ABSTRACT

Sensitivity of a Highly Compressed Xenon Gas Ionization Chamber to the Neutrinoless Double Beta Decay of 136Xe

Craig Steven Levin Yale University

1993

This thesis examines the sensitivity of a highly compressed xenon gas drift chamber to Ov PP decay of 136Xe. The design, construction, and performance of this detector are described in detail. In this detector the PP source is identical to the ionization medium, which consists of xenon gas near its critical point. Extensive charge collection and energy resolution studies were performed. The essential elements for performing a sensitive double beta decay experiment using this chamber are presented. Particular advantages of this chamber are the excellent energy resolution achieved (2% at 1 MeV, which extrapolates to 1% at 2.5 MeV, the PP endpoint energy) and high efficiency for containment of PP events (>80%, from Monte Carlo studies). The ability to drift ionization over large distances without attenuation and exceptional stability with time are demonstrated.

Above-ground background measurements were performed utilizing active and passive shielding. By treating the chamber as a 1-dimensional TPC, further background rejection was achieved using pulse shape discrimination of digitized pre-amplifier signals. Other techniques for background reduction are discussed. Based on our studies, the projected sensitivity to the Ov PP decay half-life of 13^Xe is > 1024 years for this

chamber. This is comparable with sensitivities of the two most recent germanium experiments. Adopting the nuclear matrix elements of Faessler, this sensitivity implies a Majorana electron neutrino mass parameter of < 0.4

Sensitivity of a Highly Compressed Xenon Gas Ionization Chamber to the Neutrinoless Double Beta Decay of 136Xe

A Dissertation Presented to the Faculty of the Graduate School

ofYale University

in Candidacy for the Degree of Doctor of Philosophy

byCraig Steven Levin

May 1993

To my family and Nicole

Acknowledgments

I would like to thank my thesis advisor, John Markey for his optimism throughout this project and many helpful discussions. I thank the other members of my thesis committee, C. Bockelman, A. Chodos, M. Schmidt and, especially, P. Parker, for reading my thesis and their useful questions, comments and criticisms. I am grateful to Al Howard, Dick Hyder and, particularly, Kim Lister for years of illuminating discussions.

I gratefully thank the W.N.S.L. technical support staff for their expert and friendly help. Distinguished thanks to Tom Barker and Joe Cimino for their valuable assistance in my laboratory. I would also like to express my appreciation to John Baris, Tom Barker, Joe Cimino, Phil Clarkin, Ted Duda, Bob Hamburger, Al Jeddry, Tom Leonard, Allen Ouellette and Dick Wagner for many friendly and amusing conversations. At the Gibbs Machine Shop, I would like to thank Dexter Crowley, Dick Downing Jr., Richard Downing, Walter Howe, Don Johnson and Ted Peterson for their assistance in the design and construction of the apparatus used in this project.

I am grateful to the members of the W.N.S.L. office staff, Dee Berenda, Rita Bonito, Karen DeFelice and Mary Anne Schultz for all of their help over the years. Lisa Close deserves extra thanks for the moral and secretarial support she has given. I also thank Sara Batter and Jean Belfonti for their support.

I thank Joe Germani for his work on this project. I also thank students such as, Dan Blumenthal, Ben Crowell, Ken Everding, Joe Germani, Kevin Hahn, Stuart Henderson, Nicholas Kaloskamis, Brian Lund, Bernard Phlips, Mike Smith and, particularly, Sinan Utku for their friendship and support.

Special thanks to my great friends Chris Alliegro, Pat Ennis and Jaipal Tuttle for everything they have done for me and all the good times we have had.

Most of all, I thank my parents, my brother, Jason, my sister, Korey, my grandparents and my best friend, Nicole, for their love, friendship, encouragement and support. I also thank the Arabolos family, Mike, Sharon, Tanya, Larissa and the grandparents, and the Delvecchios for the warmth and kindness they have shown me through the past several years.

Finally, I would like to extend my gratitude to D. Allan Bromley for his interest in this project and the Department of Energy for the support of this research.

Table of Contents

Acknowledgments........................................................................................ iiiChapter One: Introduction and Motivation............................................ 1

1.1. The Neutrino.................................................................................... 11.1.1. History and Physics of the Neutrino....................................... 11.1.2. Theoretical Considerations for Neutrinos............................... 3

1.2. pp Decay.......................................................................................... 81.2.1. History of PP Decay.................................................................81.2.2. Phenomenological Description of pp Decay......................... 111.2.3. Theoretical Considerations for pp Decay............................. 141.2.4. Calculation of pp Decay Rates.............................................. 20

Chapter Two: Experimental Considerations........................................ 442.1. Present Status of pp Decay - Other Experimental Searches 44

2.1.1. Introduction............................................................................442.1.2. Direct Counting Experiments............................................... 442.1.3. Geochemical Experiments.................................................... 482.1.4. Radiochemical Experiments................................................. 49

2.2. Experimental Sensitivity Issues for 13*>Xe OvPP DecaySearches..................................................................................49

Chapter Three: Condensed and Compressed Rare Gases asIonization Media................................................... 59

3.1. Previous Studies in Condensed Xenon and Argon....................... 593.1.1. Introduction............................................................................593.1.2. Electron-Ion Recombination................................................. 60

3.2. Charge Collection and Energy Resolution Studies inCompressed Xenon Gas Near Its Critical Point.................... 66

3.2.1. Introduction ...............................................................663.2.2. Thermodynamics of Compressed Xe..................................683.2.3. Apparatus and Experimental Procedure................................683.2.4. Data and Analysis..................................................................783.2.5. Results....................................................................................803.2.6. Discussion..............................................................................853.2.7. Conclusion........................................................................... 100

3.3. Relevance to Detection of the Ov PP Decay of 136Xe................101Chapter Four: Background Studies Using a High Pressure Xenon

Ionization C ham ber........................................... 1234.1. Sources of Background for 136Xe Ov pp Decay Searches 123

4.1.1. Introduction.......................................................................... 1234.1.2. Background from the Apparatus and Surrounding

Environment.................................................................... 1234.2. Background Event Identification................................................133

4.2.1. Characteristics of Cosmic and Gamma Ray Events in OurChamber.......................................................................... 133

4.2.2. Studying the Pulse Shape Discrimination Method UsingCosmic-ray Muons and an External y-ray Source:.......... 138

4.3. Background Measurements.........................................................1444.3.1. No Shielding........................................................................1444.3.2. Passive Shielding................................................................. 1454.3.3. Active Shielding................................................................... 1474.3.4. Reduction of Background Using Pulse Shape

Discrimination................................................................. 149

Chapter Five: Computer Simulations of Gamma-rayBackground and 136Xe Ov PP Event Trajectories in Compressed Xenon................... 176

5.1. Gamma Ray Background Monte Carlo........................................1765.1.1. Introduction.......................................................................... 1765.1.2. Effects Included................................................................... 1775.1.3. Number of Iterations............................................................1795.1.4. Monte Carlo Simulation.......................................................1805.1.5. Results.................................................................................. 183

5.2. Monte Carlo Simulation of Electron Trajectories in HighPressure Xenon Gas..............................................................186

5.2.1. Introduction.......................................................................... 1865.2.2. Effects Included................................................................... 1875.2.3. The Monte Carlo Simulation................................................1955.2.4. Results.................................................................................. 197

Chapter Six: Results and Conclusions................................................ 2196.1. Projected Sensitivity to the Half-life of 13 Xe Ov PP Decay. 2196.2. Comparisons with the Caltech Experiment................................. 2216.3. Extrapolations to a Larger, Underground Xenon

Ionization Chamber Experiment...........................................2246.4. Improvements: Lowering the Background Rate......................... 227

References................................................................................................ 231

CHAPTER 1 Introduction and Motivation

1.1. The Neutrino

1.1.1. History and Physics of the Neutrino

Wolfgang Pauli introduced the notion of the neutrino, a chargeless and massless lepton, in 1930 to explain the unexpected energy distribution of electrons emitted in beta decay.1 From these ideas sprang Fermi's theory of P decay incorporating a vector-like interaction, in analogy to QED .2 In 1956 Lee and Yang developed the concept of parity non­conservation in the fundamental interaction responsible for the production of the neutrinos.3 The subsequent V-A (vector minus axial vector) interaction that evolved was a product of the notion that parity was not conserved in "weak" interactions, such as that responsible for beta decay. In 1953 Reines and Cowan experimentally demonstrated the existence of the neutrino through inverse beta decay.4 The 1960's saw the Standard Model of electroweak interactions unfold.5 In 1962 Danby et al. found that the neutrino associated with pion decay was distinct from that from nuclear beta decay.6 This led to the idea of separate lepton number conservation. Currently it is believed that three flavors of neutrinos (and their anti­particles) exist, including the tau neutrino.7 The recent LEP experiments at CERN, measuring the width of the Z° boson decay, confirmed that there are three (2.9 ±0.1) types of light neutrinos.8

1

2

There still remain several unanswered questions regarding neutrino properties. The neutrino mass and charge conjugation symmetry are unknown despite numerous attempts of their measurement. In the minimal Standard Model of electroweak interactions9 neutrinos are massless and purely left-handed. Separate lepton number conservation is applied to the three generations of neutrinos implying no mixing between them. Thus, observing a neutrino mass or mixing would clearly signify new physics beyond the Standard Model. In fact, most Grand Unified Theories (GUTs)10*11 favor the existence of massive neutrinos. Using the "see-saw" mechanism 10 for neutrino mass generation, many GUTs expect a light neutrino mass

(mlepton )m v ------ ,Mqut

where miepton is the mass of a light lepton and M qut is the grand unification scale. This mechanism requires Majorana neutrino mass. No such effects have been seen to the present level of experimental sensitivity.

The idea of neutrino mass also has consequences in fields outside fundamental nuclear and particle physics, in the realm of astrophysics and cosmology. Since neutrinos interact only weakly, they are invisible as far as most astronomical observations are concerned. Massive neutrinos may thus explain the Dark Matter problem.11 The observed expansion rate of the universe gives an upper bound on its average mass density as well as the total mass of all flavors of light neutrinos (X m v < 100 eV)11. Massiveneutrinos may also play an important role in the formation of the inhomogeneities in the Universe. A finite mass for the neutrino also opens

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the possibility of neutrino flavor mixings (oscillations) which, in turn,might offer a solution to the Solar Neutrino Puzzle.11

Experiments searching for neutrino mass have been performed forthe past 25 years. All results from kinematic measurements of the 3H beta spectrum imply12 that m Ye< 10 eV. The bursts of neutrinos fromSupernova 1987 suggest13 a model dependent m Ve< 11-15 eV. Othercurrent upper limits are mv < 0.25 and 35 MeV, respectively, for the p. and x neutrinos.11 The limits on the electron neutrino mass from various double beta decay experiments will be discussed in the next chapter.

The issue of charge conjugation symmetry asks what is the fundamental nature of the neutrino; is it a Dirac (v * v ) or Majorana (v =v) particle ? This question is intimately connected with lepton number conservation, a feature of the Standard Model. Since the neutrino carries lepton number of one its charge conjugate (anti-particle) carries a lepton number of negative one. In the Majorana case, lepton number is violated and the Standard Model needs modification. In addition, Majorana neutrinos exist only if they have a non-zero mass. All experimental evidence thus far is consistent with the notion that the neutrino is a Dirac particle. In the next section we will more precisely define the above properties of neutrinos.

1.1.2. Theoretical Considerations for Neutrinos

Charge Conjugation Symmetry and Neutrino Mass

We will use the Pauli-Dirac representation of the y matrices. Neutrinos are emitted (and interact) only in the weak interactions; thus,

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only the left-handed, (l-Y5)/2 projection of the neutrino current will couple to the W-boson field. If the neutrino is massless (Standard Model), the solutions to the Dirac equations for a free neutrino will be eigenstates of the chirality operator (l-Ys)/2. The most general neutrino spinor is of the form

where a and (3 are two component spinors. The eigenstates of chirality will be

« R = ( “ ^ ) f o r i ( l + Y 5)

andU L = ( ^ % , ) f o r i ( l - Y 5)

Operating on these states with the charge conjugation operator C=i^Y2 has the effect of flipping the spin :

VL = ^(1 - Y5)“ = ( ) (V l )C = C (? l )T = ( “!)V R = | ( 1 + Y5)u = ( $ ) (VR)C=C(VR)T = ( “d

where

o l = ( i ) “ 2 = (? )

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By convention, the projection with its spin oriented parallel (anti-parallel) to the direction of the momentum is called the right (left) handed projection.

If the neutrino is given a mass the most general solution for the free particle Dirac equation is :

( \ a

- f — VV V E + m / y

a\

for the anti-particle states. These states are no longer eigenstates of the chirality operators, but the weak interaction still couples only to the left- handed projection of the particle state (if only left-handed weak couplings are present) and right-handed projection of the anti-particle state. These are called Dirac neutrinos. The neutrino and anti-neutrino are distinct.

We next form

'l'M = ^ ( V L + l ( V L )c )

from the massive Dirac neutrino states. T| is a complex phase with no physical significance. 'Em has the notable property that

u =

for the particle and

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c vf m = 7i' ^ m .

This property implies 'Em is a Majorana neutrino. Similar to a photon, the Majorana neutrino is its own anti-particle. Thus, there are only two Majorana neutrino states as opposed to the four Dirac neutrino states. As m v vanishes the Dirac and Majorana neutrino states become indistinguishable (in the Dirac-Pauli representation).

Neutrino Mass in the Standard Model Lagrangian

There are two possible ways a neutrino mass may enter into the Standard Model Lagrangian. The first case is similar to that for the charged leptons, the Dirac case :

L = m D\jhjf + h.c.

m o is the Dirac mass. This term conserves lepton number. The second way is due to the chargelessness of the neutrino, the Majorana mass case:

L = i» m (V ° V + W c ) = n>MVMVM.where

\jrc = C t y

V m = 4 ( V + V c )

andV m = C V m = V m -

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him is the Majorana mass. This term in the Lagrangian does not conserve lepton number and, in fact, introduces processes that change lepton number by two units (such as Ov (3(5 decay). The most general mass term in the Standard Model Lagrangian (that respects Lorentz invariance) will have both Dirac and Majorana terms :

Lmass= L D + L m •

The interaction term in the Standard Model Lagrangian is

L f : = l Y ,l| a - 7 5 ) W j v w +h.c.

for charged current interactions and

for neutral currents. Here, vw is the weak interaction eigenstate of the neutrino field. In general, these eigenstates are related to the mass eigenstates via a unitary transformation U

v w — ^ i j v mass J

where vmass are the mass eigenstates. If at least one of the vi w has a non­zero mass, neutrino oscillations are possible.

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The existence of neutrinoless double beta decay (Ov p p ) of a nucleus would answer the above questions regarding the mass and fundamental nature of neutrinos. For this process to occur the neutrino must be a massive Majorana particle and thus, lepton number conservation is violated. In addition, the existence of Ov p p might allow the presence of right-handed couplings (right-handed neutrinos and/or W's) in the weak interaction. It is thus one of the fundamental experiments in modem physics. A central goal of this thesis is to describe what are the elements necessary to perform a sensitive experimental search for the Ov pp decay of 136xe.

1.2. pp Decay

1.2.1. History of PP Decay

In 1932 Heisenberg explained the natural occurrence of more than one stable isobar by hypothesizing the idea of a nuclear pairing force.14 This force would make sequential beta decay energetically impossible for many cases of nuclei; for even A isobars, two nuclear mass parabolas are generated by the pairing force, as seen in Figure 1.1 for 76Ge. Odd N, odd Z nuclei are less stable (more massive) than even N, even Z nuclei. The bottom parabola in Figure 1.1 indicates that there is more than one stable A=76 isobar. Drawing from the above ideas, the possibility of nuclear double beta decay was first discussed by Wigner as a mechanism by which one stable even A isobar could decay into another less massive (more stable) one. In 1935, M. Goeppert-Mayer first calculated the rate of

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double beta decay to be of the order of lO2 years, using the Fermi theory of beta decay.15 Two years later Majorana developed the alternate theory of the two-component neutrino.16 That same year Racah first discussed the possibility of double beta decay with no neutrinos among the final products.17 Predictions for the zero neutrino decay probability, mediated by a Majorana neutrino, were made by Furry in 1939.18 Double beta decay experiments thus became a test of the Dirac/Majorana nature of the neutrino. The zero Majorana neutrino mode is favored kinematically (by a larger phase space factor) over the two Dirac neutrino mode.

The first experimental search for PP decay was initiated by Fireman in 1948.19 He originally claimed a positive result for Ovpp decay in 124Sn giving a half-life of 4 -9 x l0 15y, agreeing with Furry's prediction. This gave the impression that the electron neutrino was a Majorana particle. In the early 1950's, several cloud chamber experiments, including that of Kalstein et. al.20 and Fireman et. al.21 in 1952, set only lower bounds of 1016-2 x l0 17y on the 124Sn PP half-life. The counts seen in Fireman’s original experiment were explained by the presence of radioactive contaminants in the enriched source used. Several subsequent failed attempts in searching for the Ov PP mode in nuclei (48Ca, 96Zr, 13°Te and 238U, for example), and the Davis experiment22 in 1955 seemed to demonstrate that the neutrino was distinct from its anti-particle. The latter search was unable22 to detect the reaction v + 37C1 —» 37A + e- (neutrino capture). Since a reactor produces mostly anti-neutrinos, the conclusion v

follows.The picture changed drastically in 1956 with the discovery that the

weak interaction violated parity conservation. On the assumption of massless left handed neutrinos alone one could understand the extremely

10

long lifetimes for Ov p p decay and the Davis results. For two-component type coupling, the absence of O v p p decay depends on the form of the lepton interaction not on the Dirac/Majorana nature of the neutrino. Few searches for Ov p p were made during the next decade.

In the late 1960's the onset of gauge theories saw a rebirth of interest in Ov PP decay. The theoretical prejudice bom in GUTs10*11 is that lepton number may only appear to be conserved at low energies. This would be the result of a large unified mass scale governing the global symmetry which would be responsible for lepton number conservation. This marriage between a symmetry and a conservation law is analogous to the invariance of the Lagrangian for the electron field,

L = - rmjhj/,

under the U(l) phase transformation \y(x)—»eiay(x), implying the existence of a conserved electromagnetic current density of an electron of charge - e . Thus, conservation of charge follows from a "global" gauge invariance.

Many of the grand unified extensions of the standard electroweak model predicted massive Majorana neutrinos. This reopened the experimental question of the existence of the Ov mode of PP decay. Such efforts would provide a strict test of lepton number conservation (which is closely related to the question of the Dirac/Majorana nature of the neutrino) and a sensitive measurement of any existing mass of the Majorana electron neutrino.

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1.2.2. Phenomenological Description of pp Decay

Beta decay is a spontaneous first order process resulting from the weak interaction. Nuclear double beta decay is a second order weak effect and is not to be confused with two successive single beta decays. It is a process in which two neutrons (protons) in a nucleus (A,Z) decay spontaneously to two protons (neutrons) of a daughter nucleus (A,Z ± 2), two electrons (positrons) and either two or zero anti-neutrinos (neutrinos):

(A,Z) -> (A,Z ± 2) + 2e+ + 2v/v (A,Z) -> (A,Z ± 2) + 2e+

The emission of one positron and absorption of one orbital electron or the nuclear capture of two orbital electrons are other possible forms of a second order beta decay process. The two electrons emitted in pp decay have relatively high energies. For example, in 48Ca, 136Xe and 82Se, the decay energies are 4.3, 2.5 and 3.0 MeV, respectively. Thus, from phase space considerations, large expected decay rates result. In this work we will consider only double beta decay with the emission of two electrons.

The condition of lepton number conservation requires that the emission of two electrons is accompanied by the simultaneous emission of two anti-neutrinos, as seen in the first decay above; this process is called two neutrino double beta decay (2vpp). This decay does not require that the neutrino be a Majorana particle or massive and, thus, does not imply any necessary modifications of the Standard Model. However, detection of the 2v mode provides an extremely sensitive test of the nuclear wave functions involved. The 2v lifetimes would give information on nuclear

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structure, which may help to interpret the measurements made in experiments searching for the neutrinoless mode. The case in which no neutrinos are emitted is called neutrinoless double beta decay (OvPP). This violates lepton number conservation by two units and requires the neutrino to be a massive Majorana particle. The phase space factor for Ovpp is enhanced by many orders of magnitude over 2vpp, since there are two rather than four leptonic decay products. It is this phase space advantage which makes the Ovpp decay such a sensitive probe for Majorana neutrino mass and violation of lepton number conservation. This point will be discussed later in this Chapter.

In order for pp to take place, the transition (A*Z)-»(A,Z + 2) must be energetically allowed : M(A,Z) > M(A,Z + 2) (the atomic mass of the parent nucleus must be greater than that of its daughter isobar). Not all nuclides which meet this condition are useful in a search for double beta decay. Any experimental effort will be severely limited if the nucleus considered is unstable with respect to ordinary single beta decay: (A,Z)-»(A,Z + 1) + e- + Ve. A succession of two single beta decays can masquerade as the much rarer double beta decay. In addition, the electron or y-ray from a single P*y cascade could scatter a second electron from the source likewise imitating a double beta decay event. Thus, ordinary beta decay must be either energetically forbidden, M(A,Z+1) > M(A,Z), or strongly suppressed by spin and/or parity selection rules. Double beta decay must be the dominant decay channel.

The above situation arises in even-even nuclei where the nuclear pairing force at least severely suppresses or forbids single beta decay. Nuclei satisfying these conditions are said to form an isobaric triplet. Isobaric triplets of this kind are relatively plentiful in nature because of the

13

nuclear pairing force which causes nucleons inside the nucleus to tend to bind into pairs of opposite spin. Because of this force, nuclei that have all nucleons paired (even number of neutrons and protons or, "even-even" nuclei) tend to be more tightly bound (less massive) than their adjacent isobar neighbors that have unpaired nucleons (odd Z and/or N). Examples of typical double beta decay candidates are 82Se, 48Ca, 150Nd, 130Te, 76Ge, 124Sn, and 136Xe. Many others exist. The isobaric states of 136Xe are shown in Figure 1.2.

The experimentally most interesting case is that in which the intermediate nucleus is more massive than both the parent and daughter nuclei making single beta decay energetically impossible. Double beta decay in this case occurs through the intermediate nuclear state (A,Z+1) which lies above the ground state of the initial nucleus (A,Z). In so doing, the decay violates energy conservation in the intermediate step only as typical of all higher order processes. Such states are possible only when both (A,Z) and (A,Z+2) are even-even nuclei. (3(3 decays between ground states are then all 0+—»0 + (zero angular momentum, even parity) transitions since even-even nuclei have 0+ ground states. The parent nuclei may also pp decay to the excited states of the daughter nuclei as well giving rise to 0+->l+ and 0+->2+ transitions, provided it is energetically allowed. If the two electrons are emitted in a zero angular momentum state the final nucleus will be left in a 0+ ground state or a 2+ excited state. The latter is possible in OvPP decay only if there is some form of right-handed coupling. This will be discussed later.

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1.2.3. Theoretical Considerations for (3(3 Decay

Modes o f Double Beta Decay

Only the two-nucleon mechanism for PP decay will be examined. References 11 and 23-25 describe others. There are three modes of double beta decay considered theoretically. They are distinguished from each other by any decay products which may accompany the two P particles.

The Two-Neutrino Mode (2v(3f5) :

(A,Z) (A,Z+2) + e r + &2~ + Ve, + v e2

has an anti-neutrino accompanying each beta particle. As previously discussed, this second order weak interaction is allowed in the Standard Model, since lepton number is conserved. 2vPP decay can be visualized as a two step process consisting of two successive beta decays. In the first stage the parent nucleus (A,Z) beta decays to its isobar neighbor (A,Z + 1) emitting an electron and an anti-neutrino. Since this first step violates energy conservation it can only occur virtually. The isobar neighbor, being a virtual intermediate nuclear state, cannot live longer than specified by the uncertainty principle. The electron and neutrino are real particles since they appear in the final state. The second step consists of the beta decay of the virtual intermediate level to the final state isobar (A,Z + 2) with the emission of another electron and anti-neutrino. Energy is conserved between the initial and final states. Schematically:

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(A ,Z )-> e r+ vei + "(A,Z + 1)""(A,Z + 1)" -> e r + vC2 + (A,Z + 2)

Figure 1.3a shows a Feynman diagram of this process.

The Zero-Neutrino Mode (Ovpfi):

(A,Z) -> (A,Z + 2) + e f + t £

has no neutrinos appearing in the decay and thus violates lepton number conservation. In this mode the parent nucleus (A,Z) first beta decays to its isobar neighbor (A,Z + 1) emitting an electron and a neutrino. This step is again a virtual intermediate state since it violates energy conservation. Since the emitted neutrino will not appear in the final state it is also considered virtual in character and may have much larger energies than the neutrino emitted in 2vpp decay. In the second stage of the process the virtual neutrino is absorbed by the intermediate nucleus with the emission of a second electron. No neutrinos appear in the final state. Effectively a virtual neutrino is exchanged between the two nucleons. Schematically :

(A,Z) -» e f + "vel + (A,Z + 1)"

"vel + (A,Z + 1)" -> e2- + (A,Z + 2)

A simple argument will illustrate how this decay might occur and how its transition rate involves a massive Majorana neutrino. Consider the following decay-absorption Racah sequence within the nucleus:

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ni -» pi + ei + "v""v" + n2 -> P2 + e2

In this process one of the neutrons within the nucleus decays emitting a virtual "v" which is absorbed by another neutron. The neutrino emitted in the first step is identical to the anti-neutrino absorbed in the second. But v =v is not sufficient for this process to occur. For now, we will assume no right handed currents (RHC's) are present. Conservation of angular momentum then requires the neutrino emitted by ni to be right handed, while that absorbed by n2 to be left. This is the two-component neutrino theory which demands that a neutrino can only be in one helicity state when emitted and the opposite when absorbed. OvPP thus cannot occur unless the neutrino emitted also has a small component of the "wrong" helicity state for it to be absorbed. In order for a particle to not be in one definite state of handedness it must be massive. Then a Lorentz transformation can be made to a frame in which the spin of the neutrino entering the second stage is left handed making the absorption possible. These conditions are satisfied by a massive Majorana electron neutrino (v=v). These arguments will be made more precise in the following sub-section.

The OvPP MechanismsTwo possible Feynman diagrams for the exchange of a virtual

neutrino between the two nucleons are shown in Figures 1.3b and c. In the Standard Model a purely right-handed v e is emitted at the first vertex and only a left handed ve is absorbed at the second. This helicity (angular momentum) mismatch between the emitted and absorbed neutrinos can be

17

remedied by two mechanisms that drive Ovpp decay. As mentioned above the process can only proceed if neutrinos and anti-neutrinos are identical.

(1) Mass Mechanism (Fig. 1.3b):The electron neutrino would have a non-zero mass. The neutrino

mass eigenstate therefore would be a linear combination of the two helicity states (the presence of a right handed neutrino current). The extent of the mixing between the "wrong" helicity component is - mv/Ev , where mv is the Majorana neutrino mass parameter. The mass mechanism ejects electrons in an s-wave state with identical helicities (as conservation of angular momentum requires): AJP = 0 + selection rule. That is, this mechanism only allows 0+-»0+ transitions. Only V-A coupling is allowed at the vertices of the interaction.

(2) Right-Handed Weak Currents (right-handed Ws) Mechanism(Fig. 1.3c):

Here the weak interaction has both right and left-handed currents present. If any weak RHC's exist then a right handed neutrino could interact with the neutron via this force. The general Hamiltonian describing semi-Ieptonic weak interactions at low energies (below the W boson mass) can be written as:

” W = w [ Je(JL +K lL > + jR (l’ , L + W tn> ] + h c-’

where j t ,R = ^ V v cV“ (l + Y5)V e and j£ ,R =^V „Y |l (l + 7 5)Vi

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are the lepton and quark left/right-handed weak current four vectors, respectively, and the fields Vve »Ve»Vu»Vd are the lepton and quarkeigenstates. G=Gfcos0c is the weak coupling constant, GF=the Fermi constant, 0c=the Cabibbo angle.

The deviation from the minimal Standard Model is characterized by the dimensionless parameters k,T| and X. The parameter r| determines the extent of coupling between the right-handed lepton and the left handed quark currents; X describes that between the right handed lepton and right- handed quark currents; and k between the right-handed quark and left- handed lepton currents. Note when k,T| and X are zero the Hamiltonian shows maximal parity violation, a required condition for exact "two- component neutrino" coupling. Ovpp could not occur in this case regardless of the nature of the neutrino: the term I-Y5 would project out a neutrino state of definite helicity and, if there was V-A coupling at both vertices, the virtual neutrino could not carry any angular momentum from one vertex to the other (because the helicity must be identical at both points). We note that using the quark current impulse approximation to the nucleon current, the parameter k gives a negligible contribution to the Ovpp rate. So we need only study the parameters X and i\, involving right-handed lepton currents.

We also note a few characteristics of this interaction Hamiltonian. Both helicity states of the leptonic currents are present and mixing between the neutrino and anti-neutrino currents occurs. In general, the emitted and absorbed neutrinos have different helicity. Thus, the decay rate depends not only on the presence of a RHC but also on the occurrence of neutrino mixing between the two helicity states. This requires the existence of a non-zero neutrino mass.

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With RHC's present, we now have a variety of various spin and parity assignments. For this interaction mechanism of Ovpp decay all possible transitions are allowed (0+—»0+,l+ and 2+). With this mode V+A coupling is allowed at either of the vertices of the interaction. For example, if one of the vertices has some component of V+A coupling, then the neutrino may carry one unit of angular momentum, making the 2+ final state possible. The RHC mechanism would then eject electrons in a p-wave state with opposite helicities: AJp = 0+,l+ ,2+ selection rule. Thus, from angular momentum conservation considerations, only the RHC mechanism can mediate the 0+—>2+ transition. Present evidence from electron helicity measurements in nuclear beta decay rules out right-handed couplings down to 10-3 of the left-handed weak coupling strength.

It is important to emphasize that for OvPP decay to occur the neutrino must be a massive Majorana particle. Both mechanisms for OvpP decay require the existence of a massive Majorana neutrino. RHC's are not necessary for the decay to occur. A small admixture of right-handed currents can make the rates go faster by making the absorption of the second neutrino more probable, but non zero Majorana neutrino mass is the fundamental requirement for the decay to take place. In fact, if gauge theories describe the weak interactions, it can be shown that RHC's cannot mediate Ovpp decay unless at least one neutrino species has some mass.26

The Majoron Mode (xPPP):

(A,Z) -> (A,Z + 2) + e r + e2- + X°

20

has no neutrinos and is possible only if the neutral Majoron itself exists. The Majoron is the massless Goldstone boson produced by the spontaneous breaking of the global B-L (baryon minus lepton number) symmetry.27 Various GUT's predict processes where either B or L or both are not conserved. If this boson exists, the OvPP decay rate is determined by the

coupling to neutrinos which generates the Majorana neutrino mass. The existence of the Majoron was recently ruled out by the LEP experiments.8 Figure 1.3d shows the Feynman diagram for this process.

1.2.4. Calculation of pp Decay Rates

The details of the calculation of transition rates is developed in references 11 and 23-25. We will only outline the process here and present the theoretical results relevant to an experimental investigation of pp decay. The matrix elements for the decays are composed of leptonic and hadronic (nuclear) factors. The leptonic part is easily calculated while that for the hadronic part is non-trivial and will be discussed at the end of this chapter. We will only consider the 0+—»0+ transitions for PP since the larger phase space available usually causes it to dominate over all others. The Ov and 2v decay rates will be different because the former involves an intermediate state occupied by a virtual neutrino, the latter does not. Thus, for the Ov mode, the leptonic part of the matrix element introduces a neutrino potential in between the two nucleons undergoing the decay. In addition the phase space factors will be different in the two decays because the decay energy in the 2v process is shared among four particles versus only two in the Ov transition.

21

2 v/3/3 Transition Rate

Being a low energy process (the decay energy, To for 136Xe pp is2.48 MeV), we can sufficiently approximate the electroweak decay rate using Fermi's golden rule and second order time dependent perturbation theory:

d(D = 27t5(Eo - £ E f ) f(f|H p |m )(m |H p |i)

m ,p Ei - E m pv Ee

for the partial decay rate (a sum over virtual intermediate states m). Here H is the Fermi current-current interaction Hamiltonian, Ei, Ef, Em are the energies of the initial, final and intermediate states and pv and Ee are. the momenta and energy of the neutrino and electron emitted in the first stage of the decay. Remembering that the weak Hamiltonian is the product of the nuclear and lepton currents, the individual first order matrix elements are:

<m|H|i) = (>Pm ,e ,v |^9p (« j?e (1 - y5 )y*V v )(? p (g v ~gA TsiTnVn J ty i>

where JP and M^ are, respectively, the leptonic and hadronic four vector weak currents of the four-component fermion spinors. We must perform the sum over all possible final states and introduce a minus sign between all terms that differ only by the exchange of indistinguishable fermions in the final states:

22

d<o = 8rcGF4 cos4 e c8 ( E o - £ E f ) I M ^ m J L I

where ne,v= l,2 denotes the first and second lepton and n'e,v is the complement of ne,v. Neglecting terms linear in the lepton momenta which will disappear after integration over angles in phase space, setting the initial energy Eei+pvl carried off by the first electron and neutrino equal on average to (Ei-Ef)/2 (half the available energy for 0+—>0+ transitions), performing the required sums, and contracting the leptonic currents, we obtain the decay rate as:

M is the nuclear matrix element; its calculation is model-dependent and will be discussed at the end of this chapter:

x J o ° Eei E *2 lM |2 P v , <E 0 " E e, " E e2 “ P v , >2 dPv , •En- E , - E ,

<f|OT+ |m)(m|GT+ li) t gy (f|T+ |m)(m|T+ |i)

m Em —(Mj + M f ) / 2 g2 S E ra- ( M i + Mf ) / 2

23

F(Z,E) is a correction factor that accounts for the Coulomb attraction of the outgoing electrons to the nucleus. One such term is needed for each electron. The non-relativistic form is :

F(Z ,E) = E 2jcZaP i 2nZct

where a is the fine structure constant, Z, the nuclear charge and E and P are the energies and momenta of the outgoing electrons. Assuming this non-relativistic expression we can obtain qualitative features of the summed electron energy spectrum. The correct, relativistic factors are evaluated numerically for the outgoing electrons' wave functions in reference 25. These are needed to calculate the correct total decay rate. Evaluating the integral over phase space gives:

< ° l / 2 = [Tl/2 ( ° + 0+ )] 1 = G2v (E0 .Z)where,

m g t - ( — >2 m f v

s a

g 2v octJ 1 + Z o + ^ . + _ ^ +2 9 90 1980

L0 0 0

is the lepton four body phase space factor and, as mentioned before,

M ^ = £( O f L i g i ^ l c X c L k ^ i o r )

E ra- ( M i + M f ) / 2

and

24

are the second order Gamow-Teller and Fermi matrix elements and contain the nuclear structure information. IO+i> and IO+f> are the 0+ initial and final nuclei with masses Mi and Mf, respectively. The ll+m> are the 1+ states in the intermediate odd-odd nucleus with energies Em. Usually M f< < M q t for the two neutrino mode experimentally. M f is also predicted to be negligibly small since the matrix elements involved do not connect states of different isospin.25

The summed electron spectrum (total kinetic energy of the two electrons), which is of primary interest to the experimentalist, is obtained from G2v(Eo,Z) by integration over the total electron energy Ti+T2=K instead of over Ti and T2 separately. It is of the form

dN K K3 K K(T0 - K ) (1 + 2K + 4 + + -----)dK 0 3 3 30

where To=Eo-2 is the maximal kinetic energy and K is the sum of the kinetic energies of both electrons in units of electron mass mec2. Eo is the total endpoint energy. The spectrum of the summed kinetic energies of the two electrons is continuous and peaked at about 1/3 of the transition energy (0.8 MeV for the case of 136Xe as shown in Fig. 1.4).

The opening angle distribution also results from the V-A theory of the weak interactions and angular momentum conservation. It is approximated by ( l - p ip 2cos0 )dcos0 for the 0+—»0 + transition and (l+ p lp 2cos0/3)dcos0 for 0+—>2+, where P=p/E and 0 is the opening angle

25

between the two emitted electrons. A plot of the distribution (l-cos0)sin0 is given in Figure 1.5.

Ovpp Transition Rate

The calculation of the Ov transition rate proceeds in a similar fashion. We will consider only the mass mechanism (without right-handed couplings). The handling of the RHC mechanism is presented in references 11 and 23-25. Analogous to the 2v case we write,

where Rov is the transition amplitude including both the lepton and nuclear parts. In the leptonic part, a neutrino propagator term appears. This is the fundamental difference between the 2v and Ov processes. The lepton component of the amplitude is written as a product of two left or right- handed lepton currents (Majorana v’s assumed):

Combining this with the neutrino propagator and integrating over virtual neutrino momentum, the lepton part of the amplitude becomes

®0v — S |R qv | 5(E Cj + Ee2 + Ef Mj )d Pejd Pe2»spins

e(x)Yp i(l ± y 5 )vj (x)e(y)ya i(l ± y 5 )vk

*(x)Yp ± Y5 Xq^Yp + mj ) ^ d ± Y5 )Yae° (y)

26

where q is the four momentum carried by the virtual neutrino. Contracting the spinors and integrating leads to an expression that has a Yukawa-form of a "neutrino potential" which represents the effect of the neutrino propagation between two nucleons:

1 r l3- e iqrH (E ,r) = ——Jd q4 it q(q + E)— s H (r) = —e-rniv r

where R=1.2A1/3, the nuclear radius, is added to render H dimensionless. E=<E>-l/2(Mi+Mf), where <E> is a "typical" excitation energy of the intermediate nucleus. Assuming that the energy differences between the intermediate nuclear states and the initial state, Em-Ei (the excitation energies), are negligible compared to the energy carried by the virtual neutrino simplifies the sum over intermediate states in the nuclear matrix elements. The total rate then becomes:

[ l $ ( 0 + ->0+ )] 1 =G0v(E0 ,Z)2iiOv ®V » ,0v

m g t — r f& A

< m v > ,

with the nuclear matrix elements modified by the neutrino potential,

Mg'T = ( f | I 5 1.qc x ^ H ( r lk)|i>1,1c

- ( f l R S a i - c t T f T j / rjk|i>

l,kand

M?v = < f |S x ^ H ( r lk)|i> l,k

27

~ < f |R Z x f < / rik|i) l,k

<mv> is an effective neutrino mass (the neutrino mass parameter). The l,k summation is over all nucleons, n.k is the distance between any two. G0v(Eq,Z) is the two-electron phase space coefficient and is proportional to

G0v ~ /F (Z .E e i)peipe iEe Eei8 (E 0 - E e_ - E e, )dEe)dEe2

+ E 2 30 3 0 5

where we have assumed the non-relativistic form of F(Z,E).The summed electron energy spectrum of the Ov mode is a 8 -

fiinction peaked at the endpoint energy, To (which is 2.48 MeV for 136Xe)and is shown in Figure 1.4. This fact distinguishes experimentally the Ov and 2v modes of pp decay. Note also the phase space advantages the Ov mode has over the 2v mode. The decay rate for Ovpp is on the order of 106 times greater than that for 2v: the two-lepton final state has an Eo5 dependence while that for the four-lepton case is Eo11. The Ov decay is also faster because the higher energy available to the virtual neutrino greatly increases the available phase space; the typical nuclear excitation energies are small compared to the large possible momenta of the virtual neutrino.

The single electron energy spectrum (for each of the two electrons emitted) is determined by proper phase space integration and has the general form

and is shown in Figure 1.6. Also shown in this figure is the corresponding distribution for a particular case of the RHC coupling mechanism, which has a (Tei-Te2)2 factor present. For the RHC spectrum, note the node in the middle where the two electrons equally share the available energy. The decay rate calculation for this latter mechanism is discussed in the quoted references. The distribution of the opening angle for the Ov mode goes as 1-acosG, where a is a function of the energies of the two p's emitted and is different for the RHC and mv mechanisms.

Combining contributions from the two mechanisms of OvPP decay we can give a general formula for the transition rate

[t $ ( o+ ->o+ ) l "1 = C l <mv2>2 + c 2 < x > l ^ + c 3 < n > l ^m„ tHg m g+C4 < \ > 2 +C5 < q >2 +Cg < X > < T| >

where <mv>,<X> and <T|> are the effective parameters for the neutrino mass and right-handed coupling constants that may be extracted from the analysis of a Ovpp decay experiment. The functions Cn contain the nuclear matrix elements and the phase space integrals. For example, the mass mechanism term coefficient is

29

with MOvqt and defined above. The definitions of the other Cn can be found in reference 19.

The transition rate to the 2+ final state does not depend explicitly on the Majorana neutrino mass (even though a non-zero mass is required). The nuclear matrix elements in this case are summarized in reference 19. The total decay rate, which depends only on parameters of the right-handed couplings is

[ T ^ ( 0 + - * 2+ )]_1 = D t < X > 2 +D2 < X> < r |> +D 3 < t |> 2 .

Lepton Number Violation

The fact that the phase space for Ovpp is at least 106 times greater than that for the 2v mode gives us insight into what extent lepton number conservation (LNC) is violated in pp decay. By writing the Ov rate in terms of a lepton number violating parameter T|,

Rov = Tj2 x 106 x R2v •

When t |= l , LNC is maximally broken. 11=0 signifies lepton number conservation. So a PP decay experiment is a particularly sensitive test of LNC if it is sensitive to 2vPP decay; a tiny violation of LNC law would show up as an observable branching to Ovpp decay. Since the Ov decay is greatly favored by phase space, if we find Rov (observed) < R2v (observed), we can set limits on t| of the order < 10~3. q is then

30

interpreted as the lepton number violating amplitude of the weak interaction. This limit is more sensitive than other experiments that search for LNC violation, where limits of ti < 1(H are typical.

X^PP Transition Rate

Reference 27 discusses PP decay with the emission of the Majoron, a massless Goldstone boson that generates the Majorana mass for the neutrino. The decay rate is given by

[ Ti £ ] ’ I = R(Eo ) |M° '1 2 g ~ ’

where R is a phase space factor and gee is the coupling at the neutrino- Majoron vertex. The nuclear matrix element is similar to the 2v case. Experimentally, however, since the Majoron leaves the apparatus undetected, the summed electron kinetic energy spectrum is continuous and peaked at about 2 MeV for 136Xe, as shown in Figure 1.4. The shape is characteristic of a decay with three light particles in the final state.

Nuclear Matrix Elements

In the predictions of the PP rates, the phase space integrals can be evaluated exactly. The nuclear matrix elements, however, are difficult to calculate. Because of our lack of knowledge of the intermediate nuclear states and a consistent nuclear model to describe them, they are quite uncertain. Various authors have done calculations28 but their predictions

31

do not agree. The problem is currently under active research. The translation from Ti/2(0v) to a limit for <mv> depends on which specificcalculation one chooses. Table 1.1 shows the lifetime predictions for several candidate isotopes. Hypothetically, even in the most favorable case, M=1.0, the half-lives would be exceedingly long. In this section we give a brief description of the techniques that are being utilized to calculate the nuclear matrix elements relevant to pp decay.

All of the nuclear matrix elements defined in the previous sections contain the wave functions of the initial and final 0+ ground state even-even nuclei and some operator connecting these states (we will not consider transitions to the 2+ final states in this discussion). In the 2v case a summation over the complete set of states |m,Jm) of the intermediate odd-odd nucleus (N-1,Z+1) is also required. This summation is avoided in the "closure approximation" in which one completes the sum over the virtual intermediate nuclear states by closure after replacing Em -(Mi + Mf)/2 by some average value AE as we did for the Ov case. This leads to the same matrix element structure for 2v as for the Ov mode (see section 1.2.4) and only wave functions of the initial and final states are required. However, the closure approximation is accurate for the Ov mode because the virtual neutrino energy is high. It is a poor approximation for the 2v case and one must explicitly sum over all intermediate states.

As mentioned before, the matrix element M f in the 2v case is negligible since it does not connect states of different isospin.25 For the Ov case this is not true since the factor H(r,E) or 1/rik (see section 1.2.4) allows isospin change25; M f is still smaller than M g t by at least a factor of 4.

32

There are two approaches to the evaluation of the nuclear matrix elements of double beta decay. They will now be discussed briefly. The reader is encouraged to consult reference 28 for more details.

Shell Model Calculations

In the most ideal case one should obtain the required nuclear wave functions by solving the nuclear many body problem with a realistic nucleon-nucleon interaction without approximations. This is not feasible for heavy double beta decay candidates, such as 136Xe. In heavier nuclei, Haxton et al.28 have developed a shell model approach that allows calculation of all nuclear matrix elements of interest. They ignore higher lying configurations and spin-orbit partners and use the closure approximation. It is thus difficult to estimate the uncertainty in their calculation.

Most of the other calculations for 2v decay are concerned only with the configurations directly connected to the unperturbed ground state by the Gamow-Teller operator, ax. These calculations can explicitly describe the intermediate odd-odd nucleus. Because of the vector-isovector nature of the operator ox, the summation over the intermediate states, \m,Jm)involves only states with spin and parity I* = 1+ for the 0+->0+ and 0+—>2+ transitions. Thus, one must determine the spectrum of the 1+ states in the intermediate odd-odd nucleus and the matrix elements of the Gamow-Teller operator ax that connect these states with the 0+ ground states of the initial and final nuclei.

Tests of the shell model calculations are possible for several reasons. The quantities 311(1 ( ° / d e t e r m i n e , respectively, the

33

strength of the p” transition between the initial and the intermediate nucleus (if this transition were energetically possible) and that of the P+ transition between the final and the intermediate nucleus. These factors also determine the cross section of the charge exchange reactions (pji) and (n,p), respectively, which can be studied experimentally. An additional constraint is obtained from a sum rule which relates the total p- and P+ strengths, which are determined by the ax + and the ax~ operators, respectively.

Quasi-Particle Random Phase Approximation (QRPA)Calculations

This approximation gives a systematic procedure for calculating the matrix elements and M,v. It utilizes two necessary ingredients ofnuclear structure: pairing, which causes the extra binding of even-even nuclei; and spin-isospin polarization, responsible for the "giant Gamow- Teller resonance" of the (p,n) reaction discussed above. The QRPA method uses a few adjustable parameters that adjust the strength of the effective nucleon-nucleon interaction in the particle-particle and particle- hole channels independendy. These parameters are fitted to experimentally known nuclear properties.

Early QRPA calculations overestimated the decay rates for 2v decay. Predicted lifetimes were shorter than the experimental limits. The inclusion of a particle-particle spin-isospin polarization force by Engel et a l .28 led to the needed suppression of the 2v pp decay rate. The interaction strength of this force, gPP can be determined by requiring consistency with ordinary P+ decay. With this constraint, the matrix

34

elements M£ agree better with experiment but there is still a significant over estimate for heavy pp decay candidates, such as 136Xe.

The Ov matrix elements are different than those of 2v for several reasons. The radial dependence H(r) from the neutrino propagator means that all virtual intermediate states may possibly contribute, rather than only the 1+ states as for 2v. Thus a larger set of single particle states is required. There is, however, a general consensus that the ground state correlations, caused by the particle-particle force affect the 1+ states more than those of other multipolarities. When the particle-particle force is switched on, the components of the matrix elements associated with the intermediate 1+ states are reduced considerably while those associated with other intermediate states are less affected; the final matrix elements are then less sensitive to gPP. Thus, the evaluation of the matrix elements of Ov decay are less uncertain than for the 2v case.

Another reason that the Ov and 2v cases are different is that the isospin selection rule, which caused M? to vanish is not inhibiting Ov decay .25 Finally, the closure approximation is expected to be valid eliminating the summation over intermediate states. However, the ground states of the initial and final nucleus must be described correctly.

QRPA is a general method for the evaluation of the zero and two neutrino double beta decay matrix elements. Different authors28 apply this method using different forms and parameterizations of the nucleon-nucleon interaction, treatments of pairing and the short range nucleon repulsion, and values for other parameters involved. There is still a large theoretical uncertainty in the Ov matrix element calculations. This spread in matrix elements directly affects the uncertainty of the constants Ci - C6 of section 1.2.4 and, therefore, of the neutrino mass and right handed coupling

35

parameters <my>, <T|> and <A,>. We will now briefly describe the calculation of the matrix elements for the Ov pp decay of 136Xe by Pantis et al.29 This technique is expected to have less uncertainty for the nucleus !36Xe, in particular.

Calculation of the l^ X e Ov PP Decay Matrix Elements

We will briefly discuss the assumptions made and summarize the results obtained by Pantis et al.29 The states |m,Jm) are obtained as proton-neutron quasiparticle states. The method that was employed was the proton-neutron quasiparticle random phase approximation. They assumed a finite range interaction based on the nuclear G matrix. They have shown that with such an interaction the necessary renormalization of the coupling constants is quite small: gpp=gph=l; they do not modify the particle- particle and the particle-hole elements by the typical factors gpp and gph- The single particle energies were calculated with a Coulomb-corrected Wood-Saxon potential. The kinematic factors were taken from Doi et al.25

Results

The results for the nuclear matrix elements and M0/ and the parameter <mv> extracted from the experimentally determined half-life of 136Xe Ov pp decay, 7,%, is as follows:

and

M(3x= -1.8633 = 0.2397

36

*r*Ov*1/2

These results will be utilized in Chapter 6 to estimate the projected sensitivity of a 136Xe Ov PP experimental search, using our compressed xenon gas drift chamber, to the Majorana electron neutrino mass.

I.SQtORfi <Vogel et al.

%(>"•) *m(yr)KiapJor

<>(yr)<?t al.

76Ge 9.2 OfHX 1.3 x 1021 2.3 x 1024 3.0 x 1021

82Se 7.3 <soX 1.2 x 1020 6.0 x 1023 1.1 x 1020lOOMo 1.9 x 102* 6.0 x 1018 1.3 x 102* 1.1 x 101Sl28Te 1.8 x 1025 5.5 x 1023 7.8 x 1024 2.6 x 1024I30re 1.1 x 1024 2.2 x 1020 4.9 x 1023 1.8 x 1021136Xe 6.3 x 102* 8.2 x 1020 2.2 x 1024 4.6 x 1021

Table 1.1. Theoretical Ov and 2v half-life predictions for several pp decay candidate isotopes.

/39*'

Figure 1.1 Atomic masses o f nuclei with A=76. Parabolas connecting the even-even and odd-odd nuclear states are indicated. 76Ge and 76Se are stable with respect to ordinary beta decay; 76Ge, however, can decay by emitting two beta particles.

Figure 1.2 Isobar triplet involved in 136Xe Pp decay. Principal decay branches are indicated. Qpp = 2.479 keV for 136Xe.

v////////////////>Z Z + t Z ♦ 2

a)

l'-A

P j

b) c)

‘ V-A

nW W W w w w n :

d)

Figure 1.3 Schematic Feynman diagrams for the various modes of double beta decay in the two-nucleon mechanism: a) 2v mode, b) Ov mode with the neutrino mass mechanism (left-handed lepton current at both vertices), c) Ov mode with the right-handed weak current mechanism (a left-right current interference is shown), and d) Ov with the emission of the Majoron. The arrows represent the main neutrino helicides at each vertex.

Figure 1.4 Typical spectra of the total kinetic energy, Ti+T2, of the two electrons emitted in the various modes of double beta decay. For 136Xe the transition energy is To=2.481 MeV. Note for the Ov mode the summed electron kinetic energy is always To.

PROB

ABIL

ITY

OPENING ANGLE (DEGREES)

Figure 1.5 Opening angle distribution for 2v pp decay.

1--------1_____ I I I - I J_____ 1_____ I0 0 .5

ei/Tq

ei/To

Figure 1.6 Two typical types of the single electron kinetic energy spectrum for 136Xe Ov PP decay (0+- 0 + transition). The e jis the kinetic energy of either one of the electrons and To is the maximum kinetic energy release. The spectrum is normalized so that its integrated value is unity, a) massive neutrino mechanism, b) right-handed current mechanism. Note that the emitted electrons will most likely have the same (different) energies in the my (RHC) mode.

CHAPTER 2Experimental Considerations

2.1. Present Status of p|3 Decay-Other Experimental Searches

2.1.1. Introduction

As mentioned before, PP experiments have been performed since the late 1940's, but have received special attention only in the last 10 years. Ironically, no experiment has ever claimed an observation of Ov PP decay except the first, performed by Fireman.19 Therefore, nothing can be claimed conclusively about the neutrino mass or RHC since the neutrino may indeed be a Dirac particle. One can only compare the relative sensitivity of different Ov PP experiments. If the Ov pp process is undetected, an upper limit is placed on the mass of the Majorana neutrino. The experimental techniques utilized to search for Ov pp decay are classified as either indirect (in which the decay electrons are not observed) or direct (in which the energy and/or trajectory of the decay electrons is observed in a counter or visible tracking device).

2.1.2. Direct Counting Experiments

In these experiments one uses a beta spectrometer to directly search for the two outgoing electrons by measuring their summed energy. As mentioned before the modes of double beta decay, Ov, 2v and x°» are

44

45

distinguished by the different total kinetic energy distributions of the two electrons emitted. A large range of spectrometers have been utilized. In these experiments, very good energy resolution is required to differentiate the Ov mode (signified by a spike in the summed electron energy spectrum) from the other modes of pp decay and background processes (see Fig. 1.4).

To date, the most sensitive limits for Ov pp decay have been obtained from 76Ge experiments. The UCSB-LBL 76Ge zero neutrino double beta decay experiment that ran in the Oroville Dam in California is one of the most successful experiments to date.30 It involves the use of eight, 175 cm2 natural Ge detectors (which are 7.8% 76Ge). This system of detectors is surrounded by 15 cm of NaI(Tl) to actively veto Compton scattered internal gamma rays which are emitted from radioactive contaminants in the detector. After several years of data taking (a total Ge mass times running time = 21 kg-years), this experiment achieved a limit of T 1/2 (Ov) > 1.2 x 1024 years (90% confidence level).30 Using the set of matrix elements calculated by Haxton and Stevenson,28 this corresponds to a limit of <mv> <1.3 eV, <t\> < 0.23 x 10*6, and <X> < 0.23 x 10'5. The collaboration is now turning toward experiments to search for dark matter and thus, their mass limit may not significantly improve in the future.

Other 76Ge experiments are being performed. Two Soviet groups have obtained large quantities of enriched 76Ge. A Moscow-Yerevan team has finished an experiment achieving a lower limit of 1.3 x 1024 y for the Ov half-life (2.5 kg-yr), but at the 68% confidence level.31 They have identified the 2v decay giving a half-life of 0.9 ± 0.1 x 1021 y (68% C.L.).32 This decay was also seen by Avignone et al.,33 giving consistent results for the 2v half-life. Another Moscow group, collaborating with Heidelberg have recently reported their first results34 for 1.29 kg-yr of operation:

46

T i/2 (0 v )> 1 .4 and 4.3 x 1024 yr (90% CL) for the decay to the ground and first excited states, respectively. This experiment produced a more sensitive limit than the UCSB-LBL experiment due to a larger 76Ge source size (enriched Ge) and a smaller background rate.

A collaboration of the University of Zarazoga, Pacific Northwest Laboratory, and the University of South Carolina have organized the International Germanium Experiment (IGEX).31»33 They have acquired 5 kg of 85% 76Ge raw material (and are expecting 5 kg more). They expect a fiducial mass nearly an order of magnitude larger than that for the UCSB- LBL experiment described above. Assuming the background rates stay constant, they could achieve approximately a factor of 3 improvement in the neutrino mass sensitivity in a comparable running time.

The 2v pp mode of 82Se was observed by Elliot et al.35 at U.C.I. They observed T i/2 (2 v ) = 1.1 ± 0.5 x 1020 y with a 14 g sample of enriched 82Se. This experiment utilized a time projection chamber that can distinguish pp trajectories from single electron events (and many other background processes).

Moe35 has also studied the 2v pp decay of 10°Mo using an 8.3 g sample of enriched, radioactively pure 100M oO3 at an underground laboratory at the Hoover Dam. They have performed a coincidence experiment in which background rejection was achieved by sandwiching thin wafers of silicon detectors and foils of candidate isotopes. This experiment was limited by background gamma radiation that scattered in the source. They have determined the 2v half-life to be T1/2 = (1.16 ± 0.34) x 1019 y (68% C.L.). At LBL and Osaka 10°Mo experiments are also being p e r f o r m e d . 3 L36 Both of these use a sandwich design of detectors and lOOMo enriched electromagnetically at the Oak Ridge National Laboratory.

47

The challenge for these experiments lies in the usual U contamination of the source material at the ppb level. 10°Mo is a very strong candidate for study because of the large available energy (3.03 MeV) for the decay. Recent results from these various 100Mo experiments indicate a 2v half-life on the order of 1019 years and a half-life limit of 2.6 x 1021 y for the Ov mode.31*36

Several experiments searching for the decay of 136Xe are being performed or are under development. A Caltech-PSI-Neuchatel collaboration has built and run a large, 207 liter, time projection chamber (TPC), operating at 5 atmospheres of Xe enriched to 62.5% 136Xe.37 They are running in the Gotthard Tunnel in Switzerland for cosmic ray background reduction. This detector has adequate position resolution to allow study of individual electron tracks. As with the Irvine TPC, this technique offers advantages in background event identification (despite the large amount of multiple scattering present). However, the measured energy resolution37 is 7 % at 2.48 MeV. In addition, the detector efficiencies37 for the mass and RHC mechanisms are only 20 and 13 %, respectively (giving a fiducial mass of approximately 3 - 5 moles of 136Xe). As we will see later, these factors substantially reduce the sensitivity of their TPC to the detection of the Ov mode. This experiment has reported half-life limits of Ti/2(0v) > 2.5 and 1.7 x 1023 y for the neutrino mass and RHC mechanisms, respectively (90% confidence level).37 TTiis is the best limit so far reported in l36Xe.

Another low-density gas detector has been built by the Milan group of Fiorini et al.38 It is a multi-element proportional chamber with 61 proportional cells, hexagonal in cross section. It is operating in the Gran Sasso Underground Laboratory, at a pressure of 10 atm with xenon enriched to 64% in 136Xe and a fiducial volume of 45 I (fiducial mass of 8 moles).

48

The energy resolution is similarly rather poor (5% at 2.5 MeV) and it lacks the advantage of tracking the individual electrons. However, some background rejection is achieved by requiring that at least three and less than nine adjacent cells are triggered by the same event. The best half-life limit obtained to date by this experiment is Ti/2(0v) > 2.0 x 1022 years at the 90% confidence level.38

The Soviet group of Pomansky, working in the Baksan underground laboratory, has built and run a high pressure xenon ionization chamber to look for 136Xe PP decay.39 The chamber has an active volume of 3.1 liters and is filled with 93% enriched 136Xe at 25 atm (fiducial mass of about 3 moles of 136Xe). The gas has an admixture of 0.8% H2 to increase the electron drift velocity. The energy resolution is 4% at 2.5 MeV. The limits obtained after 700 hours of running are Ti/2(2v) > 8.4 x 1019 y and Ti/2(0v) > 3.3 x 102* y.39

2.1.3. Geochemical Experiments

In this method, total pp lifetimes are determined by measuring the abundance of daughter isotopes in an ore containing the parent. This is done using mass spectrometry techniques. This search for pp decay has the advantage of a long running or accumulation time (the age of the earth ~ 109 y), but cannot distinguish between the various modes (0v,2v). In addition, the lack of a precise sample history allows more uncertainty in the measurement. Thus far, this method has only been successfully applied to cases where the daughters are noble gases: 82Se-»82Kr, 128Te-»128Xe and l30Te—>13° X e .4 0 Positive results have been reported only in 82Se and 13°Te: Ti/2=1.3 ± 0.5 x 1020 and 2.6 ± 0.8 x 1021 y, respectively.

49

2.1.4. Radiochemical Experiments

Here the PP lifetimes are determined by directly counting the number of daughter isotopes produced in a sample of the parent during a known period of time. To accomplish this, chemical extraction or "milking" techniques are used. The only experiments performed using this method were of the transition 238u—>238pu# a controversial positive result of T1/2 = 2.0 ± 0.6 x 1021 y was recently reported4* and before that only a limit T1/2 > 6 x 1018 y was given.42

The results for the various experiments performed are summarized in Table 2.1.

2.2. Experimental Sensitivity Issues for 136Xe Ov pp Decay Searches

All pp experiments suffer from the difficulty of extremely low signal rates (much less than one event per day) and large background rates due to the presence of radioactive contamination of the source and/or the apparatus and ambient cosmic and gamma ray radiation. Any experimental effort must reduce the ambient radiation by as much as possible and to at least some extent be able to differentiate between PP decay and background events which masquerade as PP events in the detector utilized. Fortunately, PP decay has a fairly distinctive signature :

(a) the two electrons emitted originate from the same location.(b) the sum energy of the two electrons must have the proper spectrum

shape.

50

(c) the distribution of opening angles for the two electrons must have the correct form and the two-electron trajectory must exhibit the proper shape.

However, various background events may mimic the two electrons emitted in double beta decay in their trajectories or energy deposited. Excellent energy resolution and reducing the levels of the background sources are ways to cope with this problem. Differentiating the background processes from two electron events by the shapes of their tracks can to some extent be accomplished through the use of an imaging detector, such as a TPC.

If Ov PP decay occurs, the two electrons will share the total available energy, and the expected summed electron energy spectrum would be a narrow peak at the endpoint energy. One then only needs to study this small energy region in the spectrum. From an experimental point of view, the 2v decay is difficult to observe despite the shorter expected half-life of that transition; the electron intensity in the 2v decay is spread over all energies from 0 to the decay energy (2.5 MeV for 136Xe) according to the four- fermion phase space distribution (see Chapter 1); the number of electrons per energy bin changes over the spectrum and the energy resolution worsens at lower energy. Further complications arise from the larger number of background gamma-ray lines at low energy (< 2MeV). Because of these facts, the detector developed for this thesis will be more sensitive to the Ov mode of pp decay than to the 2v mode (whose summed electron energy spectrum is continuous over all energies up to the transition energy).

In the absence of any background events a detector with No pp source atoms in the sensitive region of a perfectly efficient detector, after operating

51

for one year and seeing zero counts, would allow us to place a double beta decay half-life limit, using Poisson statistics, on the order of No years. In reality, there is always a background component, and thus it will not be possible to reach this limit.

In the presence of background we define a projected "sensitivity" to the half-life limit of Ov pp decay to correspond to one standard deviation of the background counting rate in an energy bin centered on the decay energy of interest and with a width equal to the energy resolution (FWHM). This is equivalent to neglecting the error in the shape of the background counting rates in the energy region of interest, which is approximately correct in all experiments. The projected sensitivity of an experiment is thus given (in years) by:

IylI • Nq • £• t Xl/2 " V N b ' A E - t

where No is the number of candidate PP decay atoms within the sensitive volume of the detector, e is the detector efficiency for the decay, t is the running time in years, Nb is the background counting rate in counts/(keV-yr), and AE is the expected energy resolution at the endpoint energy.

The number of double beta decay candidates is limited in nature. The isotopes most commonly studied are 124Sn, 48Ca, 82Se, 100Mo, 128Te, 130Te and ?6Ge. 13*>Xe is a particularly appealing candidate (has a high projected experimental sensitivity) for many reasons:

52

(1) Sample SizeSince lifetimes of 136Xe Ovpp decay are on the order of 1023 y,

several moles of the candidate nuclei are necessary in order to have a reasonable average expected count rate in 1 year of running time. The natural isotopic abundance of 136Xe is 8.87% which allows a large number of 136Xe atoms in a sample of ordinary xenon without isotopic enrichment. In addition, xenon is commercially available, relatively inexpensive (~$20/liter in 1990) and can be cleanly and economically enriched to > 60% in 136Xe. This latter property is due to the fact that 136Xe is the end member of the stable xenon isotope series.

Xenon is also a good ionization medium possessing good electron drifting properties. Being a gas, xenon can be incorporated into large detector volumes of various geometries in which the source of 136Xe pp decay is also the ionization medium for the detector. If, in addition, the xenon is compressed or condensed, a large number of PP decay source atoms in relatively small detector volumes would result Xenon's low cost in large volumes gives a 136Xe pp decay search a distinct advantage over experiments using solid-state detectors (such as 76Ge experiments).

(2) Detector EfficiencyXenon has a large atomic number (Z=54) and when compressed or

condensed, can be made into a highly efficient electron (and/or gamma-ray) spectrometer. The design and construction of such a device will be discussed in the next chapter.

53

(3) BackgroundThe relatively high decay energy for 136Xe pp decay of 2.48 MeV

(the atomic mass difference between the parent and daughter nuclei) results in a lower background rate near the endpoint (the critical energy range for the Ov mode). Most of the y-ray lines from the natural decay chains are below 2.0 MeV, and only the 2.615 MeV line from 208T1 (originating from 228Th) lies above the 2.48 MeV transition energy. In addition, no long-lived cosmogenic radioactive daughters (analogous to 68Ge) are present in xenon, which has a high degree of radioactive purity naturally. The signature for the Ov mode would be a peak at 2.48 MeV in the measured summed energy spectrum of the two electrons emitted and must be well distinguished from background events occurring in this energy region.

In addition, being a gas, xenon can be made into a drift chamber that can to at least some extent, be able to discriminate between electrons produced by double beta decay and those produced by other means (such as, from cosmic ray and/or atomic electron-y-ray induced interactions, or P emitting radioactive decays occurring in the detector). The xenon TPC used in the Caltech-PSI-Neuchatel pp experiment,37 for example, can visually distinguish background events from good events by the shape of the electron tracks produced (by dE/dx measurements along the electron tracks).

Because a xenon detector does not require a cryostat (unlike 76Ge pp decay experiments), it is easier to implement efficient passive and active shielding to reduce events produced by ambient background radiation. In addition, there are no unusual problems associated with the radioactivity of the components in the experimental apparatus (such as cryostats), provided that the construction materials are well chosen.

54

Being a gas, xenon can be efficiently isotopically enriched in 136Xe, through the use of ultra-centrifuges. This reduces the chances of radioactive impurities being present in the PP source. This is a distinct advantage over lOOMo and 82Se experiments where the source is a solid; these experiments must live with any impurities present in their source. However, because xenon is a gas, air-born radioactive impurities such as radon can diffuse into the active region of the detector and cause problems. In this regard, solid state pp experiments (76Ge, for example) have an advantage over those using xenon gas since contaminants cannot diffuse past the surface of the solid crystal.

Clearly the sensitivity of the detector depends strongly on the level of background, and every effort must be made to reduce this as much as possible. Such efforts in background reduction will be discussed in Chapters 4 and 6.

(41 Energy ResolutionIn this thesis, we will demonstrate that xenon can be incorporated into

a detector with high energy resolution. This is especially important in distinguishing between Ov 136Xe pp decay and background events in the summed electron energy spectrum. For example, as mentioned above, the photopeak from 232Th background contamination is at 2.62 MeV. In order to be able to distinguish between a possible 136Xe Ov pp signature peak at2.48 MeV and the 208t i photo-peak at 2.62 MeV in a pulse height spectrum, the FWHM energy resolution of the detector filled with xenon must at minimum be better than 140 keV or 5.6% at the endpoint A sensitive Ov PP detector must allow as few background events as possible into the energy

55

window of interest (at the endpoint energy); the better the energy resolution of a detector, the fewer is the number of background counts allowed in AE.

In addition, since a pp event may occur anywhere in the sensitive region of the detector, a position independent electronic signal must be achieved to minimize fluctuations in the charge collected. Ways to avoid position dependent effects in charge collection and energy resolution in a xenon ionization chamber will be discussed in the next chapter.

The current experiments searching for the zero neutrino mode of double beta decay in 136Xe at Caltech, Universita di Milano and various laboratories in Russia are characterized by energy resolution at the pp endpoint, ranging from 4 to 7 % at 2.5 MeV. This obviously reduces the sensitivity for the detection of the zero neutrino mode.

The poor detector energy resolution in these experiments results from their low gas pressures and the types of ionization devices being utilized. These detector designs all run in a proportional ionization mode. Charge multiplication, space charge effects, and their variation produce larger uncertainty in energy measurements. If wires are used the fluctuation in the gain from different wires alone is expected to be on the order of 4%.43 This non-uniform charge multiplication has drastic effects on the energy resolution. In order to achieve highly uniform charge multiplication and avoid any space charge effects these detector designs require spectacular geometrical precision of wire spacing and other separations as well as clean and smooth wires (high electric fields are present). Also, often a quenching ("cooling") gas such as CH4 must be added to reduce electron diffusion, increase drift velocities and enhance the stability against high voltage breakdown. These considerations make high energy resolution seem impossible in wire chamber designs.

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In xenon gas near its critical point, the predicted FWHM energy resolution is 0.25 % at 2.48 MeV (see next chapter). The design and construction of an efficient, high resolution xenon detector that could be used in a Ov 136xe PP decay experiment is the subject of the next chapter. We will demonstrate that the energy resolution extrapolated to 2.48 MeV, in a drift chamber filled with xenon near its critical point, is 1 %.

(5) Time StabilityBecause a double beta decay experiment often has long running times

(> 1 year) it is essential that charge collection and energy resolution remain constant over that period. We will demonstrate in the next chapter that our compressed xenon gas device has this property.

(6) Expected Decay RatesThe relatively high energy release of 136Xe neutrinoless double beta

decay, compared to other candidate nuclei, results in a larger phase space factor and, thus, in a higher expected decay rate. From the point of nuclear structure calculations relevant to pp decay, 136Xe is also predicted to have a large nuclear matrix element.29 In addition, nuclear matrix element calculations in 136Xe are less sensitive to model parameters and thus more certain than in other cases such as, 76Ge, 82Se and 100Mo.29

The Experimental ChoiceOn the basis of the above considerations we chose to develop a high

pressure, parallel plate xenon ionization chamber that could be utilized in a search for the Ov mode of 136Xe pp decay. This calorimeter has one dimensional imaging capabilities which will allow some background

57

reduction as will be discussed in Chapters 4 and 6 . If the apparatus were built with ultra-low background materials it could also be quite useful for measuring the continuous 2v PP decay summed electron spectrum.

The advantages of using a xenon detector operating in the ionization mode at high pressure versus the proportional mode at low pressure, in a PP decay search, balance the lack of three dimensional imaging capabilities (the Caltech TPC, for example). The energy resolution and efficiency in a highly compressed xenon ionization chamber are (as we will demonstrate) much better than for low pressure, proportional versions. In a simple ionization chamber, nearly gainless charge measurements are made. With little charge multiplication there are much smaller uncertainties in energy measurements. The design, operation and performance of such a device is the subject of this next chapter.

Spectroscopic experiments

4*Ca 76Ge «Sc l00Mo ,J*Xe

T ini Ov) ^ x l O 21 > 1 .2 x (0 24 > 7 x l0 JI >2 .6x 1021 >2.5xlO JJ

<5mv> a <1.4 <9.3 <22.1 <3.0< m v>* <1.8 <14.4 <3.0< m v> e <(2.4-4.7) <(28-40) < - 2 7 <(3.3-5.0)

r 1/2( 2v) > 3 .6 x (0 19 0 .92 t5 j^x l0JI 1.1 ^ flx lO 20 1 . 1 6 ^ x 1 0 ” > 1 .6 x l0 20

Geochemical and milking experiments

«Se ,2*Te ,3<>r e 2,,U

7’i/2(Ov,2v) (1.3±0.05)xlOJO > 8X1024 (2.6±0.3)xl021 (2 .0±0.6)xl021

* Matrix elements of Muto et al. (89), ’axial charge* - 1.0. (33)* Matrix elements o f Suhoneo et al. (91), *axial charge* — 1.0. (34){ Matrix elements of Engel el al. (88), o',- -}75± 15 MeV fm1, ‘axial charge* - 1/1.25. (35)

Table 2.113 Experimental half-lives (in years) for some double beta decay candidates (limits are 90% CL). For references see text or Boehm et al. (13). Corresponding upper limits for the neutrino mass parameter <my> (in eV) are also shown.

CHAPTER 3 Condensed and Compressed Rare Gases as Ionization Media

3.1. Previous Studies in Condensed Xenon and Argon

3.1.1. Introduction

Liquid xenon and argon are excellent ionization media because the energy required to form an electron-ion pair in either is small: 15.6 and 23.6 eV, respectively.44 The statistical fluctuation in these numbers is also low due to the solid state properties of xenon and argon.45 A convenient expression for the statistical variation in the ionization process in any medium is through the Fano factor46

a = ^/FE0w ,

where a is the variance in the energy measurement, F is the Fano factor, Eo is the energy of the primary ionizing particle and w is the average energy required to form an electron-ion pair. The Fano factor expresses the deviation of the ionization process from independent, identically distributed events. For example, for an ionization process governed by Poisson statistics, F=l. For identical ionization events, F=0.

The estimated Fano factors in liquid xenon and argon are 0.04 and 0.11, respectively.47 These low values are due to the small number of

59

60

degrees of freedom for the de-excitation of energetic electrons and the small band gap in these materials (9.3 and 14.3 eV in xenon and argon, respectively).45*47*48 Extremely good energy resolution in liquid xenon or argon should thus be possible. Estimates based on these Fano factors are 0.2 and 0.4 % FWHM for liquid xenon and argon, respectively, at 1 MeV. However, the best energy resolution observed at 1 MeV is only ~5 and 3% FWHM, respectively, in liquid xenon and argon ionization detectors, even at extremely high electric fields.47-52 These numbers are far from the expected theoretical Fano limits. It appears that the resolution is limited by some process other than Poisson fluctuations.

The factors which might contribute most to the degradation of the energy resolution of a gridded ionization detector are charge loss mechanisms such as recombination between the electrons and positive ions resulting from the ionization process, attachment of free electrons to electronegative impurities, electronic noise and electron trapping by the grid. In addition, back scattering in the source material, variation of the rise time of pulses and imperfect grid shielding add much smaller contributions to the measured energy resolution.

3.1.2. Electron-Ion Recombination

Various attempts to explain the above discrepancy between liquid xenon and argon experiments and theory have been m a d e .5 2 -5 4 These authors believe that what is limiting the energy resolution is the fluctuation in electron-ion recombination due to the variation in ionization densities along the path of an ionizing particle from event to event. They claim the discrepancy between theory and experiment is due to an effect, resulting

61

from the production of "low energy" delta electrons, that has not been taken into account in the estimation of the Fano factor. The statistical fluctuation in the number of delta electrons produced and in the density of ionization along the track of a delta electron apparently produces a significant variation in the rate of electron-ion recombination. This, in turn, limits the energy resolution.

Electron-ion recombination was first discussed by Rutherford.55 This process has not been understood and does effect the resolution of an ionization detector. The two modes of electron-ion recombination which may limit the total charge yield are geminate and columnar recombination. Geminate or "initial" recombination involving only the initial parent ion is different from columnar or "track" recombination which involves all the ions in the track left by an ionizing particle. The theories of initial and track recombination are related because both depend on the initial distances of electron-ion separation. The extent of recombination in both cases can be computed from the laws of diffusion and migration. We now review the various theories of recombination.

The Onsager Theory o f Geminate Recombination

The geminate (initial) theory of recombination in an ionization chamber reduces to a problem of Brownian motion of one particle under the influence of the collecting field together with the Coulomb attraction of the parent ion. The fundamental assumptions in the Onsager theory56 is that each electron-ion pair created is independent and spatially separate from the others and that each electron of the pair only interacts with the parent ion via an infinite range mutual coulomb force. The application of

62

an external electric field diminishes the average field between the electron and ion of each randomly oriented pair created. At low electric fields, neglecting other charge loss mechanisms, the predicted dependency of the collected charge on electric field is linear,

Q(E) = Q0(A + B E ) ,

where A and B are numerical constants depending on factors such as the probability o f escape in absence o f an external field, the electron thermalization length and the distance at which the energy of the mutual coulomb attraction of the ion pairs is equal to the thermal energy, kT.

Several authors52*57*58 have attempted to fit data taken with liquid xenon and argon ionization detectors to the Onsager model with little or no success. There are several problems with the Onsager theory. The assumption of separated ion pairs is probably not valid in dense xenon and argon. The assumption of the 1/r Coulomb attraction is probably incorrect because the high coefficient of polarization in argon and especially xenon causes the induced dipole moments to reduce the effective charge of an ion to within a few atomic spacings.45 The resulting polarization potential falls off more rapidly than 1/r. Finally, electrons which escape geminate recombination with the parent ions may still recombine with other ions. Therefore, the application of an external electric field does not necessarily yield a linear increase of free carriers.

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The Jaffe Theory of Columnar Recombination

The columnar (track) theory of recombination leads to a non-linear system of differential equations for which Jaffe59 has made an approximate solution. Jaffe used a diffusion equation neglecting the coulomb forces entirely. In addition he included a recombination term whose rate depends on the density of the ions and electrons separately:

dn - -= +p±E • Vn± + D ± V2n± - ocn+n_ ,ot

where n+,n. are the ion and electron charge distributions, respectively, |i+,|X. are the mobilities, D=|ikT/e is the diffusion coefficient and a=87cpe is the coefficient of recombination. Jaffe attempted to solve this model by considering the recombination term as a perturbation with the boundary condition that the initial distribution of electrons and ion pairs is in a "column" of uniform charge density around the primary track. Kramers60 pointed out that in an external field the diffusion term is smaller than the recombination term so the above perturbative solution was unreliable. He solved the equations by treating the diffusion term as the perturbation, including the columnar initial conditions and assuming that the electron and ion mobilities are equal. In the high field approximation, Jaffes' model then becomes

Q(E) = - - —°— 1 + k /E

64

k is a recombination constant and Qo is the charge collected at infinite field.

Attempts to fit this equation to various data taken have also been poor.52*57'58 The failure of this model is probably in the assumption of equal electron and ion mobilities which is not the case in noble gas liquids.61*63 Also the assumption of uniform charge density along the path o f the primary ionizing particle is not realistic. It is well known that the rate of energy loss in the liquid increases as the particle slows down. In addition, sudden changes in the ionization rate may occur due to the production of delta (or knock-on) electrons produced from hard collisions.

Based on the idea that the production of delta electrons is the mechanism which severely affects the statistical fluctuations in the ionization density and, thus, the recombination rate along the primary electron track, several authors have derived expressions for the field dependence of the collected charge. Thomas et al.64 used Jaffes’ diffusion equations but neglected the diffusion terms and the ion mobility. In addition, he separated the charge collected into two parts: the charge collected from the delta electron tracks and that from everything else. Thomas derived an expression for the field dependence of the collected charge:

Here £0 and £1 describe the charge density of the minimum and heavily ionizing regions of the particle and delta electron tracks, respectively. The constant a depends on the delta electron minimum and maximum energy

65

and the energy of the initial particle. Thomas' fits of this equation to existing data are reasonable.

To take into account the possible different rate of recombination in the high charge density regions of the delta electrons, Bolotnikov65 and subsequently several other authors52*53*66 used a modified Jaffe equation of the form

q ( E ) = .Q Q ~ Q S + — .1 + k / E l + k g / E

Here Qg is the fraction of charge produced along delta electron tracks which is characterized by the recombination constant kg. k is the ordinary recombination constant for the primary particle track as before. Fits to this equation that have been performed using data taken in liquid xenon and argon have been favorable.52*53*66 However, this only demonstrates an internal consistency of the model rather than a fundamental solution to the problem of electron-ion recombination.

There are several aesthetic problems associated with these delta electron models. The values extracted from the fits for Qg and Qo, for example, indicate that a significant amount of the energy of the primary ionizing particle goes into producing knock-on electrons. This may not be true. In addition, the problems with the Jaffe-Kramers theory have been "swept" into the constants Qg and kg in an ad hoc fashion. We note that according to the above delta electron theories, the resolution and charge collection should improve only at extremely high electric fields (>50kV/cm). Experimentally, high electric fields in general become a problem for ionization detectors since at some point electron multiplication

66

or gas breakdown may begin to occur. In addition, improvements in energy resolution are always accompanied by an increase in the charge collected in the delta electron model of recombination.

In order to understand the influence of the many limiting factors on the ultimate energy resolution achievable with noble gas detectors, we have built a gridded ionization chamber to be used for charge collection and energy resolution measurements with an electron source of ionization. This detector was filled with xenon. Because we wanted the detector to be highly efficient the density had to be large. In our effort to obtain high resolution in energy measurements we chose not to utilize condensed (liquid) xenon since all previous efforts to obtain Fano factor resolution in this medium have failed.49-52 We instead chose highly compressed xenon gas as our ionization medium. The conclusions of the delta electron model will be tested. The design, construction, operation and performance of this device will now be described.

3.2. Charge Collection and Energy Resolution Studies in Compressed Xenon Gas Near Its Critical Point

3.2.1. Introduction

We have developed a high pressure xenon gas ionization chamber which could be used to study Ov pp decay in 136Xe. In such a chamber, the ability to drift ionization over large distances without attenuation, stability with time, and excellent energy resolution are essential.

67

Xenon is an especially attractive candidate for use as an ionization detection medium. It has a large atomic number (Z=54) and when compressed or condensed (high density) has a high stopping power for y- radiation. The relatively low average energy required to produce an electron-ion pair (w=21.9 eV measured for xenon gas at a pressure of a few atmospheres and room temperature, 15.6 eV for condensed xenon near its triple point)44*47 and small Fano factors46 allow good energy resolution. For example, in liquid xenon the Fano factor is estimated to be F=0.041.47*48 This translates to a predicted ultimate energy resolution of 2 keV FWHM at 1 MeV. In comparison, using the measured Fano factor in gaseous xenon (FeXp = 0.13 ± 0.01)67 gives an energy resolution of 4 keV FWHM at 1 MeV. In either case, a spectrometer densely filled with xenon should have a detection efficiency similar to Nal(Tl) crystals of the same size and an energy resolution comparable in theory to that in Ge(Li) detectors (w-F=0.64 in liquid xenon, comparable to a product of 0.61 for germanium).

Progress toward realization of high resolution liquid xenon devices has been slow. The best44*52 energy resolution results, 30 and 54 keV FWHM, respectively, for the 570 and 1064 keV photo-peaks of 207Bi, fall considerably short of the above stated Fano factor goal. It appears that the resolution is limited by some process other than Poisson fluctuations.

In this section we describe results obtained with a high purity, gaseous xenon ionization detector operating in a thermodynamic regime that has not been previously studied: near the critical point where the density is comparable to that of the liquid phase (p/ ~ 3 g/cm3). The entiresystem was designed, built and operated during the past year and a half (fall 1990-spring 1992). Using xenon gas allows better control of the

68

density. If any type of recombination plays a role in limiting the energy resolution then reducing the density of the gas should decrease its effect. The conclusions of the delta electron hypothesis will be tested. We will also demonstrate that it is possible to achieve much better energy resolution in gas than in liquid. First it is useful to review the thermodynamics of high pressure xenon.

3.2.2. Thermodynamics of Compressed Xe

Figure 3.1 displays a few isotherms of xenon.68 The temperature, pressure and density are related in such a manner as to produce a large compression, without much increase in the pressure, near the critical point (57.5 atm and 16.6°C69). The critical point is indicated in the figure along with the various densities studied in this experiment. The critical density is 1.09 g/cm3. Obviously xenon is no longer an ideal gas near its critical point. Also shown is the location of some other experiments that have been performed in liquid and gaseous xenon.52*67*70

3.2.3. Apparatus and experimental procedure

The Dual Gridded Ionization Chamber

The experimental apparatus is shown schematically in Figures 3.2 and 3.3. The detector (Fig. 3.2) is designed as two back-to-back Schintelmeister gridded ionization drift chambers (with a common signal collection anode) using the guidelines set forth in Buneman et al.71 A gridded ionization chamber is basically a drift chamber with a grid of

69

wires between the cathode and anode. The grid is needed to shield the charge collector from the drifting ionization charge. This allows a position independent electron signal that has nearly the same rise time from event to event. If the grid in our ionization detector were not there the signal induced on the anode would be composed of that from both the electrons and the positive ions drifting; the height of the output pulse would therefore be a function of how close to the anode the event occurs (since the positive ions drift at much slower velocities, this effect is expected to be small). In addition, large amplifier shaping times would be required to process events that occur far from the anode (longer rise time pulses). Position independence of the signal induced in our gridded ionization chamber is absolutely necessary, if it is to have the high energy resolution required for a Ov PP decay experiment. In section 3.2.5 we will demonstrate that the grids in our detectors efficiently shield the anodes from the effects of positive ions.

All electrodes of the detector are 11.4 cm in diameter. The anode, cathode and grid are circular disks 1.0 mm thick. The field shaping rings are annuli 1.27 cm high and 0.05 mm thick. The grids are composed of a washer with a 10.16 cm diameter aperture that has an electroformed nickel m e s h 7 2 spot welded onto the side facing the cathode. If the electric field is uniform out to the edge of the mesh, this geometry provides a sensitive detection volume 10.16 cm in diameter for both detectors. The mesh has28.2 |im wire thickness with semi-rounded wires spaced 282 pm between centers (90.1 lines/in) and is 19.3 pm thick. The anode to grid spacing is 0.64 cm in both detectors. These dimensions result in a grid shielding inefficiency71 of 0.8%. All detector components, except the mesh, are constructed out of 304 stainless steel. The two detector volumes

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configured inside the chamber have different values for the cathode to grid spacing, 2.69 and 4.97 cm and a common signal collection anode.

Because a true double beta decay event in our chamber may occur anywhere in the active detector volume, we must demonstrate that charge can be drifted, with minimal loss and fluctuation, over different distances. Charge collection characteristics in xenon were studied using 207Bi internal conversion electron sources. The sources were electroplated on the center of each cathode in a less than 2 mm diameter spot with an activity of approximately 1 and 2 nC for the smaller (D l) and the bigger (D2) detector, respectively, as shown in Fig. 3.2. Drifting ionization from the 207Bi radiation produced at the cathode over two different distances within the same chamber allows us to measure directly any charge attenuation due to the presence of electronegative impurities (the ionization electrons drift past the grid and are collected on the anode). This simulates the occurrence of a PP event at two different locations within the active detector volume. A satisfactory double beta decay experiment can be done using this detector only if we can demonstrate that the charge collected over two different drift distances from a given ionizing event is roughly the same and does not change with time.

The detectors are contained in a cylindrical 304 stainless steel pressure vessel of approximately 4.5 liters which has copper gasket seals.73 This chamber was machined out of one solid billet. The top flanges of the chamber are 6.35 cm thick and 29.0 cm in diameter and are bolted together with grade 8 strength bolts, each pre-stressed to over 200 ft-lbs. These precautions were necessary to avoid any buckling of the flange under pressure which would produce a leak by allowing the gasket to separate from the knife-edge seal.73 This problem haunted us in past designs where

71

standard 2 cm thick flanges73 were utilized. The larger the area of the flange the more serious this problem became. For example, a 20 cm diameter flange 2 cm thick that we utilized in a previously developed prototype under 800 psi of pressure experienced approximately a 0.03 cm deflection in its center. This was enough to cause a leak at the knife edge. The chamber wall and bottom thicknesses in the current chamber are 1.27 and 5.08 cm, respectively.

The combination of high voltage, high pressure, ultra-high vacuum, cryogenic temperature cycling and low noise requirements severely restricted the design of the electrical feedthrus that were used. Custom made, low corona, aluminous ceramic electrical feedthroughs74 were built for this purpose. The absence of any corona discharge under high voltage is absolutely essential for low noise performance as we painfully learned in previous work. In order to achieve this, both external and internal metalization on sections of the insulating ceramic of the feedthrough were necessary to create an equipotential gap between the parts of the ceramic exposed both to air and any conducting surfaces.

These feedthroughs were welded onto the top flange of the chamber for both the electrical connections and mechanical supports for the electrodes. All electrodes had two feedthroughs for support except for the cathode and ring of D l, which only had one each. The conductors of the feedthroughs were connected to the plates at their various heights via stainless steel extensions. These were spot welded to the feedthroughs and tig-welded to the electrodes.

The detector vessel is connected with 1/2 inch, 316 stainless steel tubing to the vacuum and xenon gas purification and handling systems (Fig. 3.3). The whole system was assembled either by welds (orbital welds for

72

nearly the entire gas handling system) or high vacuum fittings and only all metal bellows valves75 are used. All components of the chamber and gas handling system were cleaned before assembly using TCE (tricloroethyline), acetone, methanol and de-ionized water baths, in that order. The result is an apparatus made of only ultra-high vacuum components. Using a Varian leak detector, a leak rate of below lO 9 torr-liter/sec (the most sensitive scale) in the vessel and gas handling system was established before the xenon was incorporated. The entire set-up rests on a spring loaded table for vibrational isolation.

System Preparation

The system was simultaneously evacuated and baked at > 300°C for three days prior to use to remove any water present. This was accomplished using heater tape and aluminum foil. The vacuum system comprises sorption pumps for roughing and a triode-ion pump to achieve less than 10*10 torr in the vessel and gas handling system. The outgassing rate in the chamber, using these precautions, was < 10-12 torr-liter/sec. This was measured using the pressure gauge in the ion pump. By closing the valve to the chamber for a given amount of time and then opening it and observing the change in pressure, we arrived at the above rate.

Approximately 1000 STP liters of research grade xenon stored in two stainless steel cylinders was then purified using two large volume, low- flow-rate, hot metal getters76 operating at > 500°C. The transferring of the gas through the purifiers was accomplished cryogenically by simply cooling the side of the system to which the gas had to be transferred. The detector was filled by cooling the vessel with a dry ice and ethanol bath (~

73

-63°C), thereby condensing the xenon into it. The vapor pressure of xenon at this transfer temperature is approximately 7.5 atm.68 The transfer pressure of the xenon (the pressure at the location of the pressure transducer (there is approximately 5 feet of stainless steel tubing between it and the chamber) was adjusted by "cracking" the valves on either sides of the system. This transfer pressure had to be above the xenon vapor pressure at the cold end but below 250 psi which was the pressure rating of the valves.47 A 170 psi transfer pressure was used.

Each pass through the purifier took approximately 2-3 hours: the flow rate was kept below 10 liter/min to maximize the efficiency of the gettering process. Once all of the xenon was inside the chamber it was then valved off and allowed to warm to room temperature prior to a run (this warming up process took approximately 15 hours because of the large thermal lag of the chamber). The working volume and density of the xenon were held fixed. The pressure, determined by the ambient temperature68, was measured using a stainless steel transducer with a piezoelectric sensor.77 The operating pressures for most of the measurements made were 62.2 ± 0.2 atm (1.4 ± 0.04 g/cm3) at 19.0 ± 0.4°C (and went to 64.6 atm at 22.0°C). This is near the critical point of xenon which is at 58 atm, 1.1 g/cm3 and 16.6°C.

Charge Collection and Signal Formation in Ionization Detectors

The signal observed on the collector plate of an ionization detector is induced by the motion of charge carriers in the space around that electrode. In our chamber, the term charge carrier applies to electrons produced by the ionization process in the xenon gas. The induced current

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and charge can be calculated using the laws of electrostatics. In the case of a gridded ionization chamber the ionization produced at the cathode drifts past the grid and is collected on the anode. Ideally the collector does not see the motion of any charge carrier until it has passed the grid.71 If an ionization event occurs between the anode and the grid (a pp event, for example), the effect of the positive ions would be detected by the anode and a slightly smaller pulse height would be seen from that event. This could worsen the energy resolution. A possible remedy for this problem is discussed at the end of Chapter 6.

The current induced on the anode due to the motion of ionization electrons drifting past the grid with drift velocity vd under the influence of the uniform electric field Ec between the grid and the anode separated by a distance d is78*79

i = Q vd/d.The time evolution of a typical signal induced on the anode and the grid is drawn in Fig. 3.4.

Electronics

Negative high voltage for the cathodes, rings and grids was supplied from a single power supply (Spellman-RHR40N60 or VK-5900) through an external resistive divider chain. A low-pass filtering network was incorporated before the cathode and a bank of capacitors was put in parallel with the resistors on the divider chain because the high voltage ripple from the supply was too high for low noise operation. A large copper shell, 1/16" thick, shielded the top of the chamber (the entire electrical feedthrough configuration) from radio frequency noise. To

75

avoid ground loops all detector electronics were grounded to a single copper bar that was bolted to the steel vessel.

The induced current on the anode resulting from the motion of ionization electrons was integrated using a charge sensitive pre-amplifier with a long fall-time constant to maximize the ratio of signal to noise (modified ORTEC Model 120: the magnitude of the feedback resistor was doubled and the first stage FET was replaced by a lower noise version, TI- 43669). It was mounted directly on the chamber and was at room temperature. The input capacitance to the first stage FET of the pre-amp in the present experiment was measured to be 93 pf.

The pre-amp pulses were shaped and amplified using a spectroscopy amplifier (Ortec Model 572) with active differentiation and two integration stages. The shaped pulses were then fed into a multi-channel analyzer (Canberra S-100) and the spectra were stored in a computer for charge collection and energy resolution measurements. The shaping time of the amplifier was set at 10 ps since our pulses out of the pre-amp had rise- times on the order of 3-5 }is. Unipolar shaping was used. The calibration of the entire readout chain was made with a high stability test pulse generator coupled with a 1 pf capacitor to the gate of the FET. The measured electronic noise was 19.5 and 18.5 keV FWHM for D1 and D2, respectively, during most of the experiment and was independent of the applied voltage. However, due to the mechanical connections used between the electrodes and the electrical feedthroughs, noise from microphonics in D1 varied at times by as much as 15 %, especially at lower xenon densities.

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In order to achieve as large a sensitive volume as possible as well as the proper collection of charge in these two detectors the electric field between the cathode and grid must be uniform to as large a radius as possible. This will ensure that all secondary electrons drift parallel to the axis and at constant velocity. To diminish edge effects due to the finite size of the electrodes, field shaping rings were configured between the cathode and grid in each detector (see Fig. 3.2 and 3.5). The proper size, shape, separation and voltages for these rings as well as for the other electrodes was investigated using a Poisson electric field calculation program.80 (see Fig. 3.5).

We found that 1.27 cm high cylinders spaced ~ 1.1 cm apart and with voltages stepped down linearly from cathode to grid minimized the divergence of the electric field lines near the edge of the sensitive volume (between the cathode and grid and within the diameter of the mesh). D1 required only one ring while D2 required two (we neglect the non­uniformity of the electric field between the anode and the grid, since there is only 6mm between them). Figure 3.5 shows the results of an electric field calculation performed on D2 (4.97 cm between cathode and grid, 0.64 cm between grid and anode). The voltages applied to each electrode are indicated. We see the field is approximately uniform out to the edge of the sensitive volume. This is especially important when utilizing this detector in a double beta decay experiment since a PP event can occur anywhere in the sensitive volume. Uniformity of the electric field at the edges of the detector minimizes charge losses due to events that may occur near there. This is obviously important for high energy resolution at the PP decay

Uniformity of the Electric Field

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endpoint energy. The situation of incomplete charge collection near the edges of the fiducial volume will be discussed at the end of Chapter 6.

We emphasize that the same electronics were used for D l and D2 (which were configured within the same chamber with a common signal collection anode) and measurements in the different detectors were performed, by simply "turning on" either detector (applying negative high voltage to the cathode of either detector). At the relatively low applied voltages used in this experiment both detectors were operating in the direct ionization mode, without amplification.

The Source

207Bi is an electron capture source decaying to 2°7Pb with a half-life of 30 yr.81 The dominant y-ray transitions are at energies of 569.6 and1063.4 keV. There is also a weaker line at 1770.2 keV. However, in relatively small detector volumes, the lines in the pulse height spectra are mostly due to (a) K-shell internal conversion electrons at energies of 481.6 and 975.6 keV and (b) the summing o f these electrons with the K- fluorescence x-rays or Auger electrons accompanying this nuclear decay process.

From Monte Carlo studies in xenon at the densities we are considering, a 1 MeV electron is expected to have an average range of a few millimeters and is thus completely absorbed in the region between the cathode and the grid (the active or sensitive volume) in either detector. Figure 3.6 shows a typical trajectory as calculated via an electron trajectory Monte Carlo for the 976 keV electron originating from the center of the cathode in xenon at a density of 1.4 g/cm3. The projected

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range along the direction of the electric field of this track is approximately 2 mm. The details of the simulation will be discussed in Chapter 5.

A 136Xe double beta decay event on average produces two 1250 keV electrons. 2°7Bi was chosen for our ionization studies in xenon since it produces electrons of a similar energy.

3.2.4. Data and Analysis

Pulse Height Spectra, Energy Calibration and Resolution

Typical pulse height spectra in high pressure (62 atm) gaseous xenon at a density of 1.40 ± 0.04 g/cm3 are shown in Figures 3.7 and 3.8 for the two detectors. The running times were 20 and 10 hours, for D1 and D2, respectively, because of their differing source strengths. The electronic pulser peak is seen at the right, far away from the two pairs of 207Bi lines. The peak seen on the left of each pair corresponds to the K-conversion electron of 207Bi at energies of 482 and 976 keV, respectively. Those on the right result from either the detection of the y-ray from the full nuclear transition or, from the summing within the sensitive region of the detector of the energy from the conversion electron and the Pb x-ray or Auger electron produced by the filling of the K-shell vacancy. D2 has a higher y- ray efficiency than D1 because it has twice the active detector volume. The peaks corresponding to the full nuclear transition are asymmetrical with a low energy tail. This is due to the detection of the L-conversion electron (which has a reduced intensity81) and/or the incomplete charge collection from a y-event.

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In order to precisely determine the peak position and energy resolution for a given line a least squares fitting routine82 was applied that took into consideration the skewed shape of the full nuclear transition lines at 570 and 1063 keV. Only fits with 0.95 < x 2/v < 1 . 1 were accepted. Figure 3.9 shows a typical fit to the data for the 976 and 1063 keV lines. The residual between the fit and the spectrum (shown at the bottom) is small and corresponds to a reduced chi-squared value of 1.02.

We chose the 976 keV K-conversion electron line for most of our charge collection (pulse height) and energy resolution studies. Calibration of the energy deposited in the xenon is accomplished using the known energies of the lines in 207Bi and the corresponding peak positions in the pulse height spectra. There is approximately 0.59 keV/ch in Figs. 3.8 and 3.9. Figure 3.10 shows the relation between the pulse height and the energy of the line for the spectrum in D l. The linearity is excellent. There is less than 1% non-linearity present.

Presently the measured energy resolution of the 976 keV line for a given detector is obtained by subtracting in quadrature the contribution of the electronic noise from the width of the peak in the spectrum. Other factors may contribute to the broadening of the pulse heights and will be discussed later. A major goal of this work was to measure the fluctuation in collected charge due only to the fluctuation in the number of electrons liberated from the ionization process (Fano factor resolution).

Similar spectra were measured in a significantly different detector. Fig. 3.11 we show a 207Bi spectrum taken in 0.9 g/cm3 (57 atm) xenon in a small prototype that we developed previously. The grid-anode and grid- cathode spacings were 0.5 and 1.3 cm, respectively. The cathode and grid were disks 6.4 cm in diameter. The anode was a disk 2.5 cm in diameter.

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The grid had an aperture of 2.0 cm over which 63.5 pm wires spaced 635 pm apart were spot welded. Because the grid was made with wires of circular cross-section, a field ratio of 2.0 was sufficient for this detector geometry71 (see section 3.2.5). The applied electric field between the cathode and the grid for this spectrum in Fig. 3.11 was 3.0 kV/cm. The electrical noise, obtained from the width of the pulser peak was approximately 6 keV FWHM as a result of the low input capacitance of this system (approximately 20 pf). The electronic noise subtracted energy resolution obtained for the 9?6 keV peak of 207Bi was 16.6 ± 1 . 0 keV (1.7%) FWHM in this small prototype.

3.2.5. Results

Charge Collection and Energy Resolution

The presence of the grid is extremely helpful in shielding the anode from the unwanted positive ion signal. However, drifting electrons (or, equivalently, electric field lines) must not be trapped by the grid as they pass through it. The transparency of the grid to the drifting ionization electrons is calculated using Buneman's criteria71, for the geometries used in our chamber, to be near 100% when the collection electric field, Ec, between the anode and grid is at least 1.92 times stronger than the drift field, Ed, between the grid and the cathode for both detectors in the chamber. This minimizes the number of electric field lines that originate from the cathode and terminate on the grid instead of the anode. Since the ionization electrons for the most part drift along the electric field lines toward the anode with little or no diffusion83*84 this condition insures that

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few electrons are trapped by the grid. However, Buneman's formula applies to grids of wires of circular cross-sections (as was the case for the grid of our small prototype described at the end of section 3.2.4), not to the meshes used in this experiment.

In order to determine the correct field ratio to be used we first measured the saturation characteristics of the pulse height and energy resolution against the ratio Ec/Ed for the two detectors keeping Ed fixed at1.3 kV/cm. Figure 3.12 shows these curves for the two detectors measured for 62.3 atm (916psi) xenon at 19.2°C using the 976 keV peak. Above field ratios of roughly 2.4, the charge collection (Fig. 3.12a) significantly increased in D2 but not D l. The different behavior of the charge collection with field ratio in D2 was caused by a problem with the uniformity of the electric field in that detector and was physically uninteresting; the errors in the field ratio near the grid in D2 were difficult to estimate and may have been in fact much larger than shown. This problem as well as the comparison of the performance of the two detectors with field ratio will be discussed in section 3.2.6. In D l the collected charge had saturated to within 1% at a field ratio of 3.4.

Figures 3.12b displays the improvement in FWHM energy resolution (electronic noise subtracted) with increasing field ratio for the two detectors. We see that although there was only on the order of a 1% increase in charge collection in D l over the range of field ratios studied, there was a significant improvement in energy resolution. However, above a field ratio of 3.4 there was little improvement in the energy resolution (Fig. 3.12b). The error bars seen represent statistical uncertainties in the fitting routine utilized and systematic uncertainties in the applied electric field ratios in D l. On the basis of the above observations for D l (ignoring

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the performance of D2: see section 3.2.6) we chose an operating field ratio of 3.5.

Figure 3.13a displays the dependence of the pulse height of the 976 keV peak on Ed for the two detectors using a field ratio of 3.5. The ordinate is the ratio of the collected charge to the net charge Qo expected using 21.9 eV as the w-value in gaseous xenon and an absolute charge calibration that was performed. The value of Q/Qo is approximately 98 ± 4 % at Ed=1.5 kV/cm and is consistent with complete charge collection. The quoted uncertainty originates from an overall 4% uncertainty in the absolute charge calibration (pre-amp gain), not shown in the figures. This latter measurement will be discussed later in this subsection.

Figure 3.13b shows the FWHM energy resolution (electronic noise subtracted) vs. Ed for the two detectors. We see that the energy resolution improves with increasing field in approximately the same manner for detectors D1 and D2. At about 1.3 kV/cm the energy resolution has a value of 2.0 and 2.1 ± 0.1% FWHM in D1 and D2, respectively, which corresponds to 19.5 and 20.5 ±1 . 0 keV FWHM for the 976 keV peak at 62 atm (1.4 g/cm3). These values are seen to improve only slightly at higher electric fields. The errors quoted are due to statistical uncertainties in the fitting routine and systematic uncertainties in the applied electric fields (causing possibly different operating conditions for the two detectors). Near Ed=1.3 kV/cm these latter errors are insignificant since the charge collected does not vaiy much with electric field at that point.

Figure 3.14 shows the relation between the intrinsic energy resolution of the K-conversion electron peaks and their energy. The linearity and the fact that the line passes through the origin indicates that the energy resolution scales as E*1/2 to other energies. For example, the

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extrapolated energy resolution at 2480 keV, the endpoint of 136Xe double beta decay, would be 2%-(976/2480)1/2=1.2%.

The Absolute Charge Calibration

By calibrating the charge sensitivity of the pre-amplifier/amplifier combination, one may determine the energy required to create a free electron-ion pair, w, in gaseous xenon near its critical point. Using the known capacitance between the grid and the anode, we pulsed the grid with a known pulse height. The measured grid to anode capacitance in either detector was 27.1 ± 0.8 pf. We pulsed the grid with 600 ± 10 jiV pulses of ~5 |is rise times (approximately the rise time of detector signals from 207Bi). This resulted in 1.63 ±. 0.07 x 10-14 C (1.02 ± 0.04 x 105 electrons) of charge being dumped onto the grid, corresponding to an absolute charge calibration of 25.9 electrons/ch.

By then measuring at what channel the 975.6 keV peak appears in the 207Bi pulse height spectrum for Ed=1.5 kV/cm we then know how much charge Q is being dumped on the anode from that internal conversion electron line at that applied drift electric field (where the collected charge has saturated; see Fig.3.13a). Comparing this with the total charge that is supposed to be liberated from a 975.6 keV ionizing electron: Qo = 975.6keV/21.9eV = 4.45 x 104 electrons (using the measured average energy expended to create on electron-ion pair, 21.9 eV in low pressure gaseous xenon) we obtain Q/Qo= 98 ± 4%. The 4% error is mostly due to the uncertainty in the pre-amp gain (originating from the uncertainty in the capacitance between the grid and the anode). Our results are consistent with complete charge collection at Ed=1.5 kV/cm, assuming that w for

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compressed gaseous xenon near its critical point is essentially the same as its low pressure value, 21.9 eV.

Stability

Measurements were conducted over a 7 month period using Dl as the monitor. In this time there were many successive purifications of the xenon and exposures of the detector to atmosphere (there were no mechanical changes made on D l). During the first 1.5 months 7 passes through the purifier were performed and the detector was exposed to atmosphere 4 times. During the remaining 5.5 months the detector was not exposed to air and 5 purifications were done. The longest running time without purifying was approximately 5 months. In this entire 7 month period no change in collected charge was observed to within 0.1% (gain shift corrected using the position of the pulser peak centroid). For the energy resolution the variation was less than 1 keV. These changes are consistent with the overall statistical uncertainties of 0.1% in the position of the centroid and 1.0 keV in the FWHM of the 976 keV peak as extracted by the fitting routine due to the statistical uncertainties of the data. These facts indicate a very clean chamber with low residual outgassing rate and an efficient and reliable xenon purification system. This stability is obviously desirable for double beta decay experiments which routinely must remain in their low background environments for months or years at a time. Not having to repurify the gas during the running time is highly desirable.

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3.2.6. Discussion

Comparisons Between the Two Detectors: Problems with Some Electrical Feedthroughs

The collected charge in the two detectors (with 4.97 and 2.69 cm drift distances, respectively) as a function of the field ratio, Ec/Ed is presented in Figure 3.12a. We see that after a field ratio of 3.5 was imposed the two detectors collected essentially the same amount of charge (for all values of Ed) within the quoted errors. We believe the difference in charge collection between the two detectors at lower field ratios is due to field shape non-uniformities in D2, especially near its grid. This was a result of the observed malfunctioning of an electrical feedthrough connected to the field shaping ring nearest to the grid in D2.

This ring was subsequently grounded during the data taking instead of being at the required voltage of nearly 5 kV. Under these operating conditions, from Monte Carlo studies we expect the electric field lines near the grid to diverge considerably. Thus, the field ratio would have to be raised in D2 to compensate. The errors in the value of the field ratio seen by drifting electrons in D2 just before entering the grid-anode (collection) region are obviously hard to estimate; they are definitely larger than those in D l.

Eventually one of the feedthroughs connected to the other ring in D2 also became faulty, which places it under suspicion as also contributing to the problem of charge collection in D2 (even before it blew); it may not have been holding voltage well during the measurements. Once this additional ring was grounded we were only able to collect 65 % of the total

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charge rendering D2 useless. This is consistent with the hypothesis that it was the non-uniformity of the electric field that produced the effect seen in Figure 3.12a. Replacing the faulty feedthroughs in D2 was not necessary since we already had taken the required charge collection and energy resolution data for a proper comparison with D l.

The reason for the failure of the electrical feedthroughs was probably in their poor design.74 Unlike all other designs that we used with great success in the past, the custom-made electrical feedthroughs used in this experiment used un-glazed aluminous ceramic as the insulator. The un-glazed insulators absorbed any moisture in the air, especially during the gas transferring process when the chamber and the feedthroughs were often below 0°C and during the summer when the relative humidity in the room was > 70%. Once they became wet from condensation it usually took several days for the ceramic to dry out enough for operation. The advantage of a glazed insulator is the speed and extent to which it dries. When moist, the insulators were semi-conducting so that the anode, in particular, was no longer floating (which is a requirement for the proper operation of our detector). The resistance of the insulators was normally > 1012 ohms when completely dry and < 108 ohms when wet.

When the insulator of the feedthrough connected to the anode was moist or semi-conducting, the electronic noise was also much worse due to a small leakage current that the pre-amp picks up. We also found that applying high voltage to a feedthrough whose insulator is wet may damage it (i.e. bum a track into it), causing it to fail under high voltage or have a lower resistance to ground. We believe this is the reason for the failure of some of the electrical feedthroughs and what limited the operating voltages in D l and D2.

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In Figure 3.12b we plotted the energy resolution (electronic noise subtracted) in the two detectors vs. Ec/Ed. Above a field ratio of 2.4 the energy resolution improves roughly in the same manner for the two detectors. The charge collected in D1 only increased by 1% above field ratios of 2.4 (Fig. 3.12a). We assume that the same would be seen in D2 if it had the proper field ratios (i.e. if all its electrodes were at their required voltages). The values extracted at Ed=1.3 kV/cm for the 976 keV peak are 2.0 and 2.1 ± 0.1 % FWHM for D1 and D2 respectively.

Attachment of Drifting Electrons to Electronegative Impurities

Drifting ionization electrons can attach to electronegative contaminants, thus degrading the amplitude of the signals in our chamber. From the data taken with the detectors of two different drift distances, we w ill now estimate to what extent ionization electron attachment to electronegative impurities is occurring in our chamber filled with compressed xenon gas near its critical point. The loss of electrons in a swarm drifting in a constant electric field across distance x is described by the expression85:

— = e-l A - . n 0

where n is the number of the original no ionization electrons left after drifting a distance x. Xa is the attenuation length of electrons due to the attachment to electronegative impurities. X,a can be conveniently expressed

in terms of the electron lifetime due to the presence of electronegative impurites85:

x = — ,vd

where Vd is the average drift velocity of the swarm of electrons.

Drift VelocityThe drift velocity of the ionization electrons was measured by

directly observing the rise time of the output pulses from the charge sensitive pre-amplifier as displayed on a digital storage oscilloscope. From a measurement of the slope at the mid height of the pulse (where all liberated charge is in motion and located between the grid and the anode), the drift velocity as a function of the electric field between the grid and the anode was determined. The relation of Ramo78 was used yielding: i = Q-vd/d, where i is the induced current, Q is the total charge in motion, vd is the drift velocity, and d is the grid to anode distance, i = dq/dt on average can be approximated by CAV/At, where AV and At are measured from appropriate points on the pre-amp signal and C is the feedback capacitance of the preamp. Q is equal to CVm, where Vm is the maximum height of the pulse. Substituting into the expression for j and inverting, we arrive at the following expression for the measured average drift velocity of the drifting ionization electrons (from pulse to pulse):

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A typical pulse at a drift field of 1.3 kV/cm is displayed in Figure 3.15. AV and At are indicated. Compare with Fig. 3.4. The measured results for the drift velocity are plotted in Fig. 3.16 as a function of the electric field between the grid and the anode in Dl in compressed xenon near the critical point. This data was taken at a xenon density of 1.4 g/cc, at a temperature of 19.0 deg. C and at xenon pressure of 62 atm (near the critical point). Saturation of the drift velocity at about 1.5 kV/cm is clearly evident in this figure with v = 1.2 ± 0.1 x 10^cm/sec at that point. The values for drift velocities above 1.8 kV/cm were taken from drift velocity data measured in the small prototype xenon detector at 0.9 g/cc mentioned in section 3.2.4.

Also shown in Fig. 3.16 are drift velocity data taken for low pressure gaseous xenon at room temperature and for liquid xenon near the triple point.8*2’87 The drift velocities in liquid xenon are a factor of 3-4 times larger than in gas. We see that xenon near its critical point, although having a density similar to a liquid has electron transport properties nearer to a low pressure gas. These slow drift velocities are not a problem either for our measurements or for a double beta decay experiment using this detector since the expected count rates are so low. In Fig. 3.17 the saturation drift velocities are plotted as a function of xenon density in this experiment; the drift velocity did not show any systematic variation over the range of densities 0.25 < p < 1.4 g/cc.

The values obtained for the drift velocities were verified using signals generated by cosmic ray muons. The rise time of the muon signal is a measure of the time taken by the entire track of the ionization electrons (created by a vertical muon traversing the chamber) to drift to the anode. Small sodium iodide detectors were placed on top and underneath the

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xenon detector. Coincidence signals from these detectors provided the triggers for vertical muons. The values obtained in this way for the electron drift velocities were consistent with those measured using the 976 keV electrons.

Impurity ConcentrationIn order to relate the electron lifetime to impurity concentration we

use the expression:

t = m 7 ’

where ki (which will be derived below) is the reaction rate for electron capture to impurity i and p is the molecular density of that impurity.88,89

Among all possible impurities, oxygen is the most common one found in drift gases. It is also the most well understood as far as attachment to electrons is concerned. Its electron affinity is 0.43 eV. It is present in commercial gas supplies and may also be produced by outgassing from the chamber materials. For these reasons the electronegative impurity level in a drift chamber is often quoted in terms of an "oxygen equivalent" value, assuming any attenuation of the electronic signal due to attachment to electronegative impurites is caused by oxygen alone.

The reaction for electron attachment to oxygen is90*91

(1) O2 + e- -> O2'* (reaction rate ki)

followed by the two competing processes:

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(2) 02'* + M -* O2 + M + e- rate: k2

(3) 02'* + M -» 02' + M* rate: K4

M denotes the buffer gas molecule (in our case, xenon). The relative probabilities of the two processes occurring, and hence the attenuation length of the drifting electrons X,a depends strongly on the nature of the buffer gas. Electrons will be "quenched" if process (3) takes place and M* undergoes a transition to the ground state through lattice vibrations or heat dissipation (phonons generated). Complex molecules with dense vibrational energy levels favor this process. Noble gases which are fairly inert to electron attachment favor process (2). Hydrogen, water, methanol and nitrogen do not have a sizable attachment to electrons, but can act as buffer molecules that substantially enhance the cross section for process (3). The result of this two-step mechanism for attachment is that given the same level o f impurity contamination, the attenuation length is inversely proportional to the square of the gas pressure.

The effective reaction rate is given by90*91

1 k2 + K4rM ]_ 1 | 1keff k ^ M ] kj Km[M] ’

where [M ] is the molecular density of the buffer gas ki=4.8 x 10-11 cm3/sec, K m = 0 .0 8 5 x 10*30cm6/sec at room temperature59*60 and M is gaseous xenon. Note that since keff [M], p oc [M], [M] oc p, the gas pressure and X «= x 1/kp, this means X <*= l/P^ as mentioned above. In this work [M ]= 1.4 g/cm3 (mole/131gM6.023xl023/mole) = 6.4xl021 Xe atoms/cm3. This leads to an effective attachment rate to oxygen of keff =

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4.4 x lO-11 cm2/sec. Since x=l/kip and oxygen is the impurity, [O2 ] = 1/kiX. But x=A/vd implies [O 2 ] = vd/kiX, where ki=keff and the saturation drift velocity vd=l x 1 (Pcm/sec will be used.

The electron attenuation length X,, due to the presence of electronegative impurities, can be obtained by measuring the difference in collected charge between two detectors with substantially different drift distances. In our case the two different distances are xi=2.69cm and X 2=4.97 cm (we assume that the ionization is deposited in a point at the cathode). If ni and n2 are the number of ionization electrons left from the 976 keV electron radiation after drifting over distances x i and X2 respectively then ni = noe_xl/X and n2=noe~x2/X . We then form D = (n i- n2)/n i = the fractional difference in charge collected between the two detectors, from which the result

1 _ *1 ~ x 2

A i ( l - D )

simply follows.If there were ionization electrons lost to scavenging by

electronegative impurities, then there would be a difference in charge collected from detectors with different drift distances in this experiment. At a field ratio of 3.6 we saw that there was less than 1% difference in the collected charge and energy resolution measured in the two detectors (Fig. 3.12a) at 1.3 kV/cm. This is well within the quoted errors. The same conclusion can be reached by inspecting Figs. 3.13a and b: for a field ratio of 3.5 the charge collection and energy resolution are the same within statistical uncertainties (see section 3.2.5) at 1.3 kV/cm. At 1.5 kV/cm the

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difference in the collected charge in the two detectors was less than 0.1% (±0.1%). The difference in energy resolution was less than 0.4 keV. These values are well within the quoted errors. We thus conclude there is no statistically significant evidence of attachment to electronegative impurities in our experiment.

If we assume < 0.1 % difference in collected charge between the two detectors we can arrive at a limit for the electron drift attenuation length. Using the derived relation for X with xi=2.69cm, X2=4.97cm and D < 0.001 gives X, > 2.3 m. From this we can get a limit for the oxygen equivalent impurity level [O2 ] = Vd/kX < 1 0 0 parts O2 per trillion xenon atoms (100 ppt oxygen equivalent).

Factors That May Degrade the Energy Resolution

In order to determine the spread in energy of the 976 keV peak due only to the fluctuation in ionization liberated we must estimate the contribution of other sources to the measured widths and subtract them out in quadrature as we did for the electronic noise. The net result is defined as the intrinsic energy resolution of the detector.

(a) Electronic NoiseAs discussed in section 3.2.3, the measured noise of the electronics

was 19.5 and 18.5 keV for D l and D2, respectively, at room temperature and was obtained from the spectrum of test signals from the pulser (the intrinsic resolution of the pulser alone, with zero input capacitance was less than 2 keV). It was by far the largest contribution to the broadening in energy of the measured pulse height peaks. These numbers could be

94

reduced by cooling the first stage FET and by reducing the capacitive load of the preamplifier. This latter task could be accomplished simply by utilizing physically smaller, lower capacitance electrical feedthroughs connected to the collector plate and by reducing the size of the anode plate. The resulting electronic noise subtracted width of the 976 keV K- conversion electron peak in 207Bi was 19.5 ±1. 0 keV FWHM in 62 atm of xenon (small detector, D l) at 1.3 kV/cm. Other factors that might contribute to this residual spread in energy were examined.

(b) The Source EffectThe conversion electron lines from the 207Bi source were examined

using a cooled Si(Li) electron detector. The inherent width of the peaks from the source (including any backscattering in the source material) was less than 1 keV, a negligible effect for our xenon detector.

(c) ImpuritiesThis effect of impurity attachment on the energy resolution should

be relatively unimportant for measurements in a given detector (Dl or D2) since all of the charge is deposited more or less at one spot at the xenon densities we are considering. So although impurity attachment will affect absolute charge collection, the variation in the charge collected may be small for a given drift distance. That is, from decay to decay all of the charge deposited drifts about the same length for a given drift distance so the fluctuation in that detector should be low (for lower densities and thus longer electron track lengths, this may not be true). If attachment to impurites is present, charge collection and its fluctuation would depend on the drift distance, and so, would be different in Dl than in D2.

95

We saw no evidence of attachment to electronegative impurities. As indicated in Figs. 3.12b and 3.13b, for drift electric field strengths > 1.3 kV/cm and field ratios of 2.4 the intrinsic energy resolution of the 976 keV peak differed by less than 1 keV between the two detectors of different drift distances. This is consistent with an overall uncertainty in the energy resolution of 1.0 keV based on statistical errors in the fitting routine as mentioned before.

A double beta decay event may deposit its charge anywhere in the sensitive volume (between the cathode and the grid). If a significant amount of electronegative impurities were present, the further away from the anode a pp event occurs the more signal attenuation would be present. Obviously this could be devastating to the energy resolution at the endpoint of PP decay. In this experiment we simulated this variation in the location of an ionizing event by having the ionization created drift over two different distances within the same chamber. The results were extremely satisfactory because within uncertainties we saw no difference.

(d) Rise Time or Ballistic Deficit EffectThe fluctuation in the length of the trajectory of primary electrons

within the xenon between the cathode and the grid causes a variation in rise time of individual pulses from the preamplifier. This effect is determined by the drift time of the ionization electrons and the shaping constants of the amplifier. We experimented with several spectroscopy amplifiers and ran with shaping times up to 25 ps. We observed that for shaping times greater than 10 ps there was no detectable change in the energy resolution. At a xenon density of 1.4 g/cm3 the rise times measured were 3-5 ps in duration. See Figure 3.15.

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(e) Electron Trapping by the GridThe effect on the energy resolution of the trapping of drifting

ionization electrons on the grid for the field ratio utilized was also negligible in D1 and D2 as we saw from Figure 3.12b. For a fixed drift electric field there was no significant improvement in energy resolution in either detector once we were at a field ratio of 3.4. This field ratio is nearly twice as large as the Buneman criteria71 predicts.

(f) RecombinationMaintaining the field ratio constant at a value of 3.5 keeps the grid

losses small and constant. By varying the drift electric field we can then examine the effects on the resolution solely due to recombination effects. As seen in Figure 3.13b there may be a slight improvement in energy resolution at higher drift electric fields. This indicates that recombination might be limiting the obtainable energy resolution. We tried increasing Ed to values higher than 1.6 kV/cm but this only seemed to increase the effect o f microphonics in our apparatus resulting in more electronic noise, and thus, causing more uncertainty in the noise subtracted energy resolution measurements.

At higher electric fields some of the electrical feedthroughs also began to show signs of corona breakdown which appeared as large negative spikes on the pre-amp signal. This was probably due to poorly designed parameters of the electrical feedthroughs, such as the presence of burrs and points on the conductors. The presence of a leakage current on the high voltage feedthrough caused by their decreased resistance (see section 3.2.6) may also be a possible origin of this corona effect. Low noise performance is impossible with the presence of corona discharge. However, in the

97

smaller prototype (end of section 3.2.4) we were able to reach electric fields greater than 3.0 kV/cm without significant increase in noise. We observed there was only a slight improvement in energy resolution above1.3 kV/cm.

An alternative approach to understanding the effects of recombination on the energy resolution is to lower the density of the xenon. If electron-ion recombination effects were playing a role in limiting the energy resolution, these effects should diminish as the density is lowered and the energy resolution should improve. The density was gradually lowered from 1.40 to 0.25 g/cm3 and the intrinsic resolution, charge collection and drift velocities were measured at a field ratio of 3.5 and a drift field of 1.3 kV/cm. The results are presented in Figures 3.18ab and 3.19ab for D l. Both the 976 keV K-conversion electron and the 570 keV full transition peaks were studied.

From Fig. 3.18a we see that at a density of 0.49 g/cm3 the intrinsic energy resolution has improved to 1.2 ± 0.1 % FWHM for the 976 keV conversion electron peak. However, there was no indication of an increase in collected charge as seen in Fig. 3.18b. The error bars seen are due to the statistical errors in the fits used to extract the charge collection and energy resolution measurements. For the 570 keV peak the energy resolution also improved from 2.8 % at 1.4 g/cm3 to 1.8 % at 0.49 g/cm3 (Fig. 3.19a). There was also no significant increase in the collected charge from this line as seen in Fig. 3.19b (the larger spread in the collected charge versus density for this 570 keV line may have been due to larger uncertainties in the fit since the background component that this peak is sitting on is large; see Fig. 3.7,3.8 and 3.20)

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At some of the lower densities the electronic noise was as large as22.2 keV. This was most likely due to an increase in microphonics because of a decrease in the mechanical damping of electrode vibrations. The least squares fits to the data were still good, so we had no difficulty unfolding the electronic noise from the measured width of the peaks under study.

Further density reduction below 0.49 g/cm3 produced no improvements in the energy resolution. We believe this is due to the fact that as the density is reduced the longer electron tracks produce larger rise time effects. In addition the low energy tails on the full energy peaks at 1063 and 570 keV due to incomplete charge collection become larger. These two properties begin to have an effect on the measured energy resolution of the 976 and 570 keV peaks at densities below 0.5 g/cm3.

If recombination were diminishing with decreasing density we might expect an improvement in energy resolution to be accompanied by a measurable increase in the amount of charge liberated from the ionization process. This does not appear to be the case as is shown in Figs. 3.18b and 3.19b. Clearly the intrinsic resolution in our chamber is not solely determined by simple Poisson statistics in these pictures. Perhaps some other mechanism or systematic error is canceling this expected enhancement in charge collection. Evidence for ballistic deficit was again investigated at these lower xenon densities. At 0.49 g/cm3 the rise times were again roughly 3-5 p.s. If a rise time or ballistic deficit effect were playing a role we would see a low energy asymmetry in the energy peaks92 which does not appear in the pulse height spectrum in Figure 3.20 (0.49 g/cc). A shaping time of 10 p.s would produce only a ballistic deficit of 1% in pulse height92, not enough to significantly effect the charge collection or the energy resolution.

99

Any gain shift as the density was lowered was monitored by the position of the pulser peak in the spectrum. The largest gain shift was less than 1%. There also was no significant change (less than 1%) in the zero offset of the energy calibration of the ADC with xenon density. The error in the fit for these spectra with larger pulser widths (at lower densities) was not significantly different from the values obtained at higher xenon densities.

We thus conclude that the resolution improves to some extent as the density is lowered without a systematic increase in the amount of charge collected (recall we encountered a similar situation in Fig. 3.12: the energy resolution in D l improved with field ratio without a significant increase in collected charge for a fixed Ed). The average number of electron-ion pairs created and collected at the anode remains the same over the densities studied. However, because of the longer track lengths at lower densities, the average distance between each pair along an ionization track has increased. Could this possibly reduce the fluctuations in electron-ion recombination without affecting the average amount of recombination? This seems to contradict intuition.

This absence of an increase in charge collection with lower xenon pressures further demonstrates that attachment to electronegative impurities is not significant in our detector. If scavenging did occur it would diminish as the density was lowered and the amount of charge collected from a given ionization process would increase. This characteristic is not seen.

The fact that we saw no increase in collected charge as we lowered the xenon density also implies that the w value for high pressure gaseous xenon remains constant with density (21.9 eV). At 0.5 g/cm3 the energy

100

resolution of the 976 keV peak (1.2%) is near to the Poisson limit but still a factor of 3 worse than Fano factor predictions (see section 3.1.1).

3.2.7. Conclusions

We have demonstrated the ability to drift ionization electrons over large distances in highly compressed xenon at room temperature. The intrinsic energy resolution of the 976 keV K-conversion electron peak of 207Bi was measured to be 20 keV FWHM in 1.4 g/cm3 (62 atm) of xenon, independent of drift distance. No change in charge collection or energy resolution could be detected during the entire 7 month running period. These results show that the inner chamber construction and the purification system used were more than adequate to eliminate the problem of attachment to electronegative impurities which has plagued xenon detectors of the past. In addition, the chosen grid design, electric field assignments, geometries and pulse shaping parameters made most charge loss mechanisms and width broadening effects negligible.

An additional effect was observed as the density of the xenon was lowered. We found that reducing the density of the xenon from 1.4 to 0.5 g/cm3 improved the energy resolution without an increase in the average charge collected. This fact contradicts both intuition and previous assumptions of the effects of recombination. It is especially contrary to the conclusions of the "delta electron" mechanism presented in the beginning of this chapter. If the resolution improves in this model it must be accompanied by an increase in collected charge. However, this result does indicate that the w-value for xenon gas remains constant at 21.9 eV.

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The best obtained intrinsic energy resolution of the 976 keV K- conversion electron peak of 207Bi was 11.7 ± 1.0 keV (1.2%) FWHM in xenon gas at a pressure of 52 atm, density of 0.49 g/cm3, field ratio of 3.5 and drift electric field of 1.3 kV/cm. For the 570 keV full transition peak the corresponding number was 10.3 ± 0.6 keV (1.8 %) FWHM.

Further reduction of the density below 0.49 g/cm3 was possible but other problems associated with longer track lengths, such as detector efficiency for y-rays and rise time effects were expected to have a larger impact on the charge collection process. The above results are near to the Poisson statistical limit (F=l) but still a factor of 3 worse than the predicted Fano limit (see section 3.1) but are the best reported thus far in xenon, by over a factor of 4. The effect that is preventing this experiment from attaining Fano factor resolution remains a mystery.

For any future tests of such a detector, the electric fields should be raised to values well above 2.0 kV/cm as another check of the influence of recombination effects on the energy resolution. Furthermore, the noise of the electronics should be significantly lowered from its nominal values of 18.5-22.2 keV in this experiment in order to further reduce uncertainties in the measured energy resolution.

Obviously detectors having the characteristics reported in this chapter will be of importance in many different fields. Our data suggests that xenon near its critical point will be an important addition to the presently available high-resolution radiation detector media. However, our studies have mainly been part of a program directed toward a search for the Ov pp decay of 136Xe.

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Relevance to Detection of Ov p p Decay in l^ X e

We have studied the charge collection process in a high pressure xenon ionization detector using a 207Bi source deposited on the cathode. This source was chosen because the conversion electrons that are ejected at the cathode have energies of 482 and 976 keV. This is approximately the energy region of interest for electrons from a Ov PP event in xenon (where the average energy of each beta particle is approximately 1250 keV).

A PP event in xenon can occur anywhere within the sensitive region of the detector (between the cathode and grid). This was the motivation for having two different drift distances within the same gas volume. We could alternately drift the ionization created over two different distances before it is collected. It gave us an idea of how dependent the charge collection process is on the location of a given event in the detector.

We have demonstrated that under certain detector operating conditions, the amount of charge collected from a 1 MeV electron event in dense xenon does not depend on the distance it drifts before collection (within uncertainties). Ionization electrons are not lost to scavenging by electronegative impurities or any other position dependent effects. Therefore, the signal produced does not depend on where the event occurs in the sensitive region of the detector.

We have also obtained high energy resolution and stability with time. These are necessary requirements for our xenon detector to be useful as a detector for PP decay in xenon. A satisfactory double beta decay experiment using such a detector requires that the charge collected over various drift distances from a given ionizing event is identical, does not change with time and has a low statistical uncertainty. The next two

chapters discuss the two missing ingredients, low background and high efficiency.

103

P(ATM)

Fig. 3.1. Some isotherms of xenon and the location of some other xenon experiments.

H AN DLIN GANOVAC U UMSYSTEMS

.E L E C T R IC A L ' r FEEDTHO UOH

a l lELECTRODES SUSPENDED BY FEEOTHROUGH CONNECTIONS

U S

Fig. 3.2. Schematic o f the dual-gridded ionization chamber developed for the high pressure xenon gas experiments. The two drift distances are 2.7 and 5.0 cm.

MANUALVoLVES

/ X

PRESSURE TRANSDUCER

f f i T C JGETTER ^ G ETTER

XENONCYLINDER

J

TO SORPTION PUMP

TO ION PUMP

-PRESSURETRANSDUCER

CHAMBER

Fig. 3.3. Schematic of the xenon gas handling and purification system developed.

C G A(0)

Fig. 3.4. a) the drifting of ionization from in between the cathode and grid (C and G respectively at negative high voltage) to the anode (A at ground), b) the time evolution of the electron current and charge induced on the anode and c) on the grid. Also shown is the small effect of the positive ion motion induced on the grid and the effect of a non-point-like deposition of charge on the signal induced on the anode.

cathode

ring 2

ring 1

gridanode

V \ M i^ n rr r m 7 T m rrn T TI U -L U -I-U .u ijju u lu/ \Tl TTI I UI III HI M II f / > . 'O l iu u R - f r T T r i i i i ' r r n T T T T iT . i i i m u w

SimilHHIIIHIIIIHI-— — T rm iT T rn T n ii i m n r

Fig. 3.5. Semi-cross-sectional view of the result of a Poisson electric field calculation performed on the 5.0 cm detector (D2). Only the outer most electric field lines are shown for simplicity. The boundary conditions behind the rings and at the far right in the figure are of the Dirichlet type. The electrode boundaries are of the Neumann type. The electrode voltages in this calculation are 9.4,7.2,5.1,2.9 and 0 kV, respectively, for the cathode, ring2, ringl, the grid and the anode (field ratio-3.5, drift field-1.3 kV/cm).

FIG. 3.6 TRAJECTORY OF A 976KEU ELECTRON AT CATHODE

X POSITION IN CM

Fig. 3.6. A typical 976 keV electron trajectory in 1.4 g/cm3 of xenon (62 atm) from the 207Bi source deposited on the center of the cathode.

Fig. 3.7

Fig. 3.8

>0’ Bi IN (2 ATM XF.NON (2 69cm drift dm ince)

W B i IN 6 2 ATM XEN O N (4 .97cm drift d iitin cc)

Figs. 3.7,8. 207Bi pulse height spectrum in 62 atm (1.4 g/cm3) of xenon gas for two different drift distances at1.3 kV/cm. The electronic noise subtracted energy resolution is 20 keV FWHM for the 976 keV electron peak in both detectors. The corresponding number for the 570 keV full transition peak is 16 keV FWHM. The FWHM of the test pulse peak (far right) is 19.5 (18.5) keV for the 2.7 (5.0) cm drift distance.

SAMPLE FIT TO 207fii DATA

Fig. 3.9. A typical fit to the data for the upper region of a pulse height spectrum. The solid line is the best Gaussian fit to the lines. The reduced X2 value for the fit is 1.02.

Fig. 3.10 407 Bi IN COMPRESSED XENON

ENERGY(keV)

Fig. 3.10. The energy calibration of the 62 atm xenon chamber.

Fig. 3.11. 207Bi pulse height spectrum in 58 atm of xenon gas at 3.0 kV/cm for a small prototype previously developed (see text). The noise subtracted energy resolution of the 976 keV electron peak is 17 keV. The FWHM of the test pulse peak is 7 keV.

Fig. 3.12a *” Bi IN COMPRESSED XENON

Iq

38

□ D1

♦ D2

FIELD RATIO

Fig. 3.12b Bi IN COMPRESSED XENON

zo

2 -

I *

076 keV e- peak1.3 kV/cm drill Held

2.4 2.6 2.8 3.0 3.8FIELD RATIO

□ D1

♦ D2

Fig. 3.12. a) Collected charge and b) electronic noise subtracted energy resolution (FWHM) as a function of electric field ratio for 976 keV electrons in both detectors: Dl-2.7 cm, D2-5.0 cm. The performance of D2 in a) is uninteresting since it was due to known electric field non-uniformities in that detector.

Fig. 3.13a 207 Bi IN COMPRESSED XENON

IP □ D1

♦ D2

DRIFT ELECTRIC FIELD (kV/cm)

Fig. 3 .13b 207 Bi IN COMPRESSED XENON

DRIFT FIELD (kV/cm)

Fig. 3.13. a) Collected charge and b) electronic noise subtracted energy resolution (FWHM) as a function of applied electric field between the cathode and the grid for 976 keV electrons in both detectors.

Fig. 3.14 107 Bi IN COMPRESSED XENON-D1

*

1

&

8

INVERSE ENERGY (keV*1 x 1000)

Fig. 3.14. Relation between the FWHM noise subtracted energy resolution of the electron peaks of 207Bi and their energy in 62 atm of xenon gas. The linearity indicates that the energy resolution scales as 1/E1" to other energies.

Ch. l Timebase Start Vmarkerl

5.000 mVolts/div5.00 us/div -29.9000 us -28.80 mVolt3

StopVmarker2

-25.4000 us -19.70 mVolts

Of f set Delay Delta T Delta V

- -20.00 mVolts- -27.8000 us • 4.50000 us- 9.100 mVolts

Fig. 3.15. A typical pulse out of our pre-amp from the ionization 976 keV electron in 62 atm (1.4 g/cm3) of gaseous xenon. Compare with Fig. 3.4.

DRIFT

VE

LOCIT

Y (X

10* C

M/SE

C)

Fig. 3.16 ELECTRON DRIFT VELOCITY IN XENON

□ 1 atm gas

♦ gas near critical p i A liquid near triple pt.

DRIFT FIELD (kV/cm)

Fig. 3.16. The electron drift velocity in xenon at various densities as a function of electric field strength.

1.5-

i .o -

DRIFT VELOCITY IN COMPRESSED XENON

j 1 j 1 1 1

0.5-

676 keV electrons 1.3 kV/cm drift Held 3.5 field ratio

-i----------------- 1----- r0 .0 0 .5 1 .0 1 .5

DENSITY (g/cm * )

Fig. 3.17. The electron drift velocity at 1.5 kV/cm as function of the xenon densities studied.

Fig. 3.18a Bi IN COMPRESSED XENON2.2 -

1 2.0 -

I 1.8 -

o 1.6 -

i 1.4-

1 2 -

1.0 -

£ $ £

#0.4 0.6

076 keV ®-1.3 kV/cm drift Held3.S field ratio

0.8 1.0 1.2 1.4DENSITY (g/cm’ )

1.6

Fig. 3.18b Bi IN COMPRESSED XENON

0.97 -

us

0.950.4

T0.6

t---'— r0.8 1.0 1.2

DENSITY (g/cm*)

076 keV e-1.3 kV/cm drift field3.5 field ratio

T-i— 1— r 1.4 1.6

Fig. 3.18. a) Electronic noise subtracted energy resolution and b) collected charge as a function of the xenon gas density at 1.3 kV/cm for the 976 electron peak. The energy resolution improves from 2.0 to 1.2 % FWHM without a significant increase in the measured charge collected.

Fig. 3.19a 207

§

Bi IN COMPRESSED XENON3.0'

25-

2.0 -

•F

570 keV lull transition peak 1.3 kV/cm drift field 3.5 field rallo

0 .4 0.6 0.8 1.0 1.2 1 .4 1.6DENSITY (g/cm )

F ig . 3 .1 9 b * " Bi IN COMPRESSED XENON

o£s

1

1.00

0.99 -

0.98 -

0.970 .4

T0.6

l-§Hhfrl

670 keV ful transition peak 1.3 kV/cm drift field 9.5 Held ratio

T— 1— i— '— i— 1— r 0 .8 1 .0 1 .2 1 .4

DENSITY (g/cm* )1.6

Fig. 3.19. a) Electronic noise subtracted energy resolution and b) collected charge as a function of the xenon gas density at 1.3 kV/cm for the 570 full transition peak. The energy resolution improves from 2.8 to 1.8 % FWHM also without a significant increase in the measured charge collected.

207Bi IN 52 ATM XENON

CHANNEL NUMBER

Fig. 3.20. Energy Spectrum of 207Bi in 52 atm (0.5 g/cm3) of xenon gas at 1.3 kV/cm. The noise subtracted energy resolution is 12 and 10 keV FWHM for the 976 keV electron peak and the 570 keV full transition peak respectively. The FWHM of the test pulse peak (far right) is 22 keV.

CHAPTER 4 Background Studies Using A High Pressure Xenon Ionization Detector

4.1. Sources of Background for 136Xe Ov pp Decay Searches

4.1.1. Introduction

In experiments with low count rates, such as double beta decay searches, understanding the origins and effects of background radiation is essential. In this chapter we discuss the sources of the background that occur in all 136Xe PP experiments. Some comparisons to other PP experiments will be made. The results of background measurements and analyses using our xenon detector will be presented.

4.1.2. Background from the Apparatus and Surrounding Environment

Alpha, Beta and Gamma-rays

There is always some trace radioactivity in the equipment and walls of any laboratory. Alpha particles and electrons from nuclear decays external to the detector are short-ranged and do not cause any problems because the probability of penetrating inside is small. If these sources are on the inside of the detector materials or chamber they will contribute to the background. In a 76Ge pp experiment, for example, these sources of

123

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radioactive impurities might be present in the germanium crystal or its housing. In our chamber a particles could be produced from radioactive impurities in the electrode materials or the inner surface of the chamber.

Gamma rays coming from sources external to the detecting apparatus can penetrate the detection apparatus because of their relatively long attenuation lengths in materials. Passive and active shielding may be implemented between the detector and the external environment. However, gamma rays can also originate from decays within any shielding and/or detector construction materials. This source of background events must either be tolerated or be actively rejected using the detector. Because of the high xenon density, our chamber has an especially good efficiency for detecting y-ray background events (for example, Compton scattering produces single electrons).

The most dominant source of gamma ray background near the endpoint of 136Xe pp (2.5 MeV) decay comes from the possible presence of 238U and 232Th in the walls of the chamber and the detector construction materials. These isotopes are precursors of natural decay chains shown in Tables 4.1a and b.81 The various gamma lines from the U and Th chains have energies up to 3270 keV. All lines above 2.7 MeV are weak and originate from the decay of 214Bi along the 238U series:

214ei -» 214p0 + e- + v e (Q= 3.28 MeV, t i /2= 20 min)

followed by

2l4Po -> 2l0pb + a (Q=7.8 MeV, ti/2=164 us).

125

However, this type of event in our detector might be recognized by observing any delayed, post trigger activity (the trigger will be defined later). We will later demonstrate to what extent background events can be rejected in our xenon ionization chamber.

Both U and Th decay chains emit radioactive radon gas, 220Rn and 222Rn with 55 s and 3.8 day half-lives, respectively. Daughters of these latter isotopes are beta emitters. If they are emitted from the walls of the chamber or gas handling and purification system and decay inside the active volume of the detector they could contribute background events. The daughter nuclei of 220Rn (from the 232Th series) are short-lived. This small lifetime is important if the source of the radon gas is the purification system. After the gas is transferred into our xenon chamber, it is no longer exposed to the purifier. If one waits a few days before running, the amount of radioactive 220Rn present would be drastically reduced. This is not the case for the Caltech 136Xe double beta decay experiment where continuous purification is needed; the xenon gas is continuously exposed to the purification system.

One daughter of 222Rn (from 238U series) is long-lived 210Pb with a 22 year half-life and leads to the emission of a 1.2 MeV beta particle. This low energy background source poses no problem for studying the Ov mode but does for the 2v one (continuous spectrum). By surrounding the exterior of the chamber with a bag of pressurized nitrogen (inside the shielding), we can prevent the diffusing of radioactive radon gas into the vicinity of the detector.

In a background spectrum we might also observe the y lines of 40K (at 1461 keV) and 125Sn (at 428 keV) from the apparatus and laboratory walls. The long-lived 137Cs line (at 662 keV, xi/2=30y) resulting from the

126

Chernobyl incident may also be evident. The presence of 60Co in the chamber construction materials, with its y-ray lines at 1.33 and 1.17 MeV in cascade could also contribute background events near 2.5 MeV.

Another source of external background is neutrons produced by an (a ,n ) reaction or fission of uranium. Thermal neutrons captured by various nuclei often are accompanied by the emission of high energy particles. In particular, the reaction 136Xe(n,y)137Xe (c=0.16b) may produce the following beta decay in the active region of the detector:

137Xe —> 137Cs + e* + ve (Q > 3.6 MeV, t i/2=4 min).

We expect the external thermal neutron flux to be significantly attenuated by the copper and lead shielding and the stainless steel vessel walls.

The xenon itself may also be a source. Commercial xenon contains ~15 ppm krypton,93*94 of which ~1 ppt is radioactive 85Kr. This isotope is a beta emitter with transition energy of 690 keV and half-life of 10.7 y. This decay energy poses no problem for a Ov decay experiment but does for a 2v search. Using xenon isotopically enriched in 136Xe one can reduce the amount of 85Kr.93*94 This enrichment is performed centrifugally.95

As mentioned before 136Xe pp decay searches have the distinct advantage of having the source of the decay also being the detector ionization medium. In addition, because it is a gas it can be cleanly isotopically enriched which has a high efficiency of removing radioactive impurities present in the gas. Experiments searching for 10°Mo or 82Se, for example, have the disadvantage of having to use solid sources which are not an integral part of the detecting medium. These experiments must be

127

able to tolerate radioactive contaminants inherent in the source that cannot be easily removed.

If all chamber and detector construction materials are carefully chosen it is possible to have an extremely low background experiment for the search of PP decay in 136Xe. However, being a gas xenon has a disadvantage because radioactive impurities from the experimental apparatus, such as radon gas might diffuse into the gas. Being a solid, 76Ge would not have this problem and would only acquire this background contamination on the surface of the crystal.

The 136Xe pp decay endpoint energy (where the summed electron energy peak of the neutrinoless mode resides) is at 2479 ± 8 keV 96 At this energy the dominant source of gamma-ray background in our chamber is from the presence of thorium. At the very bottom of the 232Th series, 208T1 decays to an excited state of 208Pb which then gives off a 2615 keV y-ray (see Table 4.1). This is the only intense gamma source near or above the transition energy of 2.5 MeV. If this process occurs within the chamber construction materials it could contribute counts near the endpoint of pp decay, which is a problem for studying the neutrinoless mode. The y-ray could deposit approximately 2615 - 2479 = 136 keV outside and 2479 keV inside the sensitive region of the detector. For example, the y- ray might Compton scatter before entering and then eventually deposit just the right amount of energy within the detector by photo-absorbing. The possibilities are endless and will be treated in die next chapter. We will just note that at 2.6 MeV the most probable interaction a y-ray will undergo in xenon or stainless steel is a Compton scatter, the next pair- creation and the last photo-absorption 97

128

The energy resolution of the 976 keV peak of 207Bi was measured to be 20 keV, at 1.4 g/cm3. Assuming the energy resolution at other energies scales as 1/E1/2 (see Chapter 3), the extrapolated energy resolution at the 136Xe OvPP decay summed electron energy in our xenon detector (1.4 g/cm3) is 30 keV FWHM (we assume that the energy resolution depends only on the total energy of the decay and not on whether we have a one or two electron event). With this resolution, the Compton edge (2381 keV) and photoelectron peak (2615 keV) of 208x1 background gamma rays are outside the range To ± 1/2(FWHM) (the 208x1 photo peak is also well above To + FWHM), where To = 2479 keV. Therefore, we expect gamma induced events due to 208x1 will not contribute significantly to background in the Ov energy region unless the low energy tail of the photopeak (due to incomplete charge collection within the sensitive region) is large enough and/or there is significant thorium contamination in our chamber. High density xenon has a good gamma-ray efficiency. We then would expect the low energy tail of the 208x1 photo-peak, due to incomplete charge collection of the 2.62 MeV gamma-ray, to be minimal.

To minimize internal gamma background our chamber was built with relatively low background materials: stainless steel vessel, detector parts and feedthrough conductors, copper gaskets, aluminous ceramic feedthrough insulators and nickel mesh. All materials and components of our chamber have been tested for radioactive purity using glow discharge mass spectrometry98 to get a limit on the presence of uranium and thorium. Only the stainless steel vessel material showed any activity to the level of sensitivity of the measurements. 1 part per billion by weight (ppbw) of 232Th was detected in stainless steel from the chamber walls. This is unfortunate since the chamber walls constitute a large proportion by mass

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of the detector (copper may be better for low background but could not be used for a high pressure vessel). However, since this ppb level of sensitivity is the limit for the glow discharge mass spectrometry process,98 we are somewhat reserved about this measurement.

The radioactive purity of other construction materials for our chamber was investigated. We obtained samples of ultra-pure titanium and measured the background using a low background intrinsic germanium detector.99 From this measurement it was inferred that the sample contained less than 0.1 ppbw thorium. However, the stress requirements on a high pressure vessel would rule out pure titanium as the construction material (it is very brittle). A titanium-aluminum alloy would be much more realistic. We also measured the background rate of synthetic sapphire for the purpose of the insulators for the electrical feedthroughs. The purity was similar to that of the titanium sample.

To simulate how the presence of thorium might affect the spectrum of events in our detector we used a 228Th source placed in various positions around the outside of the chamber. We note that this may not be a good representation of an internal thorium source since the walls and flanges of the chamber are so thick. Figure 4.1a displays an external 228Th spectrum taken in the smaller xenon drift region (D l) at the usual electric field parameters and a density of 1.4 g/cm3. The source strength was approximately 6 pCi and was placed ~ 10 inches above the top of the chamber along its axis (the event rate was too high for closer positions). Similar spectra were obtained with the source placed at other positions around the chamber. The spectrum in Fig. 4.1a mostly represents the flux of gamma rays being Compton scattered from the chamber flange before hitting the detector. The 208T1 photo-peak is not well resolved. Beyond

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2.7 MeV the gamma flux falls sharply (the energy calibration will be described later). The lower energy structure (below 2 MeV) was due mostly to the 207Bi source that remained on the cathodes of D1 and D2 during these measurements (see Chapter 3).

A spectrum from the same thorium source was also taken using a high resolution germanium detector with 2.5 cm of steel in between the source and the detector to simulate the effect of the steel vessel walls of our xenon chamber. This spectrum is shown in Figure 4.1b. The 2615 keV 208T1 photo-peak was well-resolved in this detector (the energy resolution was better, the geometry was more favorable and there was less steel between the source and this detector than with the xenon chamber). Both spectra exhibit a prominent double escape peak due to the small detector volumes used.

As seen from the above figures the xenon ionization detector used in these measurements is not efficient for the photo-absorption of the 2.6 MeV y-rays from a source external to the chamber. This is most likely due to the high probability of scattering in the chamber flange (6.4 cm thick stainless steel) or in the dead layer of xenon (4 cm) before entering the active region of the detector. We note that a xenon ionization chamber with 1 mm thick titanium walls has been built since the above measurements were taken. In this thin-walled detector we demonstrated that the photo-peak of 208T1 was well resolved (1.4% FWHM at 2615 keV, using an external 232Th source). Several other external gamma-ray sources were also used (137Cs, 6°Co, etc.) and again we observed that all photo-peaks were well resolved. This indicates that the performance (efficiency and energy resolution) of our present xenon ionization chamber (with thick steel walls) using an external source may not be a good

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indication of what effect an internal source of thorium (in the walls of the chamber or in the detector parts) would have.

Cosmic-rays

Another important source of background near the PP endpoint, especially in ground level experiments is cosmic rays. At ground level, cosmic rays penetrate the chamber at a rate of ~1.0/cm2/min (or roughly 10 Hz in our apparatus). By "clipping" or "grazing" the active region of the detector or by the spurious operation of the spectroscopy amplifier, a cosmic ray muon event could produce counts near the endpoint energy of 136Xe pp decay. These possibilities will be discussed.

Cosmic ray muons produce straight, minimum ionizing trajectories that will penetrate the shielding. A minimum ionizing particle is one whose characteristic dE/dx value is near the minimum possible for that medium and that particle. The incident minimum ionizing cosmic-ray muons have a range of energy from 1 GeV to 1 TeV.100 High energy gamma rays may be emitted from the capture of the negative muon by the lead or copper shielding. Cosmic ray muons may also produce unstable or excited nuclei by the electromagnetic nuclear reactions101

p. + A-> p' + A* (or p' + A')

but these isotopes are usually of low decay energy and/or short-lived. By placing the experimental apparatus underground (where the muon flux is considerably diminished) and waiting several lifetimes of the excited nuclei before running, this source of background can be reduced significantly.

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The nucleonic components of the cosmic ray flux are heavily ionizing and have a higher probability of giving rise to electromagnetic showers. Cosmic ray fast neutrons interacting with the copper shielding may create radioactive isotopes whose decays could contribute background events. A list of these isotopes is given in Table 4.2. The reaction 63Cu(n,a+4n)56Co is potentially a problem if copper shielding or materials are utilized since the short lived daughter emits gamma rays of energy up to 3270 keV.

Cosmic ray muons, electrons and pions may also undergo bremsstrahlung in the atmosphere or the detection apparatus causing electromagnetic (gamma ray) showers.

In our above ground measurements we will show that the background rate was determined by cosmic ray muons penetrating the xenon chamber. The muon flux was too high above ground to see the effects of the radiation from gamma-ray background sources inherent to the experimental apparatus. Most pp experiments transfer their entire apparatus underground several thousand meters (water equivalent). Depths of various underground laboratories and their muon fluxes are shown in Fig. 4.2. Alternately, by building a highly efficient active comic ray muon veto shield, the effects of the muons can be diminished. Nevertheless, we felt it instructive to study above ground background effects in our xenon detector in order to understand how cosmic ray events may be rejected and how they might limit the sensitivity of a Ov PP decay experiment

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4.2. Background Event Identification

How do we distinguish a Ov double beta decay event from a background y or cosmic-ray event experimentally? In our high pressure xenon detector precise electron trajectory and dE/dx information (position resolution) is unavailable due to the short tracks and the one dimensionality of the ionization chamber: single-electron trajectories (from Compton scattered gamma-ray background) cannot be distinguished from two- electron, PP events. However, because an electron is a highly ionizing particle at the energies we are considering, it deposits its energy within a very localized and contiguous region in the xenon. In fact, Monte Carlo studies suggest that on average a 136Xe Ov p p event in xenon at 1.4 g/cm3 is confined within 2 mm (see Chapter 5). Figure 4.3a shows a typical simulated 136Xe Ov PP event in 1.4 g/cm3 xenon. To some extent, this characteristic of highly localized and contiguous deposition of charge distinguishes a p p decay event from a non-localized cosmic-ray muon or gamma-ray event.

4.2.1. Characteristics of Cosmic-ray and Gamma-ray Events in Our Chamber

A cosmic ray muon is a minimum ionizing particle which deposits its energy in a continuous manner. The lengths of the muon tracks through the detector are usually much longer than for a highly ionizing electron or PP event. The cos20 angular distribution of the incoming muons implies that most are entering vertically. In addition, with very little multiple scattering, the track created by a minimum ionizing cosmic ray muon is

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often straight (we will see examples of detector pulses produced by cosmic rays later).

A y-ray event also may deposit its energy over larger, non­contiguous regions than a pp event. It could, for example, Compton scatter in the detector imparting some of its initial energy to an electron (which stops almost immediately) and then either scatter again (double Compton scattering) and/or photo-absorb. It could create an e+e- pair in the detector, and one of the 511 keV photons emitted might escape and the other only be partially absorbed, etc., etc.

Thus, a gamma interaction in the chamber can often lead to a non­contiguous, non-localized charge deposition, unless only one Compton scattering event or a direct photo-absorption occurs within the detector. These types of events will lead to single electron trajectories. Fig. 4.3b depicts such an event generated by a Monte Carlo. The cross sections forthe various interactions are obtained from standard data.97 The attenuation

3lengths for a 2.6 MeV photon in lead, copper, steel and 1.4 g/cm of xenon are approximately 2.0, 3.3, 3.3 and 20 cm, respectively (at 1 MeV the numbers are 1.3, 2.0, 2.0 and 13 cm, respectively).

The many possibilities of y interactions in the detector were incorporated into a Monte Carlo simulation that was performed to see how many counts are expected near the endpoint of 136Xe Ov p|3 decay due to randomly distributed background y-ray sources present in the chamber walls (see Chapter 5). The additional requirement that all of the charge from an event is deposited in a highly localized region of the detector will reduce the number of background events; this will be described in the next section and in Chapter 5.

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The most likely occurring 208T1 gamma interaction (2615 keV) that could produce counts at our Ov pp decay energy (2480 keV) and at the same time be highly spatially localized is a double Compton scattering at the same z position within the detector. Other possible events that might occur include photo absorbing at the edge of the fiducial volume (incomplete charge collection) or pair creation followed by a partial absorption (at the same z) of the 51 l ’s produced. Most other gamma events in the chamber either produce counts at energies much different than 2480 keV or create non-localized deposition of charge in the detector (single Compton scattering of a 2615 keV gamma-ray produces electrons up to 2380 keV, well below this energy).

To produce a 2.5 MeV Compton electron it takes a gamma ray with energy greater than 2.7 MeV (see Chapter 5). However, as we noted before, the gamma flux falls rapidly beyond 2.7 MeV. To produce a 2.5 MeV pair production event, a gamma ray of 3.5 MeV is needed. However, the gamma flux at 3.5 MeV is 2 orders of magnitude smaller than at 2.5 MeV (see Fig. 4.1). The chances of either a single pair creation or a Compton background event occurring within the detector, with energy near the endpoint of Ov pp decay of 136Xe, are thus highly suppressed.

Could we distinguish the above discussed types of background events (muon or gamma) from "electron-like" pp events using our xenon drift chamber? The pulses out of our detector give a time evolution (a history along the direction of the electric field: the z-direction) of the shape of a track (how the energy was deposited) for a particular ionization event. Our chamber is basically a one-dimensional time projection chamber in the z-direction. By "capturing" the pulses arriving at the anode and inspecting

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their shape, we might be able to distinguish background events from good events (contiguous and localized). For example, we have observed that pulses from the K-conversion electrons of 207Bi have a relatively sharp rise time of 3-5 ps. They are usually constant or slowly varying in slope during this time and have a height proportional to their energy (see Fig. 3.15, for example). These features are also what we would expect for events in which all of the energy is deposited in a single localized region, such as pulses from the two electrons in Ov PP decay. Examples of Monte Carlo generated Ov PP events will be shown next chapter.

For a non-contiguous, non-localized y-ray event, the ionization deposited may be separated in the z-direction by a distance comparable to that between the anode and the grid (or, approximately, the drift velocity multiplied by the rise time). In this situation, y-ray events may be rejected. The anode collection plate encounters the ionization created in the sensitive region of the detector only after it has drifted past the grid. The resulting pulse expected after all of the charge was collected would be "multi- humped" (with one or more changes in the slope of the rise). This would be characteristic of a series of separate, localized depositions of charge from a y-ray event in our detector (several, spatially separate single electron trajectories). The y-background Monte Carlo simulation also incorporates cuts based on the spatial extent of events (i.e. events are rejected if they are made up of non-contiguous depositions of charge).

A minimum ionizing cosmic ray muon deposits its energy uniformly over a large volume. We then expect slower rise time pulses than for electrons. For a vertical muon, for example, in 1.4 g/cm3 of xenon the energy deposited in the sensitive region o f the detector is,

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approximately102 1.5 MeV-cm2/g x 1.4 g/cm3 x 2.69 cm = 5.0 MeV in D1 of Chapter 3.

There are of course cases in which the y or cosmic ray event deposits energy in a highly localized manner and effectively produces an "electron- like" pulse. For example, a y-ray coming from the walls of the chamber could photo-absorb in the detector or even deposit the energy in two locations at the same z-position. A cosmic ray muon could, for example, just graze the sensitive region of the detector. These situations would produce an "electron-like" pre-amp pulse (contiguous and localized deposition of ionization). If, in addition, such events deposit energy near the pp endpoint, they are background. How "likely" these effects are will be examined in the next chapter.

These background events we cannot distinguish from a "true event" by their pulse shape alone. We would need more information or a few more dimensions added to our only one dimensional viewing capabilities. In a 3-dimensional TPC, for example, dE/dx measurements can be made along the trajectory of the event. In such a device, hue PP events would be characterized by two tracks with a common origin and with a large blob of charge deposited at each end. However, as discussed in Chapter 2 and 5, in order to see the separate "charge blobs" (dE/dx along the trajectory), the xenon pressure cannot be higher than 5-10 atm.37 In 1.4 g/cm3 of xenon, a measurement of dE/dx along the trajectory of a 136Xe pp event would require pm position resolution: an impossible task.

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4.2.2. Studying the Pulse Shape Discrimination Method Using Cosmic-rayMuons and an External y-ray Source

From the above discussion it is evident that to some limited extent we may be able to distinguish pure electron-like events from others by analyzing the pulse shapes from the anode in our 1-D xenon drift chamber. Hie features to examine are the height, shape and duration of these signals.

We used an external 228Th source to study the efficiency for rejection of y-background events using the above categories of pulse shape discrimination. The source was placed 10" above and along the axis of the top flange. The internal207Bi source remained in place since there was no structure seen from it at the high energy regions of interest (>2MeV). We searched for events that deposit energy within a certain energy window around 2479 and 2615 keV (the decay energies for 136Xe pp and 208T1, respectively).

We emphasize that we are not attempting to simulate the residual effect of 232Th in the walls of the chamber with this source (in fact, by examining Fig. 4.1a, we hope that in a true background measurement, we would be able to resolve the 208t i photo-peak). The following experiment with an external source is only meant to demonstrate the pulse shape discrimination technique utilized and allow us look at sizes and shapes of signals that produce background counts in the energy region of interest.

The energy calibration for pulse heights out of the pre-amplifier (as well as the shaping amplifier) is determined by the location and energies of the lines of 207Bi in a pulse height spectrum (482, 570, 976,1063 and 1770 keV). Assuming the detector is linear with energy we can predict at what channel in a pulse height spectrum the transition energies of 208t 1 and

I

136Xe Ovpp decay would occur. We then adjust the pulser output amplitude to that channel and determine its corresponding height out of the pre-amp. This value is the expected height of the pre-amp pulse from either of the above decays (at 2479 or 2615 keV depending on where we set the pulser). We then "capture" (select with a timing single channel analyzer) these signals for inspection on a sampling digital storage oscilloscope. From this we may determine how many of the total number of events observed are "good" (have the correct height, shape and rise time).

The electronic configuration is shown in Figure 4.4. We use a digital storage oscilloscope (HP-5411 ID) triggered on the gate generated by a timing SCA window of 30 keV around the energy region of interest (ORTEC 427A T-SCA, LeCroy 222 gate generator). Pulses from the pre­amplifier and/or the spectroscopy amplifier (also referred to as "shaping amplifier") are then displayed and examined. Using the wave form digitizer, sufficient pre- and post-triggering information was possible by simply adjusting the time scale. The timing requirements are shown in Figure 4.5a. We require that the gate generated by the T-SCA starts/stops > 10 jis before/after the maximum of the pulse from the unipolar output of the spectroscopy amplifier. This is accomplished by using several delay amplifiers and an adjustable gate width. The amplifier pulse appears approximately 25 |is after the start of the pre-amplifier pulse (see Figure 4.5b).

Due to the failure of the SCA to properly process shaped pulses of widths greater than 20 ps, many of the pulses that appeared, with the scope triggered as above, were actually outside the window in energy. These very long pulses were usually due to cosmic-ray events in the chamber.

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We could resolve this ambiguity by looking at the shaping amplifier output simultaneously with that from the pre-amp. The shaping amplifier pulse heights determine whether or not a signal will contribute a count at the energy region of interest. Those events with shaping amplifier output pulses that are not the correct height or width are disregarded.

In addition, using 10 p.s of shaping even some of the "good" spectroscopy amplifier pulses were > 20 us in width. The T-SCA requires that the width of incoming shaped pulses be < 20 ps to operate correctly and consistently. By reducing the shaping time to 6 jxs the spec-amp pulse widths were reduced to < 20 Jis. However, in going to 6 fis shaping time we may give up some resolution in energy. This will be discussed later. It turns out that when 10 p.s shaping was used, there was more of a spread in the range of spec-amp pulse heights that were allowed into the energy window than was the case for 6fis shaping.

Observing the pulses from the pre-amp and spec-amp simultaneously resolves yet another ambiguity. If the shaping time were set at 6 fis, the spec-amp would process approximately 6 p,s of the incoming pre-amp pulse. If the time evolution of the pre-amp pulse from a background event is just right, the shaping-amp might "clip" an otherwise too large or long signal and cause it to contribute a count within the energy region of interest. This problem is avoided by checking the digitized pre-amp pulse for the required properties.

Typical pulse shapes that were seen are shown in Figures 4.5c-4.7. The difference between electron-like ("good") events (4.5c) and others is obvious. Pulses that are y-like often rise for a couple of microseconds, the slope then goes to zero for a while and then the slope rises again. This produces the "double-humped" pulses mentioned in the last section and seen

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in Fig. 4.6. Signals from cosmic ray muons (Fig. 4.7) have much longer rise times (sometimes as big as 100 ps) and larger pulse heights than those due to electrons; whether or not a change in slope appears in the pulse out of the pre-amp depends on where and at what angle the muon enters the chamber.

With the pulse height energy calibrations and other features discussed above, we summarize the requirements for "electron-like" events that contribute counts in the energy region of interest (2479 or 2615 keV):

(1) Pulses out of the pre-amp must not drastically change theirslope in the rise (this includes multi-humped pulses).

(2) Pulses out of the pre-amp must have rise times < 7 ps and the"correct" height

(3) pulses out of the shaping amplifier must have widths < 20 psand the "correct" height.

300 events were inspected manually for each of the above energies with a 6 pC 228Th source above the chamber. The small xenon detector, D l was used with the usual drift electric field of 1.3 kV/cm, a field ratio of 3.5 and a density of 1.4 g/cc. Although better energy resolution was obtained at lower xenon densities the higher efficiency at this density was considered more important. From Chapter 3, the extrapolated energy resolution at 2479 keV is 1.2 % or 30 keV, which was the width chosen for the energy window. The results were as follows:

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af.2 4 .2 S toy:39 events were due to cosmic ray muons ("cosmic ray-like" pre­

amp signal).13 events were double humped and thus most likely due to gamma

rays.248 events had "good" pulse shapes from the pre-amp and from

the spec-amp.

at 2615 keV:43 "cosmic ray-like" events 0 multi-humped pulses 257 "good" events

We note that some of the "good" events may be caused by cosmic ray muons or y-ray events that are indistinguishable in our detector from electron-like events. Also we estimate that ~30% of the cosmic ray muon­like events had pulses with the correct heights from the spec-amp but not from the pre-amp. This was due to the anomalous saturation of the spec- amp by pre-amp pulses of greater rise time than the shaping time used (as discussed earlier). The other 70 % of the "cosmic" events present were due to the failure of the SCA, as noted above. The "double-humped" pulses were double-humped in both the pre-amp and the spec-amp outputs. The corresponding spec-amp pulse sometimes had two separate pulses one of which was the "correct" height the other much smaller. This happened when the "humps" in the pre-amp pulse were separated by more than a shaping time. If they were separated by less than this amount of time, then there would be only one spec-amp pulse but it would be double-humped.

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Relatively speaking, there does not seem to be many double humped or cosmic ray muon like pulses contributing counts near the endpoint of pp decay in 136Xe. Only ~20% of the total number of events can be rejected by their pulse shapes alone. As we will see later, the rejection factor improves when the external 228Th source is removed and the residual background is studied. In the above study using an external source, quite a bit o f scattering of the y-rays may occur in the stainless steel vessel walls (6.4cm thick) before entering the xenon. In a true pp decay experiment the thorium source would be randomly distributed in the chamber walls. In this situation the y-rays would then have a better chance of directly seeing the xenon, so we may expect different results. We will study this case later in this chapter.

With the electronics used in this pulse height identification process and the spectroscopy amplifier forced to have a shaping time of 6 (is, has the energy resolution been significantly degraded? That is, should the chosen T-SCA window size be larger than 1.2% (30 keV) at 2479 keV? There was only approximately a 1% improvement in the energy resolution o f the 976 keV 207Bi line when the extra electronics requited for pulse shape discrimination (T-SCA, gate generator, delay amplifiers etc.) were removed (using 6(is shaping time). In addition, with the lower gain that we are using in the present studies, there was only a 5 % difference in the energy resolution of the 976 keV internal conversion ^ B i peak between 6 and 10 (is shaping times with the extra electronics present. The latter was the shaping time used in the energy resolution studies of Chapter 3. So we give up some energy resolution in return for proper pulse height discrimination from the T-SCA.

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With this loss in energy resolution, can we distinguish between a 2479 and a 2615 keV pre-amplifier pulse height using the T-SCA? In other words, because of a loss in energy resolution, will the spec-amp signals chosen by a T-SCA window centered on 2615 keV correspond to separate pre-amp pulse heights than those for a window centered on 2479 keV ? To answer this question, the "good" events from the two energy windows (248 and 257 events for the 2479 and 2615 keV energy windows, respectively; see Section 4.2.2) were histogrammed by pre-amplifier pulse heights and the results are presented in Figure 4.8. We see there is some overlap between what is considered a 2479 and a 2615 keV pre-amp pulse height, respectively, but for the most part, the pulse heights in the two windows are separate. This demonstrates that this method of pulse shape identification is working well enough to distinguish the two pre-amp pulse heights.

We have demonstrated that, to some extent, pulse shape discrimination is possible if the chamber is viewed as a 1-dimensional TPC.

4.3. Background Measurements

4.3.1. No shielding

With no radioactive sources present except for the low energy internal 207Bi source, we measured the natural residual background rate (in counts/(keV-kg-hr)) in our detector (D l) near the endpoint energy, 2479 keV. The 207Bi source does not contribute any counts near the energy region of interest. This is verified by the spectrum shown in Fig.

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4.9 taken at Ed = 1.3 kV/cm, a field ratio of 3.5, and a density of 1.4 g/cm3 in D l. We see no structure at energies higher than 1800 keV. The existence of the source allows us a precise, continual energy calibration. For these measurements there were 309 grams of xenon within the sensitive volume of the detector.

For a 2 % (50 keV) wide integration window around the endpoint energy and 20 hours of running time we measured a background rate of 5.4 ± 0.2 cts-keV'i-kg-l-hr1 for a spectrum taken with the unshielded detector. The uncertainty is due to the statistical inaccuracy in the summing of the counts within this window.

4.3.2. Passive Shielding

We first surrounded the sides and bottom only of the chamber with 4" of lead bricks stacked 18" high (the chamber with copper faraday cage is 16.5" from top to bottom) in an overlapped fashion (see Figure 4.10). Using the above integration window and running time gave us a background rate of 5.5 ± 0.2 cts-keV 'l-kg-fhr1 at the endpoint energy. To investigate the contribution to this value due to the presence of the lead we then surrounded the bottom and sides of the vessel with additional 1" thick copper plates 17" high inside the lead shielding. The resulting background rate was then 5.4 ± 0.2 cts-keV-1 -kg'1 -hr1. Since the above three numbers are the same within the quoted uncertainties, we conclude that neither the lead nor the copper significantly affected the background rate at 2480 keV.

We then completed the shielding by placing an additional 1" of copper and 2" of lead on top of the vessel (see Figure 4.10). The measured

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value for the background rate then became 5.1 ± 0.2 cts-keV-Lkg-l-hr1. Evidently, in this configuration (above-ground and with no cosmic ray muon anti-coincidence panels) only a very small contribution to the background rate comes from gamma rays external to the apparatus.

Nearly 2.5 inches of stainless steel and -1.5" of high density xenon surround the active region of the detector inside the chamber. This allows additional external gamma ray attenuation. In fact, 2.5" of stainless steel and 1" of 1.4 g/cm3 of xenon should reduce any 2.6 MeV gamma background flux by a factor of 10. 4" of lead and 1" of copper shielding should reduce it by an additional factor of 1000. The lead and copper together with the steel and xenon should significantly reduce any external background gamma ray flux.

This entire house of shielding weighs nearly 2.5 tons. The electronics and gas handling system were all outside the shielding. All cables and gas pipes were bent through right angles before connecting to the chamber to prevent direct illumination of any background gamma rays. To prevent radioactive radon gas from diffusing inside the shielding, the entire lead house was slightly pressurized by dry nitrogen during all background runs (unnecessary for ground level background measurements since cosmic-ray muon events dominate the rate).

Cosmic ray muon induced background counts dominate the measured background rate. If this component o f background were reduced significantly we might then begin to see a difference between the un­shielded and shielded background rate due to external gamma rays.

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4.3.3. Active Shielding

We next investigated the use of cosmic ray veto panels to further reduce the background counts near the energy range of interest. For this measurement only 2 large scintillation panels (5' x 2' x 5/16" thick) with RCA-8575 photo-multiplier tubes were available. There were two possible configurations for these elements. We could overlap them, place them on top of the passive shielding and veto on their coincidence or we could place one on top, one on the side and generate a veto on the logical OR of the two. Due to a high singles veto rate of approximately 2 kHz (mostly because of the random thermal electron noise) it was seen that the former set-up was over 2 times more efficient than the latter (the dead time in the OR set up was close to 40 %). Several settings of the discriminator levels were investigated when deciding between the two configurations.

The chamber, together with its passive and active shielding, is depicted in Figure 4.10. The two panels were overlapped by 110 cm over the configuration. The area of overlap was 6800 cm2. The electronic set­up is shown in Figure 4.11. A single power supply (Northeast Sci. RE- 5001) of negative polarity provided the high voltage for the two PMTs. The fast (1-2 ns) negative outputs from the anodes of the PMTs were fed into 2 separate constant fraction discriminators (ORTEC 473A) followed by a fast coincidence box (LeCroy 465). The output of this generated a gate (LeCroy 222) which was fed into the anti-coincidence gate input of the ADC of our Canberra data acquisition system. A > 75 ps gate width was necessary because many of the shaped cosmic ray pulses were as large as 70 j is wide (several gate widths between 75 and 100 ps were used with little or no change in veto efficiency). Figure 4.12 displays the timing between a

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typical signal from the spectroscopy amplifier and a 100 |xs gate generated by the veto signal.

The discriminator levels were first set by using a 6°Co source (y-ray energies of 1330 and 1170 keV) placed in various positions on top of the region of overlap of the two panels and optimizing the coincidence rate. The levels were at first adjusted just above random triggering of the noise. However, the best efficiency for rejection of cosmic rays was obtained with the discriminator levels turned all the way down. The veto rate was plotted against high voltage and a plateau was reached at 2700 V. We chose an operating voltage of 2950 V, well above the knee. The amplitudes out of the PMTs at this voltage were 1.2 and 2.5 V for the top and bottom scintillation counter, respectively. The veto rate was 120 Hz which leads to < 1 % dead time.

The measured background rate with the active and passive shielding implemented was 1.8 ± 0.1 ctsTceV-^kg-Uhr1. The reduction of the background after each of the above stages of shielding is displayed in Figure 4.13 in 50 keV bins. Because of the lack of structure near 2480 keV in all three spectra, the small difference between Fig. 4.13a and b, and the significantly lower rate in 4.13c (veto panels), one can strongly argue that the remaining 1.8 cts-keV-^kg-^hr1 are due to cosmic ray muons. This point will be discussed later in this chapter. Assuming this statement is true for now and comparing the resulting background rate before and after the veto panels were implemented we are led to a veto inefficiency of: (1.8 cts-keV'i-kg-Lhr1) /^ .! cts-keV’i-k g-L h r1) = (35 ± 3)%. This would imply an efficiency for rejection of cosmic-ray muon background of 65%.

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This number for the cosmic ray veto efficiency could be improved if we had enough veto panels to make a double-layered "house" around the chamber (again vetoed on the coincidence of the two overlapped panels on any one side), where all possible paths to the detector are blocked by veto panels. In the above measurement the sides of the apparatus were unshielded from non-vertical entering cosmic ray muons.

4.3.4. Reduction of Background Using Pulse Shape Discrimination

With both active and passive shielding implemented we tried to further reduce the background, using pulse shape discrimination. We will use the same idea discussed in section 4.2.2. We attempt to reduce background counts near our endpoint energy, 2480 keV, by examining the shapes of the pulses that produce them. We search for events that deposit energy within a 30 keV window around 2479 keV and are electron-like using the same requirements as before (section 4.2.2):

(1) Pulses out of the pre-amp must not drastically change theirslope in the rise (this includes multi-humped pulses).

(2) Pulses out of the pre-amp must have rise times < 7 (is and the"correct" height

(3) Pulses out of the shaping-amp must have widths < 20 (is andthe "correct" height.

In addition, we now require that there was no cosmic-rav veto signal present.

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We used a sampling digital storage oscilloscope triggered on the gate generated by the timing SCA window of 30 keV around 2480 keV for all of the following measurements. The electronic set-up is shown in Fig. 4.14. Again the T-SCA failed to properly discriminate shaped pulses of widths > 20 ps (all of the SCA's available had this trouble). This caused many pulses to appear on the oscilloscope that actually were outside the energy window. How frequently this happened must now be understood in order to make a correct estimate of how much the background rate may be further reduced by pulse shape discrimination. Three steps are required:

Step 1. Simultaneously observing pulses coming from the pre-amp and die gate generated by the coincidence of the veto panels (the veto signal).

500 events were observed manually with an average trigger rate of 1 per minute (± 0.3 min) from the T-SCA. This corresponds to an effective live-time of 8.3 ± 2.5 hours. Of these, only 8 pulses from the pre-amp were pulses typical of electrons in 1.4 g/cm3 of xenon ("electron-like") and, therefore, could not be thrown out. The rest of the observed signals were mostly pulses typical of cosmic ray muons ("cosmic-ray-like" as defined previously), with or without a veto signal present; a few were "electron-like" with a veto signal present (see Figs. 4.15-16). The cosmic- ray-like events occupied ~ 95 % o f the total. No pre-amp pulses appeared that were characteristic of y-ray interactions in the detector (see section4.2.2).

The SCA does not have trouble processing electron-like pulses from the shaping amplifier, since these have widths < 20 ps. It does have considerable problems processing shaping amplifier pulses > 20 ps wide.

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How many of the cosmic-ray muon-like pre-amplifier pulses (long rise times) lead to shaping amplifier pulses that had too large widths (or, equivalently too big rise times) for the SCA to process? Not all o f them; clearly it is possible that a pre-amp pulse may have the characteristics of a pulse from a cosmic ray muon, while the corresponding shaping-amp signal looks "good" (a pulse typical of an electron-like event). In this case the SCA would have no problems. The spec-amp is concerned only with that part of the pre-amp pulse which occurs within a time period characterized by the shaping time. If the pre-amp signal had just the correct shape to produce a spec-amp signal of the required height it could be placed correctly in the energy window by the T-SCA. We cannot answer the above question until we look at pulses from the pre-amp and spec-amp simultaneously.

Step 2. By simultaneously observing pulses coming from the pre-amp and spec-amp, estimate the percentage o f the cosmic-ray-like events appeared due to an SCA failure and how many were correctly processed.

200 events were observed. 31 % had the correct shape out of the spec-amp (the height and width were "electron-like" and were thus correctly processed by the T-SCA) but had the wrong shape from the pre­amp (the height and risetime were "cosmic-ray-like"). 69 % had the wrong spec-amp pulse (too wide) and pre-amp pulse and were thus present because the timing SCA failed to process them correctly. See Figure 4.17 for examples. However, of the above 31 (or 69) % what percentage would have had a veto signal present? Signals from the veto shield could not be displayed in this last estimate (our scope could only observe two channels at

152

a time). We are especially concerned with the number of events that do not have a veto present. These will be the background due to cosmic ray events. To answer this last question, we now must look at signals from the shaping amplifier and the veto simultaneously.

Step 3. Estimating the percentage of "good" pulses from the shaping amplifier that would not be vetoed as cosmic ray events by simultaneously observing signals from the shaping amplifier and the veto panel coincidence.

200 events were examined. This was a very slow process since many of the shaped pulses appearing were not the correct height or shape. Assuming all of these were due to cosmic rays (since we could only see two scope channels at a time, we did not know what the corresponding pulse from the pre-amp looked like), we observed 39% un-vetoed and 61% vetoed cosmic ray events (a 39% veto inefficiency).

With this last bit of information we went back to the original 500 events observed, and estimated how many of the cosmic-ray-like events seen from the pre-amp signals were correctly triggered on. For the true number of vetoed cosmic ray events, multiply the original number of vetoed cosmics (in the original sample of 500) by .31 x .61 (the fraction of events in which the SCA functioned correctly) x (the fraction of these events that had a veto present). For the correct number of un-vetoed cosmic ray events multiply the original number of un-vetoed cosmics (in the original sample of 500) by .31 x .39. The remaining number of cosmic ray events in each category were incorrectly triggered on by the SCA. The

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corrected distribution of events from the original 500 events observed in Step 1 is as follows:

Out of 500 events only an estimated 99 events were processed and triggered on correctly by the T-SCA:

8 events were electron-like with no cosmic veto present 19 events were electron-like with a cosmic veto present 31 events were cosmic-like (from the pre-amp) with no veto pres.41 events were cosmic-like (from the pre-amp) with a veto present 0 events were gamma-like

We reiterate that the numbers for the cosmic-like events were estimated from the above discussion. Those for the electron-like events were directly observed from the original sample of pre-amp signals (there was no problem with the SCA operation for these events). "Good" signals from the pre-amp necessarily implies good pulses from the spec-amp (the converse, however, is not true).

We observed no pulse shapes that matched the characteristics of a background gamma-ray event in this study. This fact further supports the claim previously made that the events near the endpoint energy were dominantly due to cosmic ray events in our chamber. If the background rate were swamped by cosmic rays muons, the contribution due to gamma- rays would be negligible in comparison. Recall, even in the pulse shape discrimination experiment using an external 6 \iC 228Th source (section4.2.2), we saw only a few of the events surveyed had characteristically y- like signals from the detector (double-humped). Above ground the ratio of cosmic-ray-muon induced background events to gamma-ray induced events

154

is much too large. Only with lower cosmic ray muon fluxes would one expect to be able to see (in the background energy spectrum or by pulse shape discrimination) gamma-ray effects on the background rate.

With as high an inefficiency of rejection as 35 % it is highly probable that at least some, if not most of the 8 electron-like events (good signals from the pre-amp and no veto) observed in the current experiment were due to cosmic ray events that just "grazed" the sensitive volume of the detector (thus entering through angles other than vertical). Only this type of cosmic ray event could produce the small and contiguous deposition of ionization in the detector that is required for an "electron-like" signal from the pre-amp. The fact that there are 19 electron-like signals that were vetoed (almost definitely due to cosmic ray events) supports the above claim that at least some of the 8 good signals were cosmic ray muon produced. There is obviously a good chance that a proven cosmic ray muon event produces a "good" signal from the pre-amplifier. Knowing that a large cosmic ray muon rejection inefficiency exists one may conclude that at least some of the 8 are probably of cosmic ray muon origin.

Using the above numbers for the correctly triggered pulses above and assuming that all background events are solely due to cosmic rays leads to an estimated veto inefficiency of : ( 8 + 31 ) / ( 8 + 19 + 31 + 41) = 0.39 (the number of un-vetoed divided by the total number of cosmic ray events). We note that this is the same as the result of Step 2 above. The numbers 31 and 41 in this calculation were estimated, 8 and 19 were not. Errors in these values describing the estimated numbers of correctly processed cosmic ray events are due to the small data samples utilized in their estimate. If we assume the errors go as Vn, the uncertainty in the newly estimated result of 39 % is ± 2 %. This compares well (within

155

errors) with the previous value of 35 ± 3 % extracted from the background measurements done earlier (section 4.3.3). This indicates that our estimate (made in Steps 1-3 in this section) of the fraction of the total background rate due only to "pulses typical of electrons" is reasonable.

We can now estimate the reduction of the background rate near the endpoint of 136Xe pp decay due to the use of the above pulse shape analysis. There were 8 un-vetoed, electron-like signals from the pre­amplifier and 31 un-vetoed cosmic ray-like events that produced electron- like spec-amplifier pulses but cosmic ray muon-like pre-amplifier pulses (and are thus disregarded). Thus, the estimated cosmic-ray background reduction factor is: 8/(8+31) = 0.21. This rejection factor is a product of a cosmic ray dominated background energy spectrum and is expected to change when the cosmic ray flux is low enough so that gamma events dominate. Applying the previous factor to the measured background rate of 1.8 ± 0.1 cts-keV^-kg^-hr1 yields 0.38 ± 0.03 cts-keV*1'kg-1-h r1 as the reduced value for the background rate.

We can arrive at yet another value for the reduced background rate. Because we had 8 good events in the 30 keV energy window after an effective live-time of 8.3 ± 2.5 hours (of pulse shape observation) in 0.31 kg of xenon, we arrive at a rate of 0.10 ± 0.03 cts-keV-1 -kg-1 -h r1. The discrepancy between the two values for the reduced background rate is most likely due to the errors in the background measurement and pulse shape analysis estimates. Averaging the two numbers (0.38 and 0.10) yields 0.24 ± 0.03 cts-keV-1 ‘k g-1 ‘h r 1 for the estimated reduced background rate in our xenon detector experiment

The background rate obtained is 2.1 x 103 cts-keV-1 -kg* U y r 1 expressed in the background unit adopted by double beta decay searches.

156

This is over 5 orders of magnitude worse than the best number achieved so far in the Caltech-PSI 136Xe TPC experiment (0.01 cts-keV-i-kg-i-yr1),37 and 3 orders of magnitude worse than that for the germanium double beta decay experiments (1.2 cts-keV-Lkg-Lyr*1) .103' 105 The half-life sensitivities will be comparable in these latter two experiments though, since germanium detectors have much better energy resolution than in the xenon TPC (2.5 keV compared to 100-200 keV). These experiments were performed in underground laboratories where the cosmic ray muon flux was attenuated by at least 6 orders of magnitude lower than that in our above-ground background measurements.

Parent Daughter Half-life Decay Mode Q Value (MeV)

JMU 234Th 4.47 x 10® y a 4.270234Th 234 Pa* 24.10 d 0~ 0.183234 Pa* 234Pa 1.18 min IT (0.13%) 0.08234 Pa* 234 u 1.18 min 0- (99.87%) 2.207234 Pa 234 u 6.70 h 0- 2.287234 U 230Th 2.45 x 105 y a 4.856230Th 226 Ra 8.0 x 104 y a 4.771226Ra 222 Rn 1600 y a 4.871222 Rn 218Po 3.83 d a 5.5912iaPo 2l4Pb 3.05 min a 6.115214Pb 214Bi 26.8 min 0- 1.024214Bi 214Po 19.7 min 0~ 3.2702l4Po 210Pb 163.7 /is a 7.834210Pb 2i°Bi 22.26 y 0~ 0.063

210Bi 210Po 5.01 d 0~ 1.1613iop0 206Pb 138.38 d a 5.408

Table 4.1a. The 238U decay chain.

Parent Daughter Half-life Decay Mode Q Value (MeV)

232Th 228 Ra 1.41 x 10l° y a 4.0812,8 Ra 328 Ac 5.76 y 0- 0.046228 Ac 228Th 6.13 hr 0- 2.137228Th 224 Ra 1.91 y a 5.520224Ra 220 Rn 3.66 d a 5.789220Rn 216Po 55.6 s a 6.405218Po 212Pb 0.15 s a 6.907212Pb 312Bi 10.64 h 0- 0.573212Bi 212Po 60.60 min 0- (64.0%) 2.246212Bi 208'J 'J 60.60 min a (36.0%) 6.207

2,2Po 208Pb 0.30 /xs a 8.954aoa«j«| 208Pb 3.05 min 0" 2.377

Table 4.1b. The 232Th decay chain.

Reaction Tk (day) E, (MeV)( > 1 MeV only )

Branching Ratio (%) ( > 1% only )

63Cu(n,ap)S9Fe 44.5 1.099 56.51.292 43.2

63Cu(n,a+4n)56Co 78.8 1.037 14.001.175 2.281.238 67.601.360 4.331.771 15.702.015 3.082.035 7.892.599 16.903.010 1.003.202 3.043.253 7.413.273 1.75

63Cu(n,a)60Co 1934.5 1.173 1001.332 100

Table 4.2. Long lived isotopes induced by cosmic ray neutrons in copper. Only gamma rays with energies above 1 MeV and branching ratios above 1 % are listed.

Fig. 4.1. a) 228Th spectrum in D l from an external source ( ^ B i produces low energy structure), b) 228Th spectrum in a high purity germanium spectrometer with 2" of steel between the source and the detector.

358a

150a

4088

Muon

flux (

m~*

y"')

Depth (mwe)

Fig. 4.2. Cosmic ray muon fluxes in various underground laboratories.

a) TRAJECTORY OF A ZERO NEUTRINO DOUBLE BETA DECAY EUENT

X POSITION IN CM

TRAJECTORY OF A COtPTON SCATTERING ECCNT

X POSITION IN CM

Fig. 4.3. a) A typical simulated 136Xe double beta decay trajectory in 1.4 g/cm3 of xenon, b) A simulated Compton scattered event (single electron). The two events are distinguished by their deposition of energy along the track.

Fig. 4.4. Electronic set-up for pulse shape discrimination using an external 228th source.

-126.114 u« -26.1138 ut 71.6862 M

-39.3000 u* -14.3000 u« 10.7000 I*

Fig. 4.5. a) Timing requirement for amplified pulses (gaussian) with respect to the gate generated by the T-SCA (square), b) Timing between the pre-amp and spec-amp signals, c) An "electron-like" pulse out of the pre-amp.

Ch. 1 Ch. 2 Tlmebase Start Vmarker1

2.000 Volts/dlv10.00 nVolts/dlv10.0 us/dlv

-30.0000 U S -32.60 mVolts

StopVmarker2

-19.2000 us 1.400 mVolts

§ffset f fset Delay Delta T Delta V

-20.00 mVolts 0.000 Volta

-31.7000 ua 10.6000 us 34.00 mVolts

-392.000 us -192.000 us 7.99993 us

. . . .H

_ ■ 10.00 mVolts/dlvCh. 2 - 2.000 Volts/dlvTlmebase - 40.0 us/dlvVmarker1 “ -38.60 mVolts

Ch. 1 i. 2

V m a r k e r ? — I S f i f t m V o H f t

Offset - -22.00 nVoltsOffset - 0.000 VoltsDelay - -192.000 ueDelta V - 22.80 mVolts

Fig. 4.6. Characteristically "gamma-like" (double-humped) pulses out o f pre-amp. Compare with Fig. 4.5c.

-43.9000 u« -18.9000 U9 8.90000 u«

-47.1000 ut -22.1000 u» 2.90000 u»

Fig. 4.7. Characteristically "cosmic-ray muon-like" (long rise- times and/or large amplitudes) pre-amp pulses. Compare with Fig. 4.5c.

PULSE HEIGHTS FROM GATED PREAMP SIGNALS

a)100

80

40 H

20

1% window set on 2479 keV

23.2 23.4 23.6 23.8 24 24.2 24.4 24.8 24.8

PULSE HEIGHT (mV)

b)

8

120

100

80

60

40 H

20

1% window set on 2615 keV

24.6 24.8 25 25.2 25.4 25.6 25.8 26 26.2

PULSE HEIGHT (mV)

Fig. 4.8. Histogram o f "good" pulse heights from gated pre-amp signals contributing counts to a) 136Xe double beta decay endpoint, b) 208ti gamma decay endpoint The two peaks are well resolved.

Fig. 4.9. Spectrum in D l o f 2°7Bj source deposited on the cathode. There is no structrure seen at energies higher than 1.7 MeV.

COPPER PLATE

tn ^ -P R E AMP.

1 I LEAD COPPER SCINTILLATOR

Fig. 4.10. a) Passive and active shielding o f the xenon ionization chamber, b) exploded view.

Fig. 4.11. Electronic set-up for the comic-ray muon vetoed xenon ionization chamber.

-5 8 .0 000 us 42 .0000 US 142.000 US

Ch. i - 2.000 Volts/div Offset - 0.000 VoltsCh. 2 - 1.000 Volts/div Offset - 2.000 VoltsTimebase - 20.0 us/dlv Delay « 42.0000 us

Fig. 4.12. Timing between a amplified pulse from a cosmic ray traversing the chamber (semi-gaussian) and the gate generated by the veto panel (square).

Fig. 4.13. Background spectra in 50 keV bins for the different stages of shielding, a) unshielded, b) shielded with 4" lead and 1" copper, c) veto panels added. The spectrum appears flat near the endpoint of 136Xe double beta decay.

Fig. 4.14. Electronic set-up for pulse shape discrimination of signals from the actively and passively shielded xenon ionization chamber that contribute counts near the endpoint of 136Xe double beta decay.

TO OBSERVE SIGNALS

TO SET ENERGY WINDOWS

120.BOO us *20.6000 us 79.2000 US

*119.600 us *19.6000 US 60.4000 us1 •

1<

111

11

t11

1 1

1

1A ‘' !

*

.. . tO. I¥?ft«t>tstS ttrt Vatrktr1

• 2.000 Volts/dlv: :i?:88°2vS!t. StOO

Vwrk«r2 :i2d3S02-u»ClVoItt

Offsst • 0.0Dffsst - 0,rK ity - -idK its T K it* Vvolt*Voit*ut

c)

Ch. 1& J .h o s tVaorkeM

2.000 Velts/dt*18:8°u:)sh*/dlv*61.20 aVOitd Vaarktr2 - -7.600 tVolttOffset ____ ___BS155* = -?*?88oov2 lt -Oslti V • 23.60 tVoltt

• 0.000 Volts

Fig. 4.15. Some signals from the pre-amp triggered on the T-SCA window around the 13^Xe double beta decay endpoint, a) electron-like but vetoed (and therefore produced by a cosmic ray. b) slightly too large and vetoed, c) one o f the 8 un-vetoed, electron-like pulses observed.

Fig. 4.16. Some characteristically cosmic-ray-like pulses, a.b) vetoed. c,d) unvetoed.

o a*

-152.000 us -52.0000 us 45.0000 us

Fig. 4.17. Pulses from the pre-amp and spec-amp. a) electron-like from both pre-amp and spec-amp. b.c) cosmic-ray-like, d) gamma- ray-like. e) comic-ray like from the pre-amp, but electron-like from the spec-amp (and therefore due to the spurious operation of the spec-amp; it was correctly processed by the T-SCA).

CHAPTER 5 Computer Simulations of Gamma-ray

Background and 136Xe Ov PP Event Trajectories in Compressed Xenon

5.1. Gamma Ray Background Monte Carlo

5.1.1. Introduction

In our above-ground experimental apparatus we saw that the measured background rate was determined by cosmic ray muons. However, there is a small component of this rate due to background gamma rays coming from radioactive impurities in the walls of the chamber. What fraction of the measured ground level rate is due to these internal gamma rays? In a low cosmic-ray background laboratory environment, background due to internal gamma rays is expected to play a much more significant role.37 Consequently, understanding how energy is deposited in our xenon detector from these background y-rays is essential. In our efforts to understand what fraction internal y-ray background (from the chamber construction materials) contributed to the measured background rate o f Chapter 4, a Monte Carlo program was written. The predicted shape of the background internal gamma ray energy spectrum will be determined as well as the corresponding background rate near the endpoint of 136Xe pp decay. These results will apply to both above ground and

176

177

underground experiments (since the internal gamma ray background rate will be the same).

The Monte Carlo method samples a number of different possible tracks the gamma ray may take through the detector. Simulations were performed to see how many counts were expected at the PP endpoint of 136Xe due to radioactive impurities such as 228Th present in the walls of the chamber and in construction materials. Because the 20871 y-ray peak appears at 2615 keV and our measured energy resolution extrapolated to 2480 keV is approximately 30 keV (see Chapter 3 and 4), we do not expect much contribution from this line unless it has a low energy tail in our detector. In addition, by requiring a contiguous and localized deposition of charge, the number of background counts may be reduced in analogy to the pulse shape discrimination methods we used in the last chapter (for cosmic ray muon background reduction).

5.1.2. Effects Included

This program currently takes into account the following types of interactions of the y-rays with matter:

1. Photo Absorption2. Compton Scattering3. Pair Creation

The incorporation of these effects will now be described.

Photoelectric EffectIn this process the incident photon is completely absorbed by the

atom with the ejection of a photoelectron of energy Ey-Es, where Eb is

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the binding energy of that electron in the atoms of the ionization medium. For y ray energies above 20 keV, usually inner shell electrons are ejected; E b is approximately 35 keV for xenon.81 The atom then relaxes producing x-rays which do not go very far in high pressure xenon. The photoelectric cross section varies as Ey'3 and in xenon is over an order of magnitude smaller than the Compton scattering effect at 2.5 MeV.

Compton ScatteringThe gamma ray may scatter off an electron bound in an atom. The

maximum energy transferred to the electron occurs when the gamma ray is back scattered. This Compton edge is given by

I -

1 +2E.m e .

Therefore, only gamma rays with energies above 2.7 MeV will produce Compton electrons with edges at 2.5 MeV or above (to some extent, the energy resolution will smear the edge out in a measured spectrum). This formula for the edge is incorporated into the simulation when assigning the energies to the scattered gamma and electron produced. The energy distribution of the electron is taken to be uniform from zero to the Compton edge.

179

Pair ProductionThis process occurs when gamma rays, with Ey > 2meC2 = 1.022

MeV interact with the nuclear Coulomb field to produce electron-positron pairs. The positron will then slow down, stop and eventually annihilate with an atomic electron producing two 511 keV gamma rays.

The probability of the above interactions occurring is characterized by their attenuation coefficients pi (i= l, 2 or 3). The values of the attenuation coefficients as a function of gamma energy are tabulated for gamma rays in xenon and the vessel97 The coefficients used for xenon in our simulation are actually those for iodine, which is the closest element for which data is available. The vessel material is stainless steel; the coefficients used are for iron. The total probability of having had any interaction after traveling a distance x in a medium of density p is given by

P ~ l - e “ MTPx

where Pt = Pi + P2 + P3-

5.1.3. Number of Iterations

As we mentioned in Chapter 4, the result of the mass spectroscopy test performed on the vessel material (stainless steel) was that 232Th was present at a level of 1 ppb by weight. Using this number, the volume (104 cm 3), and the density (8.0g/cm3) of the chamber, we can calculate the number of thorium atoms that are present in the chamber walls: N o=2.0xl017 atoms of 232Th in the chamber walls. Next the known half­

180

life of 232Th ( l.4 x l0 10yr) and the relations N=Noe-^t and X=ln2/xi/2 give dN/dt = 107 232Th decays/yr in the walls of our stainless steel chamber. After a running time tr (in years) we expect 107-tr thorium decays. For 20 hours of running our xenon detector will be exposed to approximately 23,000 232Th decays from within the vessel walls. The 232Th decay leads to 208T134% of the time which then decays to 208Pb giving off a 2615 keV gamma ray.81 Since all the half-lives in between are negligible compared to the original 232Th half-life we may assume106 that in 20 hours the xenon detector would be exposed to 8,000 208T1 decays giving off the 2615 keV gamma ray. This 8,000 will be the number of iterations used in our simulation.

5.1.4. Monte Carlo Simulation

This program simulates the internal gamma-ray background in a xenon ionization chamber to be used in a 136Xe PP decay search. The gamma rays originate from radioactive impurities in the vessel material. These y-rays can be initiated from random positions in the vessel walls or from a single point supplied by the user. Any initial gamma ray energy is accepted. The geometry is that of a right cylinder of xenon of radius R and height 2H surrounded by a cylindrical vessel (stainless steel) with a tube wall thickness TT and cap thickness TC.

The origin of coordinates is in the center of the xenon, with 0 measured from the positive z axis and $ measured from the x axis. The direction of propagation of the gammas (dg°,dg<J>) at any given point is defined with respect to the coordinate system whose origin is at the position of the gamma ray and whose axes are parallel to the fixed system.

181

The flow chart for the simulation is shown in Fig. 5.1. It begins with the starting position and direction (randomly generated) of the gamma to be emitted due to the decay of an impurity in the vessel. The next step is to calculate the distance DIST between the initial location of this gamma ray and the nearest interface along the direction of propagation. By "interface" is meant the boundary between different materials (steel, xenon, etc.). The coordinates of the intersection of the interface with the trajectoiy are determined. The total probability of interacting somewhere within this distance is then calculated using the total gamma ray attenuation coefficient for the given gamma ray energy. This value for the total probability is used as a normalization to decide whether or not the y ray interacted using the acceptance-rejection method of random probability generation. If it did interact then the distance traveled (along DIST) before the interaction occurred is calculated, and the type of interaction is determined.

When one of the three possible gamma-ray interaction processes takes place, the appropriate distributions are sampled and the energy, position, momentum and type of any scattered particle (electron or gamma) produced is stored. For example, in Compton scattering, the scattered gamma ray energy and momentum are calculated and an additional electron is produced. The gamma coordinate frame (in which 0 and <}> are determined) has to be rotated back to the fixed laboratory coordinate system and the transformed angles 0 and d> are then used to calculate the x, y, and z coordinates of the photon and the electron. The transformation is given by the following equations:

182

cos0 = -cos<J>sin9 sin0 0 + c o s 0 c o s 0 q

cos <X> = ■ [cos <j>o cos 0 q cos <t> sin 0 - sin <J>o sin 0 sin <J> + sin 0 q cos 0 cos <j)Q ]. sin©

e ^ , 0 o.«o are tlie or current previous gamma rays,respectively. These are just the familiar expressions for a rotation of coordinates. For photo-absorption or pair creation, an electron and/or positron is created at the interaction point and the original gamma ray is gone.

Several of these three types of interactions may occur during the course of the original gammas' lifetime, during which the original or secondary gamma rays may have interacted in both the vessel and/or the xenon. The entire process is continued until the primary photon leaves the apparatus or is completely absorbed. All the secondary gammas produced are tracked in the same way as above, and their secondary particles are tracked and so on until there are no particles left to be tracked. This process constitutes one event

For each of the photon related processes, an energetic electron is produced. The tracking of the electrons is handled in a somewhat different way than the photons since the electrons lose energy in small, nearly continuous steps as they ionize bound atomic electrons close to their trajectories. It is assumed that only ionization electrons which are created inside the active region of the xenon detector contribute to the pulse height spectrum. To save computer time the ionization electrons are not tracked in this Monte Carlo; the density of the xenon is assumed to be sufficiently high so that electrons liberated by the above processes immediately stop and give up all of their available energy at the point of the gamma

183

interaction. This energy is deposited into cells depending on where along the z axis of the chamber the interaction producing the electron took place. (A detailed account of electron trajectories in high pressure xenon gas will be given later in this chapter when we model Ov pp events in xenon).

A minimum detectable background gamma-ray event energy of 50 keV (low energy cutoff for spectrum) is assumed in this program and the Monte Carlo energy resolution assumed is 15 keV, for histogramming purposes (for our background estimates, we will sum the energy in 2

consecutive bins: 30 keV, the expected detector energy resolution at 2480 keV).

5.1.5. Results

In Figure 5.2a we show the result of the simulations for 8,000, 2615 keV y-rays randomly distributed in location and direction in the vessel walls of our xenon detector. Only those events that deposit energy within the sensitive volume of the detector (2.7 cm high and 10.2 cm in diameter for the ground level background measurements of Chapter 4) are considered in this energy spectrum, which is histogrammed in 15 keV bins. We see that 29 counts are expected near the endpoint of 2°8x i decay due to 232Th present in the walls of the chamber. Only 4 counts are expected at the endpoint of 136Xe Ov PP decay, 2480 ± 1 5 keV due to this background source. This low number is probably due to the fact that the Compton edge of the 208x1 gamma-ray lies at energies below 2400 keV. In Fig. 4.13 we saw the measured background spectrum which was dominated by cosmic rays. Comparing the two spectra, we see they are consistent, keeping in

184

mind that one is dominated by cosmic ray muons the other by gamma rays (with no cosmic ray muon background component).

If we require the events of this same simulation to deposit their energy in a contiguous and localized manner (all energy deposited within two consecutive slabs along the z direction) then the number of background y-rays which produce counts produced near the 208T1 photopeak energy is reduced by nearly a factor of 3 as shown in the spectrum in Fig. 5.2b. The corresponding reduction factor at the pp endpoint is 4: there is only 1 count remaining in the 1.2% energy window around 2480 keV after this cut on spatial extent of events was imposed. We investigated the specific types of interactions that produced this count at the 2480 keV pp endpoint after this cut on the spatial extent of the events was imposed. The results are as follows:

There were 4 interactions that took place that produced this 1 count (the origin is the center of the stainless steel vessel); the sum of the energy deposited by these 4 interactions occurred within the 30 keV (2 x 15keV) window around 2480 keV.

1. A Compton scattering event occurred in xenon at the point (-0.18, 4.75, 5.49cm) depositing 2379.4 keV within the detector volume.

2. A second Compton event occurred in the xenon at the point (-1.34,4.30, 5.44cm) depositing 107.9 keV within the detector volume.

3. The scattered gamma-ray then Compton scattered in the top flange of the vessel at (2.51, 3 .4 6 ,11.88cm) depositing 2.7 keV there.

185

4. Immediately the gamma-ray then photo-absorbed in the top flange at the same point depositing the remaining 124.9 keV there.

The total energy deposited from this 1 event within the detector and localized in the z-direction was 2487 keV, which is in our energy region of interest.

This is the essence of the background pulse shape discrimination ideas developed in the last chapter. By demanding a contiguous and localized event (along the z direction), the number of counts contributing to the background could be reduced. The particular localized background gamma-ray event that contributed a count at the endpoint energy was due to double Compton scattering at the same z (but not at the same x and y positions).

Our Monte Carlo predicts that this 208x1 decay within the vessel walls contributes 4 counts in our xenon detector near the endpoint of 136Xe Ov PP decay (within To+l/2(FWHM) and To+FWHM as well) after 20 hours of counting in 0.31 kg of xenon (detector D l). Assuming we could experimentally reject (by pulse shape considerations) those events that do not deposit their energy in a contiguous and localized manner, we are left with 1 event. This leads to an expected gamma-ray background rate in this chamber of 0.005 cts-keV-Lkg-l-hr1 or 50 cts-keV-Lkg-Lyr-1, roughly 2% of the measured above-ground background rate (Section 4.3.3)

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5.2. Monte Carlo Simulation of Electron Trajectories in High Pressure Xenon Gas

5.2.1. Introduction

We developed a Monte Carlo calculation to simulate electron trajectories in high pressure xenon gas. The calculation and important results relevant to high pressure xenon ionization chambers will be discussed with emphasis on a detector that could be used in a Ov pp decay experiment. Of particular interest is the calculation of the efficiency for completely containing double beta decay events for the compressed xenon gas detector used in the measurements of Chapters 3 and 4.

The design of an ionization chamber to detect Ov pp decay depends on the precise understanding of electron trajectories in the gas. The maximum extent of the trajectory of the electrons emitted in the decay and the efficiency for detection of PP events must be known as a function of the xenon gas pressure and detector size. In a TPC, precise dE/dx information along the trajectory, in addition, would help to reduce background. In Ov PP decay o f 136Xe on average each electron has an energy of 1.25 MeV. Obviously for high detection efficiency and energy resolution we must completely contain as much of the ionization created by Ov pp events as possible. These events can occur anywhere in the active (sensitive) region of the detector, between the cathode and the grid. Our goal was that this volume o f 1.4 g/cm3 xenon be large enough to entirely enclose at least 80 % of the randomly distributed Ov PP decay events.

This Monte Carlo calculation is general and may be extended to a large range of gases and gas pressures as well as electron energies. It is

187

based on the Moliere theory of multiple scattering and the Bethe-Bloch formula both of which will be reviewed in the next section. We note that in this calculation the electron is continuously multiple scattered in its trajectory through xenon even though it is occasionally interacting and losing energy in other ways, such as through inelastic, elastic and radiative collisions. These effects will be discussed below.

5.2.2. Effects included

The Moliere Theory of Multiple Scattering

The first theory of multiple scattering was given by Saunderson and Goudsmit in 1940.107 The understanding of scattering by a single isolated atom is necessary in order to apply this theory to a specific problem. Moliere presented his theory of multiple scattering in 1948.108 It described the scattering of fast charged particles by a screened Coulomb field. Five years later Bethe showed that this theory of Moliere could be obtained from the theory of Saunderson and Goudsmit by making certain simplifying assumptions. 109 In the following development we have closely followed Bethe's paper. These expressions will be incorporated into our Monte Carlo.

The probability that an electron of momentum p and velocity v is scattered into the angle 0 and angular interval d0 after traversing a thickness t in a material of atomic number Z and density of atoms N is given by

188

f ( 0 )0 d0 = 5 ^ Jo ydyJ0 (X .y)exp ^ y 2 ( - b + ln^-y2 ) j

where, y is a dummy variable, X=0/%c and

(b = In Xc

1.167Xa

Xc is the angle parameter and characterizes the minimum single scattering angle that can occur:

2 4jiNte4 Z(Z +1)Xc “ / \2(pvr

Xa is the characteristic screening angle and is given in Moliere's approximation as

Xa =X(W 1-13 + 3 -7 6 a 2 •

XO is the critical angle below which deviations from the Rutherford scattering law (with the characteristic 1/0 4 form) become apparent because of nuclear effects. It is given by

XZ° (0.885a0Z-1/3) ‘

a=Ze2/ftv, X=fi/p is the electron DeBroglie wavelength and ao is the Bohr radius.

189

In the derivation of f(0) Bethe assumed X0«X c* which is true for reasonably thick t, but will fail for y of the order of Xc/XO'-'C1/213. The quantity eb~(Xc/Xa) 2 is approximately the number of collisions Qo that occur in the thickness t of xenon atoms. By examining the above formulas we see that for a low pressure gas Moliere’s theory of small angle multiple scattering breaks down. Moliere considered his model to be valid for &o>20 and the parameter B (defined below) > 4.5. In this work we found that in 62 atm of xenon gas a 1 MeV electron that travels 2 mm, has Ho=600 and B = 8 ; so we expect Moliere’s theory to apply.

Moliere evaluated f(0) for all angles by a change of variable '0=9/(XcB1 2). B is a constant defined by : b=B-lnB. With these definitions f(-O) can be expanded in a power series in B_1:

f (fl)fldfl = 0 d 0 [f (0) (0 ) + B- 1f (1) (fl) + B- 2 f (2) (£ )+ ....] ,

where

/

f (n> (£ ) = — J^uduJo (flu)exp(-^- n! 4 — in 4

( un

with u s B ^ y . In the lim it o f large angles, the distribution function tends toward the Rutherford single scattering law: fR (0 )0 d0 = (2 /B ) d ^ M 3 . T h e ratio o f actual to Rutherford scattering is R = f/fR = l/2 $ 4 (f(l)+ f(2 )+ ^ w hich g iv es asym ptotic expressions for f 1 and f2 . Together with f(°) obtained from f(n) above w e have

190

f (0) (ft) = 2 e”d ,

ft4

f (3) ,A \ _ 16(lnft + ln 0 .4 )ft6 ( 1 - 9ft" 2 - 2 4 f t ^ ) ‘

For d>4 these expressions will be used in our simulation. For ft<4 we will use the values in Table 2 of Bethe's paper to determine f(l) and f(2).

In the simulation we will not use approximations to f(0) for small and large values of 0 since it is not a simple function for the entire angular range of interest. We will use rejection techniques for generating f(0). If x and y are random numbers (both between 0 and 1), the standard method is to generate f(x) and accept x provided f(x)/f(0) < y. But since f(x) rapidly decreases with x this method is inefficient. A better approach is to first generate x in a trial function e(x) > f(x)/f(0). We accept x provided y-e(x) > f(x)/f(0). The most appealing choice for e(x) is a Gaussian. Note that although this technique of choosing the distribution e(x) improves the efficiency of generating f(x) there will be a smaller range of values of x that will be accepted. Any error in the generation of f would probably be due to not using enough terms in the expansion.

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Energy Loss of Electrons Traversing Xenon

Inelastic Collisions—Excitation and Ionization The average energy lost per distance traversed by an ionizing

particle in a material made of independent atoms and due to only inelastic processes (ionization and excitation) is given by110

dEdx = 4 n r^ 5 5 |-N Z (A + B ) ,P

where,

A = fn P y V y “ * m c and

B = 2 y d (Y g1- + l - ( 2 y 2 + 2 y - l ) l n 2

where ro is the classical electron radius, y K l-P )'1/2, N the number density of atoms for the medium (xenon), Z the atomic number and I the average excitation potential of the medium in eV (which for Z > 12 is approxim ately111 I=Z-(9.76+58.8Z-119) = 555 eV for xenon). By studying the above formulae we see the value for dE/dx rapidly increases as the electron slows down and therefore most of the ionization created in an electron track will be towards the end.

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Elastic Collisions-Delta or "knock-on" Electrons"Relatively hard electron-electron collisions often cause the emission

of energetic secondary electrons, commonly called delta electrons. These delta electrons have the capability of producing further ionization. The number of these secondary electrons of energy Eg emitted per unit distance and created by an incident electron of kinetic energy Ti, in a medium with electron density Ne is given by112

W (Ti)O *N 5 (E 5 ,T1) =

where

Ircrnm-Np w (Ti > ~ — °p2- ■

in the units in which h - c= l. This formula is valid for Eg « T i. However, since it is derived for relatively hard collisions we will impose a lower energy cut-off of 50-100 keV, below which delta electrons are not produced. Decisions on whether or not a delta electron is ejected are made using rejection techniques based on the above formulae. If a delta electron is produced the energy of the incident electron becomes T1-E 5 . The energy, momentum and location of the delta electron produced is stored for treatment in later iterations in this trajectory simulation (where this new particle will act as the incident particle).

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Radiative Energy Loss—Bremsstrahlung Effect The electron, through Coulomb scattering with the nucleus of the

medium, may give o ff radiation. This bremsstrahlung ("braking radiation") yield, given in terms of the ratio of energy loss by radiation to the total energy of the primary electron, is 6 - 7 %. This relatively significant energy loss, if it escapes from the detector, will change the efficiency and/or the energy resolution of an ionization chamber. We have studied the effect of bremsstrahlung photon production on the efficiency of the detector (that is, how often the photons created deposit any energy outside the active volume of the detector).

An analytic expression for the probability of generating a bremsstrahlung photon was not available (reference 12 has a formula, but it is too complicated for practical Monte Carlo simulations). We instead used tabulated numerical values1! 3 of the bremsstrahlung differential cross section da/dk, where k is the photon energy. Values for da/dk are given for k/Ti from 0 to 1 and Ti from 1 to 2000 keV, where Ti is the energy of the incident electron (the average energy of each electron in Ov PP decay of 136Xe is 1250 keV). For values of Ti in between the tabulated values linear interpolation was applied to obtain da/dk.

A low energy cut-off k/Ti=0.01 was imposed for all T i. We then calculated the total cross section

c ( T i )

where ko is the cut-off for a given T i. Using the number of xenon atoms per cm3, N, we then turn a into the probability, Pb, of having a

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bremsstrahlung interaction while the electron of kinetic energy Ti traverses a distance Ax. An alternative approach would be to calculate the mean free path A,b=l/Na or "radiation length" and generate P b =l- exp(AxAb) as the above probability.

We then generate a random number x between O an l. If Pb > x, k is generated randomly between koand Ti, and the corresponding value for da/dk and Pb(k,Ti) at that k and Ti is calculated. We accept k provided that this Pb is greater than a random number between 0 and the maximum Pb(k,Ti) for that value of Ti. The energy, direction (from conservation of energy and momentum) and location of this photon produced is stored. The scattered electron has a new direction and energy (Ti-k) and continues on as before. At this stage no energy in the form of ionization has yet been deposited.

The history of the bremsstrahlung photon created is then followed using a routine incorporated into this Monte Carlo which is similar to that used for the interaction of background gamma rays in our chamber (described in the first half of this chapter). The only difference is that the electrons produced by the interaction of the y-rays do not stop immediately where the photon interacts (which is what we assumed in the gamma-ray background Monte Carlo; see section 5.1.3). Instead the energy, momentum and location of these electrons created are stored in an array and treated in later iterations of this simulation in the same manner as for the primary electron.

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5.2.3. The Monte Carlo Simulation

Armed with an understanding of the important interactions that an electron encounters while traversing a medium, we can now concentrate on the simulation. The geometry is exactly the same as for the y-background calculation. Fig. 5.3 shows the program flow chart. In this routine one has the choice of whether the primary electrons created are monoenergetic, created by Compton scattering, or generated by a Ov PP process in 136Xe. In any case the various momenta, energies and location (randomly generated within the active volume of the detector) of the event are stored in separate arrays. If an electron originates from the Ov PP process it is accompanied by a second electron. The initial energy and momentum of both electrons are dictated by the single electron energy spectrum and angular distribution of this nuclear decay. These distributions depend on the mechanism that drives the decay (neutrino mass or RHC). In Chapter 1 we saw two possible single electron energy spectra and angular correlations for the two mechanisms of Ov pp in 136Xe. These are incorporated into the routine and the user is given a choice of which is to be used. Once the energies and momenta of the two electrons are stored, each electron is then treated independently in the simulation of its trajectory.

The trajectory of an electron in high pressure xenon gas is best followed in terms of small track segments beginning at the origin of the event. The most obvious technique to accomplish this is to allow the electron to traverse a given distance and then determine the energy lost after completing that step. However, due to large values for dE/dx toward the end of an electron trajectory the length traversed for a given energy step rapidly decreases at the end of the trajectory (especially for high

196

xenon density). Since this "step" will be used as the target thickness in this calculation, the approximation Xc»Xa and, thus, the multiple scattering derivation could break down in that end region of the trajectory.

Instead, we chose to generate the electron track in the following manner (we also expect this approach to involve less computer time): Originally the electron has a given energy Ee allowed by the decay producing it. We then degrade this energy in small steps ESTEP « Ee and calculate the range R (in three dimensions) that the electron must travel in order to lose ESTEP to inelastic collisions (ionization and excitation). This R is used as the "track segment". We then check to see if any energy loss processes other than inelastic have occurred (delta electrons or bremsstrahlung) as the electron completes this step. If so, the initial electron energy is degraded accordingly, as described in the previous sub­sections. The number of electrons created from a given incident electron, as well as their locations, energy and momenta, are stored in various arrays and will be used in later iterations that treat each of these electrons as the "primary" electron.

We then evaluate %c and B in the multiple scattering calculation using R as the target thickness in the formulae. The direction 0 that the electron scatters into (due to multiple scattering) is generated using f(6 ) as discussed before and the azimuth angle <j> is randomly generated between 0 and 2tc. At the completion of this step the electron coordinate frame, in which 0 and <j) are determined, must be rotated back to the fixed laboratory coordinate system (using the same formulae for a rotation o f coordinates given before, for the ^-background calculation of section 5.1.4). The transformed angles together with R are then used to calculate the new x, y, and z coordinates of the electron. That is, given R, 0, and <}>, we find the

197

new location o f the electron after the given energy loss and length traversed using spherical coordinates. Starting from this new position the next segment is treated in the same manner using the new energy Ee- ESTEP. This entire process continues until the energies of the primary and all of the energetic secondary electrons produced are reduced to zero or until Xc/Xa reaches a given value below which the multiple scattering calculation is no longer valid.

5.2.4. Results

This electron trajectory simulation was performed to simulate electron trajectories for various electron energies and xenon pressures. In addition, we ran this simulation for several thousand events and determined what fraction of the trajectories formed by electrons emitted from Ov pp decay deposit all of their energy in the sensitive or active volume of our detector (completely contained inside the detector). This fraction is the efficiency of our detector. The "fiducial volume" of the detector is then defined as the active volume times this efficiency.

Fig. 5.4 shows the variation of f(0) with 0 in the Monte Carlo. Scattering at small angles is dominant. A typical electron trajectory in the sensitive detector region from a Ov PP !36Xe in 62 atm of xenon is shown in Figs. 5.5a, b and c in the x-z, y-z, and x-y views, respectively. It is evident that at higher energy the scattering involves mostly small angle deflections. Towards the end of the trajectory scattering at large angles becomes more frequent, and the electron’s path begins to curve around. The projected range of the track in Fig. 5.5 along the z-axis is approximately 2 mm. The energy deposited along the z-direction for this

198

trajectory is shown in Fig. 5.5d. As mentioned in the last chapter, the particular form and extent of the energy deposited in our detector from a given event determines the shape of the pre-amp output signal.

In Fig. 3.6 we showed a simulated monoenergetic electron trajectory (x-z projection only) from a 207Bi source deposited on the cathode (976 keV electron). The projected range in that case was also 2.0 mm. The average projected ranges (along z) over 10,000 simulated events (including delta-electron effects) is 0.24 and 0.14 cm for Ov pp and 976 keV monoenergetic events, respectively. Obviously the actual curve length along an electron trajectory decreases with increasing xenon density. The cathode to grid spacing in our detectors of Chapter 3 were 2.69 and 4.97cm, respectively. These distances are much greater than the above projected ranges. This is important in order to minimize positive ion effects and ambiguities in signal formation (see Chapter 3).

Multiple scattering and ionization allow a significant number of trajectories to be enclosed in a smaller volume (because of the observed curving effects and energy loss). Delta electron and bremsstrahlung photon production will affect the detector efficiency because these processes deposit energy differently than that characteristic of multiple scattering. A bremsstrahlung photon for example, has a high probability of depositing energy outside the sensitive volume of the detector.

We can estimate an optimum value for the active volume of an ionization detector for a PP decay search by observing how the efficiency for completely enclosing Ovpp events varies with its size and gas pressure. Fig. 5.6a displays how the efficiency varies with the radius r and height 2r of a hypothetical chamber for various gas pressures (excluding delta and bremsstrahlung photon production). With r and h equal to 5.1 and 2.7 cm,

199

respectively (the dimensions of the detector (D l) that was used for a background measurement in the last chapter), the efficiency for Ovpp events is over 76 % for xenon at 62 atm (1.4 g/cm3) without delta electron or bremsstrahlung photon effects included.

The effect o f the delta electron and bremsstrahlung photon production was studied. There are on average 5 (4) delta electrons ejected for a delta cutoff of 50 (100) keV for a typical Ov pp event in 62 atm of xenon (1.4 g/cm3). As there was not a significant difference in the efficiency calculated using the two cut-off values, we will choose 100 keV as our cut-off for the remaining discussion. The energy spectrum of the delta electrons ejected is shown in Figure 5.7a. The average number of delta electrons emitted as a function of the incident electron energy is shown in Fig. 5.7b. Figures 5.5a, b and c showed several delta electrons ejected at large angles to the track. Fig. 5.6b shows how the efficiency varies with the xenon density for our detector (Dl of Chapter 3). The efficiency at 1.4 g/cm3 in D l increases to 85 % (averaged over 10,000 events) with the delta electron effect incorporated. This improvement is expected since, by ejecting delta electrons at large angles to the primary track, one decreases the average range or extent of the event.

do/dk vs. k for a 1.25 MeV incident electron is shown in Fig. 5.8a for the production of a bremsstrahlung photon of energy k. Fig. 5.8b shows Pb(Ti) vs. T i. We see that the total probability of a bremsstrahlung photon being emitted as a function of incident electron energy is fairly flat. Figure 5.9a,b,c show an electron trajectory with bremsstrahlung occurring a few times; Fig. 5.9d plots the energy deposited in the z-direction for this trajectory. We see that an event with bremsstrahlung occurring is characterized by several non-contiguous charge depositions.

200

The energy spectrum of the bremsstrahlung photons produced in this Monte Carlo simulation is displayed in Fig. 5.10. The average fraction of the initial energy given to these radiative effects is 6-7% for our xenon density. This does not mean that the photon produced is not absorbed somewhere within the detector. The percentage of events with bremsstrahlung effects incorporated that are completely enclosed by the active region of the detector (the detector efficiency) is 83%, not significantly lower than that without radiative effects included. So radiative effects do not change the efficiency much, if at all; this is due to the fact that on average only one radiative photon is produced per event.

Often these radiative events were characterized by random charge depositions inside the detector, disconnected from the main tracks (similar to background gamma events). If we require that the projected range of the electron tracks from Ov pp decay is less than 1 cm (contiguous and localized charge depositions), including bremsstrahlung effects, the efficiency is reduced to 76 %.

As discussed in Chapter 4, the gamma background rejection efficiency in our drift chamber (a 1-D TPC) depends on the ability to distinguish a purely electron-produced track from a y induced one. An electron-like event will be contiguous and localized. A gamma or bremsstrahlung event may not deposit all its energy within a small volume. If we were to study the energy deposited along die z direction (along the E- field) we should be able to distinguish between the two types of events. To demonstrate this, we observe the energy deposited along the z direction for a trajectory that has a bremsstrahlung photon event present (Figs. 5.9abcd). This trajectory was produced by the massive neutrino mechanism. We see that some of the total energy is deposited far away (disconnected) from the

201

main track due to the bremsstrahlung photon propagation through the gas. Experimentally this separate deposition of charge might be seen in a digitized pre-amp pulse. These non-contiguous tracks would be rejected in an experiment that utilized pulse shape discrimination since they are not characteristic of events caused by purely electron-like interactions (see Chapter 4).

The probability of bremsstrahlung occurring depends on the energy of the electron. The two different mechanisms of Ov pp decay have distinct single electron energy distributions (Fig. 1.6). The RHC mode has on average a higher energy electron emitted than for the massive v mechanism. Thus, on average the RHC mechanism may produce electrons that bremsstrahlung more often. The detector efficiencies, including radiative effects, might be different depending on whether the decay was driven by one or the other mechanism. However, the efficiency was 83% and 80% for the my and RHC mechanisms, respectively, not a statistically significant difference.

Could we distinguish between these two mechanisms of Ov pp decay in our xenon ionization chamber by their charge depositions alone? Fig. 5.11 shows the spectrum of the extent of Ov events projected along the z- direction for the two mechanisms. We see on average they have the same structure along the z-direction. The two mechanisms cannot be distinguished in our detector by their charge distributions alone. For both modes, the maximum extent of the events is approximately 4 mm, while the average extent is roughly 2.6 mm. The reasons for this indistinguishability between the two mechanisms, both in detector efficiency and energy deposition, are due to the high density of the xenon and the flatness of the bremsstrahlung probability distribution with initial electron energy.

Start

Find Where In the Vessel the Decay Originates

Fig. 5.1. Flow chart for the gamma-ray background Monte Carlo.

GAMMA BACKGROUND ENERGY SPECTRUM IM 01a)

c0uMTS

b)

c0uNTS

108 158 | 200energy/15 keV bins 2480

WITH CUTS ON SPATIAL EXTENT OF EVENTS

100 150 t 290energy /15 keV bins 2480 keV

C0uNTs

c0uNTS

Fig. 5.2. a) Predicted gamma-ray background energy spectrum in D l (1.4 g/cm3 of xenon) due to the presence of 232Th in the walls of the chamber, b) with cuts on the spatial extent of the charge deposited in the detector.

Define En ergy Step

C a lc u la te R ange for E n e rg y step ------------

8 or BremsstrahlungProduction’ *-'-'''' Yee

Store Position, Energy and Momentum of p a rt ic le s Created

Fig. 5.3. Flow chart for the electron trajectory Monte Carlo.

»ma)3C2

ANGULAR DISTRIBUTION OF MULTIPLE SCATTERING

900

800

700

600

500

400

300

200

100

0

1 0 0 0

Fig. 5.4. Angular distribution of Moliere multiple scattering in 1.4 g/cm3 xenon.

.1 1,1 | ,--- j--- ,----1----,---

0 1 2 3 4 5 6 7

ANGLE

nnKo

zcz

TRAJECTORY OF a ZERO tCUTRIMO DOUBLE BETA DECAY EVENT

a ) 0.43 T --------------------------------------------------------------------------------

2 0.6

P0«i a.53 T 1 0 H 0.3tNCn 8.43

0.4

b) 0.63

2 0.6-P0sI 8.33 ■ T I 0 «

0.3IN

N 0.43 -

0.4 '-I

K. \• A* • mS V ../; \*

—i---- 1---- r-.4 -4.33

1 n4 .3

T 1---- 1—1.83 - 4.8 1.13

X POSITION IN CM

origin of event

/ f i tJ ''i } '* II /:

I- 0 .9

—I--- 0.8

| i | i

- 0 .7 - 0.4 - 0.3y POSITION IN CM

ENERG

Y DE

POSIT

ED

(UNITS

OF

ESTE

P)d)

ENERGY DEPOSITED AS A FUNCTION OF Z

Fig. 5.5. A typical simulated trajectory of a 136Xe double beta decay event in our compressed xenon detector, a) x-z b) y-z andc) x-y projections including delta production, d) the form of the energy deposited along the z direction.

ENERG

Y DE

POSIT

ED

(UNITS

OF

ESTE

P)

a)

a

RADIUS (cm)

b)1 .0 -

0 .9 -

0 .8 -

60 .7 -

§ 0 .6 -u

1 05-

0 .4 -

0 3

02-0.6 0.8 1.0 1.2

DENSITY (g/cc)

Fig. 5.6. a) How the detector efficiency for 136Xe double beta decay varies with radius, r in a high pressure xenon ionization chamber of height 2r.. b) detector effiency including delta electron production as a function of xenon density in D l (r,h =5.1,2.7 resp.).

deltas included deltas excluded

DELTA ELECTRON E^R G Y SPECTRUM

a)

NUMBER

680

500 -400 -

300 -

200 -

100 -

NUM0ER

1500

OELTA ELECTRON EfCRGY (KEU)

b)

w

I&»

%t---------------- r

1000 2000 3000INCIDENT ELECTRON ENERGY (keV)

Fig. 5.7.a) Energy spectrum o f delta electrons ejected, b) the average number of deltas ejected as a function of primaiy electron energy.

a) d if f e r e n t ia l bremsstrahlung x - s e c t io n

DIFF

sccT

MB

pER

KEU

2S00

2000 -

1S00 -

1000 -

500 -

SECT

M0

PER

KEU

1500

BREMSSTRAHLUNG PHOTON EtCRGY IN KEU

TOTAL BREMSSTRAHLUNG PROBABILTIES

INCIDENT ELECTRON ENERGY IN KEU

Fig. 5.8. a) Bremsstrahlung differential cross-section as a function o f emitted photon energy and b) Bremsstrahlung total probability vs. incident electron energy.

o

y POSITION

IN CM

Z POSITION IN CM Z POSITION IN CM

Z POSITION IN CM Z POSITION IN CM

TRAJECTORY Or

A NEUTRINOLESS

OOUBIE BETA

EVENT

ENER

GY

DEPO

SITED

(N

ORM

ALIZE

D U

NIT

S)

d) ENERGY DEPOSITED AS A FUNCTION OF Z

1.5 2 2.5Z—COORDINATE IN CM

Fig. 5.9. a) x-z, b) y-z, c) x-y projections of a zero neutrino double beta decay event with bremsstrahlung and delta effects included,d) energy deposited along the z-direction.ENE

RGY D

EPOSIT

ED (NO

RMALI

ZED U

NITS)

NUM

BER

BREMSSTRAHLUNG ENERGY SPECTRUM

1000

T r “ ~l ' I 1 T 100 20 0 300 400 500 6 00 700 8 0 0 90 0 1000

ENERCr RAOIATED (KEV)

Fig. 5.10. Bremsstrahlung photon energy spectrum.

NUM

BER

a) P R O J E C T E D E X T E NT OF E VE N TS I M A S S I V E N E U T R I N O /

300

250 -

in

oo

b)

1 1.5 2

Z-EXTENT IN CM

PPC'JECTEO EXTENT OF EVENTS (R H C )

=>oo

Z-EXTENT IN CM

Fig. 5.11. Spectrum of spatial extent (projected along z) o f a) a non-zero neutrino mass and b) a right-handed current zero neutrino double beta decay event. The spatial extent of the charge deposited appears almost identical for the two different mechanisms.

CHAPTER 6 Results and Conclusions

6.1. Projected Sensitivity to the Half-life of 136Xe Ov PP Decay

We have demonstrated that using compressed xenon gas near its critical point as an ionization medium for the search of the Ov pp decay of 136Xe has several appealing characteristics. A large volume of high density xenon, which is the source of the double beta decay as well as the ionization medium, can be obtained at low cost. With proper methods of gas purification, the amount of charge collected from a given event and its fluctuation is independent of drift distance in the xenon and stable with time. Because of the high degree of stability in charge collection, long run times can be achieved with little or no adjustments to the apparatus. The energy resolution is excellent and the efficiency for completely containing events is high. Furthermore, background rejection through pulse shape discrimination is possible even without detector segmentation. With segmentation, considerable gamma-ray background reduction may be possible.

We now summarize the results obtained utilizing our 62 atm (1.4 g/cm 3) xenon ionization chamber that are relevant to determining the projected sensitivity for a 136Xe Ovpp decay search. The values quoted initially will be for the small drift volume D1 of Figure 3.2 (sensitive region: 5.1 cm radius, 2.7 cm high, and 0.31 kg of xenon). Comparisons will be made with the Caltech-PSI-Neuchatel experiment,37 which currently has placed the most stringent limit for the lifetime of 136Xe Ov PP decay. We

219

220

will then extrapolate our results to a larger volume version of this detector operated in an underground laboratory.

Resulting Parameters:

1. Number of 136Xe atoms present in the sensitive detector region assuming isotope enriched xenon (63% 136Xe): 8.9 x 1023.

2. Detector efficiency for containing 136Xe Ov PP decay events for both the neutrino mass and RHC mechanisms (delta electron and breiiisstrahliing photon production effects included; see Chapter 5): 83%.

3. Measured background rate (in 0.31 kg of xenon with passive and active shielding and pulse shape discrimination rejection factor; see Chapter 4):

0.24 ± 0.03 cts-ke V- 1 -kg- 1 -hr1.

4. Energy resolution (FWHM) extrapolated to the 136Xe Ov PP decay endpoint energy, 2.48 MeV (see Chapter 3): 30 keV.

The projected sensitivity of an experiment is given by (see Chapter 2):

/n 2 • N q • e • tTl/2“ VN b - a e T '

Using the above values we arrive at ^ 1.7 x 1020 years after 20 hours of above-ground counting. After 2 months of running time, assuming the same background rate, we would obtain 1.5 x 1021 years as the projected

221

sensitivity to the half-life of 136Xe Ov PP decay in our chamber. This is over two orders of magnitude lower than that obtained by the Caltech experiment. However, considering that we performed the Yale experiment above-ground, using a very small detector volume, and ran for only 20 hours, it is remarkable that a sensitivity of over 1020 years was achieved; evidently the high energy resolution, efficiency and density of compressed xenon gas near its critical point as an ionization medium allows a high degree of sensitivity even in the presence of these limitations.

6.2. Comparisons with the Caltech Experiment

The current half-life limits of the Caltech-PSI-Neuchatel 136Xe Ov PP decay experiment (CPN) are Tn2(0v) > 2.5 x 1023 and 1.7 x 1023 y for the neutrino mass and right-handed-current mechanisms, respectively, at the 90 % C.L.37 The difference in sensitivity between the two processes is due to their different efficiencies (see Chapter 5). These limits are two orders of magnitude more sensitive than the limit obtained in our above-ground xenon ionization chamber, assuming two months running time. In fact, we would have to run continuously (above ground, with the same shielding) for over 4000 years in this small chamber to reach the same limit of 2.5 x 1023 years.A comparison between the Yale and CPN experimental parameters is summarized below.

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CPN YaleType of detector: 3-dim. imaging TPC 1-dim. drift chamberNumber of 136Xe atoms No in sensitive volume:

1.6x1025 8.9 x 1023

Detector efficiency, e (neutrino mass mode):

2 0 % 85%

Running time (yr): 0.38 0.17Sensitive volume (I): 207 0.22

Mass of xenon atoms in sensitive volume (kg):

6.1 0.31

Extrapolated energy resolution (keV) at 2.5 MeV:

164 30

Location: St.Gotthard Underground Lab

W.N.S.L second floor

W ater eq u iv a len t overburden (m):

3000 0

Veto panels: no yesOverall cosm ic-ray m uon attenuation factor

106 20

Single-electron background rejection efficiency:

97% none

Measured background rate: cts-keV-bkg-Lyr1

0.01 2.1 x 103

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The number of fiducial 13<5Xe atoms in the sensitive region of the detector (folding in efficiencies) is 3.2 x 1024 in the CPN experiment versus 7.6 x 1023 in ours. So, even though their sensitive volume is nearly 3 orders of magnitude larger than ours, their poor efficiency (a factor of 4.3 lower than ours) and low density (0.01 vs. 1.4 g/cm3) gives the small Yale detector a comparable number of fiducial candidate double beta decay atoms.

The energy resolution near the double beta decay endpoint is a factor of 5.5 better in the Yale detector; this is important to reduce the number of background counts allowed into the energy region of interest.

The reason the CPN underground experiment is so much more sensitive than Yale's above-ground apparatus is their lower measured background rate (a factor of 2 x 105 lower). This small rate is due to the highly attenuated cosmic ray muon flux (by a factor of 106) in the Gotthard tunnel and not to the efficiency of their track reconstructing TPC in rejecting single electron events (from the Compton scattering of gamma-rays). Background gamma-rays determined the background rate in the CPN experiment37 since the muon flux was so weak. The effect of the muon flux on the background measurement was smaller in the CPN experiment by a factor of 106/20 = 5 x 104 (the factor 20 is the overall cosmic-ray muon attenuation factor in our experiment, including active shielding and pulse shape discrimination, assuming only cosmic ray muons contributed). This factor, 5 x 104, would almost entirely explain the above factor of 2 x 105

lower background rate in the CPN experiment, if eveiything else were the same.

Obviously the cosmic ray muon flux in our experiment must be lowered significantly and/or the vetoing efficiency must improve. This

224

could be accomplished by performing an experiment in one of the various underground laboratories shown in Fig. 4.2 and/or by building a highly efficient "house" of veto panels which completely shielded all possible paths to the detector. Most current pp experiments use these standard techniques of cosmic ray background reduction.

If we were to place our same chamber in the St. Gotthard Tunnel, we might expect a half-life limit comparable to that achieved by the CPN experiment due to the overwhelmingly smaller cosmic-ray muon flux. If the resulting measured background rate in our chamber dropped by at least a factor of lO4 in this muon attenuated environment then, since the projected half-life sensitivity goes as the inverse square root of the background, we might expect to gain nearly two orders of magnitude in our half-life sensitivity underground. This would explain the two orders of magnitude better results obtained by the CPN experiment This factor of 104 is feasible since (a) there is strong evidence presented in Chapter 4 that the measured above-ground background rate* was determined by cosmic ray muons alone and (b) the muon attenuation factor in the tunnel is a factor of 5x104 times better than in our current experiment. But we will go further and predict what limit could be reached with a larger detector volume.

6 3 . Extrapolation to a Larger, Underground Xenon Ionization Detector

We estimate that the largest detector configured inside the existing stainless steel vessel used in this work would have a sensitive cylindrical volume of 8 cm in radius and 16 cm in height (still a relatively small volume). For our extrapolation, we will assume these detector dimensions

225

(split into two detectors with a common central anode for ease of electric field uniformity) and 1.4 g/cm3 of xenon enriched to 63% in 136Xe. If we

background rate is determined by the ambient gamma-ray radiation, we would obtain a projected half-life limit that would surpass the CPN experiment. Such a chamber would have: No = 1.3 x 1025 active 136Xe atoms; a 95 % efficiency for completely containing all Ov pp decay events (from Monte Carlo studies); assuming 30 keV energy resolution at the endpoint energy (2.48 MeV). This translates to

where t is the running time in years and Nb is the background rate in counts-keV- 1 -kg- 1 *yr1.

Clearly, the background rate will determine the sensitivity of our experiment. We will consider two values for the background rate in our estimation of the projected sensitivity to the Ov half-life and the electron neutrino mass parameter. The first will be that obtained from our background gamma-ray Monte Carlo program described in Chapter 5 (assuming all background is due to gamma-rays from the decay of 232Th in the walls of the chamber).

For a cylindrical sensitive detector region of 16 cm in diameter and 16 cm in height: assuming the same energy resolution (30 keV), xenon density (1.4 g/cm3), volume of the stainless steel comprising the chamber walls (104

cm3), percentage of thorium in the steel, and 1 year of counting, we expect 320 counts near the endpoint of 136Xe pp decay. Only 75 of these events

move the chamber to a suitable37 underground laboratory where the

226

would remain after requiring the energy to be deposited in a highly localized volume in the z-direction: a rejection factor of 4 is obtained by requiring contiguous and localized depositions of charge. This is equivalent to a pulse shape rejection factor of 4 for background gamma-rays in a xenon ionization chamber (assuming our pre-amp signals could identify those events that are characterized by a non-localized deposition of charge).

Using 75 counts in 4.5 kg (16cm x 16cm) of xenon, this translates to an expected gamma-ray background rate of 0.55 cts-keV-Lkg-Lyr1. This result translates to a half-life sensitivity of T1/2 > 1.0 x 1024 yr. Using thematrix element calculations of Pantis et a l29 (see the end of Section 1.2.4.4), a limit for the Majorana neutrino mass parameter, <mv>, of 1.2 eV would beachieved.

If we assume the same gamma-ray determined background rate as that quoted in the CPN experiment (which is plausible since the CPN vessel is approximately37 20 times more massive than ours) and 1 year of running time we should be sensitive to a Ov half-life of T1/2 ^ 7.5 x 1024 yr. Thiswould lead to an upper limit for <mv> of 0.4 eV.

The projected values obtained above for the half-life sensitivity and the electron neutrino mass parameter (using either value for the estimated gamma-ray background rate) are more sensitive than those obtained from the most recent LBL-UCSB 76Ge results: T°,v2 > 1.2 x 1024 yr, 90% C.L., mv <2.4 - 4.7 eV after three years of data t a k in g .30*114 The CPN experiment37

(r^ > 2.5 x 1023 yr, 90% C.L.) would have to run continuously for over 100years to achieve the same half-life sensitivity as our high resolution, compressed xenon gas ionization chamber.

If the goal is to identify a possible candidate Ov pp decay event then obviously a TPC is necessary since it can visually reconstruct tracks.

227

However, if the goal is to set a more stringent limit on the lifetime of Ov pp decay of 136Xe then we expect a compressed xenon gas ionization chamber, with its excellent energy resolution and high efficiency and density, to have a higher degree of sensitivity.

6.4. Improvements: Lowering the Background Rate

Improvements to the above projected sensitivities of a zero neutrino double beta decay experiment using a highly compressed xenon drift chamber could be accomplished by lowering the background rate. Assuming we are in an environment in which the background rate is determined by gamma-ray interactions, we expect to see many events characterized by a non-contiguous deposition of charge. Background reduction could then be accomplished by improving our event identification. Rejecting events by the manner in which charge is deposited along the z- direction alone is not enough to efficiently discriminate against single electron (gamma-ray induced) background events. Segmentation of the anode, for example, would improve the situation. Several electronic techniques that could be utilized to reduce background gamma ray events in our xenon detector will now be discussed.

Obviously if we had a two or three-dimensional picture of a particular background event (how charge was deposited spatially in the detector) we would have a better chance of being able to distinguish between two- electron events (a PP decay event) from single electron events (from Compton scattering, for example). However, in 1.4 g/cm3 of xenon the ionization tracks are so short (2-4 mm, on average; see Chapter 5) that most

228

precise dE/dx information along an electron trajectory is lost (one would require spatial resolutions on the order of a few pm in order to be able to reconstruct millimeter-long tracks).

The gamma background rejection efficiency might be expected to improve with increasing track lengths (lower density gas). However, the xenon pressure would have to be below 10 atm in order to be able to resolve the details of the individual tracks created in a TPC.37 In this case, precise dE/dx measurements along the trajectory of an event would then distinguish a pp event from competing gamma- or cosmic-ray background events: a 3- dimensional picture of a true pp event would be characterized by two tracks with a common origin and a large "blob" of charge deposited at each end (dE/dx is much larger at the end than the beginning of an electron track).

If we could lower the xenon density to a value where we are increasing the extent of the trajectory to greater than 1 cm, without sacrificing the efficiency and energy resolution of our chamber, then some event shape information might be obtained by electronic segmentation of the anode (spatial resolution of a few mm). Even without a significant increase in the track lengths, some position resolution in the x-y (or radial) directions would allow us to reject background y-ray events that are characterized by spatially separated depositions of charge.

If we require a gainless charge measurement (to avoid uncertainties in charge measurements and gain non-uniformities) we would not want to segment the anode into two separate sets of wires along the x and y directions (standard TPC designs). If we instead, for example, segmented the anode into small circular disks, a few mm in diameter (each electrically insulated from the others and connected to a charge sensitive pre-amp) some x-y imaging would be achieved without significantly affecting the energy

229

resolution (by minimizing charge multiplication and non-uniformity over the anode plane). This design is both feasible and simple to construct. If only a two-dimensional picture is required, the anode could be composed of a set of strips or even a set of concentric rings.

Segmentation of the anode would also allow us to eliminate events that are on the edge of the fiducial volume of the detector (defined in Chapter 5 as (the sensitive volume) x (the efficiency)). These events will lose some charge at the boundaries of the sensitive volume and might affect the energy resolution or produce a low energy tail on the background 2615 keV gamma-ray photo-peak. The signals formed by such events will appear on the outer portions of the segmented anode and would be rejected on this basis. For example, the simplest design would be an anode segmented into two parts: an outer "veto ring" to eliminate events that occur at the outer edge of the fiducial volume, and an inner anode disk.

The presence of the grid in our detector allows us a signal independent of the z-position of an event (between the grid and cathode). In order to determine where along the z-direction charge is deposited, we need a way to determine the zero time scale for an event. This could be achieved by looking at the signal induced (ion or electron) by the event on the cathode or grid, or by the detection of the primary scintillation light from the ionization and excitation process. The time evolution of the signal gives us the z- coordinates of the event (since we know the drift velocity). This, together with segmentation of the anode, would give us a multi-dimensional picture of how charge is deposited in our chamber.

The detection of the ion induced image on the grid and/or cathode would allow us to eliminate events that occur on the top and bottom extremes of the fiducial volume (where some charge loss might occur).

230

Events that occur too close to the cathode or grid will have large positive ion induced signals and fast rise times for the electron induced signals on those electrodes. Setting an upper level on the pulse heights induced on these electrodes Gower level on the signal rise times) will allow us to avoid this problem.

Signals induced by ionization electrons which were produced in the region between the grid and collector are directly affected by positive ions. We want to detect only charges produced in the sensitive region (between the grid and cathode). This can be accomplished by observing the collector signals gated by the cathode signals. This dead region between the anode and grid should me made as small as possible to avoid such problems.

231

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