Design of an Experiment to Search for Invisible Decays of Ortho- Positronium in Vacuum and Ortho-Positronium Formation Studies in Mesostructured Silica Films

Research Collection

Doctoral Thesis

Design of an experiment to search for invisible decays of ortho- positronium in vacuum and ortho-positronium formation studies in mesostructured silica films

Author(s): Gendotti, Ulisse

Publication Date: 2010

Permanent Link: https://doi.org/10.3929/ethz-a-006250397

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ETH Library Diss. ETHZ No. 14774 and DISS. ETH NO. 19067 ETHZ-IPP Internal Report 2002-05 August 2002

Design of an experiment to search for invisible decays of ortho-positronium in vacuum and ortho-positronium formation studies in mesostructured silica ﬁlms

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH

for the degree of

Doctor of Sciences

presented by

Ulisse Gendotti Dipl. Phys., ETH Zurich born 12.12.1981 citizen of Prato Leventina, TI Switzerland accepted on recommendation of Prof. Andre Rubbia, examiner Prof. G¨unther Dissertori, co-examiner

2010 ii Abstract

In this PhD thesis, the design of an experiment for the search for invisible decays of ortho-positronium (o-Ps) in vacuum is presented. Such decays could be interpreted as a signal for Mirror type Dark Matter. The goal is to reach a sensitivity in the branching ratio of Br(o Ps invisible) 10−7 to confront the annual modulation of the signal observed by DAMA/NaI− → and DAMA/LIBRA≃ (with 8.2σ significance) with Mirror Dark Matter scenarios. In case of a signal observation, the experiment would offer a unique and essential feature for a check of this signal: by changing the number of collisions of o-Ps in the vacuum cavity by a factor 2 the signal is scaled by the same factor while the background stays constant. In case of a null result, this search will provide an upper limit for the photon-mirror photon mixing strength about one order of magnitude better than presently derived from the Big Bang Nucleosynthesis. Based on the ETH Zurich slow positron beam, a special apparatus to select an appropriate target for the Ps formation has been constructed. In some targets, fractions as high as 40 % of the positrons implanted in the film were converted into o-Ps and emitted from the surface. Moreover, measurements in a temperature range of 50-400 K were performed showing that the o-Ps yield is almost independent of the film temperature. Quantum mechanical effects related to confinement of o-Ps in the pore have been observed. In particular, it has been experimentally demonstrated that the lowest possible emission energy of o-Ps is limited by the energy of its ground state in the pore confinement potential. These experimental results provide a solid ground for the future development of low temperature e+ o-Ps converters . →

iii iv ABSTRACT Zusammenfassung

In dieser Dissertation wird die Entwicklung und Planung für ein Experiment zur Suche nach unsichtbaren Zerfällen von Ortho-Positronium Atomen (o-Ps)im Vakuum vorgestellt. Solche Zerfälle könnten als Signal für Dunkler Materie in einer Spiegelwelt interpretiert werden. Das Ziel ist es, eine Empfindlichkeit im Verzweigungsverhältnis von Br(o Ps invisible) 10−7 zu erreichen, um die von den DAMA/NaI und DAMA/LIBRA− Experi-→ ≃ menten beobachtete jährliche Variation ihres Signals (mit 8.2σ Signifikanz) mit Szenarien von Dunkler Materie in der Spiegelwelt vergleichen zu können. Falls ein Signal beobachtet wird, bietet das vorgestellte Experiment eine einzigartige und wesentliche Möglichkeit, dieses Signal zu überprüfen: indem man die Anzahl Kollisionen von o-Ps mit der Vaku- umkammer um einen Faktor 2 ändert, ändert auch das Signal um denselben Faktor bei gleich bleibendem Untergrund. Falls kein Signal beobachtet wird (Null-Resultat), liefert das Experiment eine obere Grenze für die Stärke der Photon - Spiegelphoton Mischung, die etwa um eine Grössenornung besser ist, als was heute aus der Big Bang Nukleosynthese hergeleitet werden kann. Basierend auf dem Strahl von langsamen Positronen der ETH Zürich wurde ein spezieller Apparat konstruiert, um ein möglichst gutes Target für die Positronium-Formation auszuwählen. In einigen Targets bildeten bis zu 40 % der im Film implantierten Positronen o-Ps, das von der Oberfläche emittiert wurde. Zusätzlich haben Messungen im Temperaturbereich von 50 - 400 K ergeben, dass die o-Ps-Ausbeute nahezu unabhängig von der Filmtemper- atur ist. Quantenmechanische Effekte wurden beobachtet, die vom Einschluss der o-Ps- Atome in den Poren des Filmtargets herrühren. Insbesondere wurde experimentell gezeigt, dass die niedrigste Energie der emittierten o-Ps-Atome limitert ist durch die Energie des Grundzustandas von o-Ps im Potential, das die Atome in den Poren einschliesst. Diese ex- perimentellen Resultate bieten eine solide Grundlage, für die Entwicklung von zukünftigen e+ o-Ps Konvertern bei niedrigen Temperaturen. →

v vi ZUSAMMENFASSUNG Contents

Abstract iii

Zusammenfassung v

1 Mirror Matter as Dark Matter 1 1.1 PositroniumandDarkMatter ...... 2 1.2 Experimental evidence forMirrorDarkMatter ...... 7

2 Search for the invisible decay of o-Ps in Aereogel 9 2.1 Experimentaltechnique...... 9 2.2 Background estimation and dedicated engineering run ...... 17 2.3 Dataanalysis ...... 19 2.4 Results...... 20 2.5 Interpretation ...... 23

3 Design of an experiment to search for invisible decays of o-Ps in vacuum 25 3.1 Thesetup ...... 26 3.1.1 Theslowpositronbeam...... 27 3.1.2 o-Psproductiontarget...... 28 3.1.3 Thevacuumcavity ...... 29 3.1.4 Positrontaggingsystem ...... 32 3.1.5 Trigger eﬃciency and conﬁdence level ...... 34 3.1.6 Thephotondetector ...... 39 3.2 Backgroundestimation ...... 39 3.2.1 Fastbackscattered o-Ps fromthecarbonfoil ...... 43 3.2.2 Backscatteredpositrons ...... 43 3.3 Sensitivity...... 45 3.4 Summary ...... 47

4 Study of positronium emission from porous silica ﬁlms 55 4.1 Positrons and positronium in solids ...... 55 4.1.1 Positronium formation mechanism ...... 57 4.1.2 Thepick-oﬀprocess...... 58

vii viii CONTENTS

4.1.3 Positronium diffusion and thermalization in porous films ...... 59 4.2 Dopplerbroadeningspectroscopy(DBS) ...... 61 4.3 Angular correlation of annihilation radiation (ACAR)...... 61 4.4 3γ/2γ technique...... 62 4.5 Positron annihilation lifetime spectroscopy (PALS) ...... 63 4.6 Positronium time-of-flight (Ps-TOF) ...... 63

5 The slow positron beam 65 5.1 Design and construction of a 22Na positronsourcechamber...... 65 5.1.1 Thepositronmoderator ...... 69 5.2 Thepositrontransportsystem...... 71 5.3 Thevacuumsystem...... 73 5.4 Positron and positronium tagging ...... 73 5.4.1 Pulsedbeammode ...... 73 5.4.2 Continuos beam and secondary electron trigger mode ...... 74 5.5 Beam proﬁle monitoring using a MCP with a position sensitive screen . .. 77 5.6 Conclusions ...... 79

6 Design and construction of the PALS and TOF detectors 81 6.1 Monte-Carlosimulation...... 81 6.2 The magnetic transport system in the target region ...... 82 6.3 ThePALSdetector ...... 83 6.3.1 3γ/2γ detection eﬃciency correction using MC simulations . . . . . 84 6.4 The positronium time-of-ﬂight detector ...... 87 6.5 Cooling of the target using a cryocooler ...... 89 6.5.1 Position calibration of the TOF spectrometer at low temperatures. 91 6.6 TheDAQsystem ...... 92 6.7 PALSdataprocessing ...... 92 6.8 TOFdataprocessing ...... 93 6.9 Conclusions ...... 96

7 Analysis of the PALS spectra 97 7.1 Samplepreparation...... 97 7.2 Extrapolation of the pore size from the o-Ps lifetime ...... 99 7.2.1 Lifetime in sub-nanometer pores: Tau-Eldrup model ...... 99 7.2.2 Lifetime in mesoporous materials, the RTE model ...... 99 7.3 Determination of the lifetime in the pores ...... 101 7.3.1 Measured yield of the o-Ps emission into the vacuum and the o-Ps lifetimeinpores...... 107 7.3.2 Calculation of the pore size ...... 110 7.4 Conclusions ...... 111 CONTENTS ix

8 Analysis of the TOF data 113 8.1 Ortho-positronium thermalization in porous ﬁlms ...... 114 8.1.1 Theclassicalmodel...... 114 8.1.2 Positronium cooling by phonon scattering ...... 117 8.2 Determination of the o-Ps energy from the TOF measurements ...... 120 8.2.1 Lifetime and detection eﬃciency correction and TOF peak analysis 121 8.2.2 Subtractionofthetargetcomponent ...... 123 8.2.3 Subtraction of the non-thermalized component ...... 124 8.3 Lowtemperaturemeasurements ...... 127 8.3.1 Comparison with the MC simulation and reconstruction of the total o-Psenergy ...... 131 8.3.2 Ps in thermodynamic equilibrium at a temperature T in the pore . 134 8.3.3 TheP32sample...... 137 8.3.4 Conclusions ...... 138

9 Conclusions 141

10 Future perspectives 143 10.1 1S-2S transition of ortho-positronium ...... 143 10.2PsandAntihydrogen ...... 144 10.2.1 Precise o-Ps decay rate measurement ...... 145 10.3 Bose-Einsteincondensationofo-Ps ...... 145 x CONTENTS List of Figures

1.1 History of the ortho-positronium lifetime measurements and of the calculations. 4 1.2 The double degeneracy between ortho-positronium mass eigenstates of ordinary (o-Ps) and mirror (o-Ps′) is broken when a small mixing term is included...... 5 1.3 The points are the annual modulation observed by DAMA/NaI. The line is the prediction of this modulation for Mirror Matter [12]...... 8

2.1 Schematic illustration of the experimental setup: a) front view, b) top view. 10 2.2 Schematic illustration of the positron tagging system and the o-Ps formation target of the setup...... 11 2.3 Schematic view of the scintillating fiber with the 22Na source on the squeezed part in the center...... 12 2.4 Schematic illustration of the method to readout the energy deposition in the fiber...... 13 2.5 An example of the pulse shape of the FBGO signal, which is an overlap of signals from a positron and a photon, detected in the fiber and the BGO crystal, respectively. The short gate was used to measure the energy loss from positrons (shown not in scale)...... 15 2.6 The scatter plot of energy loss measured with the short versus long gate measured for the TBGO counter coupled with the front face to the plastic scintillator. Three regions corresponding to detection of a) pure positrons detected in the plastic scintillator, b) 511 keV photons contaminated by the positron energy deposited in the plastic scintillator, and c) pure photons ,i.e. without detection of positrons in the plastic scintillator are clearly seen. The ellipse indicates the one sigma countur of the 1.275 MeV peak with a barely seen tail from positrons detected in the plastic scintillator...... 16 2.7 The cuts applied to the variables. The numbers on the plot correspond to the variable defined in the text. Only the colored regions contribute...... 20 2.8 Zero energy peak measured using the EC photon as a trigger. The arrow shows the threshold at 80 keV...... 21 2.9 Distribution of time between the fiber trigger and one of the annihilation photons in the TBGO. An exponential fit (solid line) is performed in order to determine the fraction and the lifetime of o-Ps produced in the aerogel. . 22

xi xii LIST OF FIGURES

2.10 Spectrum of the sum of the total energy in the ECAL. The inset shows the magniﬁed view of the low-energy region in logarithmic scale...... 23 2.11 a) Mass–charge parameter space for the o-Ps decay into milli-charged particles, excluded with this experiment, b) Comparison of our results (the dashed region on the plot) with other experimental (SLAC [61] and previous o Ps invisible [55]) and astrophysical bounds (the plot was taken from [62]).− ...... → 24

3.1 Schematic view of the setup. The main parts of the system are: The bunched slow positron beam, the secondary electron tagging system, the target chamber and the γ detector...... 26 3.2 Timing between the secondary electrons detected in the MCP and the bunching pulse of the beam for 1 and 2 keV implantation energy of the positrons. 28 3.3 Fraction of o-Ps emitted into the vacuum from the a selected sample as a function of the positron implantation energy measured in our setup. .... 30 3.4 (a) Ps is tagged by the secondary electrons produced by the positron that hits the converter surface (target). In the case where Ps escapes the detection region, it could mimic an invisible decay due to the strongly suppressed detection efficiency of the decay photons. (b) By closing the vacuum cavity around the o-Ps converter one obtains a region of highly uniform detection efficiency and the o-Ps leakage through the aperture is suppressed. The 15 nm carbon foil acts as a barrier for the o-Ps emitted from the converter but it is nearly transparent for the incoming positron beam and for the secondary electrons used for the trigger...... 31 3.5 Schematic of the target region and the carbon foil...... 32 3.6 Schematic of the positron tagging system for the experiment using the MCP signal for secondary electrons emitted from the target and from the thin carbon foil...... 33 3.7 Trajectories of the positron (blue) and secondary electrons (red) for the new design with the carbon foil...... 33 3.8 Simulated time distributions of the secondary electrons detected in the MCP. See text for details...... 34 3.9 Setup used for the measurements with the tagging system. In order to accelerate the SEs from the target a voltage difference between the sample holder (green) and the carbon foil has to be applied. A ceramic ring electrically insulates the carbon foil holder and the target holder...... 35 3.10 Example of an event acquired with an oscilloscope. The first signal is produced by the SE from the target and defines the START signal. The second pulse is produced by the SE from the CF 15ns after the START signal. The time window ω between 15 and 22 ns∼ (i.e. between 10 and 17 ns delay from the START signal) is defined in order to calculate the trigger efficiency and the fake trigger ratio. A Gaussian fit is used in order to determine the position of the pulses (green)...... 36 LIST OF FIGURES xiii

3.11 Measured delay of the SE from the carbon foil relative to SE from the START signal. The dashed line represents the data obtained by applying the same voltage on the carbon foil and on the sample (-1.2kV). The solid line is obtained by applying -1.2 kV on the carbon foil and -3.8kV on the sample. In this case the broadening of the peak at around 15 ns is mainly due to variations of the ﬂight time of the SE from the target that produce the START signal. The peak at about 2 ns are due to the MCP deadtime (see text for details)...... 37 3.12 Charge (measured with 50 Ω termination) in pVs of the start signal versus the charge of the signal for events in the time window 12-17 ns. Top: the same voltage of 1.2 keV is applied to the target and the carbon foil. Bottom: a voltage of 3.8 keV is applied to the target and 1.2 keV to the carbon foil. 40

3.13 Top: trigger efficiency (boxes) and coincidence suppression factor κSE (circles) as a function of the threshold set on the signal in the time window 12-17 ns. Bottom: trigger efficiency (boxes) and coincidence suppression factor κSE (circles) as a function of the cut on the charge (voltage integral) on the signals in the time window 12-17 ns...... 41 3.14 Cross section of the BGO calorimeter mounted around the beam pipe. The sphere is to show that the minimal BGO thickness around the target is of the order of 200 mm...... 42 3.15 Distributions of the energy deposited in the dead material surrounding the target region (target substrate, beam pipe and copper coil) from annihilation events in the target. The upper plot shows the results of the MC simulation for a 0.84 mm thick aluminum pipe. Below the distribution for the pipe construction with 0.04 mm aluminum and 0.800 mm carbon. The total number of simulated 2γ-events is 108 in both cases. The peaks at 511 keV and 1022 keV correspond to the total photo-absorption either of a single 511 keV photon or of both of them, respectively...... 48 3.16 Energy distribution of fast o-Ps originating from backscattered e+. The pick- off probability after a collision of o-Ps with the walls is taken to be zero for o-Ps energies smaller than the 6.8 eV while for higher energies it is 0.95. . 49 3.17 Simulated decay position of o-Ps in the vacuum cavity. The escaping probability estimated with the MC simulation is 1 10−4...... 49 ≃ × 3.18 Positron backscattering coefficients (η+) versus positron kinetic energy [70]. 50

3.19 Positron backscatter coeﬃcient (η+) from a thick carbon target (black squares) and a thin carbon foil (triangles) as a function of the positron kinetic energy. The transmission probability, through the thin foil is also shown (open squares, right scale)...... 51 3.20 Top: simulation using EGSnrc. Energy spectrum of positrons backscattered from a 20 nm carbon foil for positron implantation energies in the 1-2 keV range. The cut-oﬀ energy is 300 eV. Bottom: angular distribution for backscattered positrons ...... 52 xiv LIST OF FIGURES

3.21 Escaping probability for positrons backscattered from the carbon foil as a function of the carbon foil voltage for different positron initial energies E0. 52 3.22 Backscattering coefficient η+ for the SiO2 target as a function of the positron incident energy...... 53 3.23 Escaping probability for the total number of incident positrons at the SiO2 target as a function of the implantation voltage for different positron initials energies E0...... 53

4.1 Calculated Makhovian implantation proﬁle for 10 and 15 keV incident positrons on tungsten. The parameters are α = 3.6[µg/cm2] and n = 1.6. See text fordetails...... 57 4.2 Orthopositronium lifetime dependence as a function of the mean free path l, computed with the RTE model. The pore size a for a cubic box can be 3 estimated with a = 2 l [82]...... 59 4.3 (a) In closed porosity samples Ps remains trapped in the pore. (b) In interconnected pore systems Ps can move between the pores. If it reaches the ﬁlm surface it is emitted into the vacuum...... 60

5.1 Picture of the ETH Zurich slow positron beamline. The installation is about 6 meters long and 2 meters high...... 66 5.2 Schematic diagram of the pulsed slow positron beam apparatus ...... 66 5.3 Source and moderator chambers for the 380 MBq source. The moderator chamber (yellow) is equipped with an electron beam (green) used for the moderator annealing up to 2000oC...... 68 ∼ 5.4 Section of the source chamber. The extraction optics system consists of a grid placed at a distance of 3 mm from the moderator and a first acceleration tube...... 70 5.5 Left: finite element calculation of the magnetic transport system performed with the COMSOL multi-physics program. Right: Positron trajectories calculated with GEANT4...... 71 5.6 Correction coils produce a magnetic field which is perpendicular to the beam direction. They are used for the beam positioning...... 72 5.7 Beam position with respect to the center of the beam pipe by applying a current on the correction coil. The current ranges from 0 to 5 A with a step of 0.2 A...... 72 5.8 Bunching voltage at the first and second velocity modulation gaps. The time delay between the non-linear pulse and the pulse applied to the chopper grid is tuned in order to achieve the best compression factor...... 74 5.9 Top: trajectories of the positrons (blue) and secondary electrons (red) from the Geant4 simulation; E- and B-fields calculated with the COMSOL package for our existing setup. Bottom: simulation of the secondary electron trajectories from the sample to the MCP for the PALS and TOF spectrometers described in Chapter 6...... 75 LIST OF FIGURES xv

5.10 Flight time spread introduced in the transportation of SEs from the sample to the MCP for a flight distance of 90 cm. This time distribution was measured using two different MCPs. One at the target region detecting e+ and one in the usual position for the secondary electron tagging. The voltage on the target MCP substrate was 2.4 kV. The timing shows a spread of 1.9 ns FWHM. 76 5.11 Top: principle of work of the MCP phosphor screen. Bottom: achieved improvement in the beam profile before (left) and after (right) the optimization of the magnetic transport system. The external bright circle around the beam spot is produced by light reflection of the metallic ring holding the screen. See text for details...... 78 5.12 Left: picture of the MCP substrate. Right: picture of the phosphor screen. . 78 5.13 The solenoid around the MCP chamber is used to keep the value of the magnetic field at the MCP position similar to the one in the beam pipe. This is done in order to reproduce, at the MCP position, the same beam properties as in the beam pipe. FEM calculations have been performed. In the lower plot the calculated magnetic field along the beam pipe is shown. . 79

6.1 The solenoid is wound directly on the beam pipe in order to decrease the magnetic field at the PMTs region. An additional coil is used at the interface between the 500 mm diameter coil and the solenoid on the beam pipe (7 cm diameter) in order to make the transition of the magnetic field smoother. . 83 6.2 Top: picture of the PALS detector (left) and a 3D CAD drawing of the BGO calorimeter (right). Bottom: Schematic drawing of the PALS setup. .... 85 6.3 Lifetime measured in a single BGO crystal. The apparent lifetime measured depends on the distance of the crystal from the target. The detection probability at larger distances is enhanced for long living o-Ps...... 86 6.4 Ratio of the 3γ/2γ detection efficiency as a function of the o-Ps emission energy for three different thresholds applied to the BGOs: 200, 300 and 400 keV...... 87 6.5 3D view and picture of the TOF detector...... 88 6.6 Analysis of the 511 keV peak height as a function of the collimator position. With this scan the 0-position (target) and the slit width can be monitored. . 89 6.7 Working principle of the cryocooler. See text for details...... 90 6.8 Cryocooler cold finger and sample holder. FEM calculations have been done in order to estimate the contraction of the cryocooler assembly during cooling down...... 90 6.9 Analysis of the 511 keV peak as a function of the collimator position at room temperature and after 1 hour of operation of the crycooler (45 K). The scan is performed with a 0.1 mm step...... 91 6.10 DAQ scheme used for the PALS and TOF detectors...... 93 xvi LIST OF FIGURES

6.11 The energy spectra of the 4 BGO crystals are shown. The calibration of the PALS energy spectra by ﬁtting the 511 keV peak from the 2 γ decay.The pedestal is given when no energy is deposited in the BGO. The distribution in the energy range 0 Compton scattering. .... 94 6.12 Analysis of the PALS spectra using LT9 software. Three exponential components are used to model the spectra. A fast component, an intermediate component which determines the lifetime of o-Ps in the ﬁlm and the vacuum component...... 95 6.13 TOF spectra recorded at 4 keV positron implantation energy, at room temperature on the F sample type (more details are presented in Section 7.1). . 96

7.1 The porous materials are produced by mixing a porogen to a matrix material. At the end of the film preparation the porogen is evacuated by heating the sample to 4500C...... 98 7.2 (a) Tau-Eldrup model: in the central portion of the spherical pore with radius R+∆R the annihilation rate is λ =0 (the self annihilation is neglected) while in the interaction region it is equal the to averaged spin annihilation λS+3λT rate λA = 4 . (b) RTE model: the annihilation rate in the central region λS +3λT of the pore is λT while in the interaction region it is λA = 4 . .... 102 7.3 o-Ps lifetime as a function of the pore size calculated with the RTE model with δ =0.18 nm assuming cubic pores (dotted line) and infinite rectangular channel pores (solid line) ...... 102 7.4 RTE model lifetime calculations assuming cubic pores at 0, 300 and 800K for δ = 0.18 nm. The RTE model is calibrated by demanding that at 0 K (i.e. ground state) the TE model is reproduced for pore sizes in the sub- nanometers range...... 103 7.5 (a): Uncapped and (b) capped porous silica film: o-Ps is forced to remain in the film. In interconnected pore systems, this is done in order to study the internal properties of the film by avoiding that o-Ps emitted from the surface biases the values of the lifetime related to the annihilation in the pores. . . 104

7.6 Left: measured o-Ps lifetime components, (τ2,I2) , (142ns,I3) as a function of the porogen content. Right: o-Ps-escape model calculations...... 106

7.7 Yield of o-Ps emitted into the vacuum (Yv, circles) and total yield of Ps (Itot = I2 + I3, squares) for F (upper plot) and C samples (lower plot) at room temperature and at 50K...... 108 7.8 o-Ps lifetime in the ﬁlm determined with the escape model. Values of 54 ns for the C sample and 76 ns for the F sample have been measured. In the C sample, for implantation energies above 7 keV, positrons start to be implanted in the glass substrate. In the F sample below 6 keV the calculated lifetime using the escape model is biased by surface eﬀects...... 109 LIST OF FIGURES xvii

8.1 Thermalization curves for similar pore structures coated with different chemicals. The points represent the experimental data recorded at different positron implantation energies. The solid lines are the fit with the Eq. 8.2 where the effective mass MS is left as a free parameter. The effective mass ratio between the two chemical groups used in the preparation of F38 and m-F38 has been observed to be constant for α ranging from 1 to 4...... 116 8.2 Minimal energy of Ps as function of the pore size for cubic box (circles) and square channel (dotted line) geometries. The minimal energy of o-Ps in a square channel is smaller than in the cubic box of the same side length a. 119 8.3 Comparison between the energy loss curves obtained from the classical model and the Ps-phonon interaction model. Figure from [86]. See the text for details.120

8.4 Schematic view of the collimator and of the target region: dc is the distance between the target surface and the center of the collimator slit and wc is the collimator width. In the TOF spectrum the Ps annihilation in the target, whose γs penetrate the lead collimator and produce a signal in the BGO, contribute to the target-component...... 121 8.5 Measured (raw) TOF spectra at 300K for implantation energies ranging from 0.7-7 kV. Top: F sample. Bottom: C sample...... 122

8.6 Positronium emission energy < Ez > as a function of the implantation energy at a target temperature of 300K. The triangles correspond to the energy obtained from the data by subtracting the target component (TC subtraction) and for the squares the target and the non-thermalized component were subtracted (TC+NTC subtraction). For both data sets the lifetime and detection efficiency correction factor was applied. The inserts show the plateaus with the low-energy part of the spectra cut off...... 125 8.7 Top: TOF spectra at 3,4 and 5 keV positron implantation energy. The epithermal tails on the left of the TOF-peak decrease at larger implantation energy. Bottom: Makhovian stopping profile for different positron implantation energies. At higher energies the profiles are broadened. A fraction of positrons is always implanted near the surface, resulting in non-thermalized o-Ps to be emitted into the vacuum...... 126 8.8 Calculated fraction of positrons stopping at a depth smaller than L (open squares) and larger than L (black squres) obtained from Makhovian stopping profiles. L is the minimal implantation depth to produce thermalized positronium. Top: calculations for the C sample, bottom calculations for the F sample. The density and the thickness of the film are taken into account. 128 8.9 TOF spectra from the C sample (upper two plots) and the F sample (lower two plots): The solid histogram in panels (a) and (c) correspond to the measured (raw) TOF spectra, the diamonds represent the target component, and the crosses the non-thermalized plus the target component. Panels (b) and (d) show the corrected TOF spectra attributed to thermalized o-Ps decays.129 xviii LIST OF FIGURES

8.10 o-Ps mean emission energy < Ez > as a function of the positron implantation energy for the C (dashed line) and the F sample (solid line) at 300 K, after the subtraction of the target and non-thermalized component (corresponds to the TC + NTC curves of Fig 8.6) The C sample shows a faster thermalization curve because of the smaller pore size. As expected, the minimal energy of the F sample is smaller than the one observed in the C sample. The insert shows the plateaus with the low-energy part cut off...... 130 8.11 Upper plot: Mean Ps energy < Ez > for implantation energies higher than 2 keV at 50 K and 300 K for the C sample. Lower plot: Mean Ps energy as a function of the implantation energies higher than 4 keV at 50 K and 300 K for the F sample...... 130 8.12 Upper plot: comparison between the data of the C sample at 6 keV and the MC simulating mono-energetic Ps emitted isotropically from the film surface. Lower plot: comparison between the data of the C sample at 6 keV and the MC simulating mono-energetic Ps emitted perpendicular from the film surface. In both cases, the measured target and non-thermalized components was added to the MC simulations...... 133 8.13 The correction parameter ξ between the total o-Ps emission energy < E0 > and the parallel component < Ez > obtained from MC simulations...... 134 8.14 Positronium mean energy < E0 > as a function of the mesoporous film temperature. Those results are obtained at 6 keV for the C (triangles) and 10 keV for the F sample (squares). The solid lines are the results of a fit of Eq.8.32 to the data with the pore side lengths a,b,c left as free parameters. The dashed lines were obtained fitting with Eq.8.32 with a single free side length free a = b = c (cubic box pores)...... 136 8.15 Sketch of a multilayer sample with combined porosity. (a) The interface between two layers of the same sample type acts as a blocking barrier for o-Ps (b) For two layers, one with a small pore size (e.g. a C sample), and the other with a large pore size (e.g. P32), the blocking effect might be suppressed...... 139

10.1 BEC transition temperature vs conﬁning cavity radius assuming 108 positronium atoms...... 146 List of Tables

2.1 Comparison between expected (from MC) and measured background level for the different background sources in the engineering run and expected background level for the final setup (see text for details)...... 18 2.2 Definition of cuts and the remaining fraction of events after the cut is applied. 21

3.1 Estimated ﬂight time for SE emerging from CF (1.2 kV) and from the sample 3.8 kV for a distance of 80 cm. The expected delay time is 17 ns...... 35 3.2 Summary of the expected background level for the diﬀerent background sources. 46

5.1 Beam intensity for the diﬀerent 22Na positron sources that have been used since 2006. In the last row the eﬃciency of the moderator to emit almost mono-energetic, low energy positrons is reported...... 67

7.1 Film thickness (Z), calculated o-Ps lifetime in the pores τf , and escape rate kv at50Kand300K...... 108 7.2 Pore size calculated with the RTE model using the value of τf at300K. . . 110 8.1 Comparison of the pore sizes obtained from the PALS measurements and from the ﬁt of the Ps mean emission as a function of the sample temperature (see Fig. 8.14) for both cubic box (BOX) and rectangular pores (RECT). Minimal energy < E0 > of Ps is taken at T=50 K. The errors are the combined statistical and systematic error...... 137

xix xx LIST OF TABLES Chapter 1

Mirror Matter as Dark Matter

The Dark Matter problem provides one of the strongest indications for the existence of physics beyond the Standard Model (SM). In the past years, many cosmological observations accumulated support for the existence of Dark Matter (see e.g. [1] for an excellent review); these include galactic rotational curves [2] and gravitational lensing [3, 4]. The very recent confirmation by the DAMA/LIBRA [5] experiment of the DAMA/NaI [6] observation of an annual modulation signal with a 8.2σ significance provides the first direct experimental observation of the existence of non-baryonic Dark Matter in our galactic halo. Supersymmetry is considered as one of the most attractive extensions of the SM, mainly because it provides an elegant solution to the hierarchy problem [7] and enables the cou- plings of the SM to evolve on a common scale in GUT theories [8]. Supersymmetric- particles could be viable candidates for Dark Matter (even though that’s not a compelling condition for their existence) if one forces R-parity to be conserved, leading superpartners to annihilate or be created in pairs and, therefore, the lightest supersymmetric partner (LSP) to be stable. However, the new results of DAMA/LIBRA give us a hint that probably standard neu- tralino models are not the solution of the Dark Matter puzzle. In fact, such an explanation would contradict other higher threshold experiments like CDMS/Ge [9], CDMS/Si [10] and XENON10 [11]. Among many Dark Matter candidates that have been discussed, one of the most promising, which could reconcile the null results of those experiments with DAMA, are Mirror particles [12]. In fact, Mirror baryons are naturally dark, stable and massive. Currently, it seems that this concept could explain in a natural way that the visible and Dark Matter densities in the universe are of the same order of magnitude (ΩB =0.044 and ΩDM =0.26) [13, 14]. Furthermore, if Mirror Matter is present in our universe, it would mean that parity (spatial-inversion) is an unbroken symmetry of nature. Mirror Matter was originally discussed by Lee and Yang [15] in 1956, after their discovery of parity violation (for an excellent recent review on this subject see [16]). In order to save parity conservation they suggested, that the transformation in the particle space corresponding to the space inversion x x should not be the usual transformation P but PR, where R corresponds to the transformation→ − of a particle (proton [15]) into a re-

1 2 CHAPTER 1. MIRROR MATTER AS DARK MATTER

ﬂected state in the mirror particle space. After the observation of parity non-conservation, Landau assumed [17] that R=C, i.e. he suggested to identify antiparticles with the Mirror Matter but then CP must be conserved, which we know is not the case. The idea was further developed by A. Salam [18], and was clearly formulated in 1966 as a concept of the mirror universe by Kobzarev, Okun and Pomeranchuk [19]. In their paper, they have shown that ordinary and Mirror Matter can communicate predominantly through gravity and proposed that the Mirror Matter objects can be present in our universe. Since that time, the concept of Mirror Matter has found many interesting applications and developments. In the 80’s, it has been boosted by superstring theories with E E′ 8 × 8 symmetry, where the particles and the symmetry of interactions in each of the E8 groups are identical. Hence, the idea of Mirror Matter can be naturally combined in these models [20]. Nowadays, Mirror Matter models exist in two basic versions. The symmetric version, proposed earlier, was further developed and put into a modern context by Foot, Lew and Volkas [21]. The asymmetric version was proposed by Berezhiani and Mohapatra [22]. In the following we will concentrate on the symmetric model since it is the most interesting from a Dark Matter perspective and it could provide, as it will be discussed later, an experimental signature related to positronium. In the symmetric mirror model, the idea is that for each ordinary particle, such as the photon, electron, proton and neutron, there exists a corresponding mirror particle of exactly the same mass as the ordinary particle. R-parity interchanges the ordinary particles with the mirror particles so that the properties of the mirror particles completely mirror those of the ordinary particles. For example, the mirror proton and mirror electron are stable and interact with the mirror photon in the same way in which the ordinary proton and electron interact with the ordinary photons. The mirror particles are unlikely to be produced in laboratory experiments just because they couple very weakly with the ordinary particles. In the modern language of gauge theories, the mirror particles are all singlets under the standard G SU(3) SU(2)L U(1)Y gauge interactions [21]. The mirror particles interact with a set≡ of mirror⊗ gauge particles,⊗ so that the gauge symmetry of the theory is doubled, i.e. G G (the ordinary particles are ⊗ singlets under the mirror gauge symmetry) [21]. Parity is conserved because the mirror particles experience V + A (i.e. right-handed) mirror weak interactions while the ordinary particles experience the usual V A (i.e. left-handed) weak interactions. Ordinary and mirror particles interact with each− other predominantly by gravity.

1.1 Positronium and Dark Matter

Few years after the discovery of the positron by Anderson [23], Mohorovicic predicted that the positron and the electron could form a bound state [24]. Ruark proposed to name this system positronium (Ps) and gave a qualitative discussion of the spectroscopic structure of the Ps-atom [25]. The spins of the electron and of the positron in the positronium 1 can combine to give either a singlet spin ground state S0, called para-positronium (p- 3 Ps) or a triplet ground state S1, ortho-positronium (o-Ps). For a positronium system 1.1. POSITRONIUM AND DARK MATTER 3

with orbital angular momentum l and total spin S C-parity is C = ( 1)l+S and P-parity − is P = ( 1)l+1. For para-positronium and ortho-positronium in the ground state we P C − −+ P C −− have Jp−Ps = 0 , Jo-Ps = 1 . For other positronium states the quantum numbers are 2S+1 1 3 3 3 3 3 −− n LJP C = 2 S0−+ , 2 P0++ , 2 P1++ , 2 P1+− , 2 P2++ , 2 S1 , .... The detailed calculation of the decay rate for the spin singlet state was done by Wheeler (1946) [26] and Pirenne (1947) [27]. The more difficult calculation for the lowest order decay rate of the triplet spin state was first obtained correctly by Ore and Powell [103] in 1949. The first experimental detection and the measurement of the lifetime of the ortho-positronium, which confirmed the calculation of Ore and Powell, was performed by Deutsch (1951) [29, 30]. A lot of effort has been undertaken to determine the basic properties of o-Ps like lifetime, decay modes, spectroscopy, etc. In particular, the measurement of the o-Ps lifetime caught much atten- tion. The history of these measurements and the theoretical calculations is very interesting and at the same time controversial. Fig. 1.1, summarizes all these years of theoretical and experimental efforts to determine the lifetime after Deutsch’s first detection. The measurements performed by the Michigan group in the late eighties did not agree with theory [31]. This long standing discrepancy was called “the ortho-positronium lifetime puzzle” and ignited much experimental and theoretical activity devoted to its clarification. These are: (1) new direct lifetime measurements by the Tokyo group which did not confirm the discrepancy [34] (2) new theoretical calculations by Adkins et al. [32] including higher order terms improving the theoretical precision well below experimental errors, however, confirming early theoretical estimates (3) searches for “exotic” decay modes which could explain the lifetime discrepancy at the cost of new physics (violation of basic conservation laws with decays into 1 photon, 2 photons; anomalous rate in 5 photons; millicharged particles; new bosons, ...) (4) exotic suggestions for disappearance mechanisms (mirror worlds, extra dimensions). The experiments for the determination of the decay rate are not trivial; in fact, in order to form positronium one requires matter (electrons) and consequently some corrections are needed to get the value of the lifetime in vacuum. Many effects can introduce systematic errors, e.g. the Stark effect, magnetic quenching, positronium escaping the formation cavity, time dependence of the pick-off rate (see Section 4.1.2), fast backscattered positrons, etc. It wasn’t until 2003, when the Michigan researchers [33] obtained the newest results that agreement with the theory and consistency with the Tokyo result [34] was finally achieved. The lifetime puzzle seems to be solved, however, the precision in the experimental result is 200 times worse than the theoretical uncertainty.

Para-positronium decays predominantly into two photons and its lifetime is 125 ps. Due to the phase-space and additional α suppression factors, as compared with the singlet 1 (1 S0) state, the decay time of o-Ps is 142 ns with 3 annihilation photons. Because it can be studied for a longer time, the o-Ps decay rate gives an enhancement factor 103 ≃ in sensitivity to an admixture of new interactions, which are not accommodated in the Standard Model [35]. Glashow realized that the o-Ps system provides a sensitive way to search for Mirror Mat- ter [36]. Glashow’s idea is that if a small kinetic mixing between ordinary and mirror photons exists [37], it would mix ordinary and mirror ortho-positronium, leading to maxi- 4 CHAPTER 1. MIRROR MATTER AS DARK MATTER ) -1 s

µ 7.3 Theory 7.25 Vacuum Gas Powder 7.2

7.15 o-Ps Decay Rate ( 7.1

7.05

1965 1970 1975 1980 1985 1990 1995 2000 Year

Figure 1.1: History of the ortho-positronium lifetime measurements and of the calculations. mal ortho-positronium - mirror ortho-positronium oscillations (see Fig. 1.2). Since mirror o-Ps′ decays predominantly into three mirror photons these oscillations would result in o Ps invisible decays in vacuum. Photon-mirror photon kinetic mixing is described by− the interaction→ Lagrangian density

µν ′ L = ǫF Fµν , (1.1) µν ′ where F (Fµν) is the ﬁeld strength tensor for electromagnetism (mirror electromagnetism). Together with the Higgs-Mirror Higgs quartic coupling λφφ† φ′φ′† , these are the only renormalizable and gauge invariant terms that can be added to the SM Lagrangian. The eﬀect of ordinary photon - Mirror photon kinetic mixing is to give the mirror charged particles a small electric charge [21, 37, 36]. That is, they couple to ordinary photons with charge 2ǫe1. Ortho-positronium is connected via a one-photon annihilation diagram to its mirror version (o-Ps′) [36]. This breaks the degeneracy between o-Ps and o-Ps′ so that the vacuum ′ ′ energy eigenstates are (o-Ps + o-Ps )/√2 and (o-Ps o-Ps )/√2, which are split in energy by − ∆E =2hǫf, (1.2) where f = 8.7 104 MHz is the contribution to the ortho-para splitting from the × < 1Note, that the direct experimental bound on ǫ from searches for ‘milli-charged’ particles is ǫ 10−5 [61]. ∼ 1.1. POSITRONIUM AND DARK MATTER 5

o−Ps

o−Ps’

o−Ps+ o−Ps ∆E o−Ps’ o−Ps−

Figure 1.2: The double degeneracy between ortho-positronium mass eigenstates of ordinary (o-Ps) and mirror (o-Ps′) is broken when a small mixing term is included.

one-photon annihilation diagram involving o-Ps [36]. Assuming a mixing strength of ǫ = 4 10−9 (as suggested by the DAMA results), one obtains an energy splittingof∆E =2.9 ×− × 10 12 eV. Thus, the interaction eigenstates are maximal combinations of mass eigenstates which implies that o-Ps oscillates into o-Ps′ with a probability:

′ P (o-Ps o-Ps ) = sin2 ωt, (1.3) → where ω =2πǫf. ′ The simplest case of o-Ps o-Ps oscillations in vacuum [36] leads to an apparent → increase in the decay rate because the mirror decays are not detected. The number of o-Ps N satisﬁes − N = cos2 ωt e ΓSM t exp[ t(Γ + ω2t)], (1.4) · ≃ − SM eff where ΓSM is the Standard Model decay rate of o-Ps [38, 39, 33]. Thus Γ ΓSM (1 + 2 ≈ ω /ΓSM ) leads to a branching ratio of:

2(2πǫf)2 Br(o-Ps invisible)= 2 2 . (1.5) → ΓSM + 4(2πǫf) The above calculation is not applicable to an experiment performed with a cavity conﬁning the positronium, because in this case the collision rate is not zero and the loss of coherence due to the collisions must be included in the calculation [40, 41]. Assuming the collision rate is much larger than the decay rate Γ Γ [41], the evolution of the coll ≫ SM number of ortho-positronium states, N, satisﬁes:

dN Γ N Γ Nρ, (1.6) dt ≃ − SM − coll 6 CHAPTER 1. MIRROR MATTER AS DARK MATTER

′ where the second term is the rate at which o-Ps oscillates into o-Ps (whose subsequent decays are not detected). In this term, ρ denotes the average oscillation probability over the collision time. That is,

t t − ′ ′ ′ − ′ ′ ′ ρ Γ e Γcollt sin2 ωt dt Γ e Γcollt (ωt )2dt , (1.7) ≡ coll ≃ coll Z0 Z0 where we have used the constraint that the oscillation probability is small, i.e. ωt 1. As ≪ long as t 1/Γcoll, then ≫ 2ω2 ρ 2 (1.8) ≃ Γcoll is a reasonable approximation for a cavity experiment. Thus, substituting the above equation into Eq.(1.6), we have

2ω2 2ω2 Γeff Γ + =Γ 1+ . (1.9) ≃ SM Γ SM Γ Γ coll coll SM Therefore, the branching ratio for o Ps invisible conﬁned in a cavity can be written as − →

2ω2 Br(o-Ps invisible)= 2 (1.10) → ΓSM (ΓSM Γcoll +2ω ) and, therefore, the limit on the mixing strength, for an experiment with the o-Ps conﬁned in cavity, can be expressed as:

1 Br − → Γ Γ ǫ = o Ps invisible SM coll . (1.11) 2πf 2(1 Br − → ) s − o Ps invisible ′ Note that the probability P (o-Ps o-Ps ) can also be affected by an additional splitting of o-Ps and o-Ps′ states induced by→ an external electric or magnetic field. This is similar to the phenomenon of n n [42] or muonium to antimuonium oscillations [43] in various environments: − 2 ′ ∆E Br(o-Ps o-Ps )= . (1.12) 2 2 2 → 2(∆E + ∆ +ΓSM ) Where ∆ is the breaking of the degeneracy due to the external fields. Only the second order Stark shift contributes to the positronium in the ground state. The energy shift can be calculated in the same way as for hydrogen and is given by: 1 ∆= α ǫ E2, (1.13) −2 0 0

3 where α0 = πa0 is the polarizability of o-Ps (a0 =0.1 nm is the Bohr radius of positronium), ǫ0 is the vacuum permittivity and E is the electric ﬁeld. For the electric ﬁeld of 3-5 kV/cm that we plan to use in the experiment this contribution (∆ = 1.26 10−18 eV) is 6 orders × 1.2. EXPERIMENTAL EVIDENCE FOR MIRROR DARK MATTER 7

of magnitude smaller than the energy splitting of Eq.(1.2) and, thus, its effect on the oscillation probability is negligible. A magnetic field affects only the triplet state with quantum number m=0. For the m= 1 states, the Zeeman effect is zero because the magnetic moments for positron and ± electron are opposite. The energy contribution for m=0 can be calculated with [?, zem]

A~2 A~2 2 ~2 2 2 ∆E = + ( ) + γ1 B0 (1.14) − 2 r 2 25 −1 −2 where A =4.92 10 eV s is the hyperfine splitting constant of the ground state, γ1 = 10 −1×−1 2.81 10 T s the gyromagnetic ratio, B0 the magnetic field. For the magnetic field × − of 100 Gauss applied to guide the positrons, one gets an energy shiftof∆=1.6 10 9eV. This is 3 orders of magnitude bigger than what is expected from Eq.(1.2) and,× therefore, the oscillation probability for m=0 states will be affected. This will result in a suppression of the expected signal that should be corrected by a factor of 1/3.

1.2 Experimental evidence for Mirror Dark Matter

At present, there is some experimental evidence that Mirror Matter could exist, coming from cosmology as well as from the neutrino physics [45]. Foot discussed implications of the DAMA experiment for Mirror Matter-type Dark Matter, which is coupled to ordinary matter through the interaction of Eq.(1.1) [46, 12]. It has been shown that the annual modulation signal (see Fig. 1.3) measured by the DAMA/NaI experiment [6] can be explained by mirror matter-type Dark Matter if the photon-mirror photon mixing strength is in the region of: ǫ 4 10−9. (1.15) ≃ × Those results have been very recently confirmed by the DAMA/LIBRA experiment with a 8.2σ significance [5]. Mirror Matter is a promising candidate that can reconcile the null results from the other, higher threshold experiments like CDMS/Ge [9], CDMS/Si [10] and XENON10 [11]. Interestingly, this value of ǫ is also consistent with all other known experimental and cosmological bounds, including SN1987a2 [48] and the standard Big Bang Nucleosynthesis (BBN) bound [49]. It is also in the range of naturally small ǫ-values motivated by grand unification models [13]. To note is that, to be sensitive to an invisible decay with the ǫ constrain from the DAMA results, one should measure the lifetime rate with a precision of 0.1ppm. This value id 3 order of magnitude smaller than the current precision which is 150 ppm ??. Such an high precision in the lifetime measurements exclude precise QED tests as a way to probe for o-Ps invisible decays. If ǫ is as large as in Eq.(1.15), the branching ratio Br(o-Ps invisible) for the invisible decay of ortho-positronium in vacuum can be found with Eq.(1.10)→ and is of the order: Br(o-Ps invisible) 2 10−7. (1.16) → ≃ × 2The SN1987a limit ǫ < 10−9.5 obtained in Ref. [48] is actually much weaker. For a more detailed discussion of this and other constraints see Ref. [47] 8 CHAPTER 1. MIRROR MATTER AS DARK MATTER

Figure 1.3: The points are the annual modulation observed by DAMA/NaI. The line is the prediction of this modulation for Mirror Matter [12].

For comparison, the BBN limits [49] deduced from the successful prediction of the primor- dial 4He abundance are ǫ< 3 10−8 (1.17) × and Br(o-Ps invisible) < 10−5 (1.18) → respectively. Given the indications for the mirror world coming from Dark Matter [46] and the neutrino physics anomalies [45, 51], as well as the intuitive expectation that nature could be left-right symmetric, it is obviously important to determine experimentally whether ortho-positronium is a window to the mirror world or not. Recently, Barbieri et al. [52] proposed to search for mirror particles at LHC. Chapter 2

Search for the invisible decay of o-Ps in Aereogel

The ﬁrst experiment to search for invisible decay channels of o-Ps was performed by Atoyan et al. [53]. Their result on Br(o Ps invisible) < 5.3 10−4 (90% C.L.) excluded this channel as a possible explanation− of the→ o-Ps lifetime anomaly× (for a recent review see e.g. [54]). This search was repeated by Mitsui et al. who found an upper limit for the branching ratio Br(o Ps invisible) < 2.8 10−6 (90% C.L.) [55]. Furthermore, they could place a limit on the− existence→ of milli-charged× particles and on the photon mirror-photon mixing. This result was corrected in [40] by taking into account the suppression factor for the mixing due to the presence of matter. Motivated by DAMA results and by a possibility to search for extra-dimensions, we performed an experiment with an improved sensitivity to search for positronium decays into invisible ﬁnal states. This search was the subject of another PhD thesis [56] in which the detailed descritpion of the experiment can be found. In this chapter, a concise description of the apparatus and the experimental technique are given and the results are presented. This is important because this search served as the basis to design the experiment for the search of o-Ps invisible decays in vacuum (Chapter 3).

2.1 Experimental technique

The experimental signature for a o Ps invisible decay is the apparent disappearance − → of the energy 2me expected in ordinary decays in a hermetic calorimeter surrounding the o-Ps formation target. The readout trigger for the calorimeter is produced by tagging the stopping of a positron in the target with high eﬃciency. The schematic illustration of the detector setup is shown in Figure 2.1 (the detailed description of the experimental technique and setup can be found in [56]).

Positrons were produced from a 22Na source with an activity of 30 kBq. The 22Na has a half life of 2.6 years and has a Q-value for the nuclear transition to≃21Ne of Q =2.842 MeV.

9 10 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

Aerogel Target

XP 2020

TBGO FBGO

XP 2020

Aerogel Target Inner BGO Ring Scintillating Fiber 20 cm

Figure 2.1: Schematic illustration of the experimental setup: a) front view, b) top view.

This is the maximum energy available for the particles involved in one of the three possible decay modes of 22Na: 1. Decay mode A (Br 90.6%): the β+ decay with end-point energy 0.546 MeV. The positron is always followed≃ by the prompt emission of a 1.27 MeV photon (τ 3.7 ∗ ≃ ps) from the 21Ne de-excitation to the ground state. 2. Decay mode B (Br 9.44%): the Electron Capture process (EC), where an orbital electron is captured≃ by the nucleus, and only a 1.27 MeV photon and a neutrino are emitted from the source. In some rare cases (with a probability 6 10−3), an orbital electron is ejected, due to the sudden change in the nucleus charge≃ × (shake-oﬀ) 3. Decay mode C (Br 0.056%): there is no photon emission because the transition ≃ goes directly to the ground state. The end point energy of the positron is 1.83 MeV. Therefore, in most o-Ps (p-Ps) decays we expect 3(2) photons with a summed energy equal to 2me and one photon with an energy of 1.27 MeV (see Figure 2.2). For the design of the experimental setup aiming at a sensitivity Br(o Ps invisible) 10−8, the following criteria were considered: − → ≃ (a) The probability not to detect all direct e+e− annihilation photons was suppressed to 10−9 using a thick hermetic crystal calorimeter, minimizing the dead material and with≤ a good energy resolution. The probability to loose all photons in 3γ decays is consequently even smaller. (b) The region around the target was designed with as little dead material as possible in order to reduce photon losses. (c) By the appropriate choice of a porous target material and its dimensions a high fraction of o-Ps was produced resulting in a suppression of the background from the direct e+e− annihilation and p-Ps decays and in high statistics. 2.1. EXPERIMENTAL TECHNIQUE 11

ECAL Scintillating Fiber Plastic Scintillator

γ (1.27MeV) e+ TBGO FBGO

3γ from oPs decay 22Na Aerogel 4x8x8 mm3

Figure 2.2: Schematic illustration of the positron tagging system and the o-Ps formation target of the setup.

(d) The trigger rate and the DAQ speed were maximized for statistics.

(e) An eﬃcient positron tagging system was designed to provide a clean trigger for positronium formation. A method was developed to suppress the background from the electrons emitted in the EC process (shake-oﬀ electrons).

(f) An eﬃcient identiﬁcation of the 1.27 MeV photon emitted by the 22Na radioactive source was achieved with a method to veto the charged particles entering the trigger counter, thus, the backgrounds related to them could be reduced.

Photons from the direct e+e− annihilation in flight or from the positronium decays were detected in a hermetic, segmented BGO calorimeter (the ECAL). Two endcap counters called TBGO and FBGO (see Figures 2.1-2.2) were mounted on each side of the target. At the analysis level the 1.27 MeV photon (“the triggering photon”) was required to be identified in the TBGO counter. The calorimeter was instrumented with charge and time readout. The activity of the source was chosen to maximize the trigger rate versus the inefficiency of signal detection (mostly due to pileup events). The source was prepared by evaporating drops of a 22Na solution directly on a 100 µm thick and 2x8 mm2 wide plastic scintillator (see Figure 2.3) fabricated by squeezing a 500 µm diameter scintillating fiber (Bicron BF- 12). In this way, no dead material was introduced for a source holder. The S-shape of the fiber (see Figure 2.1) was selected to avoid background from 511 keV annihilation photons back-to-back. The scintillating fiber was read out at both ends by two photomultipliers 12 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

Figure 2.3: Schematic view of the scintillating ﬁber with the 22Na source on the squeezed part in the center.

(Philips XP2020) located outside the detector (see Figure 2.1). The coincidence of the two PMT signals was used to tag the passage of a positron through the fiber and acted as a start signal for the data readout system. The use of two PMTs in coincidence, instead of a single one [55], lowered the ratio between fake and real positron triggers to < 1.9 10−10. 3 × Opposite to the source, a 4x8x8 mm SiO2 aerogel piece (type SP30, purchased from Matsushita Electric Works) was placed in contact with the squeezed fiber (see Figure 2.2 and 2.4). Positrons stopping in the aerogel target may form positronium (the formation probability is 45% [57]) which can migrate into the aerogel pores. The collisions with the walls of the pores did not appreciably quench the o-Ps: when the aerogel was flushed with N2, a fit to the distribution of the time difference between the start from the fiber and the stop from the calorimeter yielded τ = 129.1 1.8 ns. o-Ps ± The ECAL was composed of 100 BGO crystals that surrounded the target region providing a nearly isotropic sphere of radius 200-220 mm (see Figure 2.1). Each crystal had a hexagonal cross-section of 61 mm diameter and a length of 200 mm. The crystals of the inner most ring were wrapped in a 2 µm thick aluminized Mylar foil to minimize the photon energy absorption. The other crystals were wrapped with Teflon foils of 750 µm thickness. The crystals in the barrel and the FBGO were readout with ETL 9954 photomultiplier tubes. The energy deposited in the fiber is an important parameter in order to reject the background from the electrons emitted in the EC process (shake-off electrons, see Section 2.2). The mean number of photoelectrons detected in each XP2020 for a positron crossing the fiber was measured to be about 1.2, thus, a cut on the energy deposited in the fiber 2.1. EXPERIMENTAL TECHNIQUE 13 using these signals would not be meaningful. For this reason the FBGO was also used to measure the energy deposited in the fiber by the positron: the light emitted by the fiber could traverse the transparent aerogel and enter the FBGO through an aperture in the wrapping on its front face. This light was then guided by the FBGO to the PMT attached on the back face of FBGO (as illustrated in Figure 2.4). This method provided a mean number of photoelectrons equal to 13 1 for a positron traversing the fiber [56]. ±

Figure 2.4: Schematic illustration of the method to readout the energy deposition in the ﬁber.

The TBGO endcap was used in the off-line analysis to identify the 1.27 MeV photon. The energy resolution of the TBGO was an essential parameter to reduce backgrounds related to the misidentification of the 1.27 MeV photon (see also Section 2.2). To provide a better energy resolution, this crystal was coupled to an ETL 9964 PMT with a more uniform light collection and a larger quantum efficiency than the ETL 9954. For the same reason this crystal was of a better quality than the others and efforts were dedicated to maximize the light collection by keeping the amount of dead material introduced by the crystal wrapping as small as possible. The best results were achieved with the crystal wrapped in the 3M radiant mirror (64 µm thickness): the resolution at 662 keV was measured to be about 15% (FWHM). To select the triggering photon, an energy window [1275 67] keV was used in the analysis. In addition, to veto charged particles (positrons ± 14 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL and electrons) entering the TBGO, a 1 mm thick plastic scintillator (Bicron BC-400) was optically coupled to the TBGO front face (for more details see [59]), i.e. the same PMT was used to detect the light signals from the plastic scintillator and the TBGO crystal (see Section 2.2 for a discussion of backgrounds associated to charged particles entering the TBGO). For both, TBGO and FBGO counters, the signals from the plastic scintillator or from the fiber could be distinguished from the signal of the BGO crystal due to their significantly different decay times: τ 2.7 ns for plastic scintillator and τ 300 ns for BGO. To carry out the measurements≃ the outputs of these counters were≃ passively split into three signals which were fed into corresponding ADC inputs with three different integration gates, as illustrated in Figure 2.5. The first one, the normal long gate was used to measure the full energy deposition in the counter, i.e. the sum of energies deposited in the crystal and plastic scintillator. The second, a short gate, was used to measure the energy loss in the plastic scintillator or in the fiber, and the tird one, a gate delayed with respect to the trigger long gate, was used to measure the pure photon energy deposited in the FBGO counter and for better identification of the 1.275 MeV trigger photon in TBGO, respectively. The light signal corresponding to the energy deposition from a positron crossing the fiber could, in principle, contaminate through the entrance window the energy from o-Ps decay or veto information in the FBGO counter, i.e. it could be taken as an energy deposition from the positron annihilation. To study this effect, clean samples of events corresponding to detection of two 511 keV annihilation photons in any of two back-to-back BGO counters surrounding the FBGO crystal were selected. For this sample only the fiber light could give a signal in FBGO, since the two annihilation γ’s escape the FBGO and the so-called optical cross-talk was much less than 1%. The FBGO pedestal, its width, and the response to 511 keV photons were measured as a function of the long gate delay and compared for two cases - the entrance window closed and open, i.e. with and without screening of the fiber light. Finally, the delay of 15 ns was chosen to compromise the reduction of the number of detected photoelectrons in the FBGO counter and the broadening of its pedestal. The pedestal width (FWHM) measured with and without screening the fiber light changes from 11 to 12 keV, respectively. The increase was due to the contribution from the fiber light tail and possibly from the fiber afterglow. This broadening was small compared to the cut of 80 keV on the sum of all ECAL pedestals used in the analysis and results in a negligible contribution to the o Ps invisible signal efficiency loss, which was dominated by the overlap of close in time− events→ (see below). In Figure 2.6 the scatter plot of signals measured with short versus long gate is shown for the TBGO counter coupled with the front face to the plastic scintillator. Three regions corresponding to detection of a) pure positrons stopped in the plastic scintillator, b) 511 keV photons contaminated by the positron energy deposited in the plastic scintillator, and c) pure photons, i.e. without detection of positrons in the plastic scintillator are clearly seen. The ellipse indicates the one sigma contour of the 1.275 MeV peak with a barely seen tail from positrons detected in the plastic scintillator. In order to avoid a reduction of the statistics and due to the typically high pulse height from the positron energy, it was 2.1. EXPERIMENTAL TECHNIQUE 15

Short gate integration of the first 15 ns

Long gate integration without the first 15 ns Long gate integration

Figure 2.5: An example of the pulse shape of the FBGO signal, which is an overlap of signals from a positron and a photon, detected in the fiber and the BGO crystal, respectively. The short gate was used to measure the energy loss from positrons (shown not in scale). found possible to use instead of a direct charged particle veto on the energy loss measured with the short gate, a simple loose energy window cut around the 1.275 MeV photopeak. This cut results in the identification of the trigger photon with a purity better than 90%. A remaining 10% of events contaminated by positron energy are not dangerous, because they correspond≃ to positrons stopped in the plastic scintillator and are not entering the crystal. Finally, this energy window cut was enhanced by adding an energy window cut on the energy deposition in the delayed long gate, see Figure 2.6 below, resulting in a slightly improved purity of trigger photon events. A VME system interfaced to a PC was used for data acquisition (the DAQ rate was about 1800 events/s). For every trigger, five CAEN 32 channels QDC v792 modules recorded the charge of the crystal signals while a CAEN TDC v775 recorded the time information. A trigger gate length of 2.9 µs was chosen to keep the probability of o-Ps to decay after this time to . 10−9. A temperature stabilized light-tight box containing the calorimeter was built in or- 16 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

Figure 2.6: The scatter plot of energy loss measured with the short versus long gate measured for the TBGO counter coupled with the front face to the plastic scintillator. Three regions corresponding to detection of a) pure positrons detected in the plastic scintillator, b) 511 keV photons contaminated by the positron energy deposited in the plastic scintillator, and c) pure photons ,i.e. without detection of positrons in the plastic scintillator are clearly seen. The ellipse indicates the one sigma countur of the 1.275 MeV peak with a barely seen tail from positrons detected in the plastic scintillator. der to keep the temperature of the BGO crystals in the range of 0.5 0C. Water, whose temperature was controlled by two thermostats, circulated through± copper tubes welded on two copper plates inside the box. The experimental hall was air conditioned to keep temperature variations within 10C. The high-voltage dividers of all PMTs were placed outside the box in order to avoid± energy dissipation close to the crystals. The BGO crystals were equipped with LEDs that could be pulsed periodically to monitor the response. Additionally, the gains of the PMTs were also monitored to check their stability. The detector was calibrated and monitored internally using the 511 keV annihilation photon and the 1.27 MeV photons emitted by the 22Na source. Variations of the energy scale during the run period were within . 1% and corrected on the basis of an internal calibration procedure [56]. 2.2. BACKGROUND ESTIMATION AND DEDICATED ENGINEERING RUN 17 2.2 Background estimation and dedicated engineering run

In order to reach the required sensitivity, the background must be reduced and controlled at the level of 10−8. To understand the different background sources and to cross-check the simulation, we perfomed an engineering run with a simplified version of our detector. During two months of data taking, the stability of the detector and its components was investigated. The comparison between the background expected based on Monte Carlo (MC) simulations and the data of the engineering run is summarized in Table 2.1. The ECAL thickness of 200 mm provides a probability of < 10−9 for two 511 keV photons to escape detection (see background 1 in Table 2.1). For three-photon decays, this probability is consequently even smaller. If one (or more) annihilation photon (e.g. backscattered from the target) overlaps with the 1.27 MeV in the TBGO, it can fall in the trigger energy window [1275 67] keV because ± of the finite energy resolution. This introduces a background if the remaining annihilation photon gets absorbed in the dead material or escapes detection. The separation between the upper bound of the trigger energy window and the sum of a triggering 1.27 MeV and a 511 keV photon was, thanks to the good energy resolution of the TBGO, 7σ of the 1786 keV peak (1275+511 keV). Thus, the level of this background is < 5 10−9 (background 2 in Table 2.1). × In order to suppress the other sources of background related to the misidentification of the 1.27 MeV photon (backgrounds 3, 4 and 5 listed in Table 2.1), one had to veto charged particles entering the TBGO. Two processes are responsible for generating such triggers. One is associated with decay mode B (EC) when the 1.27 MeV photon interacts in the fiber, faking a positron signal. If the scattered photon and the Compton electron reach the TBGO, the sum of the energy of the two particles can be misidentified as the triggering photon without any energy in the rest of the calorimeter. Another background can occur in decay mode A if the 1.27 MeV photon is not detected: a trigger can be produced by a positron that multiple scatters (MS) in the fiber and deposits enough energy to trigger the experiment. If the positron reaches the TBGO with a kinetic energy of about 200-300 keV and the two 511 keV annihilation photons are completely absorbed in the TBGO an energy close to 1.27 MeV will be reconstructed. This will appear as an invisible decay since no energy is expected in the rest of the detector. If the 1.27 MeV photon is not present (decay mode C) a trigger can similarly be produced by the 1.83 MeV positron. To veto these backgrounds the energy window cuts of the TBGO signal described in the previous section was used such that the backgrounds 3, 4 and 5 had a probability of < 10−8 in the final setup. The photon following EC may accidentally coincide with a trigger from the fiber generated either by the PMTs noise or by some other particles emitted from possible unstable isotopes formed during the target activation. The level of this background could be reduced with the selection of two XP 2020 with very low noise (< 30 counts/s) and the requirement of the coincidence between them. In addition, a radioactive source with a controlled high 18 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL purity was chosen. From the data of the engineering run, this background was estimated to be < 1.9 10−10 (background 6 in Table 2.1). × During the decay mode B (EC) the fiber signal can be generated by shake-off electrons (background 7 in Table 2.1). Since the probability of an electron ejection steeply drops with its emission kinetic energy (more than 4 orders of magnitude in the first 100 keV) the cut on the energy deposited in the fiber by the triggering particles was used to suppress this background. The engineering run allowed to test these backgrounds as shown in Table 2.1. The expected fraction of zero energy events is 10% smaller than what was measured. This difference can be explained by the contribution from the shake-off electrons which was not included in the simulation. Indeed, in the engineering run there was no information about the energy deposited in the fiber so that no cut on the energy of the particles passing through the fiber could be applied. The last column of the table lists the expectations for the final setup. The total background is estimated to be at the level 10−8. The threshold on the energy deposited in the fiber was set considering the uncertainty due to the number of photoelectrons and the subtraction method to be sure that no electron below 100 keV could trigger the fiber; it was chosen, based on simulations, to be at 140 keV.

BACKGROUND ENGINEERING RUN FINAL SETUP SOURCE expected measured expected 1) Hermiticity Dead Material < 10−9 < 10−9 < 10−9 Resolution 2) Absorption in trigger Energy window 1.3 10−6 1.5 10−6 < 5 10−9 × × × 3) MS positron with E =546keV 2.1 10−6 < 10−8 max × 4) MS positron −7 −8 with Emax=1.83MeV 1.4 10 < 10 × − − 5) Compton EC photon 1.3 10 6 < 10 8 × 6) Accidental noise and EC photon 3.2 10−11 < 1.9 10−10 1.9 10−10 × × × 7) Shake–off electrons in EC process 10−6-10−7 10−8 Total 4.8 10−6 5.6 10−6 10−8 × × Table 2.1: Comparison between expected (from MC) and measured background level for the different background sources in the engineering run and expected background level for the final setup (see text for details). 2.3. DATA ANALYSIS 19 2.3 Data analysis

For the analysis we used a data sample of 1.39 1010 recorded ﬁber triggers collected over × a four months data taking period. For each event the following variables were used and cuts were applied to suppress background:

(1) ∆Tshort is the time from the trigger start to the end marker of the dual timer unit that generates the short gate (measuring the light from the plastic scintillator coupled to the TBGO).

(2) ∆Tlong is the pedestal of one of the QDC channels integrated using the long gate as a start trigger.

(3) ∆TXP is the time diﬀerence between the two XPs reading the ﬁber.

(4) ∆TTBGO is the time diﬀerence between the XPs coincidence and the TBGO.

(5) ETBGOc is the energy deposited in the TBGO with a gate delayed by 15 ns to measure the energy deposited in the TBGO crystal without the contribution of the plastic scintillator.

(6) ETBGO is the energy deposited in the TBGO with the full gate (long gate).

(7) EFBGO is the energy deposition in the fiber measured with the FBGO (short gate). The distributions of these variables for a reduced data sample of 106 triggers are shown in Figure 2.7. The used selection cuts are listed in Table 2.2. The cuts were selected and tuned with the help of a dedicated run with corresponding statistics of about 5% of the data. These variables can be grouped in three categories, depending on their function: (a) The first two variables check the stability of the electronics and the duration of the gate widths. The selection has been tuned experimentally looking at the obtained spectra. (b) The variables 3) and 4) suppress accidental triggers faking positrons in the fiber. The cuts have been chosen to minimize the accidentals and maximize the signal statistics. (c) The variables 5) to 7) are the cuts that reduce triggers from backgrounds that mimic the appearance of a positron in the formation cavity region. Furthermore, the upper limit of the energy window for the 1.27 MeV photon is very sensitive to the background from the “absorption” of one 511 keV γ in the trigger energy window. The cut of 1σ was selected in order to enhance good triggers to the required level. ± All the selection cuts, except 7), have been defined in terms of the sigma of the signal determined with a Gaussian fit to the data sample with 106 events. Table 2.2 summarizes the values used and the evolution of the total number of events passing the cuts. The lower cut for the energy deposited in the fiber has been chosen to reduce the probability of shake-off electrons to trigger the fiber to a level < 10−8 as discussed in Section 2.2. The measured fraction of the o-Ps produced in the aerogel is reduced by 20% applying the threshold for the energy cut in the fiber. This was expected, since the positrons that deposit the most energy are the ones stopping in the fiber. 20 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

x10{2} x10{2} 4000 5000

Events 3500 1) Events 2) 4000 3000

2500 3000 2000 2000 1500

1000 1000 500

0 0 1360 1365 1370 1375 1380 1385 1390 1395 190 195 200 205 210 ∆ Tshort (ns) Tlong (ADC counts)

50000 3000

Events 3) Events 4) 2500 40000

2000 30000 1500 20000 1000

10000 500

0 0 -30 -20 -10 0 10 20 30 -60 -40 -20 0 20 40 60 ∆ ∆ TXP (ns) TTBGO (ns)

80000 7) Events

60000

40000

20000

0 0 50 100 150 200 250 300 EFBGO (keV)

Figure 2.7: The cuts applied to the variables. The numbers on the plot correspond to the variable deﬁned in the text. Only the colored regions contribute.

2.4 Results

After imposing the above requirements a ﬁnal sample of 1.41 108 events was obtained. For these events the energies of all the 100 BGO crystals, except×the TBGO, were summed. Figure 2.8 shows the spectrum of the total energy (Etot) deposited in the ECAL. The peak at 1022 keV corresponds to the positronium mass (MPs 2me). The inset shows that no event is observed in the zero energy region. ≃ To deﬁne the upper energy cut on Etot, below which an event is considered as photonless (invisible), a dedicated run of 107 triggers was performed triggering the experiment only 2.4. RESULTS 21

Variable Selection cut Fraction of events name # σ’s value of 1σ remaining after cuts 1) ∆T 4σ 1.03 ns 99.3% short ± 2) ∆T 4σ 0.8 ADC counts 98.9% long ± 3) ∆TXP 1σ 1.87 ns 75.5% 4) ∆T ±1σ 3.71 ns 27.2% TBGO ± 5) ETBGO 1σ 74 keV 3.1% 6) E ±1σ 67 keV 2.7% TBGOc ± 7) EFBGO 140 keV < EFBGO < 400 keV 1.1% Table 2.2: Deﬁnition of cuts and the remaining fraction of events after the cut is applied.

with the 1.27 MeV photon and no requirement of the fiber [53]. The zero peak contained about 10.4 1.2% of the events passing the selection cuts defined in Section 2.3. This value was corrected± by a factor 0.8 determined using the MC simulations to take into account the different detection efficiencies of the 1.27 MeV photon in the case of the EC process and in the case of the transition with the positron. The measured value was consistent with the expected fraction of electron capture events (decay mode B). The cut Etot < 80 keV corresponding to the region containing 87% of the events in the EC peak at zero energy was used to define the photonless events, as shown in Fig. 2.8.

1400 Events 1200

1000

800

600

400

200

0 -100 0 100 200 300 400 500 Energy (keV)

Figure 2.8: Zero energy peak measured using the EC photon as a trigger. The arrow shows the threshold at 80 keV. 22 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

To determine the signal inefficiency, mostly due to pileup, 106 events have been col- ≃ lected using a random trigger formed by delaying the fiber coincidence by 16 µs (half of the mean time interval between two events). For the 80 keV threshold defined above, this gave an inefficiency of (11.6 0.5)% that was consistent with the prediction of the simulation. ± This inefficiency was measured at the beginning of the data taking and, conservatively, was not corrected for the reduction of the source intensity during that period. Finally, the signal efficiency was estimated to be ǫ (87.4 0.5)%. ≃ ± The mean fraction of o-Ps in the data sample could be evaluated from the decay time − curve by fitting the observed distribution, shown in Figure 2.9, to the function A e( t/τo-Ps)+ B (B is the accidental background) starting from the time t = 100 ns when· o-Ps was completely thermalized in the target [56]. After taking into account the estimated difference of efficiency for 2 and 3 gamma detection and the pick-off effect, the fraction of o-Ps in the data sample obtained with the cut on EFBGO by analyzing the time distribution in the TBGO (see Table 2.2) was 4.5 0.2 % [56]. ±

-t/ τ 5 10 f(t)=Ae +B

Events Constant: A= 1235.6

τ 4 Lifetime: = 129.3 ns 10 Background: B= 60.6

3 10

2 10

0 100 200 300 400 500 600 700 800 Time (ns)

Figure 2.9: Distribution of time between the ﬁber trigger and one of the annihilation photons in the TBGO. An exponential ﬁt (solid line) is performed in order to determine the fraction and the lifetime of o-Ps produced in the aerogel.

Since in the signal region no zero energy events were observed the upper limit for the branching ratio [58] is:

−7 Br(o Ps invisible)=2.3/(N − ǫ) 4.2 10 (90% C.L.) (2.1) − → o Ps · ≤ × 2.5. INTERPRETATION 23

where N = (6.31 0.28) 106 is the number of o-Ps in the selected sample. Fig- o-Ps ± × ure 2.10 shows the extrapolation into the region of the zero signal with an exponential.

x10{2}

5000

Events Entries: 1.41e+08 4000

3000 2 10 Events

10 2000

-1 1000 10 0 200 400 Energy (keV)

0 0 200 400 600 800 1000 1200 1400 1600 Energy (keV)

Figure 2.10: Spectrum of the sum of the total energy in the ECAL. The inset shows the magniﬁed view of the low-energy region in logarithmic scale.

The integral from 0 to 80 keV of the function obtained from the ﬁt gives an evaluation of the background contribution in this region. The result is N = 0.34 0.04 expected bkg ± events, where the error was evaluated from the uncertainty related to the extrapolation procedure itself.

2.5 Interpretation

No event consistent with an invisible decay was found in the large sample of events. Using Eq. (32) of Ref. [60], the bound for particles with a fraction Qx of the electron charge can be plotted as a function of their mass mX for mX < me, as shown in Fig. 2.11a. Thus, the region of the charge-mass parameter space, which was not excluded directly by the SLAC results [61] and the previous search for o Ps invisible [55], is covered by − → this experiment (see Fig. 2.11b). The strength of the photon mirror-photon mixing ǫ can be extracted from the limit on the Br(o Ps invisible) with [40]: − → 1 Br(o Ps invisible)Γ Γ ǫ = − → SM coll (2.2) 2πf 2(1 Br(o Ps invisible)) s − − → 24 CHAPTER 2. SEARCH FOR THE INVISIBLE DECAY OF O-PS IN AEREOGEL

x10{-3} ) x

0.1

0.08

0.06

0.04

0.02 Fraction of electron charge (Q

0 100 200 300 400 500 Mass (keV)

Figure 2.11: a) Mass–charge parameter space for the o-Ps decay into milli-charged particles, excluded with this experiment, b) Comparison of our results (the dashed region on the plot) with other experimental (SLAC [61] and previous o Ps invisible [55]) and astrophysical bounds (the plot was taken from [62]). − →

by substituting a conservative value of Γ =5 104 s−1 for the collision rate of the o-Ps coll × against the walls of the aerogel pores [41]. ΓSM is the decay rate of o-Ps in vacuum and f = 8.7 104 MHz is the contribution to the ortho-para splitting from the one-photon × annihilation diagram involving o-Ps [36]. Using our result one can estimate the mixing strength to be ǫ 1.55 10−7 (90% C.L.). This is a factor of 10 smaller than the BBN ≤ − × limit of ǫ < 3 10 8 [49] but does not cover all the region of interest suggested by the DAMA and CRESST× results [46] and motivated by GUT predictions [13] and by string theory [63] (ǫ> 10−9). Chapter 3

Design of an experiment to search for invisible decays of o-Ps in vacuum

The experiment presented here is based on the slow positron beam used to form o-Ps in a vacuum cavity combined with the BGO calorimeter used in our previous search for o Ps invisible decays (see Chapter 2). The great advantages of this approach compared to− the→ one, where we produced o-Ps in an aerogel target [64], are listed here: Compared to the experiment presented in Chapter 2, a factor 104 more statistics • can be collected with the same number of positrons. In the thin SiO2 films that we plan to use as a target, 10 times more o-Ps is produced per implanted positron (see Section 3.1.2) compared to the aerogel. Furthermore, there is no need to apply cuts for the 1.27 MeV photon selection and for the fiber energy deposition that reduced the number of events to less than 1% with respect to the number of positrons emitted from the source [64, 56]. In the previous experiment, the main contribution to the 12% inefficiency for the • detection of events that gave a trigger, arose from the overlap of close in time annihilation events (so called pileup events). In the beam based experiment described here, after every 300 ns bunch the chopper shuts off the positron flux for 3 µs. Therefore, the efficiency for signal detection will be close to 100% (see Section 3.3).

′ The suppression of the o-Ps o-Ps invisible conversion due to the decoherence • caused by the interaction of→ o-Ps with→ matter will be minimized. The number of collisions with the walls of the vacuum cavity undergone by the o-Ps during its lifetime is at least a factor 104 smaller than in the aerogel pores. Since the branching ′ ratio for the o-Ps o-Ps invisible decay is inversely proportional to the number → → of the o-Ps collisions (see Equation 1.10), the sensitivity on the mixing strength will be a factor 100 better for the same statistics. In case an excess of events above the MC expectation for the background is observed, • this experiment oﬀers a unique and essential feature: one can cross check experimentally if it comes from signals. More precisely, by changing the number of collisions

25 26CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

one can modify the oscillation probability while the background remains the same. We thought about two diﬀerent possibilities:

(1) taking two runs at different positron implantation energies. From 3 to 5 keV the mean velocity of the created o-Ps increases by about a factor of two, thus, the collision rate with the walls is 2 times bigger and the signal is suppressed by the same factor (see Section 3.1.2). (2) the same result can be achieved varying the length of the cavity confining positronium (see Section 3.1.3) while keeping the implantation energy of the positron fixed.

However, compared to the previous experiment, there is a clear disadvantage: the calorimeter must be mounted outside the vacuum chamber so that the vacuum pipe introduces a loss of the photon energy. Nevertheless, simulations show that with an aluminum pipe of 1 mm thickness the sensitivity of the experiment will be at a level of 10−7 (see Sections 3.1.3 and 3.3).

3.1 The setup

Figure 3.1: Schematic view of the setup. The main parts of the system are: The bunched slow positron beam, the secondary electron tagging system, the target chamber and the γ detector.

The experiment is designed with the goal to observe the o-Ps invisible decay if its branching ratio is of the order of 10−7 (see Section 3.3). According→ to this requirement, 3.1. THE SETUP 27

the apparatus has several distinct and separated parts (Fig. 3.1) that will be described in detail in the following sections: (1) the bunched slow positron beam (Section 3.1.1) (2) the target for efficient o-Ps production near thermal energy (Section 3.1.2) (3) the vacuum cavity to confine the o-Ps (Section 3.1.3) (4) the positron appearance tagging system with a high S/N ratio, based on a high performance micro-channel-plate (MCP) described in Section 3.1.4, combined with the positron bunching (5) the gamma detector, an almost 4π BGO crystal calorimeter (ECAL) surrounding the vacuum cavity for efficient detection of annihilation photons to search for invisible o-Ps decays (Section 3.1.6).

3.1.1 The slow positron beam The details and performance of the ETHZ positron beam are presented in Chapter 5. The beam is designed to operate in two modes, i.e. there are two different ways of tagging the positrons (or positronium): (1) Detection with a MCP of the secondary electrons emitted when the positrons hit the target (Section 5.4.1). (2) Positron bunching: an initial pulse of 300 ns is compressed to the target region into a 2 ns wide pulse (Section 5.4.2). In the first mode of operation, the secondary electrons (SE) produced by the positrons (about 25000 e+/s) hitting the target are accelerated to 1-10 keV by the same voltage (applied to the target relative to the grounded transport tube) that is used to implant the positrons in the positronium converter (target). The secondary electrons are then transported in the backward direction by the same magnetic field, which guides the positrons. The two operation modes described above can be combined. This is done by studying the delay between the detection of the SE at the MCP with respect to the arrival time of the positron at the target: the trigger for the positron tagging can be formed by a coincidence of the pulse from the MCP and the signal from the pulsed beam (see Fig. 3.2). This is a key point for the experiment because of the requirement to have the highest possible signal-to-noise (S/N) ratio in order to suppress fake triggers. With a fake trigger we mean that the trigger is not correlated with the presence of a positron in the o-Ps formation cavity. In this case, no annihilation photons would be detected and, as a consequence, this event would be mis-identified as an invisible decay. The requirement of this coincidence suppresses: the background generated from electrons and ions produced by ionization of the • residual gas atoms by positrons. 28CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

the accidentals due to the MCP noise to a level of 10−5. • This fundamental step of the experiment has been already tested successfully and the result is shown in Figure 3.2. As will be explained in Section 3.1.4, to reach the required conﬁdence level for the presence of a positron in the formation cavity, it is necessary to add an additional condition to the trigger scheme.

Figure 3.2: Timing between the secondary electrons detected in the MCP and the bunching pulse of the beam for 1 and 2 keV implantation energy of the positrons.

3.1.2 o-Ps production target As reported in Chapters 7 and 8, we performed systematic studies to characterize diﬀerent samples that could be used as positronium converters for this experiment. From those samples, we selected the o-Ps production target of the experiment for the following reasons: 3.1. THE SETUP 29

(1) It provides a high production rate of o-Ps in the range of 28-30 % for positron implantation energies between 3 and 5 keV (see Fig. 3.1.2), thus, the high statistics required for the experiment can be reached (Section 3.3).

(2) In the interval of implantation energies between 3 and 5 keV the fraction of o-Ps remains constant within 2% (from 30% to 28%), thus, the background coming from the 2γ decay of p-Ps remains the same for the different implantation energies. While this fraction is almost constant, the mean energy of the produced o-Ps is about a factor of 3 larger for 3 keV implantation energy that for 5 keV (see Chapter 8. We estimated with the MC simulation that for a cylindrical cavity with 30 mm diameter and 15 mm length at 5 and 3 keV one has 0.9 and 1.9 collisions per lifetime. Therefore, the collision rate with the walls is 2 times bigger for 3 keV positrons and the signal ∼ is suppressed by the same factor. It is worth noting that from 3 to 5 keV the implantation depth for the positrons varies from 165 to 300 nm (the density of our porous films is about 1.5 g/cm3) thus the background will not be affected because the difference of the energy absorbed in 150 nm of porous SiO2 is negligible.

(3) In the studied samples the o-Ps is produced near-thermal energy, thus, it experiences only few collisions per lifetime with the cavity walls minimizing the suppression of the signal.

(4) The target thickness is about 800 nm and it can be spin coated directly on the end plate of the beam pipe (Fig. 3.4) to avoid additional material of a substrate. Therefore, the absorption of photon energy in the target will be minimized.

3.1.3 The vacuum cavity An essential issue in the experiment is that the positronium produced in the target should be confined in a region of highly uniform detection efficiency, and the o-Ps leakage through the aperture where the positrons are implanted, has to be minimized. The o-Ps which escapes the detection region, could mimic an invisible decay because in this case the detection efficiency for the annihilation photons is reduced dramatically (Fig. 3.4 (a)). In their recent decay rate experiment [33], the Michigan group tried to minimize this effect to reduce the systematic error, using a double chamber-cavity, but still the escape probability for o-Ps was at 200 ppm. In our measurement such a leakage would limit the sensitivity to a Br(o Ps invisible) 10−6. Therefore, to be able to reach the aimed sensitivity of the experiment,− → one has to invent≃ a new method. We plan to completely close the o-Ps formation cavity 1 by employing a thin (15 nm) carbon film in which the few keV positrons can pass through. However, this will block even the most energetic positronium

1Only microscopic holes will be left for pumping the vacuum inside the cavity, leaving a negligible probability for the o-Ps to escape the detection region. 30CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

40 PALS F127 142 ns component

fraction of oPs 30

15 1 2 3 4 5 6 Voltage [kV]

Figure 3.3: Fraction of o-Ps emitted into the vacuum from the a selected sample as a function of the positron implantation energy measured in our setup.

(several eV). Furthermore, with this method an additional signature for the presence of a positron in the formation cavity is added to the trigger scheme: the coincidence between the SE from the target and the ones produced in the carbon foil (Fig. 3.4 (b)). Hence, the S/N ratio will be further enhanced without a dramatic loss of the trigger rate. This point is presented in Section 3.1.4, some preliminary measurements have been performed in order to test this idea. The carbon ﬁlms that are planned to be used are currently employed at PSI2 in the muonic-hydrogen experiment [65] for tagging the muons. Similar to our application they are used for detecting the SE emitted by the crossing muons. Some of those ﬁlms were kindly given to us from the PSI group and we tested their SE emission yield in the implantation positron energy range of 1-7 keV and their permeability to o-Ps. The great advantage of this technique is that the o-Ps leakage is expected to be reduced to a negligible level. In order to minimize the energy loss of the annihilation photons in the vacuum cavity, one should design the beam pipe as thin as possible. In the H1 experiment at DESY, a vacuum pipe with 840 microns wall thickness was constructed. The internal part con- sisted of 40 microns aluminum, while the external part was made of carbon (800 microns).

2PSI, Paul Scherrer Institut, CH-5232 Villingen-PSI, Switzerland 3.1. THE SETUP 31

Figure 3.4: (a) Ps is tagged by the secondary electrons produced by the positron that hits the converter surface (target). In the case where Ps escapes the detection region, it could mimic an invisible decay due to the strongly suppressed detection eﬃciency of the decay photons. (b) By closing the vacuum cavity around the o-Ps converter one obtains a region of highly uniform detection eﬃciency and the o-Ps leakage through the aperture is suppressed. The 15 nm carbon foil acts as a barrier for the o-Ps emitted from the converter but it is nearly transparent for the incoming positron beam and for the secondary electrons used for the trigger.

Similarly, we are designing the pipe for our experiment 3. To avoid problems with the magnetic field necessary to guide the positrons to the target region, the coil should be wound directly on the beam pipe, since we demonstrated with our TOF and PALS setup (Chapter 6), that in this configuration the gain of the PMTs is not affected. Therefore, the material necessary for the coil should also be minimized. A coil made with a copper wire of 100 microns can produce the necessary field of 60 Gauss with a current of 0.5 A (the diameter of a wire fusing at this current is about 20 microns). In the following discussions, we consider a beam pipe with 1 mm wall thickness, thus the expected sensitivity should be understood as a conservative result (Section 3.3). The carbon foil and its support could be suspended by some thin wires so that it is possible to move it in vacuum (see Fig. 3.5). With such a scheme one could vary the distance between the target and the carbon foil, i.e., one would change the number of

3We are also considering the possibility of making a vacuum pipe out of a scintillating material with the internal part coated with a thin aluminum foil. 32CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS collisions that o-Ps will suﬀer during its lifetime. The signal will be suppressed for shorter distances in the same way as with the method described before by applying diﬀerent positron implantation energies.

Figure 3.5: Schematic of the target region and the carbon foil.

3.1.4 Positron tagging system The positron tagging system (see Fig 3.6) is based on the high performance MCP (Hama- matsu F4655-12) as a SE detector (noise rate < 1Hz). The coincidence between the SEs produced by positrons hitting the carbon foil and the SEs emerging from the o-Ps production target will be used to tag the positron appearance in the target region. The acceleration voltage for the positrons is applied in two steps. The positrons are first accelerated to 2 keV energy by the voltage applied between the ground pipe and the carbon foil, thus the SEs emerging from the carbon foil (CF) are transported with this energy back to the MCP. In the second acceleration stage, the positrons are accelerated by a 1-3 keV voltage applied between the CF and the target. Once they hit the target, the SEs are transported back to the carbon foil and the electrons able to cross it are then additionally accelerated so that their final energy will be 3-5 keV (see Figure 3.7). Figure 3.8 shows a MC simulation of the time distribution of the MCP signals from different SE sources; the time zero point is defined by the incoming beam positron crossing the carbon 3.1. THE SETUP 33

Figure 3.6: Schematic of the positron tagging system for the experiment using the MCP signal for secondary electrons emitted from the target and from the thin carbon foil.

foil. The two prominent peaks are due to the SEs emitted when the positrons hit the target (at about 21 ns) and the SEs from the carbon foil (at about 29 ns) when a positron crosses the foil. The SEs from the target are accelerated with a higher voltage than those from the foil and reach the MCP first, although they start later and have a larger flight path. The small third peak visible in the time spectrum of the MCP is produced by additional secondary electrons generated by some SEs from the target interacting in the carbon foil. Those will be accelerated by the same voltage that accelerates the positrons and, therefore, they are detected 1-1.5 ns after the second peak (the cavity length used in the simulation was 30 mm and the positron energy is 6 keV). The broadening of the first peak is due to the angular spread of the SEs emitted from the target and scattering in the carbon foil.

Figure 3.7: Trajectories of the positron (blue) and secondary electrons (red) for the new design with the carbon foil. 34CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

Figure 3.8: Simulated time distributions of the secondary electrons detected in the MCP. See text for details.

3.1.5 Trigger efficiency and confidence level In order to estimate the trigger efficiency and fake trigger suppression of the tagging system described above, a test set-up has been constructed (see Fig. 3.9). In this set-up the distance between the carbon foil and the target was 8 mm and the distance separating the carbon foil and the MCP was 90 cm. The measurements were performed by acquiring the MCP timing with a 5 Giga sampling oscilloscope (Lecroy wave-runner 44XMi). The threshold for the acquisition was set to 10 mV and a sample of 105 events was recorded in a time window of 50 ns after the arrival time at the MCP of the first electron that was defined as START signal. The start signal can be produced by the SEs from the carbon foil or by the SE produced at the target. The probability to detect a SE coming from the target is suppressed by the angular spread introduced by crossing the carbon foil, when propagating in the backward direction. This introduces in the trajectories larger spirals along the magnetic field axis with respect to the SE from the CF, and thus, reduces the probability of the SE to hit the MCP active area. An example of an event recorded with the oscilloscope is shown in Fig. 3.10. The START signal is given by SEs produced at the target and the pulse at 20 ns is from the SEs produced at the CF. The data in Fig. 3.11 show the time delay spectrum with respect to the START signal for the electrons arriving at the MCP with 105 triggers. These results confirm qualitatively the prediction of the simulation4. Note, that in this distribution the

4As will be discussed later in this section, Geant 4 does not reproduce correctly the transmission, 3.1. THE SETUP 35

Figure 3.9: Setup used for the measurements with the tagging system. In order to accelerate the SEs from the target a voltage diﬀerence between the sample holder (green) and the carbon foil has to be applied. A ceramic ring electrically insulates the carbon foil holder and the target holder.

time is inverted with respect to the simulations. In the simulation the time t=0 is defined by the positron arrival time at the CF. The first peak at about 2ns (and a tail extending to 5 ns) is due to the MCP dead time: the first electron in the SE cloud from the target (or carbon foil) makes a START signal and after the dead time a second electron of the same cloud produces a another signal. The second peak between 10 and 17 ns is triggered by the SEs from the CF when the START signal is produced by SE from the target; only the events in this peak are used for the positron tagging. The broadening of this peak is due to the angular spread of the SEs emitted from the target and scattering in the carbon foil. The time separation of 15 ns between the START and the second peak is consistent with a simple estimation considering a straight propagation of the SE electrons produced at the carbon foil and the SEs from the sample (see Table 3.1.5).

Voltage [kV] Flight time [ns] 1.2 39 3.8 22 ∆t 17 ns

Table 3.1: Estimated ﬂight time for SE emerging from CF (1.2 kV) and from the sample 3.8 kV for a distance of 80 cm. The expected delay time is 17 ns.

To estimate the trigger eﬃciency and the fake trigger suppression of our system, we compare two measurements:

a set of data with a voltage diﬀerence between the carbon foil and the sample of -1.2 • kV and -3.8 kV, respectively (solid line in Fig. 3.11),

scattering angles and backscattering coeﬃcients of charged particles with few keV energies. 36CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

Figure 3.10: Example of an event acquired with an oscilloscope. The first signal is produced by the SE from the target and defines the START signal. The second pulse is produced by the SE from the CF 15ns after the START signal. The time window ω between 15 and ∼ 22 ns (i.e. between 10 and 17 ns delay from the START signal) is defined in order to calculate the trigger efficiency and the fake trigger ratio. A Gaussian fit is used in order to determine the position of the pulses (green). 3.1. THE SETUP 37

2500 CF:-1.2kV S:-1.2kV

CF:-1.2kV S:-3.8 kV 2000

1500

1000 w

Number of Events (Arb. units) 500

0 0 5 10 15 20 25 Time delay [ns]

Figure 3.11: Measured delay of the SE from the carbon foil relative to SE from the START signal. The dashed line represents the data obtained by applying the same voltage on the carbon foil and on the sample (-1.2kV). The solid line is obtained by applying -1.2 kV on the carbon foil and -3.8kV on the sample. In this case the broadening of the peak at around 15 ns is mainly due to variations of the ﬂight time of the SE from the target that produce the START signal. The peak at about 2 ns are due to the MCP deadtime (see text for details). 38CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

a set of data with the same voltage applied on the carbon foil and the sample (-1.2 • kV) (dashed line in Fig. 3.11).

We deﬁne the trigger eﬃciency ǫSE as:

Nw ǫSE = (3.1) Ntot

where Nw is the number of events arriving with a time delay from the start signal in a selected time window w when a voltage diﬀerence is applied between the target and the carbon foil. Ntot is the total number of START signals. The carbon foil suppression factor κSE is deﬁned as:

′ Nw κSE = (3.2) Nw

′ where Nw is the number of events in the selected time window w when the same voltage is applied to the sample and the CF (i.e. SE produced at the target can not reach the MCP). In this case the probability for SEs emitted from the sample to reach the MCP is strongly suppressed because the transparency of the foil for those electrons is practically zero. The START signal and the peak at 2 ns for the dashed line in Fig. 3.11 (the same voltage on target and CF) is produced by∼ SEs from the carbon foil, emitted by an incoming positron, since (almost) no SE from the target reach the MCP. Thus, κSE gives suppression of fake triggers obtained by the coincidence positron trigger requirement for events with a positron traversing the carbon foil, but no SE emitted from the target. It is used to estimate the background from positrons, which do not reach the target, e.g. due to backscattering from the carbon foil. This background will be discussed in Sections 3.2.1 and 3.2.2. Note, that the value κSE (see below) is not in contradiction with the requirement for the invisible decay search experiment to have a fake trigger fraction with no energy deposition in the −7 ECAL of < 10 . The suppression κSE refers to events with a positron passing the carbon foil and in these events the annihilation photons will deposit energy in the ECAL. The signals of SEs emerging from the sample and those emerging from the CF can be further discriminated by their charge. The large scattering angle acquired by the SEs from the target crossing the CF drastically reduces the probability to have, as a trigger, a signal produced by more than one electron. On the other hand, the STOP signal is composed of a larger number of SE because it is produced by the sum of:

the SE emitted by positrons crossing the CF; • the SE that are emitted when, the SE produced at the target, cross the carbon foil • in the opposite direction, since the small diﬀerence in their arrival time at the MCP (relative to the SE from the oncoming positron) is not resolved because of the small distance (8 mm) between the target and the carbon foil and the large voltage between them. 3.2. BACKGROUND ESTIMATION 39

This is clearly visible in the Fig. 3.12 where the charge of the START signal (i.e. the first electrons which hits the MCP) is plotted versus the signal in the time window of 12-17 ns for both voltage configurations. This effect can be exploited to considerably increase the confidence level for a positron in the vacuum cavity without dramatically affecting the trigger efficiency as shown in Fig. 3.13. The trigger efficiency (boxes) and the coincidence suppression factor κSE (circles) are studied for two different selection cuts on the MCP signal:

(1) by applying a threshold on the MCP stop signal;

(2) by applying a cut on the charge (integral over the signal) produced by the MCP.

In the first case the fake trigger ratio cannot be suppressed below a value of 4 10−2 while − × the trigger efficiency drops to a value of 10 2. In the second case, the cut performed on the charge shows to be much more efficient. For a cut on the charge of 40 pVs is suppressed to 5 10−3 with a corresponding trigger efficiency of 4 10−2. × ×

3.1.6 The photon detector The same BGO crystals as in our former o-Ps invisible decay search will be used to detect γ-quanta produced in positron or positronium annihilation. The geometry of the detector should be modified to accommodate the beam pipe as we proposed in [66] (see Fig. 3.1.6). Furthermore, the crystals have to be arranged perpendicularly to the B-field, since, as we confirmed in our TOF and PALS setup (see Sections 6.3, 6.4), in this configuration the magnetic field will not affect the performance of the PMTs. The γ-detector serves to veto effectively the positron annihilations into photons. It has been shown that its inefficiency due to photo-electron statistics and due its thickness is less then 10−9 for the energy threshold of 80 keV [64, 56]5. Moreover, we realized that the energy resolution of the crystals could≃ be increased by replacing the Teflon in which the crystals are wrapped with the 3M radiant foil. This reduces the amount of dead material by a factor 12. Furthermore, all the BGO crystals surface is now polished. By roughing the BGO surface except where the PMT is coupled to the crystal, the energy resolution of the calorimeter could be further improved. Therefore, the calorimeter could be refurbished in order to increase the energy resolution resulting in an improvement of the detector performance.

3.2 Background estimation

As mentioned in the previous section, we expect backgrounds which originate from the following sources:

5It is worth noting that in the experiment described in this section the threshold will be lower because the pileup will be reduced by a factor 20. 40CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

Figure 3.12: Charge (measured with 50 Ω termination) in pVs of the start signal versus the charge of the signal for events in the time window 12-17 ns. Top: the same voltage of 1.2 keV is applied to the target and the carbon foil. Bottom: a voltage of 3.8 keV is applied to the target and 1.2 keV to the carbon foil. 3.2. BACKGROUND ESTIMATION 41

0.14 Threshold levels Trigger efficiency ∈ 0.12 SE

Efficiency κ CF suppression factor SE 0.1

0.08

0.06

0.04

0.02

0 10 15 20 25 30 35 40 45 50 Threshold [mV]

0.06 Charge deposition cuts ∈ Trigger efficiency SE 0.05 κ CF suppression factor SE

0.04 Trigger Efficiency 0.03

0.02

0.01

0 10 15 20 25 30 35 40 45 50 Charge [pVs]

Figure 3.13: Top: trigger eﬃciency (boxes) and coincidence suppression factor κSE (circles) as a function of the threshold set on the signal in the time window 12-17 ns. Bottom: trigger eﬃciency (boxes) and coincidence suppression factor κSE (circles) as a function of the cut on the charge (voltage integral) on the signals in the time window 12-17 ns. 42CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

Figure 3.14: Cross section of the BGO calorimeter mounted around the beam pipe. The sphere is to show that the minimal BGO thickness around the target is of the order of 200 mm.

(1) the annihilation energy losses that are estimated to be at a level of 10−7. ≃ (2) a fake positron tagging at a level 10−7 ≃ The main contribution to the first background of the list above is coming from the thickness of the vacuum beam pipe. In Fig. 3.15, we show the simulation results of the energy deposited in a 0.84 mm thick aluminum pipe and a pipe with 0.04 mm aluminum and 0.800 mm thick carbon pipe (similar to the one that was used at the H1 experiment at DESY). Different possibilities of fake triggers that can be produced in this experiment have been identified: Fast backscattered o-Ps (see Section 4.1.1) produced at the carbon foil surface have • a certain probability to escape the detection region. Backscattered positrons from the carbon foil surface or the target have a probability • to escape the detection region. 3.2. BACKGROUND ESTIMATION 43

3.2.1 Fast backscattered o-Ps from the carbon foil As will be discussed in Chapter 4.1.1, fast backscattered o-Ps can be produced from shallow implanted positrons that capture an electron exiting the surface. The contribution to the background arising from this eﬀect has been studied with the MC simulation. We approximated the energy distribution of o-Ps with a Landau distribution peaking around 15 eV [67] (see Fig. 3.16). The probability P (E) of o-Ps to annihilate via pick-oﬀ when it collides with the cavity walls was also included. As a function of the energy, P (E) can be divided in two regions ([68]):

(1) For Eo-Ps < 6.8eV , P (E)=0

(2) For Eo-Ps > 6.8eV , P (E)=0.95

Both assumptions are conservative. In fact, even o-Ps with an energy smaller than its binding energy (6.8 eV) can undergoe pick-oﬀ annihilation. We deﬁne the escaping probability ξ as: Nescape ξo-Ps = (3.3) Ntot

where Nescape is the number of o-Ps which decay after the bending of the vacuum cavity (See Fig. 3.17) and Ntot is the total number of events simulated. Note that this approach is very conservative because the annihilation gammas produced outside the bending region have a non-zero probability to deposit some energy in the calorimeter. The escaping −4 probability estimated with the simulation (Fig. 3.17) is ξo-Ps 1 10 . In order to calculate how this value aﬀects the sensitivity of the experiment,≃ it× has to be multiplied with the fast o-Ps formation probability [69] (< 10%). In order to mimic an invisible decay, the fast o-Ps escaping event has to coincide with an accidental trigger. Thus, the carbon foil suppression factor κSE presented in Section 3.1.5 further suppresses this background to a level < 5 10−8. ×

3.2.2 Backscattered positrons The positrons are transported along the beam line with an energy that can be varied from E = 10 200 eV. The carbon foil and the target are biased with a potential with respect 0 − to the beam pipe, giving an additional acceleration to the positron, thus, their energy at the carbon foil is ET OT = E0 + ECF and at the target it is ET OT = E0 + ET arget. Ifa positron backscatters in the carbon foil (or in the target) it is decelerated by the applied voltage. In this case, it can either be re-implanted or escape the detection region. The fate of the backscattered positron depends on its energy loss in the backscattering process at the foil or target ∆E = E E : T OT − Back

(1) if EBack < ECF (T arget) the positron is re-implanted in the carbon foil (or in the target) with an energy EBack. 44CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

(2) if EBack > ECF (T arget) the positron has enough energy to escape the carbon foil (the target) voltage and it can be transported back in the beam line with an energy E E Back − CF (T arget) This second process represents a dangerous source of background. An escaping backscattered positron could give a trigger and be transported back by the magnetic field outside the detection region, and thus, it will not deposit any energy in the calorimeter. This effect can be suppressed by decreasing the beam transport energy E0 so that the minimum energy loss necessary to escape from the target voltage is smaller and consequently also the escaping probability is suppressed. In this section, a precise estimation of this effect will be carried out using MC calculations. The dominant process in the backscattering effect is the positron multiple-scattering. GEANT4 has a set of low energy classes that can be included in the Physics list using PENELOPE MC cross sections such as G4PenelopeBrehmsstrahlung, G4PenelopeComptonEffect. Unfortunately, the multiple- scattering process is not yet implemented and consequently it is not possible to estimate the backscattering coefficients with GEANT4. Accurate knowledge of the energy and angular distributions of keV charged particles is possible with the EGSnrc (Electron Gamma Shower) Monte Carlo code [70]. This code includes sophisticated low-energy physics comparable with PENELOPE. Moreover, EGSnrc is considerably faster than PENELPOPE and does not require careful tuning of the simulation parameters. In EGSnrc a special package was developed for the calculation of backscattering coefficients. The performance of EGSnrc for keV backscattering particles is presented in [70] where MC simulation data are compared to experimental results for both electron and positron backscattering (see Fig. 3.18). We define the positron escaping ratio ǫe+−esc from the detection region as:

+ ǫe −esc = NEII /Ntot (3.4) where NEII is the number of backscattered positrons whose longitudinal energy loss is smaller than the incoming positron energy before the acceleration. The eﬀect of the positron backscattering has been studied in two situations: (1) Positron backscattering at the carbon foil.

(2) Positron backscattering at the SiO2 target.

Positron backscattering from the carbon foil To calculate the backscattering probability, we assume that the carbon foil has a density of 2g/cm3 and a thickness of 20 nm. There is a substantial difference between the backscattering coefficients for semi-infinite targets and thin foils because of the transparency effect that shows a considerable suppression of the backscattering probability when the incident energy of the positron increases. In Fig. 3.19, the backscattering coefficient η+ for a thick carbon target and for a 20 nm carbon foil are compared. On the same plot the transparency of the foil for the same implantation voltages is shown. The probability of a positron to escape the carbon foil voltage depends on: 3.3. SENSITIVITY 45

the backscattering coefficient η • + the initial positron energy E before the foil acceleration E • 0 CF the backscattering energy and angular distributions • In order to estimate the escaping fraction, the whole energy distribution of the backscattered positrons has to be known (see Fig. 3.20). Figure 3.21 shows the escaping probability for positrons backscattered from the carbon foil as a function of the acceleration voltage. The calculations have been performed for different positron initial energies E0. As one can see, for a good choice of the voltage applied to the carbon foil (about 1.5 kV) and of the initial energy (the lower the better, E0 = 10 eV) the escaping probability is smaller than 2 10−5. Positrons backscattering at the carbon foil are not a direct source of background. To× result in an artificial invisible decay, such an event has to coincide with an accidental trigger. Therefore, this background is suppressed by the confidence level of the tagging system presented in Section 3.1.5 and results in a background < 10−7.

Positron backscattering from the SiO2 target After crossing the carbon foil the positron enters the cavity and it is accelerated to the SiO2 target where it may backscatter. For this estimation, we consider the SiO2 target 2 density of 2g/cm . The backscattering coeﬃcient for SiO2 is larger than the one of the 20 nm foil (Fig. 3.22). In agreement with the results reported in [71], η+ reaches a constant value of about 10% for positron incident energies larger than 4 keV. The positron escaping probability as a function of the energy is shown in Fig. 3.23. For positron energies between 3-5 keV the escaping probability is between 1 10−5 and 3 10−6. These values are larger than the maximum background level that is allowed× in order× to reach the desired sensitivity. However, this background is clearly overestimated because the energy loss of the positron crossing the carbon foil is not taken into account. An estimation of the mean energy loss [72] [70] gives values of the order of few hundred eV that are signiﬁcantly larger than the initial positron energy E0 = 10 eV.

A possible way to further suppress this background is to redirect to the target the positrons that may backscatter. This can be realized by placing an electrode with a varying potential between 0 and 10V. The repulsion voltage has to be activated every time a start signal occurs. The technology to produce such a system is very simple and the background produced by backscattered positrons from the target can be suppresses to values < 10−7. Table 3.2, summarizes the expected background level for the diﬀerent background sources.

3.3 Sensitivity

The sensitivity So−Ps→invisible of the experiment is deﬁned as the level at which the ﬁrst background event is expected:

S − → =1/(N ǫ ) (3.5) o Ps invisible o-Ps · tot 46CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

BACKGROUND SOURCE expected 1) Photon detection loss: Hermiticity Dead Material < 10−7 Resolution 2) Positron backscattered from < 10−7 carbon foil 3) Positron Backscattered from < 10−7 SiO2 4) Fast o-Ps from carbon foil 5 < 10−8 × − 5) Fast o-Ps from << 10 8 target

Table 3.2: Summary of the expected background level for the diﬀerent background sources.

where the terms in the denominator are the integrated number of produced o-Ps (No-Ps) and ǫtot is the total efficiency to detect an invisible decay. The number No-Ps is defined as a product N = R + ǫ ǫ t , where the first factor is the number of delivered o-Ps e · o-Ps · tagging · m positrons per second on the target (in bunching mode), the second one is the efficiency for o-Ps production (about 30%), and the third one is the efficiency of the secondary electron tagging system (about 4%). The last factor, tm, is the measuring time. The number of positrons/s on target depends on the duty cycle of the bunching. As in our previous search, the length of the gate for the ADCs has to be at least 3 µs in order to suppress the probability for o-Ps to decay after this time to a level of 10−9. Hence, the losses due to the 2 duty cycle will be about 10% and the rate of positrons is estimated to be Re+ =1 10 /s. Therefore, the aimed for sensitivity of 10−7 can be reached in a 92 hours run ( ×1 107 ≈ × observed o-Ps annihilations). For zero signal events observed and no event of background expected, the upper limit at 90% CL for the branching ratio assuming Poisson statistics is given by:

Br(o-Ps invisible)=2.3/(N ǫ ) 2.3 10−7. (3.6) → o-Ps · tot ≤ × Using Equation 2.2 with the estimated average number of o-Ps collisions in the cavity Ncoll 1 (for 5 keV implantation energy of the positrons), results in a limit on the photon- mirror≃ photon mixing strength of:

ǫ 4.8 10−9. (3.7) ≤ × This is about one order of magnitude more stringent than the BBN limit (1.17). Assuming that the DAMA/NaI and DAMA/LIBRA annual signal modulation is generated by elastic scattering of mirror matter, the mixing strength is of the order of ǫ ≤ 3.4. SUMMARY 47

4 10−9, thus a total number of 91 signal events would be detected in the ECAL during × ≃ six month of data taking. Given that about 45 background events are expected, a discovery with about 7 σ signiﬁcance could be possible [73]. As explained in Section 3.1, a unique feature of this experiment is the possibility to change the experimental conditions (i.e. the number of the o-Ps collisions with matter), and hence to cross check the results without aﬀecting the background. For an implantation energy of the positron of 3 keV, the number of excess events will be 2 times smaller (45 events) compared to 5 keV positrons.

3.4 Summary

In this chapter, a proposed search for Mirror-type Dark Matter, looking for o-Ps invisible decays in a vacuum cavity, is presented. In the introduction, the Mirror matter, its relevance to the dark matter problem and the link with positronium has been reviewed. The effect of the external fields (electric and magnetic) on the oscillation probability was estimated to be negligible for the field strength used in the experiment. In Section 3.1, the design and the experimental results for the different parts of the experiment have been presented. Section 3.2 includes the simulation results of the background estimation and in Section 3.3 the estimated sensitivity is presented. The goal is to reach a sensitivity in the branching ratio of Br(o-Ps invisible) 10−7 to confront the annual modulation → ≃ signal observed by DAMA/NaI and DAMA/LIBRA (with 8.2σ significance) with Mirror Dark Matter scenarios. In case of a signal observation, the experiment would offer a unique and essential feature, whereby an increase or decrease of the signal rate by a factor 2 is possible while keeping the background constant. In case of a null result, this search∼ will provide a limit on the photon-mirror photon mixing strength about one order of magnitude better than presently derived from Big Bang Nucleosynthesis. 48CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

10{8}

10{7} Events

10{6}

10{5} 0.84 mm Al Pipe

10{4}

10{3}

10{2}

1 0 200 400 600 800 1000 1200 Energy (keV)

10{8}

10{7} Events

10{6}

10{5} 0.84 mm C-Al Pipe

10{4}

10{3}

10{2}

1 0 200 400 600 800 1000 1200 Energy (keV)

Figure 3.15: Distributions of the energy deposited in the dead material surrounding the target region (target substrate, beam pipe and copper coil) from annihilation events in the target. The upper plot shows the results of the MC simulation for a 0.84 mm thick aluminum pipe. Below the distribution for the pipe construction with 0.04 mm aluminum and 0.800 mm carbon. The total number of simulated 2γ-events is 108 in both cases. The peaks at 511 keV and 1022 keV correspond to the total photo-absorption either of a single 511 keV photon or of both of them, respectively. 3.4. SUMMARY 49

Figure 3.16: Energy distribution of fast o-Ps originating from backscattered e+. The pick- oﬀ probability after a collision of o-Ps with the walls is taken to be zero for o-Ps energies smaller than the 6.8 eV while for higher energies it is 0.95.

Figure 3.17: Simulated decay position of o-Ps in the vacuum cavity. The escaping probability estimated with the MC simulation is 1 10−4. ≃ × 50CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

Figure 3.18: Positron backscattering coeﬃcients (η+) versus positron kinetic energy [70]. 3.4. SUMMARY 51

7 1 6

5 Backscatter coefficients for 20nm film 0.8 Backscatter coefficient for thick target

4 measured positron transmission probability 0.6

3 Backscatter coeff. in % 0.4 2

0.2 1 positron transmission probability

0 0 1 1.5 2 2.5 3 3.5 4 4.5 5 Incident positron Energy [keV]

Figure 3.19: Positron backscatter coeﬃcient (η+) from a thick carbon target (black squares) and a thin carbon foil (triangles) as a function of the positron kinetic energy. The transmission probability, through the thin foil is also shown (open squares, right scale). 52CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS

0.1 E=1.0kV 0.09 E=1.2kV

0.08 E=1.4kV

(E)/dE E=1.6kV

+ 0.07

η E=1.8kV 0.06 d E=2.0kV 0.05

0.04 0.03

0.02

0.01

0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Backscatter energy [keV]

0.016 Ω 0.014 )/d

θ 0.012 ( +

η 0.01 d 0.008

0.006

0.004

0.002

-80 -60 -40 -20 0 20 40 60 80 Backscatter angle [deg]

Figure 3.20: Top: simulation using EGSnrc. Energy spectrum of positrons backscattered from a 20 nm carbon foil for positron implantation energies in the 1-2 keV range. The cut-oﬀ energy is 300 eV. Bottom: angular distribution for backscattered positrons

Figure 3.21: Escaping probability for positrons backscattered from the carbon foil as a function of the carbon foil voltage for diﬀerent positron initial energies E0. 3.4. SUMMARY 53

Backscatter coefficient for SiO2. 2g/cm3 9

8 Backscatter coeff. in % 7

5 1 2 3 4 5 6 7 8 9 Incident positron energy [keV]

Figure 3.22: Backscattering coeﬃcient η+ for the SiO2 target as a function of the positron incident energy.

Figure 3.23: Escaping probability for the total number of incident positrons at the SiO2 target as a function of the implantation voltage for diﬀerent positron initials energies E0. 54CHAPTER 3. DESIGN OF AN EXPERIMENT TO SEARCH FOR INVISIBLE DECAYS OF O-PS Chapter 4

Study of positronium emission from porous silica ﬁlms

In order to select an appropriate e+ o-Ps porous converter for the invisible decay search experiment, a system to perform o-Ps→ measurements had to be constructed. Two different aspects related to the o-Ps emission from the target have to be studied: the fraction of o-Ps emitted from the converter surface relative to the number of • implanted positrons; the energy distribution of the emitted o-Ps. • There are several complementary methods to characterize porous materials (an excellent review is presented in [74]). In all these techniques, the gamma rays from the annihilation of either the positron or positronium are detected. The techniques can be divided in two groups, those which analyze the energy spectrum of the gamma rays and those which analyze the time distribution of the decay time. Following techniques are widely used: Doppler broadening-spectroscopy (DBS), angular correlation of annihilation radiation (ACAR), 3γ annihilation spectroscopy (3γ/2γ), Ps time-of-flight (TOF) and positron annihilation lifetime spectroscopy (PALS). In this chapter I‘ll briefly describe the main aspects of these techniques and their applicability for the study of o-Ps emission in vacuum will be discussed. This is done in order to motivate our choice of selecting the spectrometers presented in Sections 6.3 and 6.4, as the most suitable for our studies.

Before describing the diﬀerent experimental techniques listed above, I will brieﬂy introduce the basic concepts that describe the behavior of positrons implanted in a material, the Ps formation mechanisms and its interaction with matter in the case of porous materials.

4.1 Positrons and positronium in solids

Positrons implanted into a material may undergo diﬀerent processes that can be divided into diﬀerent characteristic time scales [75, 77]: positron backscattering; direct positron

55 56CHAPTER 4. STUDY OF POSITRONIUM EMISSION FROM POROUS SILICA FILMS

annihilation; fast Ps backscattering; positron thermalization; Ps formation; Ps diffusion; and annihilation in the material, or emission into vacuum. The positron backscattering time scale is around 10−15s. This process is given by positrons which are shallowly implanted in the material and are redirected back to the surface via multiple scattering. They represent a few % of the total number of incident positrons and their fraction increases at higher implantation energy and Z number of the material. The implanted positrons that are not reflected slow down to 10-20 eV in several pi- coseconds. In the high energy region (0.1-1 MeV), the energy loss is dominated by the conduction electron scattering and is well described by the Bethe-Bloch formula. In the low energy range the phonon scattering process dominates. Simulations of the stopping profile for positron thermalization in the range 1-50 keV incident energy were reported in [78] and were shown to obey the implantation form originally suggested by Makhov in [79] for electrons. The transmission probability ηT for a particle as a function of the implantation depth z is given by [77]:

z m η (z)= exp (4.1) T − z 0 and the implantation proﬁle is obtained by the derivative:

mzm−1 z m P (z)= exp , (4.2) zm · − z 0 0 where m is a dimensionless parameter (for W m=2) and z0 is related to the mean penetration depth z by z z0 = 1 . (4.3) Γ[( m ) + 1] Here Γ is the Gamma function 1. The mean penetration depth z depends on the incident positron energy as: α z = En (4.4) ρ · where: ρ is the density of the target in g/cm3; • E is the positron incident energy in keV; • α is a fitting parameter (for W α =3.6µg/cm2); • n=1.6. • In Fig. 4.1 the Makhovian implantation profiles for positrons with different incident energies are shown.

1 3 1 for m=2 one obtains Γ( 2 )= 2 √π 4.1. POSITRONS AND POSITRONIUM IN SOLIDS 57

Figure 4.1: Calculated Makhovian implantation proﬁle for 10 and 15 keV incident positrons on tungsten. The parameters are α =3.6[µg/cm2] and n =1.6. See text for details.

When positrons are in thermal equilibrium with the surrounding material, they start to diffuse around the stopping point (in metal the diffusion is of the order of 100 nm). During the diffusion there is a high probability that the positron will annihilate with an electron in the material (in metal the bulk lifetime is of the order of 100 ps ). Another important mechanism during the diffusion process is the trapping of positrons at the material defect points. These regions are energetically preferable for positrons because the material density is lower [75]. After being trapped the positrons annihilate with a lifetime larger than the one in the bulk material. This makes the positron an excellent tool to study the distribution of defects in metals.

4.1.1 Positronium formation mechanism The exact formation mechanism of Ps has been studied for several decades but still it is not precisely known. The Ore model and the spur model [103], have been the most competitive theories to explain this process. They have been developed to predict Ps formation under diﬀerent conditions: in low density gas and in liquid, respectively. In the Ore model, the positrons attract ionization electrons of the gas. A positron with an energy Ee+ captures an electron with ionization energy I from a molecule M:

e+ + M Ps + M + (4.5) → In order to make this process energetically possible, the positron energy has to be larger than I-6.8 eV, where 6.8 eV is the binding energy of o-Ps in the ground state. At positron energies larger than I, Ps dissociation becomes energetically possible and the formation 58CHAPTER 4. STUDY OF POSITRONIUM EMISSION FROM POROUS SILICA FILMS

probability follows the electron capture cross section [68]. This has been experimentally demonstrated in [69], where the Ps formation cross section as a function of the positron energy is studied while the theoretical interpretation is given in [76]. This has also been demonstrated by studying fast backscattered Ps from metal surfaces. It has been observed that the energy distribution peaks around 10-20 eV. Its intensity is 10% of the total Ps for 1 kV positron energy and decreases as 1/E for increasing positron∼ implantation energy. In metal, this component is originating from backscattered or very shallowly implanted positrons that capture the electron at the film surface. The spur model proposes a different picture of the Ps formation: the incident positron ionizes the atoms along its slowing down path. After the positron is slowed down, it can combine with one of the spur electrons and form Ps. The formation probability is determined by the distance between the electron and positron, and by the characteristics of the material. As mentioned above, these processes are competitive and both of them have been shown to describe Ps formation in different environments. However, the precise relationship between these two mechanisms and the material properties of the film are largely unknown. It has been argued [74] that the Ore model is dominant at positron energy of a few eV, while the spur model determines the Ps formation at lower positron energies.

4.1.2 The pick-off process When o-Ps annihilates in the media or in voids within the media its lifetime is reduced by the interaction with the environment. The bound positron of the o-Ps can annihilate with a molecular electron with an opposite spin through the 2γ decay channel, which allows a much higher decay rate, such that the effective decay rate increases. This extra Ps annihilation decay rate, (λpickoff ), has to be added to the intrinsic vacuum o-Ps decay rate (λvac) and is called the pick-off annihilation rate. The pick-off rate can be calculated, to a good approximation, assuming the Ps-atom is a point like particle of mass MPs =2me. The repulsive exchange interaction that the Ps experiences at the wall of the cavity can be parametrized as a spherical potential with a barrier of height U0 and range R. In this model the pick-off rate is given by [80, 81]:

2 Γpickoff =4πr0cρ0Zeff P0, (4.6)

where Zeff is the eﬀective number of electrons per molecule for pick-oﬀ annihilation, P0 is the overlap integral of the Ps wave function with the electrons on the pore internal surface, 2 2 r0 = e /mc is the classical electron radius, and ρ0 is the number density of molecules in the bulk. The latter is the only free parameter of the theory and has to be determined empirically using a variety of well-characterized materials. For porous materials with small pore sizes (< 1 nm), this model (Tau Eldrup model) gives good agreement with the data, but it fails for bigger pores. In fact, this approach neglects the possibility of Ps to be in excited states inside the well. For small pores this is a reasonable assumption, since the de Broglie wavelength of thermalized Ps (at room temperature) is about 6 nm (almost a factor 4.1. POSITRONS AND POSITRONIUM IN SOLIDS 59

10 bigger than the pores). Hence, the energy gap between the ground state and the ﬁrst excited sate is large compared to kT . The extension of the model to include the excited states is done by switching from spherical to rectangular pores 2 and is called Rectangular Tau Eldrup model (RTE) [82, 83]. The estimated lifetimes as a function of the pore size at 300K are shown in Fig. 4.2. Even if the predictions of this model provide an encouraging agreement with the data, deviations have been observed with lifetime measurements at low temperatures [84, 85, 86] . A limit of the RTE model is given by the assumption that o-Ps immediately thermalizes after its emission into the pores. It has been experimentally demonstrated that o-Ps spends time in the pores to cool down from its initial energy of few eV to the thermal energy of the sample. A more detailed description of the RTE model is presented in Section 7.2.

Figure 4.2: Orthopositronium lifetime dependence as a function of the mean free path l, 3 computed with the RTE model. The pore size a for a cubic box can be estimated with a = 2 l [82].

4.1.3 Positronium diffusion and thermalization in porous films In insulating materials Ps is attracted to electron deficient regions (defects, cracks, pores) because of the reduced dielectric constant which leads to a higher Ps binding energy. In porous materials, Ps is formed by injecting positrons into the film and the distribution of the implantation depth follows a Makhovian profile. Ps is formed either in the triplet spin state (o-Ps), or in the singlet spin state (p-Ps). After its formation in the bulk Ps

2This assumption is made because the calculations of the exited states in the case of a spherical potential are prohibitive. 60CHAPTER 4. STUDY OF POSITRONIUM EMISSION FROM POROUS SILICA FILMS

is emitted into the pores with energies of a few eV (e.g., for SiO2 it is 1-3 eV [87]). If the pore network is closed, Ps remains trapped in the pore (Fig. 4.3 (a)). If the pore network is interconnected (Fig. 4.3 (b)) Ps diffuses in the film. If it reaches the surface it is emitted into the vacuum with a lower energy with respect to the formation energy. A fraction of the Ps formed in the film remains trapped in pores and annihilates inside the pore structure via pick-off.

Figure 4.3: (a) In closed porosity samples Ps remains trapped in the pore. (b) In interconnected pore systems Ps can move between the pores. If it reaches the ﬁlm surface it is emitted into the vacuum.

In metals and semiconductors, the formation of Ps is suppressed by the high electron density. The formation of Ps in these solids is only a surface process. In studies performed on metals, it has been demonstrated that a fraction of the Ps produced at the surface originated from thermal de-trapping of Ps surface bound states [88, 89]. The most promising candidates for producing high fractions of o-Ps at low energies are represented by interconnected porous films. Porous films are basically achieved in two different ways: by pressing silica powder with grain sizes of 10-20 nm, • by mixing a pore generator (porogen) to a matrix (bulk material) and then selectively • evacuating the porogen. Several measurements have been performed on a variety of interconnected porous films using the Ps Time-of-flight technique. All those measurements have been performed at room temperature. Only in [90] the emission of o-Ps from SiO2 powders has been reported at low target temperatures. In this pioneering work o-Ps cooling was observed down to 4.6 K by using a very sophisticated analysis but no quantitative estimations on the thermalized fraction was reported. A classical model of the thermalization process was developed by Nagashima et al. [87]. Their calculations reproduce the behavior for the SiO2 aerogel with pore sizes of about 100 nm. However, a classical approach is not expected to give reliable predictions for Ps confined in few nm pores because quantum mechanical effects become relevant [86]. More details on this subject will be given in Chapter 8. 4.2. DOPPLER BROADENING SPECTROSCOPY (DBS) 61 4.2 Doppler broadening spectroscopy (DBS)

With DBS one analyzes the energy spectrum of the decay photons and it is sensitive to the momentum of the electron-positron pair at the moment of annihilation. This momentum is mostly determined by the momentum of the electron in free positron annihilation or by the relative formation fraction of o-Ps and hence can probe the electronic and physical environment in which positrons are implanted. DBS uses high energy-resolution gamma detectors, typically high-purity germanium detectors, to acquire the energy spectrum of the 2 γ annihilation events in a window centered around 511 keV. These 2 γ events are produced in the positron direct annihilation, p-Ps annihilation, or o-Ps pickoﬀ quenching events. In the laboratory reference system the measured energy of annihilating pairs leads to a Doppler-broadening of the 511 keV energy line. The momentum of the e+ e− system corresponds to only a few eV kinetic energy but produces larger energy shifts− for the emitted γ because of the decay from massive particles into mass-less photons. When a positron and an electron annihilate from the free state in the laboratory system they have a certain momentum p, and as a result of their collision they can undergo a two γ annihilation. According to the law of conservation of energy, in the relativistic case, the total energy ET of the pair is:

2 4 2 2 ET = (2m0) c + p c = p1c + p2c (4.7) p where m0 is the rest mass of the electron and c is the light velocity. p1 and p2 are the momenta of the emitted photons. Two parameters are deﬁned to quantify the annihilation. In order to do this we deﬁne two distinct regions in the 511 keV peak, a low momentum region characterized by a narrow energy window centered on the 511 keV peak and a high momentum region. The two parameters are:

(1) The S parameter which is deﬁned as the ratio of events in the low momentum − window with respect to the total number of 2γ events.

(2) The W parameter is the ratio of integrated events in the high momentum window to the total− peak.

The S and W parameters can give interesting informations regarding the voids in − − the ﬁlm. Annihilations in voids have less annihilations with high momentum core electrons and more o-Ps and p-Ps is formed leading to a higher S parameter. − 4.3 Angular correlation of annihilation radiation (ACAR)

The ACAR technique also measures the momentum of the electron-positron when they annihilate. Instead of measuring the energy broadening of the 511 keV γ rays, it measures the relative angle between them (i.e. the component of the pair momentum at the moment 62CHAPTER 4. STUDY OF POSITRONIUM EMISSION FROM POROUS SILICA FILMS

of the annihilations into the two gammas). At rest the positron electron pair annihilates − in two back to back photons (180o). If the center of mass of the annihilating pair is moving relative to the lab reference system, then the opening angle of the two photons will deviate from 180o by a small angle θ (several mrad). This angle is larger for high momentum annihilating pairs. A typical ACAR setup consists of two position sensitive detectors (Angers cameras) placed 5 meters apart with a milliradiant angular resolution. Due to the large distance between the annihilation point and the detector the solid angle covered by the Angers cameras is small and the detection efficiency is drastically suppressed. This means that for ACAR measurements a positron rate as large as 109 positrons per second is required in order to achieve acceptable measuring times. The ACAR technique has been used to study the p-Ps thermalization in SiO2 powders [87] and to estimate the escaping energy of p-Ps from the layers [91]. For our purpose this type of detector is not suitable for two reasons. The first is the limited positron rate of the ETHZ positron beam (Chapter 5), secondly we are interested in the emission energy of o-Ps. Due to the short p-Ps lifetime of 120 ps the emission at the surface is suppressed. As discussed in [92], a simple simulation, assuming an energy loss of 1 meV/collision (which is typical for phonons) and a pore size of 5 nm, shows that the time of thermalization is comparable to the p-Ps lifetime. This means that most of p-Ps formed inside the film bulk will decay before it thermalizes, introducing a bias between p-Ps formation in the bulk and on the surface. The long lifetime of o-Ps suppresses this effect.

4.4 3γ/2γ technique

The 3γ/2γ technique acquires the photon energy spectrum of positron annihilation in the film. This includes 2γ from p-Ps, o-Ps quenching and the 3 γ decay from o-Ps decays. Annihilation photons from the a 2 γ interacting with a detector produce a peak at 511 keV and Compton scattered events distributed from 0 to the Compton edge at 341 keV. Annihilations into 3γ produce a continuous distribution from 0-511 keV. The total energy spectrum is a combination of 2 and 3 γ events. To identify the 2γ part an integration around the 511 keV photo-peak is performed. The 3 γ / 2γ ratio is then calculated, after correction of the Compton events, by normalizing to a spectrum that contains only 2 γ events. By varying the film temperature and/or porosity the trend of the 3γ/ 2γ ratio is investigated and information on the pore structure is deduced. In films with larger pores or higher porosity, the number of events that self-annihilate in the 3γ part of the spectrum increases. This technique is relatively easy and the o-Ps production in the target can be directly estimated. However, with this method a direct evidence of o-Ps emission into the vacuum is not possible because the 3γ fraction F3γ is the product of the effective lifetime of o-Ps and its intensity:

Iτ τeff F τ = eff (4.8) 3γ 142 4.5. POSITRON ANNIHILATION LIFETIME SPECTROSCOPY (PALS) 63

Generally, if we consider samples which emit o-Ps into the vacuum, there are also 3γ decays produced by o-Ps trapped in the pores so that it is not possible to directly reconstruct the fraction of o-Ps that is emitted into vacuum. However, using an indirect method involving measurements performed on diﬀerent types of samples, one can extrapolate the o-Ps emission yield used the 3γ /2γ experimental technique [92]. This technique has been using for the preselection run of the converters, that have been later studied in detail with the spectrometers presented in Chapter 6. These measurements have been performed by using the slow positron beam located in Orleans3.

4.5 Positron annihilation lifetime spectroscopy (PALS)

The PALS technique studies the lifetime of Ps in the sample. This is obtained by measuring the delay between the time at which the positron is implanted (t0) and the time of the detection ( tγ ) of one or more gamma rays from the Ps decay. The PALS spectrum is a combination of different exponentials. Smaller confinement volumes give smaller lifetimes, due to the pick-off effect. PALS spectrometers are generally used for the characterization of samples with close pore structures (i.e., Ps decays are restricted to a well defined region). In interconnected porosity targets, where Ps can escape from the surface, conventional PALS spectrometers are not suitable. In order to reconstruct the o-Ps fraction that is emitted from the target, a large solid angle spectrometer, as the one described in Chapter 6, is needed to unambiguously observe the 142 ns lifetime component of the o-Ps decay in vacuum and its intensity. With such a detector, both, the lifetime in the pore system and the fraction of the o-Ps that leaves the target, are measured.

4.6 Positronium time-of-ﬂight (Ps-TOF)

The Ps-TOF technique consists of placing a narrow γ collimator (< 5mm) looking perpendicular to the o-Ps propagation direction and placed closed to the target surface (generally in the range of 1-3 cm). A TOF spectrum is obtained by recording the time diﬀerence between the time at which the positron is implanted, to the time given by o-Ps that escapes the ﬁlm into the vacuum and decays in the collimator opening. TOF spectrometers are normally installed on very intense pulsed beams [93, 94]. If one considers a pulse repetition rate of 1 MHz, in order to have a reasonable signal to background ratio, a beam intensity as large as 106e+/s is needed. The excellent signal to background ratio of the tagging system described in Section 5.4.2, allowed us to perform TOF measurements with a beam intensity of 2 104e+/s. ×

3CNRS-CEMHTI Site Cyclotron, 3A rue de la Frolerie, 45071 Orlans Cedex 2, France. The measurements have been performed by L. Liszkay 64CHAPTER 4. STUDY OF POSITRONIUM EMISSION FROM POROUS SILICA FILMS Chapter 5

The slow positron beam

The ETH Zürich slow positron beam is located at CERN in the experimental hall of Bld.182. Figure 5.1 shows a picture of the existing experimental setup [95] and Fig. 5.2, shows a schematic of the beam line. The 22Na source emits positrons with a continuos β+ spectrum (0-543 keV). Almost monoenergetic slow positrons (few eV kinetic energy) are produced in a moderator single crystalline tungsten foil with a thickness of 3 µm with an efficiency, with respect to the total number of positrons emitted from the source, of about 10−5. The nearly mono-energetic beam is guided through the pipe with a quasi-uniform magnetic∼ field of 70 Gauss. In the beam pipe several internal tubes serve as accelerator electrodes as shown in the schematic Fig. 5.2. The beam can be used in DC and AC mode as described in Sections 5.4.1 and 5.4.2, respectively. At the end of the beam pipe positrons are accelerated to the target with an energy ranging from 0.7-10keV. As will be presented in this chapter, several efforts have been made to improve the low energy beam intensity. This was done by increasing the source intensity and improving the moderator efficiency. The magnetic transport system was also optimized in order to compress the beam size.

5.1 Design and construction of a 22Na positron source chamber

During my PhD work, three different positron sources have been used. In 2006, a 22Na source with an intensity of 1 MBq was used. This source was prepared by bombarding a 150 µm thick foil of pure Al with a 590 MeV proton beam at the PSI accelerator. By using this source, the beam intensity was around 10 e+/s. A first improvement has been achieved by substituting this source with a source obtained with the same method but having an intensity of 20 MBq. Since at CERN only certified sealed sources are accepted, we had to perform, in collaboration with PSI, two certification procedures: ISO2919 and ISO9978. Those consist of several tests that prove the integrity of the source and exclude the possibility of contamination. Moreover, since the source was planned to be used in vacuum, a special set-up to test a possible contamination due to radioactive out-gassing

65 66 CHAPTER 5. THE SLOW POSITRON BEAM

Figure 5.1: Picture of the ETH Zurich slow positron beamline. The installation is about 6 meters long and 2 meters high.

Figure 5.2: Schematic diagram of the pulsed slow positron beam apparatus

was constructed. After all the testing needed for the source certiﬁcation and a modiﬁcation of the source holder, the beam reached an intensity of 200 e+/s . This intensity was enough to perform the tuning of the beam and to start performing preliminary measurements with the PALS and TOF detectors (Chapter 6). However, in order to collect the desired statistics 5.1. DESIGN AND CONSTRUCTION OF A 22NA POSITRON SOURCE CHAMBER67

Year Source intensity [MBq] Beam intensity [positrons/s] Mod. + extr. optics eﬀ. 2006 1 10 1 10−5 2006-2007 ∼20 ∼1 102 ∼ 1 × 10−5 ∼ ∼ × ∼ × − 2007 386 2.0 104 5 10 5 2009 250 ∼ 2.5 × 104 ∼ 1 × 10−4 ∼ × ∼ ×

Table 5.1: Beam intensity for the different 22Na positron sources that have been used since 2006. In the last row the efficiency of the moderator to emit almost mono-energetic, low energy positrons is reported. to perform systematic studies on o-Ps emission using the TOF spectrometer, this intensity was not sufficient because of the low detection efficiency caused by the TOF lead collimator. Therefore, we designed and constructed a new vacuum chamber to accommodate a 22Na source with an intensity of 380 MBq. This source was bought from IThemba1, a company based in South-Africa that is specialized in the production of isotopes. Several efforts have been made in order to make the installation of such a source possible:

a special cage to delimit the beam area as a controlled zone was constructed; • an additional external lead shielding was placed around the source region; • a special tungsten shielding inside the vacuum was constructed; • the mounting and the dismounting procedure had to be studied with the CERN • radio-protection service and described in a manual;

a filtering system was mounted on the different pumps and periodical checks of the • filter are performed by the radio-protection service.

With this new source, an intensity of 2.5 104 e+/s was achieved. In Table 5.1, the positron intensities using the diﬀerent sources are× reported . A 3D drawing of the source chamber assembly is shown in Fig. 5.3. It includes:

the source chamber with the internal tungsten shielding; • an additional chamber used for the preparation of the moderator; • an electron beam used for the moderator annealing; • a 1 meter long magnetically guided linear driver used to move the moderator from • the annealing chamber to the source chamber.

A detailed view of the shielding assembly is shown in Fig. 5.4. The radioactive material is sealed in a titanium capsule equipped with a 5 µm window of the same material that

1Laboratory for Accelerator Based Sciences, PO Box 722 Somerset West 7129, South Africa 68 CHAPTER 5. THE SLOW POSITRON BEAM

Figure 5.3: Source and moderator chambers for the 380 MBq source. The moderator chamber (yellow) is equipped with an electron beam (green) used for the moderator annealing up to 2000oC. ∼ guarantees a high transparency for the positrons emitted from the isotope. More details of the source capsule are presented in [96].

The shielding is made of a ultra-high-vacuum compatible tungsten alloy that can be machined more easily than pure tungsten metal. The shielding discs have a diameter of 20 cm and an internal hole of 3 cm in diameter that ﬁts the holder containing the capsule. In the shielding, diﬀerent parts that are essential for the positron extraction had to be accommodated without leaving any apertures. The moderator is moved on the top of the source with a magnetically guided linear driver. The distance between the moderator and source had to be minimized in order to maximize the solid angle covered by the moderator and thus, the number of positrons passing through it. Nevertheless, for safety reasons the gap between the source and the moderator foil was kept about 1 mm to avoid any contacts between them. A damage of the source capsule would have dramatic consequences 5.1. DESIGN AND CONSTRUCTION OF A 22NA POSITRON SOURCE CHAMBER69

related to contamination. A voltage of +200V with respect to the ground is applied to the tungsten disks and the moderator. A tungsten grid with 95 % transparency is placed above the moderator and a voltage difference of -10V is applied between them. A further voltage difference is set between the extraction grid and the first drift tube (-20V). All those parts are electrically isolated by UHV compatible ceramic insulators (macor). The whole shielding assembly is mounted on a CF100 flange that is screwed on a CF100 cube. The source capsule is mounted on a tungsten rod that can be independently dismounted with a CF40 flange. This was done in order to facilitate the installing procedure of the source. The CF40 flange shown in Fig. 5.4 was screwed to a 1 meter long aluminum rod in order to minimize the radiation dose during the source handling.

5.1.1 The positron moderator

In metals, positrons that reach the metal surface during the diffusion are ejected from the surface with a precise energy (several eV) depending on the material. The origin of this effect is the decreasing electron density at the metal surface while the proton density remains stable. This causes a positive charge unbalance which pushes the positron out of the material. The negative work function of positrons is exploited as a moderator process. From a continuous spectrum of a β+ emitter, whose end point energy is generally a few hundred keV, positrons which thermalize and reach the metal surface are monoenerget- ically emitted from the surface. The moderation process is very sensitive to the surface conditions of the metal and it needs a special preparation procedure in order maximize its efficiency. The emission energy of positrons from moderators is generally a few eV and its efficiency ranges from 10−3 down to 10−6 [75].

In the 2006-2008 set-up, we used a 3 µm thick tungsten foil with (1,0,0) crystal orienta- tion. In 2009, we replaced it with a more efficient moderator made of tungsten meshes [98]. The surface quality can be improved by annealing the moderator foil at a temperature of 20000C, by using a commercial electron beam. The electrons are accelerated to 10 ∼keV and the beam has a current of 0.1 mA. The electron beam is focused to a 1 mm beam∼ spot and the moderator surface is scanned several times by changing the parameters of the x-y deflection electrodes. In the last column of Table 5.1, an estimation of the total moderator efficiency is shown 2. In the 2007 set-up, we gained a factor 5 by improving the extraction optics and the moderator preparation procedure compared to our previous set-up. Due to the half-lifetime of 22Na of 2.6019 years the source intensity in 2009 had decreased to 250 MBq. Despite of this fact, the beam intensity could be further improved to 2.5 104e+/s. Similarly to what was done in [98], we used as a moderator 12 layers of high transparency× (98 %) tungsten meshes with a diameter of 20 µm .

2Those numbers also take into account the extraction optics eﬀects and the reduced solid angle covered by the moderator. Thus, they have to be carefully compared to the values reported in the literature [77] because the total moderator eﬃciency depends on the set-up. 70 CHAPTER 5. THE SLOW POSITRON BEAM

Figure 5.4: Section of the source chamber. The extraction optics system consists of a grid placed at a distance of 3 mm from the moderator and a ﬁrst acceleration tube. 5.2. THE POSITRON TRANSPORT SYSTEM 71 5.2 The positron transport system

The magnetic field system is made of Helmoltz-type coils. One problem in positron beam transport systems is to separate slow and fast positrons. The positrons that are emitted from the source with a continuos spectrum (0-543 keV) and that are not stopped in the moderator foil are called fast positrons. There are many possibilities to build a positron velocity filter. In our design a simple bend producing a curved magnetic field acts as a velocity filter (Fig. 5.5). The radius of the bending is 20 cm. The magnetic transport system consists of 10 coils with an external diameter of 500 mm and 500 turns of 2 mm diameter wire. The coils are fed by DC currents of 0-5 A. In order to produce a longitudinal magnetic field of 70 Gauss the distance between the coils along the beam line is 350 mm. An additional coil is placed around the vacuum chamber. It has an external diameter of 250 mm and 300 turns. The parameters of the magnetic transport system were calculated using GEANT4 (Fig. 5.5). To center the beam on the target we constructed correction coils that generate a magnetic field perpendicular to the beam direction (Fig. 5.6). Two correction coils are installed after the velocity filter in order to correct for the drift with respect to the center of the beam pipe, introduced by the e+ transportation through the bending. This displacement is given by the transversal velocity with respect to the magnetic field direction introduced by the 90o curved field. The other set of correction coils is installed before the target. By changing the current in the coils the beam can be displaced. Those coils are steered by power supplies connected to the slow control system. The counting rate is automatically maximized by performing a scan on the current of the coils. In Fig. 5.7 the beam position for a current ranging from 0 to 5 A with 0.2 A steps applied to the correction coils is shown. This measurement was performed using a position sensitive MCP as described later in Section 5.5.

Figure 5.5: Left: ﬁnite element calculation of the magnetic transport system performed with the COMSOL multi-physics program. Right: Positron trajectories calculated with GEANT4. 72 CHAPTER 5. THE SLOW POSITRON BEAM

Figure 5.6: Correction coils produce a magnetic ﬁeld which is perpendicular to the beam direction. They are used for the beam positioning.

Figure 5.7: Beam position with respect to the center of the beam pipe by applying a current on the correction coil. The current ranges from 0 to 5 A with a step of 0.2 A. 5.3. THE VACUUM SYSTEM 73 5.3 The vacuum system

The vacuum system produces a clean ultra-high-vacuum (UHV) of 10−8 mbar. UHV is ∼ basically required for two reasons:

(1) the positron moderator eﬃciency and its energy dispersion are sensitive to the surface quality of the tungsten foil.

(2) in order to avoid water condensation and other contamination on the porous target that could bias the measurements.

For a pre-vacuum pump we use an oil free Varian scroll pump in order to reach 10−1 mbar. At this point a turbo pump is activated and after 2 hours of operation the vacuum stabilizes around 10−6 mbar. At this vacuum level two ion pumps are put in operation and during 1 h the pressure decreases to 10−8 mbar. Before opening the system to the external atmosphere the beam pipe is ﬁlled∼ with nitrogen in order to avoid any impurities and water condesantion to enter the system.

5.4 Positron and positronium tagging

The beam was designed to operate in two modes, i.e. there are two diﬀerent ways of tagging the positrons (or positronium):

(1) positron bunching: initial pulses of 50-300 ns are compressed at the target region in 0.4-2.3 ns wide pulses [95];

(2) detection of the secondary electrons emitted when the positrons hit the target with a MCP (Micro-Channel Plate) [97].

5.4.1 Pulsed beam mode The first chopper of the pulsing system produces positron pulses with a duration of 50-300 ns from the continuos positron emission of the moderator. A schematic of the chopper system is shown in Fig. 5.2. The main parts of the chopper system are: the source, the moderator and the chopper grid. In this mode of operation a potential of +500 V is applied to the moderator. A time varying potential between 505 and 501 V is applied to the chopper grid installed 3 mm downstream of the moderator foil. This potential is modulated by applying a pulsed voltage from a pulse generator. When the potential difference between the chopper grid and the moderator foil decreases to a value lower than 3 V (maximal longitudinal energy of the positrons from the moderator) positrons reach the chopper grid and they are accelerated by a voltage applied between the chopper grid and the first drift tube. When the voltage difference between moderator and grid increases back to 5 V, positrons are stopped at the chopper grid. Applying a pulse of 50-300 ns with an amplitude of 4 V to the chopper grid, it is possible to produce positron pulses from 74 CHAPTER 5. THE SLOW POSITRON BEAM

the initial DC beam. The bunching system is formed by three drift tubes: the buncher tube and drift tubes 2 and 3 ( see Fig. 5.2). The outer two are fed by a DC voltage, while the central tube is fed by the nonlinear voltage pulse shown in Fig. 5.8. The time delay between the chopper pulse and the non linear voltage applied on the bunching tube is synchronized in order to decelerate positrons near the leading edge of the chopper pulse while accelerating positrons on the trailing edge. A compression ratio of 100 was achieved for initial pulses of 50-300 ns. Further details are reported in [95].

100

25 first gap second gap

Voltage (V) -25

-50

-75

-100 0 100 200 300 400 500 600 Time (ns)

Figure 5.8: Bunching voltage at the ﬁrst and second velocity modulation gaps. The time delay between the non-linear pulse and the pulse applied to the chopper grid is tuned in order to achieve the best compression factor.

5.4.2 Continuos beam and secondary electron trigger mode The principle of this trigger mode exploits the emission of secondary electrons (SE) when a positron hits the target as discussed in Chapter 3. The continuos beam of positrons with an energy of 200 eV is guided by the magnetic field and passes through the first region of deflection plates (DP1) with a transversal electric and longitudinal magnetic field (Fig. 5.9). The transverse electric field is generated by applying a voltage of 200 V to the plates. For the given values of electric and magnetic fields the positron± vertical displacement is 4 cm with respect to the beam pipe axis. When the positron exits the E-field region∼ of DP1 its trajectory follows the longitudinal magnetic fields lines and enters the DP2 transverse E-field. The E-field in this region has the opposite direction of the E-field in the DP1 region. Hence, the drift velocity direction is also reversed. This temporary beam displacement from the beam pipe axis prevents the positrons from hitting the MCP. After this displacement, positrons are transported to the target region and are accelerated to the desired implantation energy in a range of 1-10 keV by biasing the voltage on the sample holder. The same voltage serves to accelerate in the backwards direction 5.4. POSITRON AND POSITRONIUM TAGGING 75

Figure 5.9: Top: trajectories of the positrons (blue) and secondary electrons (red) from the Geant4 simulation; E- and B-fields calculated with the COMSOL package for our existing setup. Bottom: simulation of the secondary electron trajectories from the sample to the MCP for the PALS and TOF spectrometers described in Chapter 6. the secondary electrons (SE) produced by the positrons hitting the sample. The SE follow a helical trajectory along the magnetic field and are slightly deflected in the DP2 region. The displacement produced by the transversal electric field in the DP2 region on the SEs is strongly suppressed with respect to the displacement introduced on the incoming positron because of the different kinetic energies: 200 eV and 1-10 keV for positrons and electrons, respectively. A tagging signal for a positron hitting the target is generated by the electrons reaching the MCP. This trigger mode serves as a start signal for three different types of spectrometers (the stop signal is given by the annihilation gammas):

(1) a high time resolution PALS spectrometer, using a BaF2 scintillator coupled to a Hamamatsu R5055 photomultiplier, with a total time resolution in the 400-700 ps range, depending on the positron implantation energy; (2) a large solid angle PALS spectrometer especially designed for measurements of o-Ps 76 CHAPTER 5. THE SLOW POSITRON BEAM

emitted into the vacuum. This spectrometer uses BGO crystals as γ detector. The total time resolution is of the order of 5 ns; (3) a Ps-TOF spectrometer using a lead collimator. Also in this detector BGOs crystals are used as photon detectors. In the spectrometer (1) the sample is placed at 10 cm from the MCP (the top of Fig. 5.9) and uses as a gamma detector the fast crystal scintillator BaF2 . The flight time of the SE is thus minimized and the respective time spread introduced during the transportation is suppressed. In the detectors (2) and (3) the target is placed at a distance of about 90 cm from the MCP (bottom in Fig. 5.9). This was done to accommodate the PALS and TOF detectors. The long distance between the target and the MCP introduces a time spread in the SE time distribution and affects the total time resolution of the system. As shown in Fig.5.10, the time spread of SEs is 1.9 ns FWHM. This was precisely measured by studying the time delay between two MCPs. The first, placed at the target position, detects positrons and it is used as a start signal. The second is installed at 90 cm distance and detects the arrival time of the SEs emitted from the first MCP. Using this trigger mode, the accidental background is produced by the noise of the MCP. A high performance Hamamatsu F4655-12 with a noise between 1-10 counts/s (depending on the discriminator threshold) is used in order to achieve a signal to background ratio in the range of 103 104. −

25000 Events

20000

15000

10000

5000

0 52 54 56 58 60 62 64 Time (ns)

Figure 5.10: Flight time spread introduced in the transportation of SEs from the sample to the MCP for a ﬂight distance of 90 cm. This time distribution was measured using two diﬀerent MCPs. One at the target region detecting e+ and one in the usual position for the secondary electron tagging. The voltage on the target MCP substrate was 2.4 kV. The timing shows a spread of 1.9 ns FWHM. 5.5. BEAM PROFILE MONITORING USING A MCP WITH A POSITION SENSITIVE SCREEN77

Secondary electron rate and tagging eﬃciency

The secondary electron yield strongly depends on the positron implantation energy and from the target material. In the case of mesoporous silica ﬁlms the counting rate at implantation energies of 1keV is between 1.5-2 104e−/s and the tagging eﬃciency was × − estimated to be around 80%. At 10kV the secondary electron rate drops to 1 103e /s. ∼ ×

5.5 Beam proﬁle monitoring using a MCP with a position sensitive screen

In the design of the o-Ps invisible decay experiment, the e+ beam has to be injected to the o-Ps formation cavity through an aperture with a diameter of 1 cm (Section 3.1.3). For this purpose we monitored the beam spot size with a position sensitive MCP (Hamamatsu F2222-21P with an active substrate diameter of 2 cm, see Fig. 5.12). A solenoid was wound around the MCP chamber in order to reproduce at the MCP position the same magnetic field as along the beam pipe. This was done in order to reproduce at the MCP position, the same beam properties as in the beam pipe (Fig. 5.13). The magnetic transport system has been modified in order to compress the beam size. The working principle of an MCP phosphor screen is shown in Fig. 5.11, a picture of the set up used for this measurements is shown in Fig. 5.12. The incident e+ beam produces secondary electrons inside the substrate channels that are multiplied and accelerated by a 2 stage system (V1=-1kV and V2=0 in Fig. 5.11). A further acceleration is applied between the substrate and the phosphor screen (V3=+1.4kV) in order to give the electrons enough energy to produce fluorescence when they hit the phosphor screen. The fluorescence on the screen is monitored with a digital camera connected to a computer. A normal web- cam with a resolution of 640x480 pixels and 8-bit dynamic range was used. The image is recorded in a bit map (.bmp) which is then converted into an ASCII file containing the pulse height (which is assumed to be proportional to the number of positrons that hit the phosphor screen) information for each pixel. The data are then processed with ROOT. Fig. 5.11 shows the improvement of the beam profile after the optimization of the magnetic system. 95 % of the beam is compressed to 5 mm diameter. A Gaussian fit of the beam profile gives a FWHM of 2.9mm in the horizontal∼ direction and 3.1 mm in the vertical direction. Different parameters have been changed in order to optimize the beam diameter:

the coils that were used for the beam positioning (correction coils) generated a non- • uniform transversal magnetic ﬁeld;

a quadrupole field is used to obtain a round beam profile: the deflection plates in the • tagging system deform the beam to an oval shape. 78 CHAPTER 5. THE SLOW POSITRON BEAM

Figure 5.11: Top: principle of work of the MCP phosphor screen. Bottom: achieved improvement in the beam proﬁle before (left) and after (right) the optimization of the magnetic transport system. The external bright circle around the beam spot is produced by light reﬂection of the metallic ring holding the screen. See text for details.

Figure 5.12: Left: picture of the MCP substrate. Right: picture of the phosphor screen. 5.6. CONCLUSIONS 79

Figure 5.13: The solenoid around the MCP chamber is used to keep the value of the magnetic ﬁeld at the MCP position similar to the one in the beam pipe. This is done in order to reproduce, at the MCP position, the same beam properties as in the beam pipe. FEM calculations have been performed. In the lower plot the calculated magnetic ﬁeld along the beam pipe is shown.

5.6 Conclusions

Several efforts have been made during 2006 and 2007 in order to increase the beam intensity. A special vacuum chamber for a source with an intensity of 380MBq was constructed. The positron intensity was increased from 10e+/s to 2.5 104e+/s. The magnetic transport system has been modified in order to optimize the beam× spot. This was done by using a MCP with a phosphor screen to monitor the beam profile. Furthermore, a system to tag the positrons with secondary electrons emitted after a positron hits at the target surface was developed [97, 99]. This tagging system showed to have an excellent signal to noise 80 CHAPTER 5. THE SLOW POSITRON BEAM ratio of the order of 103 104. − Chapter 6

Design and construction of the PALS and TOF detectors

Based on the existing slow positron beam described in Chapter 5, a system to perform studies on the o-Ps emission from porous targets into the vacuum has been constructed. We developed two types of detectors to study the diﬀerent aspects related to the o-Ps emission into vacuum from the target:

(1) a large solid angle PALS detector used for the evaluation of the fraction of o-Ps emitted fraction and the characterization of the pore structure;

(2) a Ps-TOF spectrometer used to study the emission energy and angular distribution.

Both of these detectors are used with the secondary electron trigger mode described in Section 5.4.2.

6.1 Monte-Carlo simulation

A MC simulation has served as a powerful tool for the design of the PALS and TOF spectrometers as well as for the interpretation of the results. In the MC simulations, the 3D E- and B-ﬁelds were calculated with the COMSOL multi-physics program [100], and the positron/electron trajectories in the beam were simulated with GEANT4. The simulation of the photon detection in the apparatus was based on the same package [101]. New classes were written in order to simulate the o-Ps production, propagation in the beam pipe and reﬂection on pipe walls. Furthermore, the decay channels of a positron implanted in a porous material are included, both, the 2γ and 3γ decay channels:

2γ direct e+-e- annihilation ; • 2γ decay of para-positronium ; • 2γ and 3γ decays of o-Ps annihilation trapped in the pores for a given pick oﬀ rate ; • 81 82CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

3γ annihilation of o-Ps emitted into vacuum from the sample surface. • The events for the o Ps 3γ process were generated taking into account the decay − → matrix element [102] and assuming decays at rest. The photon momentum distributions of the o-Ps 3γ decay can be calculated using the matrix element: → 2 2 2 m w1 m w2 m w3 M → = − + − + − , (6.1) ops 3γ w w w w w w 2 · 3 1 · 3 1 · 2 th where ωi (i =1, 2, 3) is the momentum of the i photon from the o-Ps annihilation and m is the mass of the electron. Integrating (6.1) over w2 and w3, the energy spectrum for one of the photons can be derived. The total probability that a photon has an energy in a given interval dw1 [103] is

2 dE w1(m w1) 2m(m w1) m w1 2m w1 2m(m w1) m w1 =2 − 2 − 3 ln − + − + −2 ln − . dw1 · (2m w1) − (2m w1) m w1 w1 m − − (6.2) The geometries of the beam transport pipe, the photon detector, the positron tagging system and its material were coded into the simulations. The simulation results were validated with our experimental measurements for both, the photon detection [64, 56, 104] and the particle transport [95, 97, 99]. The propagation of the emitted o-Ps, its interaction and its reflection with the walls of a vacuum cavity is implemented. The user can define the energy emission distribution (e.g., monoenergetic or Maxwell-Boltzmann) and the angular distribution as well as the reflection process, like e.g. Knudsen and specular reflection [104].

6.2 The magnetic transport system in the target region

In the original configuration, the magnetic transport system at the detector region was produced by a 500 mm diameter coil. This configuration was not suitable for two different reasons:

space constraints for the PALS and TOF detectors; • the magnetic ﬁeld drastically suppresses the gain of the PMTs that readout the • crystals.

In Fig. 6.1, the new magnetic field configuration is shown. The last part of the beam pipe, with a diameter of 7 cm, is wound with one layer of 1 mm copper wire. With this modification the magnetic field at the region of the PMTs was calculated to be smaller than 3 Gauss and thus, the PMTs gain was not affected. The transition of the magnetic field from the 500 mm diameter coils to the solenoid wound around the beam pipe was studied with FEM calculations. In order to make the transition of the magnetic field smoother, 6.3. THE PALS DETECTOR 83

Figure 6.1: The solenoid is wound directly on the beam pipe in order to decrease the magnetic ﬁeld at the PMTs region. An additional coil is used at the interface between the 500 mm diameter coil and the solenoid on the beam pipe (7 cm diameter) in order to make the transition of the magnetic ﬁeld smoother.

an additional coil was installed. This was done in order to avoid large variations in the magnetic field that could introduce positron reflections due to magnetic mirror effects. The current in the solenoid winding the beam pipe is 5 Amps. The transition coil has 1000 windings, an external diameter of 250 cm, an internal diameter of 150 mm, and 4 cm thickness. A current of 0.7 Amps is applied to it.

6.3 The PALS detector

Conventional beam based PALS spectrometers are usually constructed for the characterization of polymers, defects studies in semi-conductors, metals, and materials with pore sizes in the sub-nanometer range. For the characterization of these materials the lifetimes that have to be measured are shorter than 1 ns. The PALS spectrometers used in these studies need a time resolution of the order of 300-600 ps and use as a gamma detector fast BaF2 crystals. It is important to stress that, in closed porous systems o-Ps, that is formed inside the target, cannot escape from the surface and thus, the solid angle covered by the detector can simply be restricted to the target region and the decay type is mostly 2 γ. The PALS spectrometer that we developed was designed to precisely estimate the fraction of o-Ps emitted into vacuum.

Fig. 6.2, shows a picture of the PALS spectrometer (left) and a 3D CAD drawing of the BGO assembly (right). The four crystals are enclosed in a light tight aluminum 84CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS box. The start for the detectors is triggered by the MCP detecting the secondary electrons emitted when the positrons hit the target . The stop is given by one (or more) annihilation photons depositing some energy in the BGO calorimeter (ECAL). A delay of 100 ns was introduced in the stop signal to form the logic for the trigger (Section 6.6). The ECAL consists of 4 BGO crystals with hexagonal shape, 61 mm external diameter and 200 mm length. The time resolution of the system MCP-ECAL was measured to be around 2 ns ∼ FWHM convoluted with an exponential decay of 4 ns. The 2 ns spread is introduced by the propagation of the SE from the target to the MCP(See∼ Section 5.4.2). The exponential component is caused by the low number of photo-electrons produced in the BGO. The energy resolution of the crystals for annihilation photons is about 25-30% (FWHM).

6.3.1 3γ/2γ detection efficiency correction using MC simulations A precise evaluation of the fraction of o-Ps emitted into vacuum and the reconstruction of the 142 ns o-Ps vacuum lifetime, has to take into account different effects that affect the sensitivity of the detector. These are: (1) emitted o-Ps that could escape from the detection region and is not detected by the spectrometer; (2) the values of the measured lifetime depend on the detector position with respect to the emission point; (3) the dependence of the detector acceptance on the number of photons produced in the two types of decays: since the solid angle covered by the detector is smaller than 4π, the probability to detect one photon in a 3γ decay is larger than in a 2γ decay; (4) the different photon energies of the two decay types, which gives different interaction probabilities of the photons with materials such as the beam pipe, the light shielding around the detector and the detector itself. In the design of the PALS detector all these aspects have been considered. Fig. 6.3, shows that the measured lifetime of o-Ps emitted from the target depends on the detector position. The lifetime value measured in the BGO at larger distances is artificially overestimated because o-Ps that lives longer has a greater probability to travel a longer distance. By summing the spectra obtained in the single BGOs the 142 ns lifetime is correctly reconstructed. With the help of the MC simulation the 3γ/2γ detection efficiency has been calculated [104]. A pure 2 γ spectrum of events confined in the sample and a 3γ spectrum originating from the emitted o-Ps in vacuum is simulated. The calculations are performed considering a Maxwell-Boltzmann o-Ps energy distribution with a mean energy ranging from 0.03 to 1 eV. Fig. 6.4, shows that the dependence of the ratio of 3γ/2γ detection efficiencies on the energy of the emitted o-Ps is very weak, of the order of 2 %. The dependence of the 3γ/2γ detection efficiency ratio is calculated for different energy thresholds on the total energy deposited in the BGOs. 6.3. THE PALS DETECTOR 85

Beam pipe with solenoid Sample holder 1−11 kV 1 0 0

Deflection plates +/− 200V Heater

200 eV

MCP Cold finger BGO Cryocooler expander Coils

Figure 6.2: Top: picture of the PALS detector (left) and a 3D CAD drawing of the BGO calorimeter (right). Bottom: Schematic drawing of the PALS setup. 86CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

Figure 6.3: Lifetime measured in a single BGO crystal. The apparent lifetime measured depends on the distance of the crystal from the target. The detection probability at larger distances is enhanced for long living o-Ps. 6.4. THE POSITRONIUM TIME-OF-FLIGHT DETECTOR 87

Figure 6.4: Ratio of the 3γ/2γ detection eﬃciency as a function of the o-Ps emission energy for three diﬀerent thresholds applied to the BGOs: 200, 300 and 400 keV.

6.4 The positronium time-of-ﬂight detector

Existing Ps-TOF spectrometers use very intense pulsed positron beams (107 108 e+/s) based on LINACs or nuclear reactors [93, 94]. These positron ﬂuxes are more than− 3 orders of magnitude larger than the intensity of the ETHZ positron beam. However, with the excellent signal to background ratio achieved with the secondary electron tagging system presented in Section 5.4.2, TOF measurements have been successfully performed with our set-up. In the TOF spectrometer the stop is given by one (or more) annihilation photons depositing some energy in the calorimeter (ECAL) that is placed behind a lead slit at a distance z from the target (see Fig. 6.5). The ECAL is composed of 5 BGOs. The 5 crystals are covered by a light tight housing and they are screened by four 4 half cylinders of lead surrounding the beam pipe. The collimator assembly is mounted on a linear mover steered with a step motor interfaced to a computer: this allows an automatic and precise positioning. The width of the collimator is 5 mm. The position calibration of the collimator with respect to the sample has been performed by determining the height of the 511 keV peak in the total energy spectrum as a function of the collimator position (Fig. 6.6) for1 106 triggers. With × this method the number of events depositing 511 keV in the ECAL is determined. Note that the maximum height of the 511 keV peak is not observed when the target position is in the center of the collimator (0-position) because the solid angle for detecting both of the two back-to-back gammas is maximized and thus, the maximum is observed for 1.022 MeV total energy deposition. 88CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

Sample holder 1−11 kV 1 0 0 BGO

z 200 eV o−Ps

MCP

Lead collimator Cryocooler expander Coils

Figure 6.5: 3D view and picture of the TOF detector. 6.5. COOLING OF THE TARGET USING A CRYOCOOLER 89

Figure 6.6: Analysis of the 511 keV peak height as a function of the collimator position. With this scan the 0-position (target) and the slit width can be monitored.

6.5 Cooling of the target using a cryocooler

The working principle of the cryocooler is sketched in Fig. 6.7. The cryocooler used in the setup is a two-stage cryogenic refrigerator that operates with the Giﬀord-McMahon refrigeration cycle. After 1 hour of operation the thermal equilibrium is reached and three diﬀerent temperatures are established on the cryocooler assembly: (1) 300 K on the expander;

(2) 80 K on the ﬁrst stage;

(3) 45 K on the second stage. For our purpose an additional extension has been added to the second-stage. This extension consists of a copper rod, a first sapphire interface, a second copper rod, another sapphire interface, and finally the copper sample holder 6.8. The sapphire interface is used to electrically insulate the cryocooler assembly from the heating station, which is used to control the temperature of the cold finger by applying a current from 0-0.5 Amperes in a filament wound around the copper rod. The second sapphire interface insulates the heating station from the sample holder, where the voltage for the positron acceleration is applied (1-10kV). Sapphire is used because of its characteristics at low temperatures that guarantee good electrical insulation and rather good thermal conductivity. The measurements were taken in a clean vacuum of 10−9 mbar. To avoid water contamination of the films during the cooling down, the target was kept at room temperature for an hour using a heater before lowering its temperature. 90CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

Figure 6.7: Working principle of the cryocooler. See text for details.

Figure 6.8: Cryocooler cold ﬁnger and sample holder. FEM calculations have been done in order to estimate the contraction of the cryocooler assembly during cooling down. 6.5. COOLING OF THE TARGET USING A CRYOCOOLER 91

Figure 6.9: Analysis of the 511 keV peak as a function of the collimator position at room temperature and after 1 hour of operation of the crycooler (45 K). The scan is performed with a 0.1 mm step.

6.5.1 Position calibration of the TOF spectrometer at low temperatures

In the low temperature regime ( 50 K) the position of the sample with respect to the lead collimator is shifted from the∼ reference obtained at room temperature because of the significant thermal contraction of the cryocooler finger during cooling down. The geometry and materials have been implemented in a finite element program and the contraction at the thermal equilibrium has been calculated. The thermal conduction is also considered in the calculation. From the FEM calculation a shrinking of the cryocooler system and cold finger of 1.64 mm was predicted. This value has been compared with a precise scan around the sample region at 300K and 45 K (Fig. 6.9). Similar to the reference scan at room temperature, this measurement was performed by analyzing the peak of the 511 keV line at different positions. In order to be sensitive to the contraction predicted by the finite elements calculation, a step of 0.1 mm has been chosen. We observed a contraction of 1.3 mm (Fig. 6.9) compatible with the prediction of the FEM calculation. In the measurements presented in Section 8.3, the scans were performed 30 min after the temperature was set on the sample. This technique was very important in order to correct the collimator position with respect to the sample surface with a precision of 0.1 mm. ± 92CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS 6.6 The DAQ system

The data acquisition (DAQ) is based on a VME system interfaced with a computer via the optical link CAEN v2708. Both, time and energy are recorded, with a TDC (CAEN v775) and a QDC (CAEN v792). The DAQ software is coded with Labview on a Linux computer. In order not to slow down the DAQ, the analysis is then performed off-line by another computer using ROOT. The event per event storage of data has the great advantage to allow off-line cuts to be applied and to cross-check their evolution with the simulation. The disadvantage is that the maximum DAQ rate we could achieve recording 64 channels (32 TDC and 32 ADC) was about 8000 events/s. However, the SE trigger rate was larger than this value only at positron implantation energies smaller than 3 keV. Thus, in most of the measurements, the acquisition time was not limited by the DAQ rate. The DAQ scheme is shown in Fig. 6.10. The signal from the MCP is plugged in the discriminator with a threshold of 5 mV. The pulse from the discriminator is passed to a coincidence unit and then to the dual timer. The output of the dual timer is divided: the first signal is used to produce a common gate for the TDC and ADC; the second signal is used as a VETO in the coincidence unit. This is done in order to avoid a loss of correlation between time and energy from the same event. In fact, the conversion time in the TDC is faster than in the ADC. Therefore, a second trigger could start a conversion for a new event in the TDC that the ADC could miss. The BGOs signals are passively divided in two signals: one signal is used for the timing and the other for the energy maeasurements. The signals are delayed by 100 ns because of the transportation time of the electrons from the sample to the MCP and the time needed to form the logic for the trigger.

6.7 PALS data processing

A typical PALS spectrum consists of a sample of 10 runs with 106 triggers each. The acquisition time depends on the secondary electron rate as described in Section 5.4.2, and on the DAQ speed limitation (Section 6.6). The raw data are then processed and stored in a tree format (ROOT program [105]) in which, the timing and deposited energy of each event are correlated. The energy calibration of the BGOs is performed by fitting the 511 keV peak from the two gamma annihilation and the 0-energy pedestal for every measurement (Fig. 6.11). For every run the time spectra of each crystal are calibrated by fitting the position of the prompt peak generated by the “fast” 2 γ that defines t0. This is needed because of the different flight time of the SEs from the target to the MCP. A cut of 300 keV on the energy sum deposited in the calorimeter is applied in order to improve the detector time resolution 1. PALS spectra are then analyzed with an exponential fit program (Lt9 [106]). The lifetimes of the decay components are resolved by fitting the final PALS time spectrum with 3 exponentials. The sum of the exponential functions is convoluted with the resolution function of the spectrometer. The three components are shown in Fig. 6.12, and we identify them as follows:

1This is due to the very low number of photo-electrons produced by the BGO crystal 6.8. TOF DATA PROCESSING 93

Figure 6.10: DAQ scheme used for the PALS and TOF detectors.

Prompt decay component given by the direct e+ e annihilation, p-Ps decay and • e+ annihilation in the bulk of the ﬁlm. − −

Intermediate component with a lifetime τ2 of the order of 10-20 ns given by the o-Ps • lifetime in the ﬁlm. In the used sample with a pore size of 3-6 nm one would expect a lifetime larger than 50 ns. This discrepancy between the measured lifetime and the expected lifetime originates from o-Ps atoms which escape into the vacuum, and will be discussed in details later in Section 7.3.

Vacuum component with a lifetime of τ =142 ns. • v

6.8 TOF data processing

The TOF spectra are composed of 30 runs with 106 triggers each. The data are processed in the same way as for the PALS measurements. The energy calibration is performed at the beginning of the measurements by positioning the center of the collimator slit in front of the sample surface. This is done in order not to screen, with the lead shielding, the 511 keV γ‘s produced in the target. An energy window of 300-550 keV was found to be optimal in order to suppress the background from Compton scattering events coming from the target without drastically suppressing the intensity of the signal given by the o-Ps decaying in front of the collimator slit. Fig. 6.13, shows the TOF spectrum acquired 94CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

106 106

5 Det. #1 Events 105 Events 10 Det. #0 Pos(511keV) = 1243.86; Zeropos = 293.34 Pos(511keV) = 1399.72; Zeropos = 279.00 4 Cd23a_315K_11000V_0_10 104 10 Cd23a_315K_11000V_0_10 3 103 10

2 102 10

10 10

1 1 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 Channel Channel

Det. #2 105 5 Det. #3

Events Events 10 Pos(511keV) = 1954.96; Zeropos = 277.68 Pos(511keV) = 2098.83; Zeropos = 282.78 4 Cd23a_315K_11000V_0_10 10 104 Cd23a_315K_11000V_0_10

3 10 103

102 102

10 10

1 1 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 Channel Channel

Figure 6.11: The energy spectra of the 4 BGO crystals are shown. The calibration of the PALS energy spectra by ﬁtting the 511 keV peak from the 2 γ decay.The pedestal is given when no energy is deposited in the BGO. The distribution in the energy range 0

Figure 6.12: Analysis of the PALS spectra using LT9 software. Three exponential components are used to model the spectra. A fast component, an intermediate component which determines the lifetime of o-Ps in the ﬁlm and the vacuum component. 96CHAPTER 6. DESIGN AND CONSTRUCTION OF THE PALS AND TOF DETECTORS

3000 F127-TEOS 300K-4 keV

2000

1000 Detected oPs (arbitrary unit)

0 0 100 200 300 400 500 600 Time [ns]

Figure 6.13: TOF spectra recorded at 4 keV positron implantation energy, at room temperature on the F sample type (more details are presented in Section 7.1).

with the collimator position at dc=18 mm from a mesoporous silica sample, a positron implantation energy of 4 keV and at room temperature. The spectrum can be divided in two main contributions. The peak around t=0 is generated by direct e+ e− annihilation, − p-Ps decay and o-Ps decay in the sample. This component is suppressed by the lead shielding and we will refer to it as target-component. The broad peak around 160 ns is given by the decay of the emitted o-Ps (TOF-peak), its intensity and position depends on the implantation energy. The distance dc=18 mm between the sample and collimator has been chosen in order to minimize the overlap of the target-component with the TOF-peak. Note, that large collimator distances dramatically suppress the intensity of the TOF peak.

6.9 Conclusions

Two different detectors have been constructed in order to study the different aspects related to the o-Ps emission into vacuum. A large solid angle PALS detector suitable for the precise evaluation of the fraction of o-Ps emitted into the vacuum and a Ps-TOF spectrometer used to study the emission energy and angular distribution have been constructed. Both detectors are used in the secondary electron trigger mode described in Section 5.4.2. The system is equipped with a cryocooler that allows to perform measurements in a range between 50K-400K. MC simulations were essential in order to study the different aspects related to the detection of o-Ps, in particular to understand the detection efficiency of the PALS spectrometer in the case where o-Ps is emitted into the vacuum. Chapter 7

Analysis of the PALS spectra

In this chapter, the measurements performed with the spectrometer described in Section 6.3 are presented. Different mesoporous silica films have been studied and their o-Ps yield has been investigated at different positron implantation energies and temperatures. The chapter is organized as follows. In Section 7.1, I will briefly describe the technique used to produce the targets that have been measured. The main concepts of the RTE model (rectangular Tau-Eldrup model) will be reviewed in Section 7.2.2. This model correlates the o-Ps lifetime with the pore size. In Section 7.3, a novel model that we developed is presented, that serves to determine the o-Ps lifetime in the film in the case where a high fraction of o-Ps escapes from the surface. By combining the two models, the pore size of the films is determined. This has been done for two samples, having different pore sizes (see Section 7.3.1). In Section 7.3.1, I will describe the measurements performed at low target temperatures and their deviations from the RTE model will be briefly discussed. In Section 7.4, this chapter is summarized with the conclusions.

7.1 Sample preparation

The samples measured during my thesis have been prepared at CEA Saclay1 by experts in the field of thin film growing technologies. The understanding of the technical details related to the production of those films implies a deep knowledge of chemistry and material science. A detailed description of these topics is beyond the scope of this thesis. In [107], an overview of the mechanisms involved in the formation of meso-structured films is presented. The idea is to prepare a solution with a pore generator (porogen) and a matrix (Fig. 7.1). This mixture is centrifuged on a glass substrate (spin coating). At the end of the film preparation the sample is heated (calcination) to several hundred degrees and the porogen is selectively evacuated . The concentration of the porogen defines the porosity of the film. The measurements reported in Sections 7.3.1 and 8.2.2, have been performed on two different types of mesoporous thin films. Both of them are produced using the same matrix material: tetraethoxysilane (TEOS) mineral source for the silica network skeleton precur-

1IRFU/SPP, C.E.A. Saclay F91191 Gif-sur-Yvette Cedex France

97 98 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

Figure 7.1: The porous materials are produced by mixing a porogen to a matrix material. At the end of the ﬁlm preparation the porogen is evacuated by heating the sample to 4500C.

sor: CTACl-TEOS and F127-TEOS. The density of the CTACl sample is approximately 1.2 g/cm3 and the F127 sample has a density of 1.5 g/cm3. Both samples were spin- coated on a glass substrate with a size of 2 x 2 cm2. The CTACl-TEOS (called hereafter C samples) were prepared through the sol-gel process using cetyl trimethyl ammonium chloride (CTACl) cationic surfactants as the organic pore generator (porogen) agent [108]. A pure aqueous method is used. The CTACl/TEOS molar ratio for the ﬁlms prepared is 0.22. After deposition, the CTACl-TEOS/Glass samples are treated at 130 0C and stored in air. The F127-TEOS (called hereafter F sample) use non-ionic Pluronic F-127 (EO106PO70EO106) as surfactant and were prepared in the same way as described in [109]. Both samples were calcinated for 15 minutes at 450 0C in air immediately before the e+ measurements. Symmetry in pore organization is absent from the recorded X-ray diﬀrac- tion patterns. The thickness of the samples were estimated by comparing measurements on similar samples using optical refraction with 600 nm light [110]. The C sample was found to have a thickness of 700 nm. The thickness of the F sample was estimated to be 1000 nm. The measurements∼ presented in Section 7.3, were performed on samples produced∼ with the CTACB porogen [108]. A systematic study on a set of samples with porogen concentrations ranging from 0.03 to 0.14 CTATB/Si mole fraction was performed. The samples obtained with those concentrations were found to have a hexagonal three- dimensional structure for low porogen fractions (0.1 CTATB/Si ) and a less organized cubic arrangement at higher porogen contents (0.14 CTATB/Si). 7.2. EXTRAPOLATION OF THE PORE SIZE FROM THE O-PS LIFETIME 99 7.2 Extrapolation of the pore size from the o-Ps lifetime

The correlation between the o-Ps lifetime and the pore size is presented by Gidley et al. [82], where the Tau-Eldrup (TE) [80, 81] model, which is restricted to o-Ps quenching in sub-nanometer pores, is extended to any pore size at any ﬁlm temperature (RTE). In this section the diﬀerence between these two models is presented. The comparison between experimental data and other models [111] is presented in details in [82].

7.2.1 Lifetime in sub-nanometer pores: Tau-Eldrup model The TE model correlates the lifetime of o-Ps with the pore size as it would be trapped in the pore ground state described by an inﬁnitely deep spherical potential well of radius R + ∆R. The following assumptions are made in the model:

The o-Ps has inﬁnite lifetime in the central region of the potential well with radius • R.

Within a distance ∆R of the walls of the potential well the o-Ps has a lifetime of 0.5 • ns.

Excitation of Ps to higher states is neglected. • The annihilation rate is calculated by squaring of the wave function in the shell ∆R. •

The calculated annihilation rate λTE in a spherical pore with radius R + ∆R is given by: R 1 2πR λ (R)= λ 1 + sin (7.1) TE A − R + ∆R 2π R + ∆R h i where λA = (λS +3λT )/4 is the spin averaged vacuum lifetime of the singlet and triplet state (1/142 ns and 1/125 ps). The lifetime in the pore is given by τTE(R)=1/λTE. The interacting pore portion ∆R is empirically determined to be 0.16-0.17 nm by comparing the model to diﬀerent known pore materials with nanometer and sub-nanometer pore sizes. As described above, the assumption that the Ps population in higher states inside the potential well can be neglected is motivated by the energy gap between the ground and the ﬁrst excited state. In sub-nanometer pore sizes this gap is of the order of 100-200 meV and it is larger than the thermal energy kT that would allow excitements in higher states.

7.2.2 Lifetime in mesoporous materials, the RTE model An attempt to consider only the ground state in the pore for calculating the Ps wave function fails for larger pore sizes because the energy gap between the states in the pores reduces and thus the higher levels have to be included in the calculations. The extension of the TE model calculations to include excited states is not feasible because it is necessary 100 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA to calculate high order Bessel functions for describing the wave function in the spherical potential well. The diﬃculty related to the high order Bessel function can be avoided by approximating the spherical pore geometry by a rectangular shape and in the same way cylindrical pores to square channels. This extension of the TE model is called RTE model (Rectangular Tau-Eldrup model). To calculate the Ps wave function we consider the three momentum directions x, y and z in an inﬁnitely deep rectangular well of sides a, b, c. The general form of the wave function is:

Ψijk = φi(x)φj(y)φk(z) (7.2) where: 2 iπx 2 jπy 2 kπz φi(x)= sin φj(y)= sin φk(z)= sin (7.3) ra a r b b r c c The energy of these states (characterized by the quantum numbers i, j and k) is: i2 j2 k2 E = β + + (7.4) ijk a2 b2 c2 2 2 where β = h /16mPs =0.188eV mm , and mPs is the positronium mass. Similar to the ∆R interaction region of Ps described in the TE model, a distance δ is deﬁned in the RTE model. However the annihilation rates in the two parts of the pores (central region characterized by x < a δ etc.) are described in a diﬀerent way because the − assumption made in the TE model to neglect the self annihilation rate λT of o-Ps is not possible anymore. The lifetime of o-Ps in larger pores can not be neglected with respect to the vacuum lifetime of o-Ps. The annihilation rate is described by:

λ(x, y, z)= λ Λ(x, y, z) (7.5) A − where: λ λ Λ(x, y, z)= S − T for δ x a δ, δ y b δ, δ z c δ (7.6) 4 ≤ ≤ − ≤ ≤ − ≤ ≤ − Λ(x, y, z)=0 otherwise (7.7) We assume that o-Ps is in thermal equilibrium with a reservoir at temperature T. Higher levels in the pore potential can be reached because of thermal excitation that will statistically sample all states with a probability governed by the Boltzmann equation. The non-zero elements of the density matrix are:

exp( Eijk/kT ) ρ = ∞ − (7.8) ijk,ijk exp( E /kT ) i,j,k=1 − ijk P β i2 j2 k2 exp kT a2 + b2 + c2 = − (7.9) ∞ 2 hexp β i2 + j +ik2 i,j,k=1 − kT a2 b2 c2 P h i 7.3. DETERMINATION OF THE LIFETIME IN THE PORES 101

The density matrix is assumed to be diagonal for a system in thermal equilibrium. The diagonal elements of the annihilation rate matrix are:

λ =< ijk (λ Λ(x, y, z)) ijk > (7.10) ijk,ijk | A − |

λ λ a−δ b−δ c−δ = λ S − T dx dy dzφ2(x)φ2(y)φ2(z) (7.11) A − 4 i j k Zδ Zδ Zδ λ λ = λ S − T G (a, δ)G (b, δ)G (c, δ) (7.12) A − 4 i j k where 2δ 1 2nπδ G (x, δ)=1 + sin (7.13) n − x nπ x It is now possible to calculate the expectation value of the annihilation rate Tr(ρλ):

∞ λ λ λ (a, b, c, T )= ρ λ = λ S − T F (a, δ, T )F (b, δ, T )F (c, δ, T ) (7.14) RT E ijk,ijk ijk,ijk A − 4 i,j,kX=1 where: ∞ 1 2iπδ 2 2 2δ i=1 iπ sin x exp( βi /x kT ) F (x, δ, T )=1 + ∞ − (7.15) − x exp( βi2/x2kT ) P i=1 − These calculations are equivalent to weightingP the annihilation rates in each region of the pore with the square of the wave function and then average this mean annihilation rates with the occupancy probability of the diﬀerent levels calculated with a Boltzmann population as sketched in Fig 7.2. Eq. 7.14 allows us to calculate the lifetime of o-Ps for cubic, channel-like and planar pores. In the limit x the function F(x) described in Eq. 7.15 is equal to 1. Fig. 7.3 shows the o-Ps lifetime→ ∞ as a function of the pore size for two diﬀerent geometries: rectangular channels and cubic pores. For both curves δ is set to 0.18 nm. This value is determined by imposing that at low pore sizes the ground state of the rectangular model (i.e for T=0 K) agrees with the TE spherical model (which has been empirically calibrated with known sub-nanometer pore size materials such as zeolites). Fig 7.4 shows the temperature dependence of the lifetime assuming cubic boxes. At lower temperature the lifetime is expected to increase.

7.3 Determination of the lifetime in the pores

In interconnected porous systems (see Fig. 7.5 (a) ) there is a discrepancy between the measured values of the lifetime which should represent the lifetime in the film τ2, see Section 6.7) and the lifetime that one would expect considering the pore size in the film. This effect has been experimentally observed by using the capping layer technique [112]: this technique consists of covering with a 20 nm thick silica layer the surface of the sample. The goal of the measurements in capped mode is to determine the characteristics of the 102 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

Figure 7.2: (a) Tau-Eldrup model: in the central portion of the spherical pore with radius R + ∆R the annihilation rate is λ = 0 (the self annihilation is neglected) while in the λS+3λT interaction region it is equal the to averaged spin annihilation rate λA = 4 . (b) RTE model: the annihilation rate in the central region of the pore is λT while in the interaction λS +3λT region it is λA = 4 .

160

140

120

100

80 [ns] f τ 60 T=300 K 3-D Cubes 40 T=300 K 2-D Channels 20

1 10 102 Side length [nm]

Figure 7.3: o-Ps lifetime as a function of the pore size calculated with the RTE model with δ =0.18 nm assuming cubic pores (dotted line) and inﬁnite rectangular channel pores (solid line) 7.3. DETERMINATION OF THE LIFETIME IN THE PORES 103

160

140

120

100

80 TE regime [ns] f τ 60

40 T=0 K (Ground state) T=300K 20 T=800K

1 10 102 Side length [nm]

Figure 7.4: RTE model lifetime calculations assuming cubic pores at 0, 300 and 800K for δ = 0.18 nm. The RTE model is calibrated by demanding that at 0 K (i.e. ground state) the TE model is reproduced for pore sizes in the sub-nanometers range.

o-Ps lifetime and intensity inside the sample by forcing the formed o-Ps to remain in the pore system (Fig. 7.5). It has been observed that the values of the intermediate lifetime component measured in capped mode are larger than the ones when o-Ps has the possibility to leave the target, and hence the escape rate contributes to the disappearence rate of o-Ps in the pores.

We introduced a novel model to describe o-Ps emission from mesoporous silica film [113]. It allows the determination of the yield and rate of escaping o-Ps into vacuum as well as the annihilation decay rate of o-Ps trapped in the film in the case, where a large fraction of o-Ps produced in the pore system leaves the target. As mentioned above, the intermediate component τ2 obtained by the exponential decay analysis presented in Section 6.7 should represent the lifetime of o-Ps which remains trapped in the pores. In the case where Ps can escape into the vacuum this is not true. Interconnected pore structures allow Ps to escape into the vacuum which leads to a disappearance that is not given by the decay rate. This results in an extra decay rate and causes an apparent lifetime of o-Ps in the mesopores that is smaller than the one expected from the pore size. This effect is interpreted using a kinetic model that describes the o-Ps escape process as a transition between two o-Ps states 2, both of which can independently decay via annihilation. In the present model, the initial state is the film bulk o-Ps state characterized by the o-Ps annihilation lifetime τf . The final state is the o-Ps ground state in vacuum characterized

2This is done similarly to the model that describes the positron trapping in defects. 104 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

Figure 7.5: (a): Uncapped and (b) capped porous silica film: o-Ps is forced to remain in the film. In interconnected pore systems, this is done in order to study the internal properties of the film by avoiding that o-Ps emitted from the surface biases the values of the lifetime related to the annihilation in the pores.

by the τv=142 ns annihilation lifetime. The transition probability per time from the ﬁlm state to the vacuum state, i.e., the escape rate of o-Ps into vacuum, is given by the rate κv. The occupancy probability of the ﬁlm state nf decreases via annihilation at a rate λf nf −1 (λf = τf ) and via escape to the vacuum state at a rate κvnf . The occupancy probability −1 of the vacuum state nv decreases via annihilation at a rate λvnv (λv = τv ) and increases at the rate κvnf . dn f = (λ + κ )n (7.16) dt − f v f dn v = κ n λ n (7.17) dt v f − v v The solution of Equations 7.16 and 7.17 with the initial conditions

nf (0) = 1, nv(0)=0 (7.18) is −(λf +κv) t nf (t)= e (7.19)

κv −λvt −(λv +κv)t nv(t)= e e (7.20) λf + κv λv − − h i The measured lifetime spectrum is given by the probability of annihilation at time t:

dn(t) − − − = I λ e λ1t + I λ e λ2t + I λ e λ3t (7.21) − dt 1 1 2 2 3 3 By diﬀerentiating Eqs. 7.19 7.20, and comparison with Eq. 7.21, one can express the parameters of the model τf and κv in terms of ﬁtted parameters τ2 , τv, I2 and I3: dn(t) d(n (t)+ n (t)) = f v (7.22) − dt dt 7.3. DETERMINATION OF THE LIFETIME IN THE PORES 105

The observed disapparence rates of the o-Ps components are:

1 λ2 = = λf + κv (7.23) τ2

1 λ3 = . (7.24) τv The lifetime in the ﬁlm is then expressed by the observed values as:

− τ = (τ −1 τ −1)I /(I + I )+ τ −1 1 (7.25) f 2 − v 2 2 v v and the escape rate is described by:

κ =(τ −1 τ −1)I /(I + I ) (7.26) v 2 − v 3 2 3 The fraction (Yield) of o-Ps emitted into the vacuum is described by:

Y =(τ −1 τ −1)I /(I + I ) (7.27) v 2 − v 3 2 3

Note, that Yv differs from the extrapolated intensity I3 because the initial condition described in Eq. 7.18 requires that at t=0 the vacuum state occupancy is nv = 0. This model has been tested by performing measurements with various concentrations of porogen i.e porous volume fractions. The concentration of the porogen, i.e. the CTAB/Si mole fraction varied over a range between 0.03 x 0.14. For each x PALS spectra at implantation ≤ ≤ energies 1 Ee+ 5 keV are recorded and the spectra are analyzed as described in Section 6.7, using 3≤ exponential≤ functions convoluted with the detector resolution. The results are summarized in Fig. 7.6. Panels (a), (b) and (c) show the obtained fit parameters τ2,I2,I3 as a function of the porogen concentration. The drop in the lifetime τ2 and I2 is correlated with an increasing fraction of o-Ps emitted into vacuum. At porogen concentrations 0.06 x 0.1 I3 increases by an order of magnitude. This transition is interpreted as a threshold≤ ≤ concentration where the pore system starts to be interconnected. On the right side of Fig. 7.6, panels (d) (e) (f), the extrapolated values of τf , κv and Yv using the model of escaping o-Ps are shown. The calculated lifetime of o-Ps in the film increases from 40 ns for low porogen concentration to 70 ns for x 0.10. This implies an increase in the volume that localizes o-Ps. The validity of this model≥ has been cross checked with PALS measurements performed in capped mode (Fig. 7.5) at the AIST beam3 and a lifetime of 68 ns has been measured. The positronium escape model, discussed above, allows the determination of the o-Ps lifetime in the film even in the case when a significant amount of positronium escapes from the film into the vacuum. By using the correlation between the pore size and the lifetime of localized o-Ps [82], the effective pore size in mesoporous films can be determined in highly porous films.

3AIST, Tsukuba, Ibaraki 305-8568, Japan 106 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

͑ ͒ ͓ ͑ ͒ ͑ ͔͒ ͓ Figure 7.6: Left: measured o-Ps lifetime components, (τ2,I2) , (142ns,I3) as a function of the porogen content. Right: o-Ps-escape model calculations. 7.3. DETERMINATION OF THE LIFETIME IN THE PORES 107

7.3.1 Measured yield of the o-Ps emission into the vacuum and the o-Ps lifetime in pores The theoretical considerations described in the previous sections are used to characterize the two types of samples that have been studied: CTACl-TEOS and F127-TEOS. In the next chapter, the TOF measurements performed on the same samples will be discussed. As will be shown later, the information extrapolated with the PALS measurements are very important in order to understand the data recorded with the TOF spectrometer, these are: the fraction of o-Ps emitted into the vacuum; • the estimation of the pore size in the film, determined with our model describing the • o-Ps escape into the vacuum. The PALS measurements performed on those samples showed an extremely high o-Ps yield. For example, the C sample, at low implantation energies, showed that almost 50% of positrons implanted in the film form o-Ps. This fraction is calculated by summing the intensities of the two longer components obtained from the fit of the PALS spectra:

Itot = I2 + I3 (7.28) A very large fraction of o-Ps formed in the pores is emitted into the vacuum (See Fig. 7.7). For the C sample, fractions as high as 40%, with respect to the number of implanted positrons have been observed to leave the target. The F sample showed an o-Ps emission yield around 30% at low implantation energies. The emitted fractions decrease at higher implantation energies because part of the positrons are implanted in the glass substrate where no o-Ps is formed. Interestingly, the measurements performed at 50 K demonstrate that the o-Ps yield can be considered as independent of the target temperature (see Fig. 7.7). Measurements performed on porous materials using the 3γ/2γ technique [114] showed, that the total 3γ fraction dramatically decreases at low temperatures, suggesting a substantial increasing of the pick-off effect. In [84] the same effect has been reported in closed porosity samples while the opposite effect has been observed in samples with interconnected pores. At 10K an increase in the 3γ fraction of 50%, with respect to the total 3γ fraction measured at room temperature, has been measured. In [114] a water condensation in the porous material that biases the measurements at low temperatures can not be excluded. This is supported by the fact that the results could not be reproduced by repeating the cooling cycles. In [84] the substantial increase of the 3γ fraction only in the open porosity sample could also be attributed to a systematic error introduced by the dependence of the detection efficiency on the o-Ps energy. After these initial considerations on the o-Ps formation yield at different temperatures, the lifetime and the escape rate parameter, using the model presented in Section 7.2.2, are calculated. In Fig. 7.8 we show the values of τf at different implantation energies. The effect of the positrons annihilating in the glass substrate is clearly visible for the C sample at implantation energies larger than 6 keV. This effect is not observed in the F 108 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

50 F127-TEOS

Itot 300K

40 Yv 300K Itot 50K

30 Yv 50K 20

Fraction (%) 10 0 0 2 4 6 8 10 12

50 CTACl-TEOS I 300K 40 tot Yv 300K I 50K 30 tot Yv 50K 20

Fraction (%) 10 0 0 2 4 6 8 10 12 Implantation energy [keV]

Figure 7.7: Yield of o-Ps emitted into the vacuum (Yv, circles) and total yield of Ps (Itot = I2 + I3, squares) for F (upper plot) and C samples (lower plot) at room temperature and at 50K.

sample because of the larger film thickness and higher film density. In order to make the discussion simpler we use the results of the fits of the PALS spectra at 6 keV for the C sample and 10 keV for the F sample at 50 K and 300 K. At these energies the majority of the positrons are still implanted within the films (see Fig. 7.7) and the o-Ps emission energy is in the constant region (this point will be discussed in Chapter 8). The values of τf at 300K and the escape rate κv at 300K and 50K are summarized in Table 7.1. The values of τ at 300K are in a good ( 2ns)agreement with measurements performed in capped f ± mode performed at the AIST beam [112] and [115].

Table 7.1: Film thickness (Z), calculated o-Ps lifetime in the pores τf , and escape rate kv at 50 K and 300 K. 300K 50K 300K −1 50K −1 Sample Z[nm] τf [ns] τf [ns] kv [ns ] kv [ns ] C 700 54 1 60 1 0.027 0.025 F ∼1000 74±1 82±1 0.017 0.013 ∼ ± ± 7.3. DETERMINATION OF THE LIFETIME IN THE PORES 109

Figure 7.8: o-Ps lifetime in the ﬁlm determined with the escape model. Values of 54 ns for the C sample and 76 ns for the F sample have been measured. In the C sample, for implantation energies above 7 keV, positrons start to be implanted in the glass substrate. In the F sample below 6 keV the calculated lifetime using the escape model is biased by surface eﬀects.

As one can see, at lower temperature the lifetime in the film increases as predicted by the RTE model. This can be understood in the following way: the overlap of the o-Ps wave function with the volume contained within a distance δ =0.18 nm [82, 83] from the walls, for which the annihilation rate is assumed to increase, is less for o-Ps confined in the pores occupying the ground state than for o-Ps in excited states. Since at lower temperatures the population of the ground state is higher, the pick-off rate decreases (Fig. 7.4). However, the measured lifetimes are lower than expected from the calculations. For the C sample, the discrepancy is less than 10% but for the F sample the measured value is 20% lower, suggesting that the pick-off rate increases. The explanation of this underestimation of the lifetime at low temperatures is not clear. In [116] the RTE model has been tested with samples having pore sizes of 2-27 nm in a temperature range of 50-500K. Interestingly, it has been observed that the temperature dependence of the lifetime predicted by the RTE has not been reproduced. The samples with smaller pore size (2 nm) showed longer lifetimes than predicted from the RTE model while the sample with 5 nm pore size showed almost no temperature dependence. These measurements are qualitatively in agreement with our observations. In fact the C sample shows a stronger dependence on the temperature than the F sample.

The escape rate parameter kv decreases at low temperatures, suggesting that the emission of o-Ps into the vacuum at low energy is less eﬃcient. A tentative explanation of this 110 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA

effect can be found if we consider that o-Ps reaches the sample surface by tunneling from pore to pore. If one considers, similar to the RTE model, that the o-Ps wave function overlaps with the pore surface, the probability of tunneling to a next pore would be larger at higher sample temperatures. It is still not clear, if the interconnection that we are considering is given by an aperture between different pores. As observed in Fig. 7.6, with measurements performed on samples with different porogen concentrations, at a certain pore density the o-Ps escaping rate drastically increases. This could also be explained by considering that at a certain porogen concentration the wall thickness between the pores is thin enough, so that quantum mechanical tunneling of o-Ps becames possible. Even in the case where the connection between the pores is given by an aperture smaller than the pore size, the effect of the temperature would manifest itself in the same way as tunneling through the walls. This has been demonstrated in theoretical calculations where the tunneling of particles between two boxes joined with a long thin tube has been studied [117]. However, the experimental data and the information about the pore morphology that we have are not enough to draw any conclusions about this subject. Further work is needed to understand this effect.

7.3.2 Calculation of the pore size

The pore size of the samples are calculated using the value of τf reported in Table 7.1 at 300K. The difference between τf at 300K and 50K leads to different pore sizes calculated with the RTE model (see Fig. 7.4). Two different reasons support the idea to use the value at 300K:

the parameter δ of the RTE model is calibrated at room temperature; • deviations from the RTE model have been observed in diﬀerent studies performed at • low temperatures;

a small contamination of the pore surface in the cooling phase can not be totally • excluded.

In Table 7.2 the values of the pore size obtained from modeling the pore structure as a square channel and a cubic box are reported:

Table 7.2: Pore size calculated with the RTE model using the value of τf at 300K. Sample a[nm] Channel a [nm] Box C 3.3 0.5 4.2 0.5 F 4.8 ± 0.5 6.4 ± 0.5 ± ±

In the literature we found that samples produced with the same porogens and studied with the 2D X-ray scattering technique and transmission electron microscopy (TEM) show to have channel like structures. In [108] and [109] values of 2.7 and 5.2 nm are reported 7.4. CONCLUSIONS 111 for the pore size of the C and F sample, respectively. These are qualitatively in agreement with our results. However, one has to consider that the production of such samples is very sensitive to diﬀerent parameters, such as the porogen concentration and conditions during the ﬁlm growing. In the next chapter a more detailed discussion on the pore shape with the help of the results obtained with the TOF measurements is presented.

7.4 Conclusions

In this chapter it has been shown that the PALS spectrometer constructed during these years is suitable for the determination of the o-Ps emission fraction into the vacuum. A model was developed in order to reconstruct the o-Ps lifetime in the film for highly interconnected pore systems without using the capping layer technique. Measurements performed at 300K and 50K showed that the o-Ps yield can be considered as independent of the temperature. These results are qualitatively in agreement with the RTE model. However, at low temperature the measured lifetime in the film is shorter than estimated with RTE model. A similar effect has been reported in [116]. The pore sizes obtained with the PALS measurements show, that the pore size of the C sample is smaller than for the F sample. A satisfactory agreement with the values reported in the literature was found. Furthermore, due to their high o-Ps yield, the samples studied in this chapter are good candidates to be used as o-Ps converters in the invisible decay experiment. In particular the F sample, that shows a nearly constant o-Ps emission yield over a broad range of positron implantation energies. 112 CHAPTER 7. ANALYSIS OF THE PALS SPECTRA Chapter 8

Analysis of the TOF data

The goal of the the TOF data analysis is to determine the energy distribution of o-Ps emitted from the film into the vacuum. At the present stage there are two models describing the o-Ps thermalization in porous materials. In 1995 Hydo et al. [87], based on measurements performed on aerogel, proposed a model that describes Ps thermalization from a classical point of view through elastic scattering. Recently, Brusa et al. [86] performed calculations to describe o-Ps thermalization with acoustic phonon scattering, and thus, the classical idea of o-Ps colliding with the pore walls was replaced with a quantum mechanical description of the energy loss process. It is important to highlight that the energy loss of Ps through phonon scattering has been previously proposed, but the rigorous mathematical description of this process has been presented for the first time in [86]. By switching from the classical picture to a quantum mechanical approach, effects related to the confinement of Ps in a nanometer size potential emerge. In fact, in the classical model a complete thermalization of o-Ps is expected while in [86] thermalization stops when o-Ps reaches the lowest accessible quantum level in the potential of the pore. This is related to the fact that the de Broglie wavelength of Ps at room temperature is about 6 nm, and thus the confinement effect should be visible in nanoporous films with pore sizes comparable with this value. Even though various measurements have been performed on the o-Ps emission energy into vacuum from porous films, the existence of a minimal emission energy has never been unambiguously proved. The measurements presented in this thesis represent the first experimental evidence of the minimal emission energy of o-Ps from nano-porous films. Very recently, Cassidy et. al. [118], by studying samples similar to the one presented in this thesis, confirmed our results observing a minimal emission energy above room temperature. However, our results [119] are supported by temperature dependent measurements giving to the observed minimal energy a more solid foundation. As we will show later in this chapter we observed a weak dependence of the o-Ps emission energy on the sample temperature. Furthermore, as shown in Chapter 7, we studied samples with different pore sizes and the results confirmed the idea that for larger confinement potentials (i.e larger pore size) the minimal energy that Ps can reach is smaller. The idea to consider o-Ps in a confined potential well is a concept that has already been extensively used as a base assumption of the TE and later in the

113 114 CHAPTER 8. ANALYSIS OF THE TOF DATA

RTE model (Section 7.2), however, only in recent publications this concept is discussed from the point of view of emission energy [86, 118, 120]. This is probably related to the increasing interest in e+ o-Ps converters triggered by a new generation of experiments involving cold o-Ps (Chapter→ 10). In previous studies of Ps emission into vacuum using the TOF technique, the emission from the surface of different materials [90]-[121] was investigated. Recently, this technique was applied to study mesoporous and hybrid silica films [122]-[123], to evaluate the conti- nuity barrier [120] and the effect of thermalization for pore surfaces coated with different chemicals groups [124]. However, the influence of the temperature on Ps emission into vacuum from mesoporous thin films was never studied in detail. To our knowledge, only the work of Mills et al. [90], with SiO2 powders revealed a dependence on the temperature of the Ps emission into vacuum. The fraction of Ps in the low energy tail was estimated, but no quantitative estimate on the value of the minimal emission energy was obtained.

This chapter is structured as follows. In Section 8.1, the Ps thermalization models are described in more details. In Section 8.2 the analysis method used to determine the o-Ps emission energy is presented. The TOF measurements have been performed on the samples described in Section 7.1. For those samples we analyzed the o-Ps emission energy at diﬀerent implantation energies ranging from 0.7 to 10 keV. Furthermore, as described in the Chapter 6, the TOF measurements were performed at temperatures ranging from 50 to 400K. In Section 8.3.2, I will present the model we developed for the interpretation of the measurements performed at diﬀerent temperatures.

8.1 Ortho-positronium thermalization in porous ﬁlms

8.1.1 The classical model In 1995 Hyodo et al. [87] developed a classical model to describe the slowing down of Ps through collisions with the silica grains in pressed silica powder and aerogel filled with different gas molecules. In order to measure the Ps energy as a function of time, the lifetime of o-Ps was controlled with a varying magnetic field strength by quenching o-Ps into the fast decaying p-Ps state. With this method the energy of Ps could be studied with the precise ACAR technique, the applicability of which is restricted to the analysis of the 2γ decays (the principle of the ACAR technique is presented in Section 4.3). It is important to note, that this model was not developed for the purpose of describing o-Ps emission into vacuum from porous films. However, it can be adapted to this situation by replacing the time spent by Ps in the aerogel before being quenched by the magnetic field with the diffusion time of o-Ps in the film before it is emitted into the vacuum. This approach has been proposed by He et al. in [124] where the diffusion time is expressed in terms of implantation energy of the e+ beam in the film and the diffusion constant of o-Ps. Furthermore, the energy loss in the classical model is described by the elastic collision of the Ps atom with a molecule of the pore surface having an effective mass MS. 8.1. ORTHO-POSITRONIUM THERMALIZATION IN POROUS FILMS 115

According to this model, the average Ps energy loss per collision with the silica pore surface at temperature T is described by:

2 2mPs mPsv 3 < ∆E >= kBT (8.1) − MS 2 − 2 !

The average energy of Ps emitted from the ﬁlm after a diﬀusion time t is given by:

1+ Ae−bt 3 E (t)= k T (8.2) av 1 Ae−bt 2 B − where A is a constant that is determined by the Ps formation energy E0 at the time t=0. The parameter b describes the interaction of Ps with the pore surface:

3 √E0 2 kBT A = − (8.3) q 3 √E0 + 2 kBT q 2 b = 3mPskBT (8.4) lMS p The emission energy of Ps depends on its formation energy E0, on the number of collisions during the diffusion and on the energy-loss per collision. Those parameters depend on the chemistry and on the pore size of the sample. In [124] N is defined as the number of 2 collisions Ps undergoes during the diffusion. N is proportional to (Leff /l) , where Leff is the effective Ps diffusion length from the point where Ps is formed to the film surface and l is the mean free path of o-Ps in the porous film. Leff = Lα where L is the mean implantation depth of the e+ beam assuming a Makhovian profile, and α is an additional parameter that represents the morphology of the pore system and evaluates the effective ”distance” that Ps has to move divided by the linear distance between the formation point and the emission point (tortuosity). Examples of thermalization curves are shown in Fig. 8.1 for different pore sizes and effective masses. Similar pore structures have been coated with different chemicals groups in order to prove the effect of the effective mass parameter. In Fig. 8.1, the data measured at different positron implantation energies, are fitted with the formula of Eq. 8.2 with MS as a free parameter. The data are only qualitatively in agreement with the model. However, it was demonstrated that the thermalization of o-Ps depends on the chemistry of the pore surface. Since a precise determination of the α parameter is rather difficult, the fit results have been presented for alpha ranging from 1 to 4, demonstrating that the ratio between the extrapolated effective masses remains constant. Furthermore, the time predicted by the model for complete thermalization is in fair agreement with the data. The model predicts for samples with pore sizes of a few nanometer that the complete o-Ps thermalization is achieved in less than 1 ns diffusion time. 116 CHAPTER 8. ANALYSIS OF THE TOF DATA

Figure 8.1: Thermalization curves for similar pore structures coated with different chemicals. The points represent the experimental data recorded at different positron implantation energies. The solid lines are the fit with the Eq. 8.2 where the effective mass MS is left as a free parameter. The effective mass ratio between the two chemical groups used in the preparation of F38 and m-F38 has been observed to be constant for α ranging from 1 to 4. 8.1. ORTHO-POSITRONIUM THERMALIZATION IN POROUS FILMS 117

8.1.2 Positronium cooling by phonon scattering In a recent publication Brusa et al. [86] proposed a new picture to interpret the Ps cooling in nano-structured films by studying the phonon scattering of Ps within the silica matrix of the pore structure. This model moves away from the classical picture represented by collisions of Ps with molecules and a quantum mechanical approach is proposed. They consider Ps cooling in two types of porous morphologies: cubic and channel like pores. As will be shown later, there is a substantial difference in the calculations of these two shapes. A central subject presented in this paper is the existence of a minimal energy that Ps can reach during the thermalization process, caused by the confinement of the o-Ps in the pores. In this model the pore geometry is modeled, similarly to the RTE model, with a square geometry (i.e closed pores are treated as cubic boxes and channel pores as rectangular channels). The Ps atom is considered to be confined in a potential and the Ps wave function is assumed to overlap with phonons in a region R from the wall of the potential. In this model only the scattering with acoustical phonons is considered. The Ps- phonons interaction near the wall surface region can be treated in terms of a deformation potential: ℏ W = E iq(a ei~q·~r a+e−i~q·~r . (8.5) d 2NMω q − q q "s q # X Here Ed is the interaction energy term and it is material dependent. For SiO2 it has been estimated to be around 3.6 eV [125]. N is the number of atoms in the sample, M is the effective mass of the molecules, ~q is the phonon momentum and ωq its angular frequency. + aq and aq are the destruction and creation operators, ~r represents the Ps position. When Ps undergoes a phonon scattering, it can increase or decrease its energy by creating or I destroying phonons. The transition probability PkkI from the Ps momentum k to k is calculated by using the first-order perturbation theory:

t i − ℏ I − ℏ I [i(E oP s final E oP s inital+P ωq(nq nq))t]/ ] 2 P I = e ( ) ( ) q dt (8.6) kk | − ℏ | | | 0 q Z X An attentive analysis of Eq. 8.6, shows that there is a maximal energy that Ps can exchange in a phonon scattering process (the mathematical details are presented in [86]): 2v m k kI = s Ps 1.7 108m−1 (8.7) || |−| ||MAX ℏ ∼ ×

Where vs is the sound speed in the medium (i.e amorphous SiO2). The consequences of Eq. 8.7, are discussed for closed pores (box) and channels in the following paragraphs.

Cubic box pores The distance between two energy levels of a Ps trapped in an inﬁnite potential well with side length a is compared to the value calculated in Eq. 8.7. At a certain point of the cooling, the energy between the levels becames larger than the maximum energy Ps can 118 CHAPTER 8. ANALYSIS OF THE TOF DATA

exchange and further thermalization is not anymore possible. The diﬀerence between the momenta k and kI of Ps is given by: π k kI = n2 + n2 + n2 (n α)2 +(n β)2 +(n γ)2 (8.8) || |−| || a | x y z − x − y − z − | q q π = √n2 n2 + α2 + β2 + γ2 +2αn +2βn +2γn (8.9) a | − x y z| p 2 2 2 where nx, ny and nz are the principal quantum numbers (n = nx + ny + nz), and α, β and γ their variations related to the change of the momentum from k to kI . The smallest momentum change of Ps when it is in the state n is given by 1:p π k kI = [√n2 √n2 1] (8.10) || |−| || | a − ± | At this point we can obtain the condition on the level number n at which the thermalization stops, by combining equations 8.7 and 8.10:

2v m π s [√n2 √n2 1] (8.11) ℏ ≥| a − ± |

The solution of this equation gives the quantum numbers nm(a) where the cooling stops. The minimal energy Emin depends on the side length of the rectangular potential and thus, on the pore size (see Fig. 8.2) and is described by the formula:

ℏπ2 n E = m (8.12) min 2m a Square channels For a square channel the calculations are simpler. In the direction of the channel axis (z-direction), there exists no confinement of the Ps atoms. The consequence is that the Ps can exchange any amount of energy in the phonon scattering process by changing the energy in the z direction. The confinement in the other directions remains and the minimal energy that Ps can have corresponds to the ground state of the planar wave in the square potential. In the infinite well the minimum momentum has a magnitude k = √2π/a. This corresponds to a minimal energy of:

ℏ2π2 E = (8.13) min m2a2 The comparison of the minimal energy in boxes and channels as a function of the pore side length a for cubic and square channel pore is shown in Fig. 8.2. As one can see, channels show lower minimal energies compared to boxes.

1This is an approximation that underestimates the momentum distance. 8.1. ORTHO-POSITRONIUM THERMALIZATION IN POROUS FILMS 119

3.5 3D box 3 2D square channel 2.5

1.5

1 Mninimal Energy [eV] 0.5

0 0 2 4 6 8 10 Side length [nm]

Figure 8.2: Minimal energy of Ps as function of the pore size for cubic box (circles) and square channel (dotted line) geometries. The minimal energy of o-Ps in a square channel is smaller than in the cubic box of the same side length a.

Energy loss as a function of the time for a channel-like pore In [86] a calculation of the o-Ps energy as a function of the time spent in the porous material is presented. The energy loss as a function of the o-Ps energy < ∆E(k) > is calculated by considering phonon scattering. I will present here only the end result of the calculations. The time t of o-Ps spent in the interaction region R with the phonon can be approximated by: R Rm t = 2 (8.14) v ∼ ℏk where v is the velocity of o-Ps. By using a relaxation time approach one gets:

dE ∆E(k) =< >, (8.15) dt τ where τ is the time needed to cross the well τ = a/v 2am/ℏk. The R parameter ∼ is assumed to be in the range 0.15-0.2 nm, according to the estimation of the overlap between the o-Ps wave function and the surface region [80]. The total time that o-Ps takes to thermalize is comparable to the one obtained with the classical model. However, the shape of the thermalization curves as a function of the time are diﬀerent. In Fig. 8.3, the comparison between the classical model and the Ps-phonon interaction model is presented for channels with a side length a=25 nm. The Ps formation energy is set to 3.27 eV. The curves are presented for diﬀerent R parameters: 0.15 and 0.2 nm. The energy loss curve for the classical model is shown assuming M=25 amu, according to He et al. [124]. 120 CHAPTER 8. ANALYSIS OF THE TOF DATA

Figure 8.3: Comparison between the energy loss curves obtained from the classical model and the Ps-phonon interaction model. Figure from [86]. See the text for details.

8.2 Determination of the o-Ps energy from the TOF measurements

A schematic view of the target region and of the collimator used for the TOF measurements is shown in Fig. 8.4. Fig. 8.5 shows the data acquired with the TOF spectrometer at a distance dc = 18 mm for the C and F samples and for different positron implantation energies. These spectra are obtained after applying an energy cut on the total energy deposition in the BGOs, as explained in Section 6.8. Different components characterize the TOF spectra: The target component at t=0 that is produced by γs originating from Ps or direct • e+ annihilation in the target. The γ‘s cross the lead collimator and are detected in the BGO calorimeter (see Fig. 8.4). Thermalized o-Ps which produces the broad peaks between 50 ns and 200 ns, de- • pending on the positron implantation energy. Non-thermalized component originating from positrons that are implanted at small • depth in the porous film. Flat accidental background. • To obtain a clean sample of thermalized o-Ps in the vacuum, two different components have to be subtracted from the raw data (in addition to the flat background): the target component. It is subtracted by generating in the TOF geometry MC sim- • ulation the fractions and lifetimes recorded in the PALS measurements (see Section 8.2.2). 8.2. DETERMINATION OF THE O-PS ENERGY FROM THE TOF MEASUREMENTS121

Figure 8.4: Schematic view of the collimator and of the target region: dc is the distance between the target surface and the center of the collimator slit and wc is the collimator width. In the TOF spectrum the Ps annihilation in the target, whose γs penetrate the lead collimator and produce a signal in the BGO, contribute to the target-component.

the non-thermalized component. It is subtracted by analyzing the fraction of positrons • implanted below a certain implantation depth. This subtraction is presented in Sec- tion 8.2.3.

After subtraction of these backgrounds the remaining spectra are corrected with the o-Ps lifetime in vacuum and the detection probability in the collimator slit in order to extrapolate the energy at the emission from the target surface (Section 8.2.1).

8.2.1 Lifetime and detection eﬃciency correction and TOF peak analysis In the conventional analysis applied to previous TOF measurements of o-Ps , the energy of the emitted o-Ps is estimated by taking the maximum of the time distribution after having corrected the time spectra by a factor:

1 t e τo-Ps (8.16) t for t >0. This correction is applied in order to reconstruct the time distribution corresponding to the o-Ps emission velocity from leaving the target, taking into account two diﬀerent aspects : 122 CHAPTER 8. ANALYSIS OF THE TOF DATA

TOF spectra F127-TEOS 300K 0.7 keV 1 keV 2 keV 3 keV 5 keV 7 keV Detected o-Ps (arbitrary units)

0 50 100 150 200 250 300 350 400 Time [ns]

TOF spectra CTACl-TEOS 300K 0.7 keV 1 keV 2 keV 7 keV 0 keV Detected o-Ps (arbitrary units)

0 50 100 150 200 250 300 350 400 Time [ns]

Figure 8.5: Measured (raw) TOF spectra at 300K for implantation energies ranging from 0.7-7 kV. Top: F sample. Bottom: C sample. 8.2. DETERMINATION OF THE O-PS ENERGY FROM THE TOF MEASUREMENTS123

(1) The population of o-Ps decreases exponentially during the ﬂight time. Therefore, multiplying the spectra with the exponential factor of Eq. 8.16, the initial number of o-Ps emitted with velocity corresponding to a detection time t.

(2) The probability to detect a o-Ps decay as a function of the ﬂight velocity v. This corrections takes into account, that o-Ps decays are mainly detected during the time wc tc spent by o-Ps in the collimator slit with a width wc (see Fig. 8.4): tc = v . If dc is the distance of the collimator slit from the sample surface, the detection time td is dc given by td = v . The detection probability D(v) can then be written as a function of the detection time: wc wc D(v) tc = = td (8.17) ∝ v dc The detection probability D(v) is proportional to the detection time and thus this eﬀect can be corrected by scaling the time spectra with the factor 1/t.

After having performed the spectra correction, the position tmax of the maximum of the time distribution is determined and the velocity is calculated by considering the center of the collimator: dc vo-Ps = (8.18) tmax A parabolic fit is used to determine the position of the maximum. The statistical error of the fit gives an uncertainty on the calculation of the kinetic energy. The main source of the systematic error is given by the uncertainty on the determination of the slit position of 0.1 mm. This analysis is rather simple and gives an estimation for the mean value of the ± o-Ps energy perpendicular to the sample surface (hereafter we will refer to it as < Ez >). Thus, different aspects of the o-Ps emission velocity, such as the total energy and the angular distribution, are not taken into account by this analysis. As will be shown later in this chapter, the data suggest that o-Ps is emitted isotropically from the film surface. With the help of the MC simulation the total energy of o-Ps is reconstructed.

8.2.2 Subtraction of the target component

The measurements were performed at dc = 18 mm distance between the sample surface and the center of the collimator. The analysis is performed after a first correction of the measured spectra by subtracting the flat background from the accidentals. The subtraction of the target component is performed by simulating o-Ps decays at the target position according to the fractions and lifetimes determined from the PALS measurements. The subtracted spectra are weighted with the intensities I1 +I2, where I1 and I2 are the fractions of the two decay components related to the e+ and Ps annihilation in the target. With this simple subtraction the remaining spectra represent the o-Ps emitted into the vacuum. In a second step the correction factor for the o-Ps lifetime and the detection probability is applied (as discussed in the previous section). The resulting distribution is fitted with a parabola yielding the peak position. Assuming that this peak position corresponds to the average time of o-Ps to get from the target surface to the center of the collimator slit, one 124 CHAPTER 8. ANALYSIS OF THE TOF DATA

mP s 2 obtains the average z-component of their velocity, and the mean energy < Ez >= 2 vz . The triangles in Fig. 8.6 show the < Ez > as a function of the implantation energy. Two thermalization trends as a function of the implantation energy. For low implantation energy < E > decreases linearly from 0.1 eV to 1 eV; for larger implantation energies z ∼ ∼ (i.e., > 2 keV for the C sample and >3 keV for the F sample), the energy < Ez > is (almost) independent of the implantation energy.

8.2.3 Subtraction of the non-thermalized component Fig. 8.7 (bottom) shows that the Makhovian implantation profile is strongly broadened with increasing positron energies. Even if the mean positron implantation energy increases, a fraction of the positrons is always implanted near the surface region of the film and produces non-thermalized o-Ps which is emitted into the vacuum. This effect is qualitatively shown in the top of Fig. 8.7, where a comparison between the TOF data for implantation energies of 3, 4 and 5 keV is presented. One observes, that the tails on the right of the TOF-peak are similar while the left part (epithermal tail) decreases at larger implantations energies. This supports the idea that after a certain implantation depth the o-Ps energy stops to decrease while the fraction of the non-thermalized part decreases with increasing implantation energy. The non-thermalized component biases the extrapolated energy from the TOF measurements. This effect has also been qualitatively discussed in [33] for implantation energies of 2 and 4 keV, on a sample with pore size similar to the one discussed in this thesis. In our case a quantitative estimation of the non-thermalized component is needed in order to isolate the thermalized part of o-Ps in the TOF spectrum. The idea is to perform a subtraction of the target and the non-thermalized fraction of the spectrum. First, we have to identify the minimal implantation depth L of the positron that produces thermalized o-Ps. This depth corresponds to the implantation energy where the thermalization curve of Fig. 8.6 starts to rise: 2keV for the C sample and 3 keV for the F sample. As will be shown later, the non-thermalized fraction is about a few percent of the total TOF spectrum but it strongly biases the extrapolated o-Ps energy: because of its higher energy the probability to reach the collimator slit is larger than for the ”slow” (thermalized) component. To estimate these non-thermalized contributions, we suppose that the shape of their TOF distribution, NT(t), is represented by the TOF spectrum obtained at a low implantation energy (2 keV and 3kV for C and F sample, respectively). At these energies 95% of the positrons are implanted at depths smaller than L2keV =200 nm and L3keV =350 nm, as calculated from a Makhovian stopping profile, taking into account the density and the thickness of the film. For a given implantation energy Ei, NT(t) is scaled down by the fraction of positrons implanted at depths smaller than L2keV and L3keV (open squares in Fig. 8.8). Fig. 8.9 shows all TOF components for the C sample at an implantation energy of 6 keV (lower two plots) and for the F sample at an implantation energy of 10 keV (upper two plots). The solid histograms in panels (a) and (c) correspond to the uncorrected, measured TOF spectra, the diamonds correspond to the target component, and the crosses represent the target plus the non-thermalized component. Panels 8.2. DETERMINATION OF THE O-PS ENERGY FROM THE TOF MEASUREMENTS125

Figure 8.6: Positronium emission energy < Ez > as a function of the implantation energy at a target temperature of 300K. The triangles correspond to the energy obtained from the data by subtracting the target component (TC subtraction) and for the squares the target and the non-thermalized component were subtracted (TC+NTC subtraction). For both data sets the lifetime and detection eﬃciency correction factor was applied. The inserts show the plateaus with the low-energy part of the spectra cut oﬀ. 126 CHAPTER 8. ANALYSIS OF THE TOF DATA

TOF spectra CTACl-TEOS 300K 3kV 4 keV Epithermal tails 5 keV Detected oPs (arbitrary unit)

0 100 200 300 400 500 Time [ns]

1000

Makhovian implantation profile 800 1 kV 3 kV 6 kV 600 Events 400

200

0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Depth (nm)

Figure 8.7: Top: TOF spectra at 3,4 and 5 keV positron implantation energy. The epithermal tails on the left of the TOF-peak decrease at larger implantation energy. Bottom: Makhovian stopping profile for different positron implantation energies. At higher energies the profiles are broadened. A fraction of positrons is always implanted near the surface, resulting in non-thermalized o-Ps to be emitted into the vacuum. 8.3. LOW TEMPERATURE MEASUREMENTS 127

(b) and (d) show the corrected TOF spectra attributed to decays of thermalized o-Ps in vacuum: target and non-thermalized components are subtracted. After correcting these spectra with the o-Ps lifetime and detection efficiency (as explained in 8.2.1), the mean energy < Ez > of the thermalized o-Ps emitted into the vacuum is determined. The results of the analysis after subtraction of the non-thermalized part are shown as the squares in Fig. 8.6. A clear plateau of the emission energy as a function of the implantation energy is observed starting from 3 keV for the C sample and from 5 keV for the F sample (Fig. 8.10). In terms of the diffusion time the plateau starts at 0.5 ns for the C sample and 2 ns for the F sample. These values are qualitatively in agreement∼ with the thermalization∼ time predicted by the models presented in Section 8.1. Moreover, as expected from the model described in Section 8.1.2, the minimal energy of the F sample is slightly smaller than the one observed in the C sample. The values of the minimal energy are higher than the thermal energy of 25 meV, expected if no confinement effects would be present. Fur- ther support to this idea∼ is given by the measurements performed at low temperatures (see next section). At implantation energies above 3 keV, the statistical error of the fit is typically 9 ns for the F and 6 ns for the C sample. The uncertainty on the determination of the slit± position ± of 0.1 mm results in a systematic error of the order of 1 meV in the determination of ± ± the Ps mean emission energy < Ez >. Thus, the combined statistical and systematic error is at a level of 2.5 meV for the F and 1.9 meV for the C sample. ± ±

8.3 Low temperature measurements

A complete set of measurements as a function of the implantation voltage has been performed at 50K as well. The comparison between 300K and 50K measurements is presented in Fig. 8.11. Also in this case a plateau in the energy distribution is observed. The values for the mean energy < Ez > in the plateau are smaller at 50K than the one at room temperature. However, this difference is very small (around 10 meV). This behavior further supports the idea of a minimal energy o-Ps can reach for a given confinement potential (pore size). Further measurements have been performed as a function of the sample temperature for a fixed implantation voltage: 6kV for the C sample and 10kV for the F sample. At these energies the majority of the positrons are still implanted within the films (see Fig. 7.7) and the emission energy is in the constant region (Figs. 8.10-8.11). The scan is performed in the temperature range between 50K and 400K. To understand the behavior of the value of the minimal energy as a function of the film temperature we developed a simple model that describes Ps in thermodynamic equilibrium at a temperature T in rectangular boxes (Section 8.3.2). 128 CHAPTER 8. ANALYSIS OF THE TOF DATA

0.8

C sample: Implanted fraction 0.6 x > 200 nm x < 200 nm Fraction 0.4

0.2

0 0 2 4 6 8 10 12 14 Implantation energy [keV]

0.8

0.6 F sample: Implanted fraction x > 350 nm Fraction 0.4 x < 350 nm

0.2

0 0 2 4 6 8 10 12 14 Implantation energy [keV]

Figure 8.8: Calculated fraction of positrons stopping at a depth smaller than L (open squares) and larger than L (black squres) obtained from Makhovian stopping proﬁles. L is the minimal implantation depth to produce thermalized positronium. Top: calculations for the C sample, bottom calculations for the F sample. The density and the thickness of the ﬁlm are taken into account. 8.3. LOW TEMPERATURE MEASUREMENTS 129

1000 900 data: CTACl-TEOS 300K-6kV 800 TC correction 700 TC + NTC correction 600 (a) 500 400 300 200 100

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

1000 900 Thermalized o-Ps spectrum 800 700 (b) 600 500 400 300 200 100

Detected oPs (arb. units) 0 100 200 300 400 500 600 700 time[ns]

1000 data: F127-TEOS 300K-10kV 800 TC correction TC + NTC corrections 600 (c)

400

200

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

1000

Thermalized o-Ps spectrum 800

600 (d)

400

200

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

Figure 8.9: TOF spectra from the C sample (upper two plots) and the F sample (lower two plots): The solid histogram in panels (a) and (c) correspond to the measured (raw) TOF spectra, the diamonds represent the target component, and the crosses the non-thermalized plus the target component. Panels (b) and (d) show the corrected TOF spectra attributed to thermalized o-Ps decays. 130 CHAPTER 8. ANALYSIS OF THE TOF DATA

1.8 0.14 1.6 0.12 1.4 0.1 0.08 1.2 0.06 1 0.04

> [eV] 2 3 4 5 6 7 8 9 10 z 0.8

0.4 CTACl-TEOS 300K 0.2

0 0 2 4 6 8 10 Implantation energy [keV]

Figure 8.10: o-Ps mean emission energy < Ez > as a function of the positron implantation energy for the C (dashed line) and the F sample (solid line) at 300 K, after the subtraction of the target and non-thermalized component (corresponds to the TC + NTC curves of Fig 8.6) The C sample shows a faster thermalization curve because of the smaller pore size. As expected, the minimal energy of the F sample is smaller than the one observed in the C sample. The insert shows the plateaus with the low-energy part cut oﬀ.

CTACl-TEOS 300K 0.1 CTACl-TEOS 50K > [eV] z

2 3 4 5 6 7 8 9 10

F127-TEOS 300K 0.06 F127-TEOS 50K > [eV]

z 0.04

Figure 8.11: Upper plot: Mean Ps energy < Ez > for implantation energies higher than 2 keV at 50 K and 300 K for the C sample. Lower plot: Mean Ps energy as a function of the implantation energies higher than 4 keV at 50 K and 300 K for the F sample. 8.3. LOW TEMPERATURE MEASUREMENTS 131

8.3.1 Comparison with the MC simulation and reconstruction of the total o-Ps energy As mentioned in Section 8.2, we reconstructed only the parallel component of the emission energy < Ez > from the TOF measurements. In order to obtain the total energy E0 of the o-Ps atoms when they leave the target surface, the angular distribution has to be known. It is important to note that in previous studies [124, 120], this problem has not been considered. The values obtained from the peak position of the TOF spectra have been interpreted as the total energy. Measurements of the samples performed with x-ray diffraction show no structure in the pore system and suggest that the direction of the pores at the sample surface (e.g for channel-like pores) are randomly distributed. This supports the idea that o-Ps is emitted from the target with a large angular spread. With MC simulations we tried to determine the angular distribution of o-Ps emitted from the target. This was done by comparing the measurements with the spectra generated with different angular distributions. In Fig. 8.12 the comparison between the MC simulation and the data for two different angular distributions is shown: o-Ps emitted isotropically and for a fixed angle perpendicular to the target surface. We observed a good agreement with o-Ps isotropically emitted from the target surface. The MC simulation includes all the components that compose the TOF spectra:

(1) the background from the accidentals;

(2) the target component;

(3) the non-thermalized component (this component is obtained by the experimental data as discussed in 8.2.3;

(4) mono-energetic o-Ps with isotropic angular distribution and ﬁxed angle (perpendicular to the target surface).

The o-Ps fraction corresponding to items 3 and 4 in the list are simulated according to the 142 ns fraction observed in the PALS measurements.

Another important point that has to be discussed is the total energy distribution of the o-Ps atoms that leave the target. The data presented in Fig. 8.10, show that above a certain implantation voltage the mean energy < Ez > stabilizes. We interpreted this plateau as a minimal energy due to the conﬁnement of Ps in the pore potential. Thus, one would expect that the o-Ps energy distribution is mono-energetic. The comparison between the data and the MC supports this idea, however, we observed that the spectra are better reproduced by introducing a small spread in the simulated energy. As shown in Section 8.1.2, the minimal energy as a function of the pore size (for square channel pores) is given by : ℏ2π2 E = . (8.19) min m2a2 132 CHAPTER 8. ANALYSIS OF THE TOF DATA

In the ideal case where the size of all the pores is the same, one would expect mono- energetic o-Ps. However, if we consider that there is a distribution in the side length of the pores we can introduce a spread in equation 8.19. The spread is introduced by assuming that the pore size is Gaussian distributed with a mean value a, and a standard deviation σpore: ℏ2π2 ESpread = 2 2 . (8.20) m G(a, σpore)

By analyzing the residuals obtained by subtraction MC spectra with different σpore from C F the data, we observed that for values of σpore = 0.3 nm for the C sample and σpore = 0.5 nm for the F sample the measurements are best reproduced. However, the main difference between data and MC simulation arises in the region around 80-100 ns. We attribute this difference to the approximation in the subtraction method, where the contribution of the non-thermalized o-Ps is underestimated, since only a spectrum of a fixed implantation energy is used for the correction of the non-thermalized component. Moreover, the shape of the Makhovian stopping profile in the region < L2keV and < L3keV for the 2 and 3 keV stopping profile is clearly different than the one at higher implantation energies. After these considerations on the angular and energy distributions, the MC simulation is used to reconstruct from the extrapolated < Ez > the total o-Ps energy E0. The idea is to generate with the MC simulations o-Ps spectra at different emission energies and then analyze these spectra in order to find a correction parameter ξ that allows to calculate the total energy of o-Ps from the parallel component obtained from the TOF peak analysis. A linear relation:

< E0 >= ξ < Ez >, (8.21)

with constant ξ was found. Fig. 8.13, shows the fit to the MC generated data. The ξ parameter for mono-energetic o-Ps emitted perpendicularly to the sample surface is around 1, as expected. This demonstrates that the analysis correctly extrapolates the parallel component of the Ps energy. For o-Ps leaving the surface isotropically (with an angular spread proportional to cos(θ) ) we observe that the ξ factor is 1.71. In Fig. 8.13 we also show that the ξ correction parameter is constant over a broad range of emission energies for a given angular distribution. Interestingly, we found a very weak dependence of ξ on the spread introduced in the pore size parameter σpore. This is an important point because, even if the spread in the energy distribution is not well known, the correction with the ξ factor can be applied without significantly biasing the reconstructed < E0 >. This has been cross-checked for values of σpore ranging from 0 to 0.7 nm. A variation of ξ smaller than 2% has been observed. It is important to note that the correction factor ξ extrapolated from the MC simulation also takes into account other important effects related to the propagation and detection efficiency of o-Ps in the beam pipe. In fact the effect of o-Ps colliding with the walls of the beam pipe is included in the MC simulation. Furthermore, the simulation takes into account the detector acceptance for o-Ps decays occurring outside the collimator slit. This is important because the probability for events decaying before or after the collimator aperture to be detected is not negligible. 8.3. LOW TEMPERATURE MEASUREMENTS 133

1000

data: CTACl-TEOS 300K-6kV

Monte-Carlo + NTC: =75 [meV] 500

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

data: CTACl-TEOS 300K-6kV

1500 Monte-Carlo + NTC

Eo-Ps=75 [meV]- no angular spread 1000

500

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

1000

data: F127-TEOS 300K-10kV

Monte-Carlo + NTC: =58 [meV] 500

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

data: F127-TEOS 300K-10kV 1000 Monte-Carlo + NTC

Eo-Ps=58 [meV]- no angular spread

500

Detected oPs (arb. units) 0 0 100 200 300 400 500 600 700 time[ns]

Figure 8.12: Upper plot: comparison between the data of the C sample at 6 keV and the MC simulating mono-energetic Ps emitted isotropically from the ﬁlm surface. Lower plot: comparison between the data of the C sample at 6 keV and the MC simulating mono- energetic Ps emitted perpendicular from the ﬁlm surface. In both cases, the measured target and non-thermalized components was added to the MC simulations. 134 CHAPTER 8. ANALYSIS OF THE TOF DATA

Fit: ξ = 0.14 z 0 no angular spread

0.12 isotropic emission

> [eV] ξ = 1.71 0 0.1

0.08

ξ = 1.01 0.06 Simulated

0.04

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Extrapolated [eV] z

Figure 8.13: The correction parameter ξ between the total o-Ps emission energy < E0 > and the parallel component < Ez > obtained from MC simulations.

8.3.2 Ps in thermodynamic equilibrium at a temperature T in the pore In order to understand the data obtained at low temperatures we developed an extension of the idea of the confinement effect proposed by [86], which includes the effect of the sample temperature in the case of a square channel. Similar to the extension of the Tau-Eldrup model with the RTE model, we include in the minimal energy model Ps excitation to higher levels. This idea has been triggered by the temperature dependence of the minimal emission energy [119] observed on both, C and F samples.

Statistical mechanics enables us to characterize the state of Ps conﬁned in a 1D inﬁnite potential well in contact with a reservoir at a temperature T by a statistical mixture of −En/kT stationary states ϕn > with weights proportional to e , where k is the Boltzmann constant and E the| energy of the state ϕ >. The corresponding density operator is then n | n written: ρ = Z−1e−H/kT (8.22)

where H is the Hamiltonian operator, and Z is the partition function:

Z = T re−H/kT (8.23)

which insures that: T rρ = 1 (8.24) 8.3. LOW TEMPERATURE MEASUREMENTS 135

The energies E for a state ϕ > are equal to n | n h2n2 En = 2 (8.25) 8mPsa where h is the Plank constant, mPs the positronium mass and a the pore size. According to Eq. 8.22 the partition function can be written as:

∞ − h2n2 2 /kT Z = e 8mP sa (8.26) n=1 X The mean value of the Hamiltonian can be calculated with:

= Tr(Hρ)= Z−1Tr(He−H/kT ) (8.27)

Writing the trace explicitly in the ϕ > basis, we obtain: | n ∞ 2 2 − h2n2 −1 h n 2 /kT = Z e 8mP sa (8.28) 8m a2 n=1 Ps X To calculate the quantity, we diﬀerentiate both sides of Eq. 8.26 with respect to T

∞ 2 2 − h2n2 dZ h n 1 2 /kT = e 8mP sa (8.29) dT 8m a2 2 n=1 Ps kT X We see that: 1 dZ = kT 2 (8.30) Z dT To calculate the mean value of the energy for the 3D case we can use

= + + (8.31)

To calculate and one can substitute the pore side length a in Eq.8.26 with b and c. For the 3D case of Ps confined in a rectangular pore, one obtains: 1 dZ(a) 1 dZ(b) 1 dZ(c) = kT 2 + + (8.32) Z(a) dT Z(b) dT Z(c) dT For the case of a cubic box one can set < Hx >=< Hy >=< Hz >. When Ps is emitted into the vacuum, the confinement energy converts into kinetic energy. To compare the experimental data with the model described above one has to use the correction ξ described in Eq. 8.21. A detailed scan shows that the mean Ps energy (< E0 >= ξ < Ez >) decreases with the sample temperature to a minimum level (see Fig. 8.14). The solid lines in Fig. 8.14, represent the fits to the data using Eq. 8.32 where the pore side lengths (a,b,c) are left as free parameters. The fit was repeated assuming cubic box pores and the results are shown as the dashed lines in Fig. 8.14. As one can see, the fit to the data suggest that 136 CHAPTER 8. ANALYSIS OF THE TOF DATA

0.14

F127-TEOS 0.12 CTACl-TEOS RECTANGULAR PORES 0.1 CUBIC BOX PORES

0.08 o-Ps mean energy [eV] 0.06

0.04

50 100 150 200 250 300 350 400 450 Sample Temperature [K]

Figure 8.14: Positronium mean energy < E0 > as a function of the mesoporous film temperature. Those results are obtained at 6 keV for the C (triangles) and 10 keV for the F sample (squares). The solid lines are the results of a fit of Eq.8.32 to the data with the pore side lengths a,b,c left as free parameters. The dashed lines were obtained fitting with Eq.8.32 with a single free side length free a = b = c (cubic box pores).

the pores of both samples are better modeled as rectangular pores than as cubic boxes. The pores side lengths obtained in this way are reported in the Table 8.1. In particular, the ﬁt of the experimental data with the function described in Eq. 8.32, suggest that the pores seem to have a channel structure (see solid line in Fig. 8.14). The pore side length in one direction (c) obtained from this ﬁt is much longer than the substrate thickness. This could indicate that the axis of the pore channel is oriented parallel to the sample surface. This pore structure was also observed in samples produced using the F127 porogen by transmission electron microscopy (TEM) [126, 127].

According to the quantum mechanical model for Ps thermalization [86], the lowest possible index n in the sum of Eq. 8.26 could differ from 1 for cubic pores if the level separation of two close Ps energy levels is higher than the maximum momentum that a single phonon can exchange. Fits performed with different n>1 did not improve the results, supporting the calculation that the pores do not have a cubic box structure. As proposed in [118], to compare the side lengths obtained from the temperature fit with the ones extracted from the PALS measurements, one has to add to the extrapolated pore size from the fit twice the parameter δ, which is the interaction overlap region of the Ps wave function with the electrons on the pore internal surface (Section 7.2.2). For the C sample one obtains a square channel of 2.7 0.5 nm while for the F sample the fit gives a rectangular pore size of 2.9 0.6 nm by± 3.6 0.6 nm. Both values are systematically ± ± 8.3. LOW TEMPERATURE MEASUREMENTS 137

Table 8.1: Comparison of the pore sizes obtained from the PALS measurements and from the ﬁt of the Ps mean emission as a function of the sample temperature (see Fig. 8.14) for both cubic box (BOX) and rectangular pores (RECT). Minimal energy < E0 > of Ps is taken at T=50 K. The errors are the combined statistical and systematic error. C Sample TOF PALS a [nm] 3.3 0.1 4.2 0.5 BOX ± ± (a, b)RECT [nm] (2.7 0.5, 2.7 0.5) (3.1 0.5, 3.1 0.5) < E > [meV]± 73 4 ± ± ± 0 ± F Sample TOF PALS aBOX [nm] 4.1 0.1 6.4 0.5 (a, b) [nm] (2.9 0.6,± 3.6 1.5) (3.3 0.5,± 4.1 0.5) RECT ± ± ± ± < E > [meV] 48 3 0 ± lower than the pore sizes extracted by the lifetime method (PALS), where we obtained 3.1 0.5 nm (Table 8.1) for the C sample. For the F sample 3.3 0.5 nm by 4.1 0.5 nm were± obtained from the PALS measurements (by applying the RTE± model to calculate± the measured lifetime of 74 ns, assuming the ratio a/b which was extrapolated from the ﬁt shown in Fig. 8.14). Nevertheless, considering the approximations made in the model, the assumption that the pores can be treated as rectangular boxes and the uncertainty in the determination of the pore size, we conclude that the results summarized in Table 8.1 are still in reasonable agreement.

8.3.3 The P32 sample The observation of a minimal o-Ps emission energy in samples with ”small” pore sizes triggered the need to investigate samples with larger conﬁnement potentials in order to achieve colder o-Ps. A sample with pore diameter around 32 nm was produced at Ecole Politechnique 2. The technology used for the production of this type of sample is diﬀerent from the one used for the C and F samples. In this case the silica skeleton is mixed with spheres of 30 nm and later evacuated in the same way as explained in Section 7.1 3. The porosity is determined by the amount of spheres added to the silica skeleton. The maximum layer thickness that can be produced with this technique is around 300 nm. A simple extrapolation from the measurements performed on the C and F sample shows, that with a 32 nm diameter pore, the implantation depth needed for a complete thermalization should be larger than 1300 nm. An attempt of growing 4 layers with this technique has been

2Laboratoire de Physique de la Matire Condense, cole PolytechniqueCNRS, UMR 7643, 91128 Palaiseau, France 3This type of sample is still in a development phase and thus, no details about the preparation procedure were given. 138 CHAPTER 8. ANALYSIS OF THE TOF DATA

made. However, the measurements performed on this multilayer sample showed that the interface for the different layers acted as blocking barrier for the o-Ps. This was supported by PALS measurements that showed the same 142 ns fraction for the 300 nm sample and the multilayer sample. Even if a solution would be found to make the interface between the different layers transparent, the implantation energy needed to achieve thermalized o-Ps would be very large. This implies a very broad implantation profile that leads to small thermalized fractions in vacuum.

8.3.4 Conclusions We show that due to the confinement of Ps in the pores, the emission energy into vacuum has a minimal value that depends on the pore size and very weakly on the target temperature. As expected, the minimal energy is higher for the sample with smaller pores and this constant value is reached at a lower positron implantation energy. The results are in fair agreement with a model of Ps in rectangular boxes in thermal equilibrium with the sample. The measured minimal energy at 50 K for the C sample was found to be 73 4 meV while for the F sample it is 48 3 meV. These experimental results provide a solid± ground to ± understand how to produce Ps at lower temperature and could serve to develop a more realistic model to interpret the data. An idea for the future development of e+ > Ps − converters would be to use multilayer samples with combined porosity. A first attempt could be to produce a 400 nm thick C layer and deposit on its surface a layer of P32 porous material. As observed in our measurements the o-Ps yield of the C sample is very good. Moreover, small pores, as the ones of the C samples, guarantee a fast o-Ps slowing down within few hundreds of nanometers. The technology of growing different layers with different pore sizes has never been investigated. The fact that the multilayer technique does not work for films of the same pore size does not exclude that, in a transition from a smaller to a larger pore size, this barrier effect would not be observed. The interface between small and large pores (see Fig. 8.15) would intuitively work better because:

the large pore would cover the surface of many small pores on the surface of the • deeper layer;

the potential energy of o-Ps decreases at lower density materials. In the same way • as o-Ps is ejected very efficiently from the silica matrix (having sub-nanometers pore sizes) into the mesopores, the interface between smaller and larger pore layers could act as a potential decreasing step. This would theoretically push o-Ps in the direction of the large pore layer and act as a ”mirror”, reflecting o-Ps which is diffusing back towards the small pore layer.

This could result in a very efficient “cold” o-Ps converter for the new generation o-Ps experiments described in Chapter 10. For example, in the case where a P32 layer is used as an outer film, no confinement effect would be observed down to o-Ps temperatures of few a K. 8.3. LOW TEMPERATURE MEASUREMENTS 139

Figure 8.15: Sketch of a multilayer sample with combined porosity. (a) The interface between two layers of the same sample type acts as a blocking barrier for o-Ps (b) For two layers, one with a small pore size (e.g. a C sample), and the other with a large pore size (e.g. P32), the blocking eﬀect might be suppressed. 140 CHAPTER 8. ANALYSIS OF THE TOF DATA Chapter 9

Conclusions

In Chapter 3, the design of an experiment for the search for mirror-type Dark Matter via o-Ps invisible decays in vacuum is presented. The experiment is based on the ETHZ slow positron beam used to form o-Ps in a vacuum cavity combined with the BGO calorimeter used in our previous search for o Ps invisible decay in aerogel (see Chapter 2). The diﬀerent parts that compose the experiment− → have been studied in detail (Section 3.1), these are:

the bunched slow positron beam (Section 3.1.1) • the target for eﬃcient orthopositronium production near thermal energy (Section • 3.1.2)

the vacuum cavity to conﬁne the o-Ps (Section 3.1.3) • the positron appearance tagging system with a high S/N ratio, based on a high • performance micro-chanel-plate (MCP) described in Section 3.1.4, combined with the positron bunching

the gamma detector, an almost 4π BGO crystal calorimeter (ECAL) surrounding the • vacuum cavity for eﬃcient detection of annihilation photons to search for invisible o-Ps decays (Section 3.1.6).

A new idea to confine o-Ps in a region of highly uniform detection efficiency is presented in Section 3.1.3. This was achieved by employing a 20 nm carbon film in which the few keV positrons can pass through while even the most energetic o-Ps is blocked. Furthermore, with this method an additional signature for the presence of a positron in the formation cavity is added to the trigger scheme by using the coincidence between the SE from the target and the ones produced in the carbon foil. In order to test this idea an experimental set-up has been constructed (Section 3.1.4). In Section 3.2, the possible sources of background have been investigated with the help of MC simulations. It has been demonstrated that the background source generated by the positron backscattering at the carbon foil (Section 3.2.2) and the fast o-Ps formed at the carbon foil (Section 3.2.1) is suppressed

141 142 CHAPTER 9. CONCLUSIONS

by a factor 5 10−3 with a corresponding conicidence trigger eﬃciency of 4 10−2 (relative × × to the single SE rate from the target alone). The goal of the experiment is to reach a sensitivity in the branching ratio of Br(o Ps invisible) 10−7 to confront the annual modulation signal observed by DAMA/NaI− and→ DAMA/LIBRA≃ (with 8.2σ signiﬁcance) with Mirror Dark Matter scenarios.

In order to select an appropriate e+ Ps converter for the invisible decay search experiment a system, based on the ETH→ Z¨urich slow positron beam, to study the o-Ps emission from an interconnected porous target has been constructed :

a large solid angle PALS detector used for the evaluation of the fraction of the o-Ps • emitted into the vacuum and the characterization of the pore structure;

a Ps-TOF spectrometer used to study the emission energy and angular distribution. • The performance of the PALS and TOF detectors is presented in Chapter 6. Both of these detectors are based on the secondary electron trigger mode described in Section 5.4.2. In order to perform systematic studies on different targets several efforts have been made to improve the low energy beam intensity (see Chapter 5). This was done by increasing the source intensity and improving the moderator efficiency. A special vacuum chamber for a source with an intensity of 380MBq was constructed. The technical details of the source chamber are presented in Section 5.1. With these modifications the slow positron intensity was increased from 10e+/s in 2006 to 2.5 104e+/s in 2009. Furthermore, the magnetic transport system was also optimized in order× to compress the beam size. The slow positron beam target chamber was equipped with a cryocooler that allows to perform measurements in a temperature range of 50-400K. In Chapters 7 and 8, the results of the measurements performed on mesostructured silica films having different pore sizes are presented. In some targets, a fraction as high as 40 % of the positrons implanted in the film was converted into o-Ps and emitted from the surface. Furthermore, it has been shown that due to quantum mechanical confinement in the pores, the Ps emission energy into vacuum has a minimal value. As expected, the minimal energy is higher for the sample with smaller pores and this constant value is reached at a lower positron implantation energy. Chapter 10

Future perspectives

A deep understanding of the positronium formation mechanism and emission into vacuum is essential for any experiment that aims to study the o-Ps basic properties. This also motivated us to design and construct the apparatus presented in Chapter 6 to precisely investigate ortho-positronium (o-Ps) formation in vacuum. If a high fraction of positronium at controllable temperature would be available, a new generation of experiments could be performed:

(1) A measurement of the 1S-2S transition providing precise QED, CPT and an antigravity test.

(2) Anti-hydrogen formation via the charge exchange process with Ps.

(3) Precise test of bound state QED measuring the o-Ps decay rate with a precision of tens of ppm.

(4) Bose-Einstein condensation of o-Ps .

10.1 1S-2S transition of ortho-positronium

In 1993 S. Chu and A. Mills used o-Ps at 600K to perform their measurement of the 1S-2S transition by two photon excitation of o-Ps with a precision of 2.6 ppb (1233 607 216.4 3.3 ± MHz) [128]. Having a source of colder positronium will result in a higher statistics since the excitation probability is inversely proportional to the o-Ps temperature. Therefore, a better line splitting would be possible reducing the statistical error of the measurement. Furthermore, the sources of line broadening which introduce systematic eﬀects would be suppressed for the following reasons:

The second order Doppler broadening is proportional to √T . • The time of ﬂight broadening is also proportional to √T . • 143 144 CHAPTER 10. FUTURE PERSPECTIVES

The laser intensity could be reduced with respect to the previous experiment because • of the higher excitation probability. This would suppress the dynamic stark shift (so called AC stark shift) and thus, a better line splitting would enhance the precision of the measurement.

If an improvement in the precision of the 1S-2S energy diﬀerence of a factor 10, with respect to the previous measurement, would be achieved, it would result in the most stringent test of CPT in the leptonic sector that is now provided by the anti-protonic helium. The deviation of the positron/electron mass ratio will be limited to 10−10. Furthermore, such a precision will provide a model-independent limitation on antigravity [129] [130]. One should be able to observe a clear signature of antigravity as an annual variation of the ratio of the 1S-2S transition energies in hydrogen and positronium (or antihydrogen) due to the change in distance between the Sun and the Earth, which changes by about 5 million kilometers during the year. That is related to a change in the gravitational potential in fractional units by: (U(r ) U(r ))/c2 =3.2 10−10 (10.1) max − min × The shift of all material clocks (including hydrogen) is a blue shift for r = rmax with respect to r = rmin, while a positronium clock would experience no shift and the antihydrogen clocks would be red shifted.

10.2 Ps and Antihydrogen

As antihydrogen has now been created [131] and a number of parameters of the produced atoms determined [133], the next steps of investigation with antihydrogen will focus on the long range goal of studying the spectroscopy (1S-2S transition, hyperﬁne splitting) and the gravitational interaction of antihydrogen. The necessary technical steps for achieving these goals are under development [134]-[135]. The two mechanisms for low energy antihydrogen production used in the current experiments are the radiative recombination (SRR) [131]- [133]: p¯ + e+ H¯ (10.2) → and the three-body recombination (TBR):

p¯ + e+ + e+ H¯ + e+ (10.3) → The cross-sections for these processes are inversely proportional to the relative velocity between the antiproton and the positrons [132]. For example, supposing thep ¯ at rest and the positron in a 15 K environment as in the ATHENA experiment [131] the cross-sections −18 2 −17 2 are of the order of σSRR 10 cm and σT BR 10 cm , respectively. In both reactions, the antihydrogen is produced≃ isotropically. ≃ However, it was pointed out that a process involving positronium [137]:

Ps +p ¯ H¯ + e− (10.4) → 10.3. BOSE-EINSTEIN CONDENSATION OF O-PS 145 is more eﬃcient. The cross-section is about σ 10−15cm2 [136]. These calculations were ≃ conﬁrmed in an experiment using the charge conjugate reaction of Equation 10.4 [145] :

Ps + p H + e+ (10.5) → Moreover, if the positronium is excited in a Rydberg state via laser excitation [138]:

Ps∗ +p ¯ H¯ ∗ + e− (10.6) → the cross section increases with n4, where n is the principal quantum number of the Ps. For Ps in an excited state with n = 30 one can estimate that the cross-section will be about σ 8 10−8cm2. Therefore, one could expect that this process would yield a more substantial≃ × amount of antihydrogen that could be trapped. A positronium cloud could be used as a target for the antiprotons, thus, one can create a beam of antihydrogen that will have the same direction as thep ¯ because thep ¯ are much heavier than the positronium atoms. Furthermore, the antiatoms are produced in Rydberg states in a controlled way since their excitation level depends on the excitation level of the positronium. In addition, because Rydberg atoms are sensitive to electric ﬁeld gradients, the velocity of the antihydrogen beam could be changed accelerating or decelerating the antiatoms with a time dependent inhomogeneous electric ﬁeld [139]. Another very interesting feature of using positronium is that H¯ + can be produced with the reaction:

Ps + H¯ H¯ + + e− (10.7) → The predicted cross-section for this reaction is of the same order as for the three-body recombination reaction of Equation 10.3 [140]. Even though, this is much lower than for the reactions Equation 10.4 and 10.6, it would be much easier to trap the positive antihydrogen atoms in a usual ion trap and then cool them by sympathetic cooling (i.e. collision of the atoms in a buﬀer gas) using ordinary ions [141] [142]. The trapped H¯ + could then be used for gravity measurements of antimatter as proposed in [143, 141] .

10.2.1 Precise o-Ps decay rate measurement As mentioned before, a new more precise measurement of the o-Ps lifetime could provide a very stringent test of bound state QED. Currently, the experimental uncertainty for the determination of the o-Ps decay rate is at 200 ppm level; this exceeds the theoretical uncertainty (1 ppm level) by two orders of magnitude.

10.3 Bose-Einstein condensation of o-Ps

A step further would be to achieve Bose-Einstein condensation (BEC) of Ps [144]. This will allow to explore for the ﬁrst time the eﬀects of the collective properties of a matter- antimatter system. BEC of a quantum gas is achieved when the de Broglie wavelength of the particles is comparable to their spacing. The fundamental condition in terms of 146 CHAPTER 10. FUTURE PERSPECTIVES

104

103 BEC transition temperature [K]

102

102 103 Confining cavity radius [nm]

Figure 10.1: BEC transition temperature vs conﬁning cavity radius assuming 108 positronium atoms.

temperature T and density n (=N/V, where N is the number of atoms in a confining volume V) is given by: 2 2π~ 2 T < n 3 (10.8) 1.897 mk · B where m is the atom mass, kB the Boltzmann constant and ~ the Planck constant. The low mass of Ps makes the critical BEC temperature much higher than for hydrogen or alkali metals of the same density. As one can see from Fig. 10.1, if 108 positronium atoms could be confined in a spherical cavity of about 1 µm diameter, they would condensate at room temperature. This could be feasible thanks to the recent advances in positron accumulation and positron production [141, 146] if a very efficient Ps converter at room or lower temperature would be available. Bibliography

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I would like to express my deep gratitude to Prof. Dr. Andr´eRubbia not only for his guidance during this years but also for giving me the unique possibility to make my PhD Thesis working on this wonderful project. I was given the chance to work on a project of which I could contribute to all the components, the design, the construction, the simulation, the data acquisition, the data analysis.

I would like to thank Prof. Dr. G¨unther Dissertori as a co-referee of this thesis.

My sincere gratitude goes to Prof. Dr. Paolo Crivelli for his guidance during these years of work, for his support and for his endless help in all aspects related to this thesis. I would like to thank so much Patrice Perez and Laszlo Liskay for all the useful discussions, encouragement and for the many visits at the beam. I’m deeply in debt to Dr. Andreas Badertscher for his terrific work in helping to correct this thesis. I’m in dept with Leo Knecht for all the help in the mechanical part of the project. Rosa Bächli for taking care of all the administrative aspects and helped me to overcome to my intrinsic problem of always being late with administrative issues. Furthermore, I cannot forget my formers colleagues Anselmo, Rico, Marcello, Lilly...without forgetting the new colleagues: Pippo-Filippo, Devis, Lukas, Ursina, Claudia, Claudia, Alessandro and last but not least my office colleague in the last period of my stay at CERN Federico Padrino. A big hugh goes to my friends Nando, Giules, Alan & Sonia (they always been ready to partecipate to my thesis defense ;-) ) , Bruno, CaD, Peppe, Mamo, Pol and Robbo for their encouragements. A special thanks goes to my sweet Patty for her moral support and for the many kilometers she had to drive for visiting me in Geneva! Finally, I would like to warmly thank my parents, Margherita and Ino Gendotti, who always supported and encouraged me throughout my education. My sister Camilla and my brother Adamo (always welcome in my flat for his working visits :-) ) that have been extremely important for me in these years of work. Thanks once more to all the people listed here, this thesis could not have been done without them.