefore, a higher (lower) value ofτngives a higher (lower) freeze-out

temperature and thus an increase (a decrease) in the n/p ratio at this time. The n/p ratio

continues to decrease after the freeze-out due to neutron decays. Near the end of the second

phase,n/p∼1/7.

The third and final phase of BBN takes place fromt∼1 to 3 min (T ∼0.3 to 0.1 MeV). At

this point the production rate of the light elements begins to exceed their NSE values. Almost

all of the neutrons that are present at the end of the second phase bind to eventually form4He. For this reason, it is simple to estimate the mass fraction of 4He resulting from this process:

M4He

Mtotal

= 4n4

nN

= 4(nn/2)

nn+np

= 2(n/p)N U C 1 + (n/p)N U C

(1.18)

where nn is the number of neutrons, np is the number of protons, and (n/p)N U C = 1/7 [37].

This gives a4He mass fraction M

4He/Mtotal≈0.25.

In computer simulations, the time-evolution of this state is studied and predictions are

made regarding the relative abundance of the light elements,2H,3He, 4He, and7Li. A detailed description of these calculations can be found in References [26, 64, 37].

The neutron lifetime is the most important experimentally determined input parameter to

models of BBN. This parameter determines the weak interaction rates that give then/p ratio

(33)

predicted using these models directly depends on the value of the neutron lifetime used as input.

1.7

Summary

Neutron beta decay contributes to several important tests of the Standard Model.

Measure-ments of the lifetime τn and the ratio of the coupling constants λgive an independent test of

the unitarity of the CKM matrix by measuring Vud. The neutron lifetime is also an

impor-tant input parameter in simulations of the early universe that predict the primordial elemental

abundances. The sensitivity of these tests to the precision of τn motivates the multitude of

experimental techniques that seek to measure the lifetime to a precision<1 %.

Currently, seven measurements using two types of techniques contribute to the world average

ofτnreported by the Particle Data Group. However, significant discrepancy exists between the

two types of techniques that is not yet well understood, necessitating the need for new types of

measurements. The work presented as the subject of this dissertation discusses the preliminary

results of one such measurement. In the following chapter, the current state of the neutron

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Chapter 2

Present Status of the Neutron

Lifetime

Measurements of the beta-decay lifetime of a free neutron have continued to improve in

preci-sion since shortly after the discovery of the neutron itself by James Chadwick in 1932 [16, 6].

The neutron lifetime has been measured using three broadly classified experimentally distinct

techniques which we denote as the beam method, the bottle method, and the magnetic

con-finement method. Using the beam technique, experimenters count the number of neutrons

that decay and measure the total beam fluence as a cold neutron beam passes through a well

defined region of space. In the bottle technique, one counts the number of ultracold neutrons

remaining in a material or magnetic container after a specified holding time. In the magnetic

confinement technique, a population of neutrons is trapped by a magnetic field and neutron

decays are counted in situ.

The apparatuses used to perform beam measurements allow detection of either the decay

electrons, protons or both. The decay products are counted with known efficiency, providing a

measure of the number of neutrons that decay within the beam volume. Simultaneously, the

neutron fluence is also measured. The lifetime is extracted from the ratio of the number of

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Bottle type measurements allow one to confine a population of ultracold neutrons inside of

a container made with materials that either have an effective Fermi potential, or magnetic fields

with a ~µ·B~ interaction energy, greater than the kinetic energy of the neutron. The neutron

population decreases in time due to beta decays plus losses due to wall interactions. The

measurement is performed by filling the bottle with a consistent number ultracold neutrons

(UCN). The population of neutrons remaining in the trap after some time t is counted by

opening the bottle and detecting the remaining neutrons. The lifetime of neutrons in the bottle

is extracted from the measurements, varying the delay time between the fill and empty phases

of the experiment. The neutron beta-decay lifetime can be separated from wall interactions by

varying the geometry of the trap, typically the surface area to volume ratio [53, 67, 73, 42, 47].

The third technique uses the interaction between the neutron’s magnetic moment and a

magnetic field to create a conservative potential well. The decay rate of a population of trapped

neutrons is measured in-situ by detecting signatures of the neutron decays in the trapping

volume. The neutron lifetime is then extracted by fitting to the time dependent decay rate

[48, 24, 55, 40].

Each of these techniques is subject to a unique set of systematic effects. Precise

measure-ments using multiple techniques are important in establishing the true value of the neutron

lifetime. This chapter will briefly survey and describe the neutron lifetime measurements that

currently contribute to the average value reported by the Particle Data Group (PDG) [6].

2.1

Beam Measurements

The earliest detection of neutron beta decay in a beam occurred at the graphite reactor at Oak

Ridge National Laboratory by Snell and Miller in 1948 [76]. The experiment used an

electro-static potential (+4000 V) to accelerate decay protons to a negative bias electron-multiplier

type of detector. A pair of gas-filled beta detectors provided beta particle counting as well as

limited directional resolution [81]. While they were only able to provide a crude estimate of the

(36)

observa-Figure 2.1: Early apparatus used by Robsonet al. to measure the neutron lifetime [69].

tion of free neutron decay. The technology developed in this application was important to the

beam-type neutron lifetime measurements that followed. This experiment was also important

in that it demonstrated the feasibility of detecting neutrons decaying in a beam of particles and

extracting the lifetime based on these measurements.

While earlier experiments had reported limits on the value of the neutron lifetime, the first

“precision” measurement was performed by Robsonet al. in 1951 [69]. A neutron beam passed

through a vacuum chamber where decay electron and proton coincidences were detected (see

Figure 2.1). An electron multiplier was used to detect protons incident on the face of the

de-tector and beta-particles were detected using scintillation counters. The decay chamber was

evacuated to <10−6 mm Hg to minimize interactions of the neutron beam with the

surround-ings. The neutron flux was measured separately by activating thin foils of manganese and

(37)

because it demonstrated that the positive particles observed in neutron decay were indeed

pro-tons. This experiment dramatically improved the knowledge of the neutron lifetime over Snell’s

work, reporting a value of τn= (1108±216) s.

A second experimental technique was devised shortly thereafter by D’Angelo et al. at

Ar-gonne National Laboratory. This group measured decay events in a beam of neutrons produced

by the CP-5 nuclear reactor [19]. The decay volume was a cloud chamber roughly 1.32 m in

length, and filled with methyl alcohol vapor in a mixture of oxygen and helium at 60◦C. A

lead wall provided passive shielding of the cloud chamber on all sides, reducing backgrounds. A

photographic camera took stereo pictures of the cloud chamber at a rate of 2 frames per second.

Neutrons decaying within the cloud chamber produced ionization tracks that could be seen on

film. The beam flux was measured separately by activating gold foils. Neutron detection in a

cloud chamber was a clever detection scheme that allowed for counting of neutron decays while

simultaneously identifying decay products.

The primary uncertainty in the number of neutron counts was related to how well the

ionization tracks could be identified. Since decay events had to be counted individually by eye,

illumination non-uniformities caused some decay events not to produce tracks that were visible

on the film. This led to uncertainty due to the subjective nature of identifying certain events.

This was compensated for by performing independent analyses of the data several weeks apart.

Also, while care was taken to place the plane of projection in the beam, this type of alignment

could not be tested in-situ. The flux measurement that was extracted through measurements

of the foil activation was limited by uncertainties related to foil mass, background events, and

counter efficiency. Ultimately, the precision of the experiment was limited by poor counting

statistics. The final result of this experiment wasτn= (1100±165) s.

Over the years, the in-beam measurement has evolved into a precision technique with well

understood systematic effects. In a modern-day beam type experiment, decay products are

counted as a neutron beam passes through a well defined region of space. In addition to the

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Figure 2.2: Neutron bottle used by Nicoet al. for measurement of the neutron lifetime [63].

the decay volume. For this reason a precise measurement of the neutron flux is also needed.

Neutrons spend an amount of time in the trap inversely proportional to their velocity. One

must thus use either a monochromatic energy neutron beam, or compensate for the energy

spectrum of neutrons in the beam using a 1/v dependent flux monitor.

The two most recent experiments detect the decay proton as well as account for the 1/v

-weighted fluence using neutron capture in a thin foil. The lifetime of the neutron can then be

extracted from measured quantities using the following relation:

τn=

L ρf oilσthvth

Rn

Rp

p

n

(2.1)

whereLis the length of the trap,ρf oilis the density of the foil,σthandvthare the thermal cross

section and velocity, Rn is the rate of neutron detection, Rp is the rate of proton detection,

n is the neutron detection efficiency, andp is the proton detection efficiency. Knowing these

parameters, one can extract the neutron lifetime.

Byrne et al. report a lifetime of τn= (893.6±5.3) s, counting neutron decays by trapping

decay protons in a Penning trap [13, 12]. An updated version of this type of measurement

was constructed at NIST in Gaithersburg MD [63]. Here, a neutron beam passed through a

well defined region of space as defined by an electrostatic trap. The lifetime was extracted

(39)

variable length electrostatic potential was used in conjunction with a 4.6 T magnetic field to

confine these decay protons (see Figure 2.2). The protons were accumulated for approximately

10 ms and subsequently accelerated and detected using a silicon surface barrier detector.

Independently of the proton counting, the neutron beam flux was continuously monitored

using a thin 6LiF foil-based detector to determine the number of neutrons in the beam. The thin foil has a mass density ofρ= (39.30±0.10)µg/cm2 that minimizes the attenuation factor of the beam in the target. The absorption cross section of the foil is given by:

σabs(v) =

σthvth

v (2.2)

where σabs is the velocity dependent absorption cross section, and σth is the absorption cross

section at the thermal velocityvth= 2200 m/s. This 1/v proportional neutron detector cancels

out the effect of the neutron energy spectrum exactly. The result published in 2005 by Nicoet

al. stands atτn= (886.3±3.4) s.

These two measurements were designed to allow for in-situ determination of several

impor-tant systematic effects. Since the measurement depends strongly on precisely knowing the total

number of neutrons in the Penning trap at any given time, the trap was built with a variable

electrode system that allowed for the trap length to be changed, thus allowing one to minimize

the end effects of the trapping region. The shape of the potential in a given configuration is

known from precision measurements of the dimensions of the trap electrodes. By taking data

over a range of trap lengths, the decay rate per unit length can be extracted.

Additional systematic uncertainties arise from the foil mass as well as the7Li cross section. Early versions of this experiment could only reach uncertainties at the±5.3 s level due primarily

to the flux measurement. The result currently reported by Nico et al. stands atτn= (886.3±

3.4) s, and is included in the PDG world average [6]. Although the current result does not

significantly affect the PDG’s average value, it is important to include due to its unique set of

(40)

used in this experiment was made recently that reduces the uncertainty due to the calibration

of the flux monitor. The forthcoming result of the reanalysis will likely reduce the overall

uncertainty in the Nico et al. result, increasing its significance in the PDG world average.

2.2

Material Bottle Measurements

Neutrons with sufficiently low energy can be totally internally reflected from materials due to

their strong interaction with atomic nuclei. Ultracold neutrons have wavelengths that are long

compared to the interatomic spacing of commonly used wall materials. Neutrons incident on a

surface thus effectively sample a ‘forest’ of delta-function potentials [35]. This interaction can

be described in terms of a Fermi potential similar to the way an optical potential describes the

way light is reflected from surfaces. As a result of this interaction, neutrons can be stored in

containers for times comparable to their beta decay lifetime.

Neutron bottles of this type are typically constructed using materials such as beryllium

or stainless steel that have large Fermi potentials (244 neV and 188 neV respectively). The

chambers have ports for filling and emptying the bottle. UCN are loaded into the bottle and

are confined using a combination of the material potential and/or gravitational interaction1. After a fixed amount of time, the bottle is opened and the number of remaining neutrons is

counted. The lifetime is extracted by measuring the number of neutrons remaining in the trap

as a function of the storage time. A similar type of neutron lifetime measurements that use

magnetic instead of material walls is discussed in Section 2.3.

The first successful neutron bottle was constructed by Kosvintsevet al. and they published

a measurement of the neutron lifetime using this apparatus in 1980 [47]. The bottle was a

cylindrical vessel 29 cm in radius and 30 cm tall. It was constructed out of aluminum which has

a Fermi potential of 54 neV. The container was inserted into a vacuum jacket that was evacuated

to a pressure of 3×10−5 torr. The walls of the vessel were processed and annealed in oxygen

1

(41)

Figure 2.3: Neutron bottle used by Mampeet al. for measurement of the neutron lifetime [53].

to minimize neutron absorption from impurities on the surface. The geometry of the trap was

such that removable aluminum fins could be inserted into the bottle to vary the wall collision

rate. In this way, the effect of neutrons lost due to wall interactions could be characterized. The

total number of neutrons present in a given trapping cycle could be measured by inserting a

neutron absorbing gas. Heating of UCN was also a concern, but the contribution to the overall

uncertainty did not exceed 0.9 %. The result reported by Kosvintsevet al. wasτn= (903±13)

s. While this group demonstrated the importance and feasibility of measuring the wall loss

rates, their result was ultimately statistically limited.

The Mampeet al. group improved the neutron bottle technique by incorporating a moving

wall that could be used to vary the surface area to volume ratio of the bottle (see Figure 2.3)[53].

This bottle (known as MAMBO) was built using glass walls that were coated with Fomblin oil,

a fluorinated polymer with a material potential of 106 neV. Bottles coated with this type of

oil exhibit high reflectivity and neutron storage times comparable with the beta-decay neutron

lifetime. The bottle was filled with UCN from the neutron turbine at the Institut Laue-Langevin

(42)

Measurements using the MAMBO neutron bottle increased the statistical precision of the

neutron lifetime over the Kosvintsev technique by over an order of magnitude. They also had

the advantage that many of their systematic effects could be studied directly, namely neutron

losses from wall interactions. This bottle was constructed with a rectangular geometry, where

the movable back wall allowed for the surface area to volume ratioS/V to be changed.

Addi-tionally, the surface structure of the walls was modified to ensure the uniformity of the neutron

population in velocity phase space. This allowed one to change the rate of wall interactions of

the neutrons in the bottle, thus changing the proportion of neutrons lost due to this effect. This

procedure was performed for several surface to volume ratios. The data was then extrapolated

to the case of an infinitely large bottle corresponding to no wall collisions, allowing one to

remove the effect of this wall loss mechanism. The MAMBO group reported a measurement of

τn= (882.5±2.1) s.

The method initially developed by Mampe et al. was expanded upon by Pichlmaier et

al. [67]. The Pichlmaier bottle also incorporated a glass-walled box coated with Fomblin oil.

Their new apparatus (MAMBO II) incorporated improvements over the previous version for

further reducing systematic effects. A pre-storage volume (1 m3) was incorporated to ensure a consistent initial energy spectrum for the UCN loaded in the bottle. This was done specifically to

avoid UCN energies close to the material potential, and also to regulate the velocity-dependent

wall losses across different S/V configurations. The new result reported for the MAMBO II

apparatus was τn= (880.7±1.8) s [67].

The Gravitrap experiment by Serebrov et al. utilized two bottles to vary the surface area

to volume ratio. In addition, to probe the energy spectra of the UCN, they designed their

apparatus such that one could detect neutrons from different parts of the energy spectrum

separately (see Figure 2.4) [73, 42]. This was achieved by employing a tilt-able bottle, allowing

for neutrons in a particular energy band of the spectrum to be emptied at separate times.

Neutrons with total energy E > mg(htop) will escape the trap, where htop is the height of

Figure

Figure 1.1:Examples of the lowest order weak vertices. (a) shows charged lepton - neutrino interac-tions, (b) shows quark interactions , and (c) shows charged lepton - charged lepton, neutrino - neutrinoscattering.
Figure 1.2:Feynman diagram depicting the decay of a free neutron. The conversion of a downto up quark inside the nucleon occurs by emission of a virtual W − boson, which promptlydecays into an electron and antineutrino.
Figure 2.1:Early apparatus used by Robson et al. to measure the neutron lifetime [69].
Figure 2.3:Neutron bottle used by Mampe et al. for measurement of the neutron lifetime [53].
+7

References

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