Detector for positronium temperature measurements by two-photon angularcorrelationG G Cecchini A C L Jones M Fuentes-Garcia D J Adams M Austin E Membreno and A P Mills

Citation Review of Scientific Instruments 89 053106 (2018) doi 10106315017724View online httpsdoiorg10106315017724View Table of Contents httpaipscitationorgtocrsi895Published by the American Institute of Physics

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REVIEW OF SCIENTIFIC INSTRUMENTS 89 053106 (2018)

Detector for positronium temperature measurementsby two-photon angular correlation

G G Cecchini1a) A C L Jones1 M Fuentes-Garcia1 D J Adams2 M Austin3E Membreno1 and A P Mills Jr11Department of Physics and Astronomy University of California Riverside California 92521 USA2College of Natural and Agricultural Sciences Machine Shop University of California RiversideCalifornia 92521 USA3Department of Physics Marquette University Milwaukee Wisconsin 53233 USA

(Received 29 November 2017 accepted 16 April 2018 published online 10 May 2018)

We report on the design and characterization of a modular γ-ray detector assembly developed foraccurate and efficient detection of coincident 511 keV back-to-back γ-rays following electron-positronannihilation Each modular detector consists of 16 narrow lutetium yttrium oxyorthosilicate scintilla-tors coupled to a multi-anode Hamamatsu H12700B photomultiplier tube We discuss the operationand optimization of 511 keV γ-ray detection resulting from testing various scintillators and detec-tor arrangements concluding with an estimate of the coincident 511 keV detection efficiency for theintended experiment and a preliminary test representing one-quarter of the completed array Publishedby AIP Publishing httpsdoiorg10106315017724

I INTRODUCTION

To realize the goal of producing identifying and studyinga positronium (Ps) Bose-Einstein condensate (BEC)1 we willneed to produce a dense cold spin polarized source of Ps Fora 2D BEC of Ps at areal density n2D = 1012 cm2 or a 3DBEC at density n3D = 1018 cm3 the critical temperature forcondensation is T c sim 15 K23

To accomplish this pulses of sim108 positrons from anaccumulator4 compressed by a rotating electric field56 atsim50 MHz (to a plasma 1 mm in diameter) will be accel-erated and temporally bunched7 to sim10 ns FWHM and thenextracted from the accumulator through a small aperture ina micro-metal shield89 The beam will then be electrostaticallyfocused to a radius of lt01 mm onto a transmission re-moderator10 After about 15 of the positrons emerge fromthe re-moderator foil with low energy they will be acceleratedand electrostatically focused again a process known as bright-ness enhancement11 to a sim10 microm diameter spot at the targetwhere they become trapped within a cavity sim10 microm in diam-eter and 10ndash100 nm deep The final areal density at the targetwill be 2 times 1013 cm2 about 100 times greater than previouslyachieved12

Once implanted in the target up to 50 of the positronsmay be expected to form Ps at cryogenic temperatures1314

Roughly one-quarter of the Ps atoms formed are in the 11S0

state and are rapidly (τ = 125 ps) lost to annihilation Theremaining three-quarters form 13S1 with a vacuum lifetimeof 142 ns The high-density of Ps expected in the cavitywill lead to spin-exchange quenching15 and di-positroniumformation16 reducing the amount of triplet Ps until theseprocesses are exhausted leaving pure m = 1 triplet Ps12

a)Author to whom correspondence should be addressed gabrielcecchiniucredu

The combination of processes leading to rapid annihilationmeans that the delayed signal that we hope to observe willcome in addition to a substantial prompt background of511 keV γs however the prompt signal will rapidly decay sothat aftersim40 ns we will be able to unambiguously detect coin-cident annihilation γs from long lived triplet Ps quenched17

by a delayed 10 ns 1 T pulsed magnetic field transverse to thepolarization direction of the triplet Ps

As Ps will be confined within a cavity probing the tem-perature of the atoms cannot be trivially achieved via spectro-scopic techniques (eg measuring the Doppler width of the1Sndash2P transition of Ps emitted from the target into vacuum18)and the Doppler spectroscopy of Ps within a cavity is furthercomplicated by saturation and line-narrowing19 Rather the Pstemperature will be measured using the Angular Correlationof Annihilation Radiation (ACAR)2021 method to measure themomentum of Ps atoms at the instant of annihilation Account-ing for the non-zero momentum of a Ps atom at the time ofannihilation the annihilation photons with momenta~p1 and~p2

deviate from collinearity by the angle θ asymp pPsperpmec where pPsperp is

the magnitude of the Ps momentum component perpendicularto the line joining the difference of the momenta of the nearlycollinear photons

For Ps cooled to 10 K the FWHM of the angular distribu-tion is sim014 mrad so the angular resolution of the apparatusneeds to be about 01 mrad In this paper we describe the con-struction and testing of a modular detector assembly whichwill form the basis of the detector arrays necessary for theplanned experiment In Sec II we present the design and con-struction of the assembled detector and characterize the crosstalk between neighboring channels In Sec III we presentdetails of a data analysis routine and the optimization andcharacterization of its performance Preliminary data collectedwith a one-quarter scale version of the final experimentalarrangement are presented in Sec IV

0034-6748201889(5)0531068$3000 89 053106-1 Published by AIP Publishing

053106-2 Cecchini et al Rev Sci Instrum 89 053106 (2018)

II DESIGN AND CHARACTERIZATIONOF THE DETECTOR ASSEMBLY

The planned experiment will involve two detector arraysseparated by 20 m positioned diametrically opposite andequidistant from the target chamber Each array contains 19230 times 22 times 2 mm3 lutetium-yttrium oxyorthosilicate dopedwith 005 cerium [Lu18Y02SiO5Ce (LYSOCe hereafterldquoLYSOrdquo for short)] scintillator channels We anticipate onedelayed detected 2γ annihilation event per 74 times 104 singletPs atoms annihilating immediately at the target For pulsesof sim107 positrons this would result in a prompt signal ofsim1 single γ per shot per channel In developing the detec-tor we reviewed several possible candidate scintillators leadtungstate (PbWO4) LYSO purchased from Shanghai ProjectElectronic Technology Company and thallium-doped sodiumiodide (NaI(Tl)) as well as a plastic scintillator (EJ-230) pur-chased from Eljen Technology In the following discussionwe describe the characteristics of several different scintilla-tors in various configurations and describe the final assemblyproduced

A Testing of scintillators and mountingarrangements

To test and characterize a modular detector it is first posi-tioned sim5 cm away from a 13 microCi 22Na positron source Pulsewaveforms from the test assembly are recorded when detectedin coincidence (∆t le 20 ns) with the unambiguous observa-tion of a 127 MeV γ in a NaI(Tl)-based detector orientedperpendicular to the test assembly The combination of a weaksource and detection coincident with the birth of a positrongreatly reduces the observed background resulting from cos-mic radiation and scintillator self-signal (as seen in LYSO)We average over sim103 waveform records to generate compos-ite pulses with high signal-to-noise ratios allowing a precisecomparison of the performance of each test system An exam-ple illustrating three such measurements comparing a varietyof LYSO arrangements is plotted in Fig 1

Each scintillator tested was approximately three absorp-tion lengths long yielding a sim95 chance of interaction for511 keV γs entering the scintillator along its longest axisFor the inorganic scintillators LYSO and PbWO4 which have511 keV attenuation lengths of sim1 cm the scintillators mea-sured 30 times 22 times 2 mm3 The plastic scintillators with anattenuation length of sim10 cm measured 300 times 22 times 2 mm3Scintillators were coupled to a Hamamatsu H12700B 64 anodephotomultiplier tube (PMT) for testing

The energy deposited from a γ-ray can be inferred fromthe resulting pulse area calibrated from the measured pulsearea spectrum as indicated in Fig 2 To make a fast and accurateestimate of the energy of a given γ detection pulses are fitwith a simple function with characteristic rise and decay timeswhich are derived from the composite pulses as illustrated inFig 1 Table I lists a summary of the fitted rise and decaytimes of the different scintillator materials tested LYSO wasselected for its large light output and moderate rise time twoimportant qualities for multi-peak detection

When testing LYSO it was found that the observed life-time (sim46 ns) was longer than 40 ns reported in the literature25

FIG 1 Mean photopeak signals (black line) along with a fit (red dashed line)from various LYSOCe scintillator arrangements coupled to a HamamatsuR1924A PMT Fits are a product of an exponential decay and an error func-tion Pulses presented include (a) a block of LYSOCe (15 times 15 times 30 mm3)(b) a sliver of LYSOCe wrapped in 99 reflective enhanced spectroscopicreflective tape (2 times 22 times 30 mm3) and (c) another similarly sized sliver ofLYSOCe left bare

This led us to investigate LYSO response times and energyresolutions for various scintillator geometries Annihilationenergy spectra were generated using two similar HamamatsuR1924A single channel PMTs each coupled to one of the twodifferent sizes of LYSO a block measuring 30 times 15 times 15 mm3

and a thin rectangle measuring 30times 22times 2 mm3 coupled to thePMT at the 2 times 22 mm2 face Typical 511 keV pulse areas areaveraged and analyzed for signal pulse rise and decay timesBoth LYSO samples exhibited similar rise times decay timesand energy resolutions but it was noted that the thin LYSO pro-duces smaller pulses There are several possible explanations

FIG 2 Distribution of pulse areas from a 30 times 22 times 2 mm3 LYSOCe scin-tillator The LYSOCe sample is covered in ESR film on its sides and coupledon its 22 times 2 mm2 face to a Hamamatsu H12700B PMT biased at 900 V Thelargest peak seen at a low pulse area is a consequence of cross talk betweenneighboring channels We set a discriminating limit for genuine data equiva-lent to 14 Ep The plateau between the two peaks is attributed to the Comptonscattering within a scintillator with the Compton edge Ec = (23) Ep The peakat 8 nV s results from a full absorption of 511 keV γs and has a resolution∆EEp of sim16 FWHM

053106-3 Cecchini et al Rev Sci Instrum 89 053106 (2018)

TABLE I Rise and decay times measured from data contributing to the photopeak presented in Fig 2 Data givenwithout error estimates are from Ref 22 Rise times indicate the average time elapsed for a pulse to rise from 12to 88 of the maximum amplitude The NaI(Tl) scintillator was mounted to a Hamamatsu R1924A PMT whilethe other scintillators were coupled to a Hamamatsu H12700B PMT We list here fundamental properties of thescintillators pertinent to the optimization of the detector light output in photons per keV attenuation length (λ)and relative refractive index (nr )22ndash24 nr is the ratio of the scintillatorrsquos index of refraction relative to that of theborosilicate window of the PMT (nb sim 153)

Scintillator Rise time (ns) Decay time (ns) PhotonskeV λ (cm) nr =n

nb

LYSOCe 290 plusmn 001 463 plusmn 011 32 11 12PbWO4 110 plusmn 003 635 plusmn 003 05 14 146EJ-230 094 plusmn 002 349 plusmn 012 2 10 066NaI(Tl) 591 plusmn 021 250 38 25 123

for this UV light bounces fewer times on average within theblock sample leading to higher efficiency as compared to thethin scintillator sample Also the block sample covers a greaterportion of the center of the PMTrsquos face ensuring that virtuallyall light incident on the glass face is detected Energy spectrawere recorded with a bare scintillator surrounded by flat blackpainted isolators or wrapped in a reflective film The reflectivefilm Vikuiti Enhanced Specular Reflector (ESR)26 purchasedfrom 3M Optical Systems is a 65 microm thick non-metallic100 polymer that has a minimum 98 reflectance across thevisible spectrum The results of these tests are summarizedin Table II Bare thin scintillators exhibited the narrowest risetime (29 ns) but longer decay time (46 ns) Using black sur-faces rather than ESR leads to a comparable rise time (31 ns)and a shorter decay time (43 ns)

In Fig 2 a typical energy spectrum is plotted with datataken from a 30 times 22 times 2 mm3 LYSO scintillator The LYSOis wrapped in an ESR film with no adhesive or coupling(ie with an air gap) and then the LYSO crystal is coupledon its 22 times 2 mm2 face to a Hamamatsu H12700B 64 anodePMT with polydimethylsiloxane (PDMS) ldquogluerdquo27 Individ-ual channels are separated by 4 mm thick tungsten isolatorsThe PMT was biased at 900 V for these tests A peak inthe plotted pulse area spectrum at 8 nVs is attributed to a fullabsorption of 511 keV γs and is known as the photopeak (Ep)or full energy peak A Gaussian fit to the peak indicates a meanphotopeak pulse area of 808 plusmn 001 nVs with a full width athalf maximum (FWHM) energy resolution of sim16 (∆EEp)The photopeak area accounts for sim45 of the total counts

TABLE II Tabulated LYSOCe characteristics for various geometries andsurface coatings LYSOCe blocks and thin rectangles measure 15 times 15 times30 and 2 times 22 times 30 mm3 respectively Data are collected with scintillatorsmounted on a Hamamatsu R1924A PMT Data presented here are collectedfrom isolated photopeak signals

Scintillator Rise time (ns) Decay time (ns) Energy resolution

BlockBare 323 plusmn 002 4648 plusmn 038 104 plusmn 01

ThinBare 290 plusmn 001 4630 plusmn 011 100 plusmn 02Black cover 310 plusmn 002 4309 plusmn 040 130 plusmn 03ESR film 308 plusmn 002 4336 plusmn 039 121 plusmn 04

after correcting for cross talk attributed to scattered light fromneighboring scintillators which causes the large peak locatedat sim10 of the photopeak centroid A typical photo-peakevent resulting from a 511 keV γ produces a pulse witha 345 mV amplitude Assuming that the pulse area scaleslinearly with γ-energy deposited the Compton edge whichoccurs at Ec = 340 keV is found at sim539 nVs and corre-sponds to a sim230 mV amplitude There is nonlinearity in theenergy scale relating the observed pulse area and the energydeposited by an incident γ-ray described in Ref 28 Howeverin the energy range from 340 keV to 511 keV the correc-tion is only sim3 and is neglected here The plateau belowthis cutoff is due to the Compton scattering of γs within thescintillator

B Detector assembly

Each of the final detector assemblies comprises an array of16 LYSO scintillators (30 times 22 times 2 mm3) arranged in 2 rowsof 8 Scintillators are coupled to the PMT29 window alongone 22 times 2 mm2 face with a thin layer of PDMS all of theremaining scintillator faces are covered in the ESR film tomaximize the scintillation light reaching the PMT The layoutof one such detector is illustrated in Fig 3 Neighboring rowsof 8 scintillators are separated by tungsten plates measuring38 times 22 times 4 mm3 The assembly is encased within two2 times 52 times 30 mm3 tungsten plates After the 2 components ofPDMS are thoroughly mixed it is set aside forsim1 h to allow airbubbles formed during mixing to escape While this processis occurring the LYSO scintillators along with the tungstenisolators are assembled within a 53times 53times 125 mm3 cavity ina 50 times 100 times 100 mm3 block of Lucite After sim1 cm3 PDMS ispoured on top of the scintillator assembly the glass face of theH12700B PMT is placed on top with the interface taped Theunit is then inverted and left to cure for 24 h with a sim4 kgweight placed atop the Lucite block As illustrated in Fig 3each of the completed detector assemblies is then housed in ablack light-tight ABS (acrylonitrile butadiene styrene) plas-tic casing held together with tongue and groove joints andblack nylon screws minimizing light leakage Small holesat the rear of the assembly allow RG174U BNC cables toconnect to the modular detector Following assembly theseholes are sealed with black silicone caulk to ensure the entiredetector is light tight The face of the ABS casing nearest the

053106-4 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 3 (a) Anterior view of the detector assembly with the plastic casing halfcut away to show the details of the scintillator assembly 2 mm thick LYSOscintillators (white) with faces covered with the ESR film (not shown) andseparated by 4 mm tungsten (black) The isolators are painted flat black onthe faces in contact with the phototube window to reduce light scattering(b) Cutaway lateral view of the multi-channel scintillator-PMT detectorassembly (1) Feedthrough holes aligned diagonally along back for connec-tions Holes are sealed after assembly with black PDMS caulk (2) Light-tighttongue and groove connections (3) ABS plastic (crosshatched) (4) Hama-matsu H12700B PMT (5) Scintillator assembly complete with LYSO scintil-lators (white) and black painted tungsten isolators (black) (6) Plastic (ABS)face with 3 mm pockets cut out to eliminate a 5 scattering loss and to indicatethe location of LYSO channels

scintillators has 3 mm wide blind pockets cut into it above eachchannel reducing the 5 attenuation of γs incident normal tothe detector to sim1 and providing a visual indicator of theposition of each channel In the final design a 2primeprime thick leadcollimator (not shown) with 1 mm wide slits centered overeach scintillator channel is carefully aligned in front of eachdetector an established technique20 used to measure positronACAR distributions to cryogenic temperatures30

Figure 4(a) illustrates the positioning of the scintillatorswith respect to the PMT anodes Each LYSO scintillator iscentered over a group of four PMT anodes electrically con-nected together to yield one channel (other geometries wereconsidered including those with scintillators centered betweenchannels as well as directly over channels however it wasobserved that signals from various forms of cross talk impairedthe time resolution) Figure 4(b) shows the layout of the anodeconnections for a single LYSO channelrsquos output with theaccompanying electrical schematic illustrated in Fig 4(c)Each channel has a cable back termination resistor and a pairof back-to-back Si diodes that provide over-voltage protectionfor the digital oscilloscopes An RC filter is built into the highvoltage (HV) input and is represented in Fig 4(d)

C Cross talk characterization

Within each modular detector unwanted signals fromadjacent scintillator channels (ie ldquocross talkrdquo) can resultfrom the absorption of Compton scattered γs reflection andor refraction of scintillation light at the PMT window andcapacitive pickup Light leakage between nearby channels isexacerbated by refraction on entering the PMTrsquos borosilicate

FIG 4 [(a) and (b)] Scintillators (blue) centered over 4 anodes (numberedsquares) constituting one channel (c) Detail of the PMT anode output elec-tronics R1 = 536 Ω provides impedance matching while D = 1N4151 Sidiodes protect the scope (d) High voltage supply circuit with low pass filterR2 = 100 kΩ and C = 001 microF

glass face (nsim 153) Light from LYSO with a refractive indexofsim182 can be expected to refract into a neighboring channelwhenever its incident angle at the glass window is amp50

We detected scattered light cross talk occurring as faras two channels away from the source scintillator Figure 5provides a summary of data resulting from signals observedin neighboring channels when only 1 photopeak event wasrecorded on the PMT From this data it is evident that crosstalk due to scattered light will not pose a significant problemsince the average pulse area detected in the nearest neighboringchannel represents only sim25 of the original signal

We have simulated γ-rays depositing energy within thescintillator assembly with scintillators measuring 2 times 30 mm2

separated by an isolator (air lead or tungsten) measuring4 times 30 mm2 In the simulation 106 511 keV γs are uniformlydistributed with trajectories normal to the 2 mm face repre-sentative of a positron source placed far away and comparableto the geometry of the expected experiment Attenuation coef-ficients extracted from NIST data are interpolated to describea continuous energy spectrum31 Upon entering a material(either scintillator or isolator) a γ-ray has a chance of beingabsorbed with a probability dependent on its energy and thelength traversed Based on data obtained with a 16 channelLYSO-PMT detector we find that sim45 of γ-ray interactionsare full energy photopeak events resulting from full absorp-tion of an incident γrsquos energy The differential cross sectionof γ-rays scattered from a single free electron and the ratio ofthe energy before and after scattering are determined from theKlein-Nishina32 formula From this we create a probabilitydistribution function (PDF) for the energy deposited that is inagreement with the experimental observations shown in Fig 2but without the low energy peak due to scattered light crosstalk Results are summarized in Table III

Based on the simulation we find that Compton scatter-ing events lead to the subsequent deposition of more energyin a neighboring channel than the channel they are initially

053106-5 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 5 (a) Typical cross talk matrix The Y-axis is the channel that wasdirectly above a 22Na source The X-axis is the channel in which a Comptonscattered γ or scattered light was observed The Z-axis is the average pulsearea in a channel relative to the average pulse area detected by the scintillatorexposed to the Na22 source This defines the crosshatched diagonal as unityThe remaining data are plotted on gray-scale (b) Sample data along the dashedline in (a) showing that the average signal observed in the nearest neighboringchannel is sim25

TABLE III Percentage of time that a neighboring channel absorbed specifiedenergy in keV (E) after the Compton scattering (simulation results)

Isolator 51 lt E 51 lt E le 170 170 lt E le 340 340 lt E

Air 298 104 122 72Lead 57 19 22 16Tungsten 37 13 15 09

scattered from 23 of the time when scintillator channels areseparated by lead and just 12 of the time with tungsten iso-lators With lead isolators the simulation indicates that sim2of incident γs will deposit at least 170 keV (12 Ec) into oneof the nearest neighboring channels in close agreement withobservation Using tungsten isolators the simulation indicatesa reduction to 14 Short time scales and large energy distri-butions make it difficult to correct for Compton events beyondrejecting suspect results Lead isolators were used in prelim-inary testing but are substituted with tungsten isolators in thefinal design to minimize the Compton scattering

III DATA ANALYSIS

During an experiment to measure the momentum distri-bution of Ps formed in the sample and following each burst

of positrons the annihilation photon scintillation signals fromeach channel will be recorded on a set of 96 Teledyne LeCroyWaveAce 2024 4-channel 8-bit digital storage oscilloscopes(DSOs) The 96 DSOs will be arranged in 2 banks with eachbank recording data from 12 modular detectors One computerwill download data for each array of 48 DSOs every 10 s Toaccomplish this software has been developed that will allow192 channels consisting of 1024 data points each to be acquiredin sim830 ms The raw data collected by each computer occupy200 KB per shot At a shot rate of 1 Hz this would consumesim16 GBday To reduce the storage requirements the data arecompressed before storage as follows

Immediately after downloading data from a DSO eachchannel is adjusted for the measured cross talk and relativegain Each recorded waveform is then fitted to the function

V (t)=imaxsumi=0

Ai

2

[1 + erfc

(∆tiradic

2σ

)] [exp

(minus∆tiτ

)](1)

using a least square trust-region-reflective algorithm33 Thefit parameters Ai and ti represent the amplitudes and timesof the prompt pulse (i = 0) and up to 3 delayed pulses whileσ and τ are obtained from the fits in Fig 1(b) To avoid fit-ting an excessive number of peaks bounds are set such thatAi ge Amin and |ti ti1| equiv ∆ti ge ∆tmin where Amin correspondsto a pulse area equivalent to 14 Ep (see Fig 2) and∆tmin = 5 nsThe minimum pulse amplitude Amin is selected to reject eventslikely caused by the Compton scattering into neighboringchannels In order to determine the number of peaks imax werequire that χ2 of the fit for each i le imax must reduce χ2 byat least a factor η such that

η χ2i+1 le χ

2i (2)

FIG 6 (a) Fit success as a function of the first delayed pulsersquos amplitude(A1) Average photopeak pulse height 345 mV Compton edge 230 mV(b) Fit success as a function of the time delay ∆t1 between the prompt and thefirst delayed pulse The fitting routine was most successful for η = 13 (redfilled circles)

053106-6 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 7 Success efficiency for η = 13 (a) and η = 21 (b) Assuming thepulse height scales linearly with the energy deposited by a γ-ray the averagephotopeak pulse and the Compton edge correspond to a peak amplitude of345 mV and 230 mV respectively

Neighboring points in the waveform record are strongly cor-related due to the inability to resolve individual photocathodeevents As such we assign the uncertainty in the individualvoltage readings to be

δVi = δV0 + αradic|Vi | (3)

where δV0 is intrinsic to the DSO (ge1 bit corresponding to1256 of the full voltage scale) and the term proportional to thesquare root of the signal accounts for the expected contributionfrom the Poisson statistics associated with the collection ofindividual photo-electrons scaled by a factor α where α istuned such that a fit to a typical 511 keV pulse has a reducedχ2 = 1

We systematically adjusted η such that the fitting algo-rithm remained both reliable and efficient In Fig 6 the prob-ability of a successful fit for a selection of values of η is plottedas a function of (a) the amplitude of the first delayed pulse (A1)and (b) the time delay ∆t1 The value chosen for η noticeablyaffected the fitting routinersquos success against both Ai and tiand the minimum η is chosen to eliminate the anomalies rep-resented within Fig 6(a) for η = 11 Increasing numbers offitted pulses must have at least a 25 better χ2 to be deemeda better fit In Fig 7(a) contour lines (and a color gradient)

illustrate the fit success as a function of both time delay andpulse amplitude for η = 13 Figure 7(b) illustrates the impactof a more stringent fit condition η = 21 which has a dra-matic effect on small pulses occurring shortly after the promptsignal Even in this case the fitting routine is at least 50effective for Compton scattered γs for ∆t ge 50 ns The bestresults are found with η = 13 for which the efficiency is 70for Compton scattered gammas and well above 90 for mostdelayed photopeak events An overall efficiency of detectinga 511 keV γ is calculated using results from the 2D simula-tion described in Sec II C along with the pulse area dependentefficiencies illustrated in Fig 6(a) For γs depositing between100 and 511 keV arriving 3ndash120 ns after a prompt signal con-sisting of 1-3 simultaneous prompt γs our algorithm correctlydetects the arrival time of up to 3 subsequent pulses to within12 ns FWHM with an efficiency of sim90

IV PRELIMINARY RESULTS

We conducted a preliminary experiment to test the per-formance of our detectors and data collection and analysisroutines The experiments made use of three pairs of modu-lar detectors as described earlier situated on either side of aCu(110) target heated to 860 K in our pulsed positron beam34

at distances of sim2440 mm indicated in Fig 8 To eliminatethe small asymmetry in the angular correlation due to a fewpercent γ absorption in the Cu sample the target is tiltedat 10 with respect to a line joining the detectors With the22 times 2 mm2 face of the LYSO crystals facing the target andLYSO crystals separated by interleaved Tungsten plates eachscintillator channel subtended an angular range of 08 mradwith 24 mrad between each channel

Bursts ofsim105 positrons every 4 s were implanted into theCu sample with kinetic energies of 3-5 keV ensuring that morethan half of the positrons annihilate within the target35 Datawere collected over the course of 72 h resulting in sim30 000coincident events To cover the full angular range one bank ofdetectors was set on a translational stage and scanned from 0to 4 mm by hand in 2 mm (08 mrad) steps The resulting

FIG 8 Setup for a preliminary experiment having one-quarter of the detectors described in Fig 3 placed 4 times closer than 10 m that will be used in theintended experiment One bank of multi-element detectors (right) is placed on a translation stage to explore the full spectrum detailed in Fig 9 The 2 mm widescintillating channels subtend 08 mrad and are separated by 24 mrad

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-3 Cecchini et al Rev Sci Instrum 89 053106 (2018)

TABLE I Rise and decay times measured from data contributing to the photopeak presented in Fig 2 Data givenwithout error estimates are from Ref 22 Rise times indicate the average time elapsed for a pulse to rise from 12to 88 of the maximum amplitude The NaI(Tl) scintillator was mounted to a Hamamatsu R1924A PMT whilethe other scintillators were coupled to a Hamamatsu H12700B PMT We list here fundamental properties of thescintillators pertinent to the optimization of the detector light output in photons per keV attenuation length (λ)and relative refractive index (nr )22ndash24 nr is the ratio of the scintillatorrsquos index of refraction relative to that of theborosilicate window of the PMT (nb sim 153)

Scintillator Rise time (ns) Decay time (ns) PhotonskeV λ (cm) nr =n

nb

LYSOCe 290 plusmn 001 463 plusmn 011 32 11 12PbWO4 110 plusmn 003 635 plusmn 003 05 14 146EJ-230 094 plusmn 002 349 plusmn 012 2 10 066NaI(Tl) 591 plusmn 021 250 38 25 123

for this UV light bounces fewer times on average within theblock sample leading to higher efficiency as compared to thethin scintillator sample Also the block sample covers a greaterportion of the center of the PMTrsquos face ensuring that virtuallyall light incident on the glass face is detected Energy spectrawere recorded with a bare scintillator surrounded by flat blackpainted isolators or wrapped in a reflective film The reflectivefilm Vikuiti Enhanced Specular Reflector (ESR)26 purchasedfrom 3M Optical Systems is a 65 microm thick non-metallic100 polymer that has a minimum 98 reflectance across thevisible spectrum The results of these tests are summarizedin Table II Bare thin scintillators exhibited the narrowest risetime (29 ns) but longer decay time (46 ns) Using black sur-faces rather than ESR leads to a comparable rise time (31 ns)and a shorter decay time (43 ns)

In Fig 2 a typical energy spectrum is plotted with datataken from a 30 times 22 times 2 mm3 LYSO scintillator The LYSOis wrapped in an ESR film with no adhesive or coupling(ie with an air gap) and then the LYSO crystal is coupledon its 22 times 2 mm2 face to a Hamamatsu H12700B 64 anodePMT with polydimethylsiloxane (PDMS) ldquogluerdquo27 Individ-ual channels are separated by 4 mm thick tungsten isolatorsThe PMT was biased at 900 V for these tests A peak inthe plotted pulse area spectrum at 8 nVs is attributed to a fullabsorption of 511 keV γs and is known as the photopeak (Ep)or full energy peak A Gaussian fit to the peak indicates a meanphotopeak pulse area of 808 plusmn 001 nVs with a full width athalf maximum (FWHM) energy resolution of sim16 (∆EEp)The photopeak area accounts for sim45 of the total counts

TABLE II Tabulated LYSOCe characteristics for various geometries andsurface coatings LYSOCe blocks and thin rectangles measure 15 times 15 times30 and 2 times 22 times 30 mm3 respectively Data are collected with scintillatorsmounted on a Hamamatsu R1924A PMT Data presented here are collectedfrom isolated photopeak signals

Scintillator Rise time (ns) Decay time (ns) Energy resolution

BlockBare 323 plusmn 002 4648 plusmn 038 104 plusmn 01

ThinBare 290 plusmn 001 4630 plusmn 011 100 plusmn 02Black cover 310 plusmn 002 4309 plusmn 040 130 plusmn 03ESR film 308 plusmn 002 4336 plusmn 039 121 plusmn 04

after correcting for cross talk attributed to scattered light fromneighboring scintillators which causes the large peak locatedat sim10 of the photopeak centroid A typical photo-peakevent resulting from a 511 keV γ produces a pulse witha 345 mV amplitude Assuming that the pulse area scaleslinearly with γ-energy deposited the Compton edge whichoccurs at Ec = 340 keV is found at sim539 nVs and corre-sponds to a sim230 mV amplitude There is nonlinearity in theenergy scale relating the observed pulse area and the energydeposited by an incident γ-ray described in Ref 28 Howeverin the energy range from 340 keV to 511 keV the correc-tion is only sim3 and is neglected here The plateau belowthis cutoff is due to the Compton scattering of γs within thescintillator

B Detector assembly

Each of the final detector assemblies comprises an array of16 LYSO scintillators (30 times 22 times 2 mm3) arranged in 2 rowsof 8 Scintillators are coupled to the PMT29 window alongone 22 times 2 mm2 face with a thin layer of PDMS all of theremaining scintillator faces are covered in the ESR film tomaximize the scintillation light reaching the PMT The layoutof one such detector is illustrated in Fig 3 Neighboring rowsof 8 scintillators are separated by tungsten plates measuring38 times 22 times 4 mm3 The assembly is encased within two2 times 52 times 30 mm3 tungsten plates After the 2 components ofPDMS are thoroughly mixed it is set aside forsim1 h to allow airbubbles formed during mixing to escape While this processis occurring the LYSO scintillators along with the tungstenisolators are assembled within a 53times 53times 125 mm3 cavity ina 50 times 100 times 100 mm3 block of Lucite After sim1 cm3 PDMS ispoured on top of the scintillator assembly the glass face of theH12700B PMT is placed on top with the interface taped Theunit is then inverted and left to cure for 24 h with a sim4 kgweight placed atop the Lucite block As illustrated in Fig 3each of the completed detector assemblies is then housed in ablack light-tight ABS (acrylonitrile butadiene styrene) plas-tic casing held together with tongue and groove joints andblack nylon screws minimizing light leakage Small holesat the rear of the assembly allow RG174U BNC cables toconnect to the modular detector Following assembly theseholes are sealed with black silicone caulk to ensure the entiredetector is light tight The face of the ABS casing nearest the

053106-4 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 3 (a) Anterior view of the detector assembly with the plastic casing halfcut away to show the details of the scintillator assembly 2 mm thick LYSOscintillators (white) with faces covered with the ESR film (not shown) andseparated by 4 mm tungsten (black) The isolators are painted flat black onthe faces in contact with the phototube window to reduce light scattering(b) Cutaway lateral view of the multi-channel scintillator-PMT detectorassembly (1) Feedthrough holes aligned diagonally along back for connec-tions Holes are sealed after assembly with black PDMS caulk (2) Light-tighttongue and groove connections (3) ABS plastic (crosshatched) (4) Hama-matsu H12700B PMT (5) Scintillator assembly complete with LYSO scintil-lators (white) and black painted tungsten isolators (black) (6) Plastic (ABS)face with 3 mm pockets cut out to eliminate a 5 scattering loss and to indicatethe location of LYSO channels

scintillators has 3 mm wide blind pockets cut into it above eachchannel reducing the 5 attenuation of γs incident normal tothe detector to sim1 and providing a visual indicator of theposition of each channel In the final design a 2primeprime thick leadcollimator (not shown) with 1 mm wide slits centered overeach scintillator channel is carefully aligned in front of eachdetector an established technique20 used to measure positronACAR distributions to cryogenic temperatures30

Figure 4(a) illustrates the positioning of the scintillatorswith respect to the PMT anodes Each LYSO scintillator iscentered over a group of four PMT anodes electrically con-nected together to yield one channel (other geometries wereconsidered including those with scintillators centered betweenchannels as well as directly over channels however it wasobserved that signals from various forms of cross talk impairedthe time resolution) Figure 4(b) shows the layout of the anodeconnections for a single LYSO channelrsquos output with theaccompanying electrical schematic illustrated in Fig 4(c)Each channel has a cable back termination resistor and a pairof back-to-back Si diodes that provide over-voltage protectionfor the digital oscilloscopes An RC filter is built into the highvoltage (HV) input and is represented in Fig 4(d)

C Cross talk characterization

Within each modular detector unwanted signals fromadjacent scintillator channels (ie ldquocross talkrdquo) can resultfrom the absorption of Compton scattered γs reflection andor refraction of scintillation light at the PMT window andcapacitive pickup Light leakage between nearby channels isexacerbated by refraction on entering the PMTrsquos borosilicate

FIG 4 [(a) and (b)] Scintillators (blue) centered over 4 anodes (numberedsquares) constituting one channel (c) Detail of the PMT anode output elec-tronics R1 = 536 Ω provides impedance matching while D = 1N4151 Sidiodes protect the scope (d) High voltage supply circuit with low pass filterR2 = 100 kΩ and C = 001 microF

glass face (nsim 153) Light from LYSO with a refractive indexofsim182 can be expected to refract into a neighboring channelwhenever its incident angle at the glass window is amp50

We detected scattered light cross talk occurring as faras two channels away from the source scintillator Figure 5provides a summary of data resulting from signals observedin neighboring channels when only 1 photopeak event wasrecorded on the PMT From this data it is evident that crosstalk due to scattered light will not pose a significant problemsince the average pulse area detected in the nearest neighboringchannel represents only sim25 of the original signal

We have simulated γ-rays depositing energy within thescintillator assembly with scintillators measuring 2 times 30 mm2

separated by an isolator (air lead or tungsten) measuring4 times 30 mm2 In the simulation 106 511 keV γs are uniformlydistributed with trajectories normal to the 2 mm face repre-sentative of a positron source placed far away and comparableto the geometry of the expected experiment Attenuation coef-ficients extracted from NIST data are interpolated to describea continuous energy spectrum31 Upon entering a material(either scintillator or isolator) a γ-ray has a chance of beingabsorbed with a probability dependent on its energy and thelength traversed Based on data obtained with a 16 channelLYSO-PMT detector we find that sim45 of γ-ray interactionsare full energy photopeak events resulting from full absorp-tion of an incident γrsquos energy The differential cross sectionof γ-rays scattered from a single free electron and the ratio ofthe energy before and after scattering are determined from theKlein-Nishina32 formula From this we create a probabilitydistribution function (PDF) for the energy deposited that is inagreement with the experimental observations shown in Fig 2but without the low energy peak due to scattered light crosstalk Results are summarized in Table III

Based on the simulation we find that Compton scatter-ing events lead to the subsequent deposition of more energyin a neighboring channel than the channel they are initially

053106-5 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 5 (a) Typical cross talk matrix The Y-axis is the channel that wasdirectly above a 22Na source The X-axis is the channel in which a Comptonscattered γ or scattered light was observed The Z-axis is the average pulsearea in a channel relative to the average pulse area detected by the scintillatorexposed to the Na22 source This defines the crosshatched diagonal as unityThe remaining data are plotted on gray-scale (b) Sample data along the dashedline in (a) showing that the average signal observed in the nearest neighboringchannel is sim25

TABLE III Percentage of time that a neighboring channel absorbed specifiedenergy in keV (E) after the Compton scattering (simulation results)

Isolator 51 lt E 51 lt E le 170 170 lt E le 340 340 lt E

Air 298 104 122 72Lead 57 19 22 16Tungsten 37 13 15 09

scattered from 23 of the time when scintillator channels areseparated by lead and just 12 of the time with tungsten iso-lators With lead isolators the simulation indicates that sim2of incident γs will deposit at least 170 keV (12 Ec) into oneof the nearest neighboring channels in close agreement withobservation Using tungsten isolators the simulation indicatesa reduction to 14 Short time scales and large energy distri-butions make it difficult to correct for Compton events beyondrejecting suspect results Lead isolators were used in prelim-inary testing but are substituted with tungsten isolators in thefinal design to minimize the Compton scattering

III DATA ANALYSIS

During an experiment to measure the momentum distri-bution of Ps formed in the sample and following each burst

of positrons the annihilation photon scintillation signals fromeach channel will be recorded on a set of 96 Teledyne LeCroyWaveAce 2024 4-channel 8-bit digital storage oscilloscopes(DSOs) The 96 DSOs will be arranged in 2 banks with eachbank recording data from 12 modular detectors One computerwill download data for each array of 48 DSOs every 10 s Toaccomplish this software has been developed that will allow192 channels consisting of 1024 data points each to be acquiredin sim830 ms The raw data collected by each computer occupy200 KB per shot At a shot rate of 1 Hz this would consumesim16 GBday To reduce the storage requirements the data arecompressed before storage as follows

Immediately after downloading data from a DSO eachchannel is adjusted for the measured cross talk and relativegain Each recorded waveform is then fitted to the function

V (t)=imaxsumi=0

Ai

2

[1 + erfc

(∆tiradic

2σ

)] [exp

(minus∆tiτ

)](1)

using a least square trust-region-reflective algorithm33 Thefit parameters Ai and ti represent the amplitudes and timesof the prompt pulse (i = 0) and up to 3 delayed pulses whileσ and τ are obtained from the fits in Fig 1(b) To avoid fit-ting an excessive number of peaks bounds are set such thatAi ge Amin and |ti ti1| equiv ∆ti ge ∆tmin where Amin correspondsto a pulse area equivalent to 14 Ep (see Fig 2) and∆tmin = 5 nsThe minimum pulse amplitude Amin is selected to reject eventslikely caused by the Compton scattering into neighboringchannels In order to determine the number of peaks imax werequire that χ2 of the fit for each i le imax must reduce χ2 byat least a factor η such that

η χ2i+1 le χ

2i (2)

FIG 6 (a) Fit success as a function of the first delayed pulsersquos amplitude(A1) Average photopeak pulse height 345 mV Compton edge 230 mV(b) Fit success as a function of the time delay ∆t1 between the prompt and thefirst delayed pulse The fitting routine was most successful for η = 13 (redfilled circles)

053106-6 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 7 Success efficiency for η = 13 (a) and η = 21 (b) Assuming thepulse height scales linearly with the energy deposited by a γ-ray the averagephotopeak pulse and the Compton edge correspond to a peak amplitude of345 mV and 230 mV respectively

Neighboring points in the waveform record are strongly cor-related due to the inability to resolve individual photocathodeevents As such we assign the uncertainty in the individualvoltage readings to be

δVi = δV0 + αradic|Vi | (3)

where δV0 is intrinsic to the DSO (ge1 bit corresponding to1256 of the full voltage scale) and the term proportional to thesquare root of the signal accounts for the expected contributionfrom the Poisson statistics associated with the collection ofindividual photo-electrons scaled by a factor α where α istuned such that a fit to a typical 511 keV pulse has a reducedχ2 = 1

We systematically adjusted η such that the fitting algo-rithm remained both reliable and efficient In Fig 6 the prob-ability of a successful fit for a selection of values of η is plottedas a function of (a) the amplitude of the first delayed pulse (A1)and (b) the time delay ∆t1 The value chosen for η noticeablyaffected the fitting routinersquos success against both Ai and tiand the minimum η is chosen to eliminate the anomalies rep-resented within Fig 6(a) for η = 11 Increasing numbers offitted pulses must have at least a 25 better χ2 to be deemeda better fit In Fig 7(a) contour lines (and a color gradient)

illustrate the fit success as a function of both time delay andpulse amplitude for η = 13 Figure 7(b) illustrates the impactof a more stringent fit condition η = 21 which has a dra-matic effect on small pulses occurring shortly after the promptsignal Even in this case the fitting routine is at least 50effective for Compton scattered γs for ∆t ge 50 ns The bestresults are found with η = 13 for which the efficiency is 70for Compton scattered gammas and well above 90 for mostdelayed photopeak events An overall efficiency of detectinga 511 keV γ is calculated using results from the 2D simula-tion described in Sec II C along with the pulse area dependentefficiencies illustrated in Fig 6(a) For γs depositing between100 and 511 keV arriving 3ndash120 ns after a prompt signal con-sisting of 1-3 simultaneous prompt γs our algorithm correctlydetects the arrival time of up to 3 subsequent pulses to within12 ns FWHM with an efficiency of sim90

IV PRELIMINARY RESULTS

We conducted a preliminary experiment to test the per-formance of our detectors and data collection and analysisroutines The experiments made use of three pairs of modu-lar detectors as described earlier situated on either side of aCu(110) target heated to 860 K in our pulsed positron beam34

at distances of sim2440 mm indicated in Fig 8 To eliminatethe small asymmetry in the angular correlation due to a fewpercent γ absorption in the Cu sample the target is tiltedat 10 with respect to a line joining the detectors With the22 times 2 mm2 face of the LYSO crystals facing the target andLYSO crystals separated by interleaved Tungsten plates eachscintillator channel subtended an angular range of 08 mradwith 24 mrad between each channel

Bursts ofsim105 positrons every 4 s were implanted into theCu sample with kinetic energies of 3-5 keV ensuring that morethan half of the positrons annihilate within the target35 Datawere collected over the course of 72 h resulting in sim30 000coincident events To cover the full angular range one bank ofdetectors was set on a translational stage and scanned from 0to 4 mm by hand in 2 mm (08 mrad) steps The resulting

FIG 8 Setup for a preliminary experiment having one-quarter of the detectors described in Fig 3 placed 4 times closer than 10 m that will be used in theintended experiment One bank of multi-element detectors (right) is placed on a translation stage to explore the full spectrum detailed in Fig 9 The 2 mm widescintillating channels subtend 08 mrad and are separated by 24 mrad

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-4 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 3 (a) Anterior view of the detector assembly with the plastic casing halfcut away to show the details of the scintillator assembly 2 mm thick LYSOscintillators (white) with faces covered with the ESR film (not shown) andseparated by 4 mm tungsten (black) The isolators are painted flat black onthe faces in contact with the phototube window to reduce light scattering(b) Cutaway lateral view of the multi-channel scintillator-PMT detectorassembly (1) Feedthrough holes aligned diagonally along back for connec-tions Holes are sealed after assembly with black PDMS caulk (2) Light-tighttongue and groove connections (3) ABS plastic (crosshatched) (4) Hama-matsu H12700B PMT (5) Scintillator assembly complete with LYSO scintil-lators (white) and black painted tungsten isolators (black) (6) Plastic (ABS)face with 3 mm pockets cut out to eliminate a 5 scattering loss and to indicatethe location of LYSO channels

scintillators has 3 mm wide blind pockets cut into it above eachchannel reducing the 5 attenuation of γs incident normal tothe detector to sim1 and providing a visual indicator of theposition of each channel In the final design a 2primeprime thick leadcollimator (not shown) with 1 mm wide slits centered overeach scintillator channel is carefully aligned in front of eachdetector an established technique20 used to measure positronACAR distributions to cryogenic temperatures30

Figure 4(a) illustrates the positioning of the scintillatorswith respect to the PMT anodes Each LYSO scintillator iscentered over a group of four PMT anodes electrically con-nected together to yield one channel (other geometries wereconsidered including those with scintillators centered betweenchannels as well as directly over channels however it wasobserved that signals from various forms of cross talk impairedthe time resolution) Figure 4(b) shows the layout of the anodeconnections for a single LYSO channelrsquos output with theaccompanying electrical schematic illustrated in Fig 4(c)Each channel has a cable back termination resistor and a pairof back-to-back Si diodes that provide over-voltage protectionfor the digital oscilloscopes An RC filter is built into the highvoltage (HV) input and is represented in Fig 4(d)

C Cross talk characterization

Within each modular detector unwanted signals fromadjacent scintillator channels (ie ldquocross talkrdquo) can resultfrom the absorption of Compton scattered γs reflection andor refraction of scintillation light at the PMT window andcapacitive pickup Light leakage between nearby channels isexacerbated by refraction on entering the PMTrsquos borosilicate

FIG 4 [(a) and (b)] Scintillators (blue) centered over 4 anodes (numberedsquares) constituting one channel (c) Detail of the PMT anode output elec-tronics R1 = 536 Ω provides impedance matching while D = 1N4151 Sidiodes protect the scope (d) High voltage supply circuit with low pass filterR2 = 100 kΩ and C = 001 microF

glass face (nsim 153) Light from LYSO with a refractive indexofsim182 can be expected to refract into a neighboring channelwhenever its incident angle at the glass window is amp50

We detected scattered light cross talk occurring as faras two channels away from the source scintillator Figure 5provides a summary of data resulting from signals observedin neighboring channels when only 1 photopeak event wasrecorded on the PMT From this data it is evident that crosstalk due to scattered light will not pose a significant problemsince the average pulse area detected in the nearest neighboringchannel represents only sim25 of the original signal

We have simulated γ-rays depositing energy within thescintillator assembly with scintillators measuring 2 times 30 mm2

separated by an isolator (air lead or tungsten) measuring4 times 30 mm2 In the simulation 106 511 keV γs are uniformlydistributed with trajectories normal to the 2 mm face repre-sentative of a positron source placed far away and comparableto the geometry of the expected experiment Attenuation coef-ficients extracted from NIST data are interpolated to describea continuous energy spectrum31 Upon entering a material(either scintillator or isolator) a γ-ray has a chance of beingabsorbed with a probability dependent on its energy and thelength traversed Based on data obtained with a 16 channelLYSO-PMT detector we find that sim45 of γ-ray interactionsare full energy photopeak events resulting from full absorp-tion of an incident γrsquos energy The differential cross sectionof γ-rays scattered from a single free electron and the ratio ofthe energy before and after scattering are determined from theKlein-Nishina32 formula From this we create a probabilitydistribution function (PDF) for the energy deposited that is inagreement with the experimental observations shown in Fig 2but without the low energy peak due to scattered light crosstalk Results are summarized in Table III

Based on the simulation we find that Compton scatter-ing events lead to the subsequent deposition of more energyin a neighboring channel than the channel they are initially

053106-5 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 5 (a) Typical cross talk matrix The Y-axis is the channel that wasdirectly above a 22Na source The X-axis is the channel in which a Comptonscattered γ or scattered light was observed The Z-axis is the average pulsearea in a channel relative to the average pulse area detected by the scintillatorexposed to the Na22 source This defines the crosshatched diagonal as unityThe remaining data are plotted on gray-scale (b) Sample data along the dashedline in (a) showing that the average signal observed in the nearest neighboringchannel is sim25

TABLE III Percentage of time that a neighboring channel absorbed specifiedenergy in keV (E) after the Compton scattering (simulation results)

Isolator 51 lt E 51 lt E le 170 170 lt E le 340 340 lt E

Air 298 104 122 72Lead 57 19 22 16Tungsten 37 13 15 09

scattered from 23 of the time when scintillator channels areseparated by lead and just 12 of the time with tungsten iso-lators With lead isolators the simulation indicates that sim2of incident γs will deposit at least 170 keV (12 Ec) into oneof the nearest neighboring channels in close agreement withobservation Using tungsten isolators the simulation indicatesa reduction to 14 Short time scales and large energy distri-butions make it difficult to correct for Compton events beyondrejecting suspect results Lead isolators were used in prelim-inary testing but are substituted with tungsten isolators in thefinal design to minimize the Compton scattering

III DATA ANALYSIS

During an experiment to measure the momentum distri-bution of Ps formed in the sample and following each burst

of positrons the annihilation photon scintillation signals fromeach channel will be recorded on a set of 96 Teledyne LeCroyWaveAce 2024 4-channel 8-bit digital storage oscilloscopes(DSOs) The 96 DSOs will be arranged in 2 banks with eachbank recording data from 12 modular detectors One computerwill download data for each array of 48 DSOs every 10 s Toaccomplish this software has been developed that will allow192 channels consisting of 1024 data points each to be acquiredin sim830 ms The raw data collected by each computer occupy200 KB per shot At a shot rate of 1 Hz this would consumesim16 GBday To reduce the storage requirements the data arecompressed before storage as follows

Immediately after downloading data from a DSO eachchannel is adjusted for the measured cross talk and relativegain Each recorded waveform is then fitted to the function

V (t)=imaxsumi=0

Ai

2

[1 + erfc

(∆tiradic

2σ

)] [exp

(minus∆tiτ

)](1)

using a least square trust-region-reflective algorithm33 Thefit parameters Ai and ti represent the amplitudes and timesof the prompt pulse (i = 0) and up to 3 delayed pulses whileσ and τ are obtained from the fits in Fig 1(b) To avoid fit-ting an excessive number of peaks bounds are set such thatAi ge Amin and |ti ti1| equiv ∆ti ge ∆tmin where Amin correspondsto a pulse area equivalent to 14 Ep (see Fig 2) and∆tmin = 5 nsThe minimum pulse amplitude Amin is selected to reject eventslikely caused by the Compton scattering into neighboringchannels In order to determine the number of peaks imax werequire that χ2 of the fit for each i le imax must reduce χ2 byat least a factor η such that

η χ2i+1 le χ

2i (2)

FIG 6 (a) Fit success as a function of the first delayed pulsersquos amplitude(A1) Average photopeak pulse height 345 mV Compton edge 230 mV(b) Fit success as a function of the time delay ∆t1 between the prompt and thefirst delayed pulse The fitting routine was most successful for η = 13 (redfilled circles)

053106-6 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 7 Success efficiency for η = 13 (a) and η = 21 (b) Assuming thepulse height scales linearly with the energy deposited by a γ-ray the averagephotopeak pulse and the Compton edge correspond to a peak amplitude of345 mV and 230 mV respectively

Neighboring points in the waveform record are strongly cor-related due to the inability to resolve individual photocathodeevents As such we assign the uncertainty in the individualvoltage readings to be

δVi = δV0 + αradic|Vi | (3)

where δV0 is intrinsic to the DSO (ge1 bit corresponding to1256 of the full voltage scale) and the term proportional to thesquare root of the signal accounts for the expected contributionfrom the Poisson statistics associated with the collection ofindividual photo-electrons scaled by a factor α where α istuned such that a fit to a typical 511 keV pulse has a reducedχ2 = 1

We systematically adjusted η such that the fitting algo-rithm remained both reliable and efficient In Fig 6 the prob-ability of a successful fit for a selection of values of η is plottedas a function of (a) the amplitude of the first delayed pulse (A1)and (b) the time delay ∆t1 The value chosen for η noticeablyaffected the fitting routinersquos success against both Ai and tiand the minimum η is chosen to eliminate the anomalies rep-resented within Fig 6(a) for η = 11 Increasing numbers offitted pulses must have at least a 25 better χ2 to be deemeda better fit In Fig 7(a) contour lines (and a color gradient)

illustrate the fit success as a function of both time delay andpulse amplitude for η = 13 Figure 7(b) illustrates the impactof a more stringent fit condition η = 21 which has a dra-matic effect on small pulses occurring shortly after the promptsignal Even in this case the fitting routine is at least 50effective for Compton scattered γs for ∆t ge 50 ns The bestresults are found with η = 13 for which the efficiency is 70for Compton scattered gammas and well above 90 for mostdelayed photopeak events An overall efficiency of detectinga 511 keV γ is calculated using results from the 2D simula-tion described in Sec II C along with the pulse area dependentefficiencies illustrated in Fig 6(a) For γs depositing between100 and 511 keV arriving 3ndash120 ns after a prompt signal con-sisting of 1-3 simultaneous prompt γs our algorithm correctlydetects the arrival time of up to 3 subsequent pulses to within12 ns FWHM with an efficiency of sim90

IV PRELIMINARY RESULTS

We conducted a preliminary experiment to test the per-formance of our detectors and data collection and analysisroutines The experiments made use of three pairs of modu-lar detectors as described earlier situated on either side of aCu(110) target heated to 860 K in our pulsed positron beam34

at distances of sim2440 mm indicated in Fig 8 To eliminatethe small asymmetry in the angular correlation due to a fewpercent γ absorption in the Cu sample the target is tiltedat 10 with respect to a line joining the detectors With the22 times 2 mm2 face of the LYSO crystals facing the target andLYSO crystals separated by interleaved Tungsten plates eachscintillator channel subtended an angular range of 08 mradwith 24 mrad between each channel

Bursts ofsim105 positrons every 4 s were implanted into theCu sample with kinetic energies of 3-5 keV ensuring that morethan half of the positrons annihilate within the target35 Datawere collected over the course of 72 h resulting in sim30 000coincident events To cover the full angular range one bank ofdetectors was set on a translational stage and scanned from 0to 4 mm by hand in 2 mm (08 mrad) steps The resulting

FIG 8 Setup for a preliminary experiment having one-quarter of the detectors described in Fig 3 placed 4 times closer than 10 m that will be used in theintended experiment One bank of multi-element detectors (right) is placed on a translation stage to explore the full spectrum detailed in Fig 9 The 2 mm widescintillating channels subtend 08 mrad and are separated by 24 mrad

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-5 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 5 (a) Typical cross talk matrix The Y-axis is the channel that wasdirectly above a 22Na source The X-axis is the channel in which a Comptonscattered γ or scattered light was observed The Z-axis is the average pulsearea in a channel relative to the average pulse area detected by the scintillatorexposed to the Na22 source This defines the crosshatched diagonal as unityThe remaining data are plotted on gray-scale (b) Sample data along the dashedline in (a) showing that the average signal observed in the nearest neighboringchannel is sim25

TABLE III Percentage of time that a neighboring channel absorbed specifiedenergy in keV (E) after the Compton scattering (simulation results)

Isolator 51 lt E 51 lt E le 170 170 lt E le 340 340 lt E

Air 298 104 122 72Lead 57 19 22 16Tungsten 37 13 15 09

scattered from 23 of the time when scintillator channels areseparated by lead and just 12 of the time with tungsten iso-lators With lead isolators the simulation indicates that sim2of incident γs will deposit at least 170 keV (12 Ec) into oneof the nearest neighboring channels in close agreement withobservation Using tungsten isolators the simulation indicatesa reduction to 14 Short time scales and large energy distri-butions make it difficult to correct for Compton events beyondrejecting suspect results Lead isolators were used in prelim-inary testing but are substituted with tungsten isolators in thefinal design to minimize the Compton scattering

III DATA ANALYSIS

During an experiment to measure the momentum distri-bution of Ps formed in the sample and following each burst

of positrons the annihilation photon scintillation signals fromeach channel will be recorded on a set of 96 Teledyne LeCroyWaveAce 2024 4-channel 8-bit digital storage oscilloscopes(DSOs) The 96 DSOs will be arranged in 2 banks with eachbank recording data from 12 modular detectors One computerwill download data for each array of 48 DSOs every 10 s Toaccomplish this software has been developed that will allow192 channels consisting of 1024 data points each to be acquiredin sim830 ms The raw data collected by each computer occupy200 KB per shot At a shot rate of 1 Hz this would consumesim16 GBday To reduce the storage requirements the data arecompressed before storage as follows

Immediately after downloading data from a DSO eachchannel is adjusted for the measured cross talk and relativegain Each recorded waveform is then fitted to the function

V (t)=imaxsumi=0

Ai

2

[1 + erfc

(∆tiradic

2σ

)] [exp

(minus∆tiτ

)](1)

using a least square trust-region-reflective algorithm33 Thefit parameters Ai and ti represent the amplitudes and timesof the prompt pulse (i = 0) and up to 3 delayed pulses whileσ and τ are obtained from the fits in Fig 1(b) To avoid fit-ting an excessive number of peaks bounds are set such thatAi ge Amin and |ti ti1| equiv ∆ti ge ∆tmin where Amin correspondsto a pulse area equivalent to 14 Ep (see Fig 2) and∆tmin = 5 nsThe minimum pulse amplitude Amin is selected to reject eventslikely caused by the Compton scattering into neighboringchannels In order to determine the number of peaks imax werequire that χ2 of the fit for each i le imax must reduce χ2 byat least a factor η such that

η χ2i+1 le χ

2i (2)

FIG 6 (a) Fit success as a function of the first delayed pulsersquos amplitude(A1) Average photopeak pulse height 345 mV Compton edge 230 mV(b) Fit success as a function of the time delay ∆t1 between the prompt and thefirst delayed pulse The fitting routine was most successful for η = 13 (redfilled circles)

053106-6 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 7 Success efficiency for η = 13 (a) and η = 21 (b) Assuming thepulse height scales linearly with the energy deposited by a γ-ray the averagephotopeak pulse and the Compton edge correspond to a peak amplitude of345 mV and 230 mV respectively

Neighboring points in the waveform record are strongly cor-related due to the inability to resolve individual photocathodeevents As such we assign the uncertainty in the individualvoltage readings to be

δVi = δV0 + αradic|Vi | (3)

where δV0 is intrinsic to the DSO (ge1 bit corresponding to1256 of the full voltage scale) and the term proportional to thesquare root of the signal accounts for the expected contributionfrom the Poisson statistics associated with the collection ofindividual photo-electrons scaled by a factor α where α istuned such that a fit to a typical 511 keV pulse has a reducedχ2 = 1

We systematically adjusted η such that the fitting algo-rithm remained both reliable and efficient In Fig 6 the prob-ability of a successful fit for a selection of values of η is plottedas a function of (a) the amplitude of the first delayed pulse (A1)and (b) the time delay ∆t1 The value chosen for η noticeablyaffected the fitting routinersquos success against both Ai and tiand the minimum η is chosen to eliminate the anomalies rep-resented within Fig 6(a) for η = 11 Increasing numbers offitted pulses must have at least a 25 better χ2 to be deemeda better fit In Fig 7(a) contour lines (and a color gradient)

illustrate the fit success as a function of both time delay andpulse amplitude for η = 13 Figure 7(b) illustrates the impactof a more stringent fit condition η = 21 which has a dra-matic effect on small pulses occurring shortly after the promptsignal Even in this case the fitting routine is at least 50effective for Compton scattered γs for ∆t ge 50 ns The bestresults are found with η = 13 for which the efficiency is 70for Compton scattered gammas and well above 90 for mostdelayed photopeak events An overall efficiency of detectinga 511 keV γ is calculated using results from the 2D simula-tion described in Sec II C along with the pulse area dependentefficiencies illustrated in Fig 6(a) For γs depositing between100 and 511 keV arriving 3ndash120 ns after a prompt signal con-sisting of 1-3 simultaneous prompt γs our algorithm correctlydetects the arrival time of up to 3 subsequent pulses to within12 ns FWHM with an efficiency of sim90

IV PRELIMINARY RESULTS

We conducted a preliminary experiment to test the per-formance of our detectors and data collection and analysisroutines The experiments made use of three pairs of modu-lar detectors as described earlier situated on either side of aCu(110) target heated to 860 K in our pulsed positron beam34

at distances of sim2440 mm indicated in Fig 8 To eliminatethe small asymmetry in the angular correlation due to a fewpercent γ absorption in the Cu sample the target is tiltedat 10 with respect to a line joining the detectors With the22 times 2 mm2 face of the LYSO crystals facing the target andLYSO crystals separated by interleaved Tungsten plates eachscintillator channel subtended an angular range of 08 mradwith 24 mrad between each channel

Bursts ofsim105 positrons every 4 s were implanted into theCu sample with kinetic energies of 3-5 keV ensuring that morethan half of the positrons annihilate within the target35 Datawere collected over the course of 72 h resulting in sim30 000coincident events To cover the full angular range one bank ofdetectors was set on a translational stage and scanned from 0to 4 mm by hand in 2 mm (08 mrad) steps The resulting

FIG 8 Setup for a preliminary experiment having one-quarter of the detectors described in Fig 3 placed 4 times closer than 10 m that will be used in theintended experiment One bank of multi-element detectors (right) is placed on a translation stage to explore the full spectrum detailed in Fig 9 The 2 mm widescintillating channels subtend 08 mrad and are separated by 24 mrad

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-6 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 7 Success efficiency for η = 13 (a) and η = 21 (b) Assuming thepulse height scales linearly with the energy deposited by a γ-ray the averagephotopeak pulse and the Compton edge correspond to a peak amplitude of345 mV and 230 mV respectively

Neighboring points in the waveform record are strongly cor-related due to the inability to resolve individual photocathodeevents As such we assign the uncertainty in the individualvoltage readings to be

δVi = δV0 + αradic|Vi | (3)

where δV0 is intrinsic to the DSO (ge1 bit corresponding to1256 of the full voltage scale) and the term proportional to thesquare root of the signal accounts for the expected contributionfrom the Poisson statistics associated with the collection ofindividual photo-electrons scaled by a factor α where α istuned such that a fit to a typical 511 keV pulse has a reducedχ2 = 1

We systematically adjusted η such that the fitting algo-rithm remained both reliable and efficient In Fig 6 the prob-ability of a successful fit for a selection of values of η is plottedas a function of (a) the amplitude of the first delayed pulse (A1)and (b) the time delay ∆t1 The value chosen for η noticeablyaffected the fitting routinersquos success against both Ai and tiand the minimum η is chosen to eliminate the anomalies rep-resented within Fig 6(a) for η = 11 Increasing numbers offitted pulses must have at least a 25 better χ2 to be deemeda better fit In Fig 7(a) contour lines (and a color gradient)

illustrate the fit success as a function of both time delay andpulse amplitude for η = 13 Figure 7(b) illustrates the impactof a more stringent fit condition η = 21 which has a dra-matic effect on small pulses occurring shortly after the promptsignal Even in this case the fitting routine is at least 50effective for Compton scattered γs for ∆t ge 50 ns The bestresults are found with η = 13 for which the efficiency is 70for Compton scattered gammas and well above 90 for mostdelayed photopeak events An overall efficiency of detectinga 511 keV γ is calculated using results from the 2D simula-tion described in Sec II C along with the pulse area dependentefficiencies illustrated in Fig 6(a) For γs depositing between100 and 511 keV arriving 3ndash120 ns after a prompt signal con-sisting of 1-3 simultaneous prompt γs our algorithm correctlydetects the arrival time of up to 3 subsequent pulses to within12 ns FWHM with an efficiency of sim90

IV PRELIMINARY RESULTS

We conducted a preliminary experiment to test the per-formance of our detectors and data collection and analysisroutines The experiments made use of three pairs of modu-lar detectors as described earlier situated on either side of aCu(110) target heated to 860 K in our pulsed positron beam34

at distances of sim2440 mm indicated in Fig 8 To eliminatethe small asymmetry in the angular correlation due to a fewpercent γ absorption in the Cu sample the target is tiltedat 10 with respect to a line joining the detectors With the22 times 2 mm2 face of the LYSO crystals facing the target andLYSO crystals separated by interleaved Tungsten plates eachscintillator channel subtended an angular range of 08 mradwith 24 mrad between each channel

Bursts ofsim105 positrons every 4 s were implanted into theCu sample with kinetic energies of 3-5 keV ensuring that morethan half of the positrons annihilate within the target35 Datawere collected over the course of 72 h resulting in sim30 000coincident events To cover the full angular range one bank ofdetectors was set on a translational stage and scanned from 0to 4 mm by hand in 2 mm (08 mrad) steps The resulting

FIG 8 Setup for a preliminary experiment having one-quarter of the detectors described in Fig 3 placed 4 times closer than 10 m that will be used in theintended experiment One bank of multi-element detectors (right) is placed on a translation stage to explore the full spectrum detailed in Fig 9 The 2 mm widescintillating channels subtend 08 mrad and are separated by 24 mrad

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-7 Cecchini et al Rev Sci Instrum 89 053106 (2018)

FIG 9 Results from preliminary ACAR experiment on Cu(110) (detailedin Fig 8) using 6 of the modular detectors discussed in Sec II The data arecompared with the results of Stewart20 (solid line) with a uniform backgroundof 0007 added

measurement of the angular correlation of the annihilationgammas is plotted in Fig 9

Our preliminary results (filled circles with error bars)are compared with a previous measurement of the ACARspectrum of Cu (solid line)20 To directly compare our mea-surement with the measurement of Stewart the curve fromRef 20 is rescaled and a flat background is added to fit ourdata With 31 degrees of freedom the reduced chi-squared ofthe fit is 107 indicating a statistically reasonable fit ACARmeasurements on simple metals36 are explained as arisingfrom annihilations with conduction and core electrons yield-ing spectra comprised of two major components For Cu thecomponent resulting from positron annihilation with core elec-trons produces a broad Gaussian background distribution witha FWHM of sim15 mrad while annihilations with conductionelectrons produce a narrow spread (sim8 mrad FWHM)20 Bothdistributions are centered about an angular deviation of zeroradians corresponding to back-to-back gamma-rays In a 1DACAR measurement which the present geometry approxi-mates the narrow component approximates the shape of aninverted parabola

V CONCLUDING REMARKS

We selected our detector configuration from the arrange-ments considered herein by comparing various scintillator andPMT attributes LYSOrsquos short rise time (sim3 ns) along with itsgood light output (sim32 photonskeV) and short attenuationlength of sim116 cm resulting in sim95 of all incident 511 keVγs producing a signal from the photomultiplier tube make itthe best choice for the planned experiment The presence ofsim25 light cross talk between neighboring PMT channelsis easily accounted for given its consistency The Comptonscattering of γs causing simultaneous signals in neighbor-ing scintillators is greatly reduced by using 4 mm tungstenshielding plates between scintillators A subset of 6 modulardetectors has been fully tested and the entire set of 24 mod-ular detectors has been assembled and is ready for the firstexperiments The final apparatus will consist of a total of 386channels covering sim17 times 104 sr with 1 mm wide slits in a508 cm lead collimator placed in front of each detector anddetectors placed 10 m away from a target to yield an angu-lar resolution of 01 mrad The detection efficiency is sim47for a single pair of back-to-back annihilation γs depositing100ndash511 keV after considering the efficiencies associated witha single LYSO channel and the analysis routine We have

avoided providing an estimate of the expected count rate inthe final experiment as there are a number of factors thatwould need to be addressed (eg the size of the prompt pulsethe background rate as a function of time etc) which wouldnecessitate a comprehensive simulation

ACKNOWLEDGMENTS

This work was supported by the US National Sci-ence Foundation under Grants Nos MRI 1429718 and PHY1505903 GGC was partially supported by a UCR GraduateResearch Mentorship Fellowship EM and MF-G are sup-ported by an NSF MPS AGEP-GRS Supplement Award No1664515 and an NSF Graduate Research Fellowship respec-tively The travel expenses of MA were supported in part bythe Ronald E McNair Scholars Summer Research InternshipProgram at Marquette University

1P M Platzman and A P Mills Jr ldquoPossibilities for Bose condensation ofpositroniumrdquo Phys Rev B 49 454ndash458 (1994)

2P Kruger Z Hadzibabic and J Dalibard ldquoCritical point of an inter-acting two-dimensional atomic Bose gasrdquo Phys Rev Lett 99 040402(2007)

3V Bagnato and D Kleppner ldquoBose-Einstein condensation in low-dimensional trapsrdquo Phys Rev A 44 7439ndash7441 (1991)

4C M Surko and R G Greaves ldquoEmerging science and technology ofantimatter plasmas and trap-based beamsrdquo Phys Plasmas 11(5) 2333ndash2348(2004)

5F Anderegg E M Hollmann and C F Driscoll ldquoRotating field confine-ment of pure electron plasmas using Trivelpiece-Gould modesrdquo Phys RevLett 81 4875ndash4878 (1998)

6R G Greaves and C M Surko ldquoInward transport and compression of apositron plasma by a rotating electric fieldrdquo Phys Rev Lett 85 1883ndash1886(2000)

7A P Mills Jr ldquoTime bunching of slow positrons for annihilation life-time and pulsed laser photon absorption experimentsrdquo Appl Phys 22(3)273ndash276 (1980)

8D Gerola W B Waeber M Shi and S J Wang ldquoQuasidivergency freeextraction of a slow positron beam from high magnetic fieldsrdquo Rev SciInstrum 66(7) 3819ndash3825 (1995)

9W Stoeffl P Asoka-Kumar and R Howell ldquoThe positron microprobe atLLNLrdquo Appl Surf Sci 149(1) 1ndash6 (1999)

10P J Schultz E M Gullikson and A P Mills Jr ldquoTransmitted positronreemission from a thin single-crystal Ni(100) foilrdquo Phys Rev B 34442ndash444 (1986)

11A P Mills Jr ldquoBrightness enhancement of slow positron beamsrdquo ApplPhys 23(2) 189ndash191 (1980)

12D B Cassidy V E Meligne and A P Mills Jr ldquoProduction of a fully spin-polarized ensemble of positronium atomsrdquo Phys Rev Lett 104 173401(2010)

13R Ferragut A Dupasquier A Calloni G Consolati F Quasso M PPetkov S M Jones A Galarneau and F D Renzo ldquoHomogeneous poroussilica for positronium production in AEGISrdquo J Phys Conf Ser 262(1)012020 (2011)

14A P Mills Jr E D Shaw R J Chichester and D M ZuckermanldquoPositronium thermalization in SiO2 powderrdquo Phys Rev B 40 2045ndash2052(1989)

15D B Cassidy S H M Deng R G Greaves T Maruo N NishiyamaJ B Snyder H K M Tanaka and A P Mills Jr ldquoExperiments with ahigh-density positronium gasrdquo Phys Rev Lett 95 195006 (2005)

16D B Cassidy and A P Mills Jr ldquoThe production of molecular positron-iumrdquo Nature 449 195ndash197 (2007)

17J Wheatley and D Halliday ldquoThe quenching of ortho-positronium decayby a magnetic fieldrdquo Phys Rev 88 424 (1952)

18D B Cassidy T H Hisakado V E Meligne H W K Tom and A P MillsJr ldquoDelayed emission of cold positronium from mesoporous materialsrdquoPhys Rev A 82 052511 (2010)

19R H Dicke ldquoThe effect of collisions upon the Doppler width of spectrallinesrdquo Phys Rev 89 472ndash473 (1953)

053106-8 Cecchini et al Rev Sci Instrum 89 053106 (2018)

20A T Stewart ldquoMomentum distribution of metallic electrons by positronannihilationrdquo Can J Phys 35(2) 168ndash183 (1957)

21S Berko M Haghgooie and J Mader ldquoMomentum density measurementswith a new multicounter two-dimensional angular correlation of annihilationradiation apparatusrdquo Phys Lett A 63 335ndash338 (1977)

22Saint-Gobain Ceramics and Plastics Inc Scintillation Materials andAssemblies 2014 URL wwwcrystalssaint-gobaincom

23A Annenkov M Korzhik and P Lecoq ldquoLead tungstate scintillationmaterialrdquo Nucl Instrum Methods Phys Res Sect A 490(12) 30ndash50(2002)

24Eljen Technology Fast Timing Plastic Scintillator EJ-228 EJ-230 2016URL wwweljentechnologycom

25C W Van Eijk ldquoInorganic scintillators in positron emission tomogra-phyrdquo in Radiation Detectors for Medical Applications (Springer 2006)pp 259ndash274

263M Optical Systems Vikuitireg Enhanced Specular Reflector (ESR) 2017URL www3Mcom

27Dow Corning Corporation Sylgardreg 184 Silicone Elastomer 2007 URLwwwdowcorningcom

28C M Pepin P Berard A-L Perrot C Pepin D Houde R Lecomte C LMelcher and H Dautet ldquoProperties of LYSO and recent LSO scintillatorsfor phoswich PET detectorsrdquo IEEE Trans Nucl Sci 51(3) 789ndash795 (2004)

29J B Birks The Theory and Practice of Scintillation Counting InternationalSeries of Monographs on Electronics and Instrumentation (MacmillanNew York 1964) Vol 27

30P Kubica and A T Stewart ldquoPositron motion in metalsrdquo Can J Phys61(7) 971ndash978 (1983)

31J Hubbell and S Seltzer Tables of x-ray mass attenuation coeffi-cients and mass energy-absorption coefficients 2004 URL httpphysicsnistgovxaamdi[2016]

32O Klein and Y Nishina ldquoUber die streuung von strahlung durch freie elek-tronen nach der neuen relativistischen quantendynamik von Diracrdquo Z Phys52(11-12) 853ndash868 (1929)

33J J More and D C Sorensen ldquoComputing a trust region steprdquo SIAM JSci Stat Comput 4(3) 553ndash572 (1983)

34A C L Jones H J Rutbeck-Goldman T H Hisakado A M PineiroH W K Tom A P Mills Jr B Barbiellini and J Kuriplach ldquoAngle-resolved spectroscopy of positronium emission from a Cu(110) surfacerdquoPhys Rev Lett 117 216402 (2016)

35A P Mills Jr and R J Wilson ldquoTransmission of 1-6-keV positrons throughthin metal filmsrdquo Phys Rev A 26 490ndash500 (1982)

36S DeBenedetti C E Cowan W R Konneker and H Primakoff ldquoOn theangular distribution of two-photon annihilation radiationrdquo Phys Rev 77205ndash212 (1950)