PHYS 4909 Final ReportEXO Scintillation Simulation

Rick Ueno - 100607696

April 10, 2007

1 Physics Overview of the Project

As a fourth year honours project, I was involved in EXO (Enriched Xenon Observatory)project at Carleton University. The objective of EXO project is to seek for signs of neutrino-less double beta decay using enriched xenon gas, 136Xe. Many experiments have proven thatneutrinos are not massless particles, but previous experiments on solar and atmospheric neu-trinos measure only the mass difference of neutrino generations. If EXO succeeds to discoverthis particular decay mode, it proves that massive neutrinos are Majorana particles (particlewhose antiparticle is identical to itself) and also answers the absolute neutrino mass scalequestion by measuring the effective Majorana mass (will be discussed later). Basic physicsoverview of the project is given below.

1.1 Neutrino and Weak Interaction

The neutrino is a subatomic particle that is a neutrally charged lepton. It was first suggestedby Pauli because of the continuous energy spectrum of the decay. In case of two-particledecay, the energy spectrum of the decay should be quantized. However, the continuous spec-trum of the beta decay suggests that there is a third “ghost” particle that carries some ofthe energy which Fermi named “neutrino” [1]. In Standard Model, neutrino is treated as amassless particle. However, many recent experiments have proven that neutrinos undergooscillations, which indicates existence of neutrino mass and mixing [2] [3].

If the neutrinos have mass, then there will be a mixing of neutrino flavours that is anal-ogous to quark flavour mixing. That is, a weak eigenstate |νl〉 is a linear superposition ofmass eigenstates |νi〉

|νl〉 =∑

Ul,i |νi〉 (1)

where Ul,i is 3 × 3 leptonic mixing matrix known as Pontecorvo-Maki-Nakagawa-Sakata(PMNS) matrix. In the case of two neutrinos (case where tau neutrino is neglected forsimplicity), the leptonic mixing matrix is

U =

(cosθ sinθ−sinθ cosθ

)(2)

and the resulting transition probability between different flavours are written as

P (να → νβ) = sin22θsin2

(∆m2L

4E

)(3)

where ∆m2 ≡ m21 − m2

2, L is the source-detector length in m, E is neutrino energy inMeV and θ is the neutrino mixing angle. The probability that να remains να is simplyP (να → να) = 1 − P (να → νβ) [2]. Neutrino oscillation experiments such as SNO andSuper-Kamiokande measures the parameter ∆m2 for solar neutrino and atmospheric neutri-nos respectively. However, since the absolute neutrino mass is not known, this leaves two

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Figure 1: Left: Normal (left) and inverted (right) hierarchy of neutrino masses. Right:Effective Majorana mass 〈mν〉 as a function of lightest mass eigenstate m1 [4].

possibilities for neutrino mass hierarchy; normal and inverted (see figure 1 left). Thereforea new experiment is needed to determine this hierarchy as well as a proof that massiveneutrinos are Majorana particles. Figure 1 on the right also illustrates that if the effectivemajorana mass is less than 0.5 eV, then the neutrino hierarchy can be distinguished [4].

1.2 Neutrinoless Double Beta Decay

Double beta decay (2νββ) is a process in which two simultaneous beta decay occurs. It isa transition of a nucleus of (Z,A), where Z is the nuclear charge and A is the mass number(both Z and A must be even), into another nucleus of (Z+2,A). This process

(Z,A) → (Z + 2, A) + 2e− + 2νe (4)

produces four leptons. In this decay process, the two electrons are detected, which, in thisdecay mode, gives a continuous distribution. This has been observed in different isotopesincluding the decay of 136Xe →136 Ba [5].

On the other hand, neutrinoless double beta decay (0νββ) involves no neutrinos in thefinal state. Figure 2 shows the difference between the two distinct double beta decays. 0νββdecay occurs only if there is a non-conserving lepton number process so that the anti-neutrinoemitted is identical to a neutrino to annihilate with the other antineutrino [1]. The differencebetween the 2νββ decay and 0νββ decay can be seen graphically in figure 3. In 0νββ decay,we look for what is called effective Majorana neutrino mass, which is

〈mν〉 =

∣∣∣∣∣∑j

mjU2ej

∣∣∣∣∣ (5)

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Figure 2: Differences between double beta decay (2νββ)(left) and neutrinoless double betadecay (0νββ)(right). In 0νββ, two neutrinos annihilate because their anti-particles are iden-tical.

Figure 3: Energy spectrum of electrons in double beta decay. The 2νββ case is a continuousspectrum as highlighted in yellow, where 0νββ case has a spike at the end [4].

where the sum is only for light neutrinos with mj < 10MeV . The rate of the 0νββ decay is

proportional to 〈mν〉2 and it is related to T 0νββ1/2 , the half-life of 0νββ as:

[T 0νββ

1/2

]−1

= G0νββ (E0, Z)

∣∣∣∣M0νββGT − g2

V

g2A

M0νββF

∣∣∣∣2 〈mν〉2 (6)

where G0νββ (E0, Z) is a known phase space factor depending on the end-point energy E0

and the nuclear charge Z, and M0νββGT and M0νββ

F are Gamow-Teller and Fermi nuclear Matrixelements for the process, and this is what is measured by the 0νββ decay experiment [5] [6].

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1.3 Xenon Gas as Detector Medium

The ultimate objective of EXO is to observe the 0νββ decay using 136Xe gas. Xe can beused as an ionization medium to track the electron produced from the decay as well as ascintillator medium. Another attractive feature of the enriched xenon gas is that it can beused as both the decay source and detector. Since there is only one material, this minimizesthe background.

Scintillators in general works as following: A particle passing through the scintillator mediumdeposits energy in the form of ionization, which forms dimers. De-excitation in the subse-quent process emits photons which can be detected [1]. 136Xe produces scintillation lightcentered around 176nm, well into the ultraviolet region. This is somewhat problematic sinceit requires ultraviolet sensitive photomultipliers to detect the photons in the region, or oth-erwise require wavelength shifter such as TPB (tetraphenyl-butadiene) coating to output alonger wavelength.

Electrons produced by the decay will drift toward the end of the time projection cham-ber (TPC) where they are detected. This is done by applying electric field between the twoend of the active volume (one end is applied a high voltage while the other end is grounded).

By coupling these two signals together, we can get better resolution of energy spectrumof the decay. One can also reconstruct the energy and particle tracks from the two types ofsignals since they can give information about the position of the event. The drifted electronis detected by the two-dimensional read-out plane, so the x-y position of the event is readilyknown. The time it took for the electron to drift from the source to the detector gives infor-mation about the position in the z direction. Position reconstruction from the scintillationsignal will be discussed later in this report. Furthermore, we know that the decay processalways produces a pair of electrons (see previous section). Therefore, we can use this trackinformation to reject the event if the two tracks does not form a vertex.

2 Scintillation Counter Design

To understand the scintillation process of xenon gas, a separate detector was designed. Be-cause scintillation process is a major component in the overall detector design, completeunderstanding of this process is essential. A simplistic design of a detector is preferred forthis application so that the result obtained from this study will be easier to understand. Thecounter design consists of a stainless steel tee (Lesker T-0800 [8]) sandwiched between twoidentical PMTs (Electron Tube 9390B [9]).

The stainless tee is basically a cylindrical shell of thickness 1/8 inch, diameter of 6 inchesand length of 12 inches, with another sleeve that comes out in the middle of the cylinder,making the shape of a “T”. This “T” is important for two reasons: It is used to connect

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Figure 4: A typical PMT efficiency as a function of wavelength, showing a unique curve fordifferent PMT model [9].

to the vacuum piping to evacuate gas and to fill it with pure xenon gas; this sleeve is alsoused to mount an alpha source inside a detector to that we can study the scintillation signalproduced by the alpha source at a precise location.

There are two types of PMTs that could be considered this study. One is PMTs thatare sensitive to wavelengths produced by scintillation process of xenon gas (around 178nm)and the other is PMTs that are sensitive to more common wavelength of about 400nm. ThePMTs of the former type in general have lower quantum efficiency, but they do not requirewavelength shifter (WLS). WLS is a material that absorbs photons in a certain range andre-emits photons of another wavelength at a certain efficiency, so this also contributes to thefinal efficiency associated with the PMT. WLS considered for this application is tetraphenylbutadiene (TPB) because it has relatively high absorption efficiency at the UV region [10].Another disadvantage of UV sensitive PMTs is their cost.

It turns out that combination of regular PMTs (sensitive to wavelengths around 400nm)and WLS has better efficiency than that of UV sensitive PMTs by carrying some simple cal-culations. Figure 4 shows the quantum efficiency of PMT and figure 5 shows absorption andemission efficiencies for WLS under consideration. Since equipments needed for applicationof WLS is already available, it was decided that we use regular PMT and manually coat itwith WLS.

After putting all of the above components together, we have a final scintillation counteras in figure 6.

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Figure 5: Left: Relative absorption efficiency of TPB compared to Sodium Salicylate. Right:Emission spectrum of TPB [10].

Figure 6: Construction of scintillation counter designed for our study.

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3 Monte Carlo Simulation

For the most part, my involvement in the project was development of monte carlo simulationof scintillation counter to study the behaviour of scintillation signal produced by the xenongas. Simulation is an important step towards understanding of the actual data obtained,and to give an idea of what to expect from the data. This simulation was programmed inC++ and it made use of GEANT4 package[7] developed by CERN (Conseil Europeen pourla Recherche Nucleaire).

3.1 Overview of GEANT4

GEANT4 is a C++ toolkit for simulation of particle behaviour and interaction with othermaterials. Its main application areas include high energy, nuclear and accelerator physics[7]. It is essentially a package that includes physics of particle interaction that is used duringvarious simulation scenarios. The design of GEANT4 allows users to easily customize thesimulation to their specifications, and it also allows users to pick and choose only the neededprocesses for particles of interest (electrons, neutrinos, photons) and their properties.

The simulation requires at least three components: Detector construction, physics processes,and event initialization. Additional modules are added to tailor the simulation for its needs.Such examples are implementation of wavelength shifter and detector behaviours.

3.2 Detector Construction

For the study of scintillation signals, a simple stainless tee detector was designed, as it wasin previous section. For simulation purpose however, the “T” design was simplified to acylinder with the same dimension. The stainless steel has certain reflectivity that dependson a wavelength of the photon. As in the real detector, a PMT module is mounted on eitherside. In GEANT4, this PMT module is simplified to a glass plate of thickness 1/4 inchesand metallic photocathode at the back which picks up the signal at certain efficiency thatis also sensitive to the photon wavelength. Inside the cylinder is filled with pure xenon gaswith properties as described in table 1.

Between the end of the cylinder and PMT, there is a “thin film” of WLS coating madeof TPB. This WLS has non-zero absorption efficiency distribution at 178nm, while its emis-sion efficiency is equivalent to zero at 178nm and maximum at around 430nm (refer to figure5). Figure 7 visualizes the final simulated detector construction.

3.3 Event Initialization, Detection and Outputs

One of the main challenges in the development of simulation is to obtain some reasonableresults by applying appropriate physical processes to the initial state. For instance, if a phys-ical process of creation of scintillation photon was not included in the simulation, PMTs will

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Property ValuesDensity 4.7 mg/cm3

Photon Energy 7.07 eV (≈ 178 nm)Scintillation Yield 29000 /MeV [12]

Refractive Index 1.6Absorption Length 100.0 cmScattering Length 30.0 cm

Prompt Timing Constant 2.2 nsLate Timing Constant 4.0 ns

Table 1: Some physical properties of simulated xenon gas. The values are taken fromGEANT4 simulation example[7] unless otherwise specified.

Figure 7: Visualisation of the final detector construction. There are two PMTs mounted oneither end of the detector with WLS (light blue) in between.

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not detect photons that should have been created by scintillation process. In the same way, ifthe process of photon detection was applied incorrectly, the output will also be incorrect. Incase of our study, the intial state is precisely known. An Americium alpha source is mountedat some position inside a detector and it emits an alpha particle carrying an energy of 5.4MeV at random direction. This initial state is defined in the simulation program, but can bemanually changed at the GEANT4 user interface. Optionally, an external macro file can beread by GEANT4 to do some simple loop commands to avoid complexity.

The PMTs having a certain efficiency is made to only pick up scintillation photon at cer-tain wavelength. This is done in GEANT4 by defining the PMT efficiency as a function ofphoton momentum (which is related to photon wavelength by De Broglie relation p = h/λ).The program must also distinguish which PMT detected a photon (recall that there are twoPMTs, one on either side of the cylinder). This is done by assigning each PMT a copy num-ber, and when a program calls for detection sequence, it looks up the copy number, therebyidentifying the PMT that detected the photon.

At the end of the simulation, the program outputs most important information, which isnumbers of scintillation lights detected by each PMT, into an ASCII data file which canbe in turn imported by ROOT data analysis package (also developed by CERN [11]) to beanalysed.

4 Results and Analysis

One of the most important goal of this simulation is to estimate the number of scintillationlight that would be detected by the PMTs in real situation and to draw a baseline forunderstanding of physics of scintillation process. This depends on various parameters; thushow they affect the final results is thoroughly investigated. The second goal of the simulationis to reconstruct the initial position and energy of the particle (alpha partcle in this case) bylooking at the relative intensities of light collected by the two PMTs.

4.1 Model Simulation of Alpha Particles

Using a macro file to make use of loop function, eight independent simulation was executedat varying energy from 1 MeV to 8 MeV with zero stainless steel reflectivity to study theenergy dependence of scintillation light generation. Each simulation produced 10 eventseach consisting of one alpha particle with initial position at the centre of the detector. It isassumed that the error on PMT signal for each event is

√n where n is the number of detected

signals. Thus the error on average of 10 events is Σn/102. As it can be seen in figure 8, theresult gives almost perfectly linear relation when total detected signal is plotted as a functionof energy. It can be concluded that the energy is proportional to the number of generatedphotons, and this linear relation becomes important when reconstructing the initial energyof the particle.

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Figure 8: Total event signal detected as a function of energy.

Similar set of simulation was executed but this time varying the initial position of the alphaparticle at a given energy to study the position dependency. For this study, again by usinga macro file, initial position of alpha particle was changed in the z direction (along the axisof the cylinder) from -14 cm to 14 cm in 2 cm increment (total of 15 positions) on the z-axis(position in x and y direction both equal to zero). This time we plot the ratio of scintillationsignal detected by one of the PMT and the total scintillation signal detected by the twoPMTs as a function of position. The error is calculated in the same manner as previously.As it can be seen in figure 9 on the left, this gives a smooth curve. Furthermore, this relationcan be readily used to estimate the z-position of the initial event since it is independentof initial energy of the particle. Another useful plot is the total signal detected at a givenposition normalized by the total signal detected at the center of the detector as a functionof z position. Figure 9 on the right shows such a relation.

Lastly, we look at the total detected scintillation signal as a function of position away fromthe central axis (x position not zero). This is simulated by following the same step above,but repeating by varying x value from -6 cm to 6 cm in 3 cm increment (y can stay zerosince the detector is axi-symmetric). The same error calculation was carried as the previoustwo. As it is seen in figure 10, the most light is detected when the event occurs along thecentral axis, and reduces as the event occurs near the edge. Furthermore, this reduction ismore significant as the event occurs farther in the z direction from the centre of the detector.

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Figure 9: Left: ratio of PMT1 vs the total detected signals. Right: ratio of total detectedsignal compared to those detected at the centre of the detector.

4.2 Reconstruction of Initial Position and Energy

In this section, we derive a preliminary empirical model for reconstruction of initial positionand energy of alpha particle from signals obtained from the two PMTs. As mentioned before,reconstruction of initial position in the z-direction is possible by looking at the distributionof signal ration between PMT1 and the total signal as a function of z position (Figure 9 left),which, by inspection, has a form

hitsPMT1

hitsPMT1 + hitsPMT2

= a = [1 + exp (α + βz)]−1 (7)

where a is calculated from the simulation data (hitsPMT1 and hitsPMT2 are the detectedsignal of PMT1 and PMT2 respectively) and α and β are constants that are obtained fromperforming fits on graph that is obtained from model simulation in section 4.1. This can besimply rearranged to find the initial position z assuming that the event has occurred alongthe central axis (x=y=0) as following:

z =1

β

[ln

(1

a− 1

)− α

](8)

To reconstruct the initial energy, we refer to graph in figure 9 on the right. We can estimatewhat the detected signal would be if an event with the same initial energy was to happenat the centre of the detector since the graph plots the ratio normalized at the centre. Byinspection, it is a fourth order polynomial relation of the form

ratio = c1 + c2 · z + c3 · z2 + c4 · z3 + c5 · z4 (9)

where c1 through c5 are constants from the fit on the model simulation, and z is the initialz position calculated from above. By dividing the total detected signal by this ratio, we get

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Figure 10: Distribution of detected signal across the diameter of the cylinder. Total hitsratio is the total PMT signal normalized by the total signal at x=0.

the estimated signal of the particle with the same energy at the centre of the detector, thatis, hitscentre = hitstotal/ratio. Now we come back to the graph in figure 8, which is the linearrelation between the total hits at the centre and the initial energy of the particle.

hitscentre = a0 + a1 · E (10)

where a1 is once again a constant from the fit. a0 ≡ 0 since PMT should not detect anyphotons if the particle has no energy. This can be rearranged to find the initial energy of thealpha particle

E =hitscentre

a1(11)

Thus we empirically reconstructed the initial position and energy of the particle given thatit was created along the centre of z-axis. Table 2 summarizes all the values of constants thatwere found and their uncertainties. The uncertainties on these constants and reconstructedparameters are calculated standard error propagation formula:

∆f =

√∑ (∂f

∂xi

)2

∆x2i (12)

4.3 Analysis and Discussion

To verify this model, another simulation was run which generated 100 independent eventsof alpha particle at 5.4 MeV at centre of the detector. Applying the algorithm developed inthe previous section to reconstruct the initial position and energy, we get a distribution as infigure 11. As it is obvious, the algorithm works fairly accurately when it is near the centre

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Constant Value Uncertainty Constant Value Uncertaintyα (eq. 7) 0.0006642 ± 0.01266 c3 (eq. 9) 0.008396 ± 0.0003697β (eq. 7) -0.2177 ± 0.001429 c4 (eq. 9) 2.773 ·10−6 ± 1.845 ·10−5

c1 (eq. 9) 1.017 ± 0.008265 c5 (eq. 9) 8.033 ·10−5 ± 2.429 ·10−6

c2 (eq. 9) -0.0004271 ± 0.001821 a1 (eq. 10) 167 ± 0.6811

Table 2: Values of constants for empirical formula and their uncertainties.

Figure 11: Result of position (left) and energy (right) reconstruction algorithm applied to100 events of alpha particles of 5.4 MeV at position (0,0,0).

of the detector.

Figure 12 shows the result of a similar simulation trial where 50 events (due to time-restriction) of alpha particle at 5.4 MeV at initial position of (0, 0, -10cm) were simulated.As it can be seen, the reconstructed position and energy agrees within a reasonable errorwith the initial position and energy of the alpha particle.

However, when the simulation tested 100 events of alpha particle at position of (5cm, 0, 5cm)(that is, initial position is off-centre with respect to the z-axis), the reconstructed positionis fairly close to the expected value but the reconstructed energy does not agree (figure 13).The reason for this is because the PMT does not detect as many scintillation signal as if theparticle was along the axis (refer to figure 10).

Another issue is that the graphs that were fitted to determine the value of constants for theempirical model is highly sensitive to parameters such as reflectivity of the stainless steel. Asit can be seen in figure 14, there is a drastic difference in shapes of the curve for reflection 0%case and reflection 70% case. Therefore, it is important that the reflectivity of the stainlesssteel is set correctly in the simulation.

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Figure 12: Result of position (left) and energy (right) reconstruction algorithm applied to100 events of alpha particles of 5.4 MeV at position (0,0,-10cm).

Figure 13: Result of position (left) and energy (right) reconstruction algorithm applied to100 events of alpha particles of 5.4 MeV at position (5cm,0,5cm).

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Figure 14: Repeat of figure 9 with results for 0% reflection case and 70% reflection casesuperimposed.

There are a number of possible systematic errors associated with the setup of this simula-tion. Firstly, for simplification, we have assumed the wavelength-independent constant suchas index of refraction and absorption length of materials. However, these parameters changeslightly with wavelength of the photon. Secondly, the efficiency of the PMT and WLS wereread in the simulation from a data file containing finite number of data points. To com-promise with the speed of the simulation, the efficiency plot of the PMT and WLS has a“step”, resulting in loss of information in between. Lastly, the quality of the random numbergenerator used in GEANT4 is unknown. Because monte carlo method is largely dependedon random number generator, quality of such algorithm becomes important. In addition,due to the lengthy simulation time (simulation of 100 events takes approximately 24 hours),only samples with 100 events were drawn. For this reason, the chi square fit to compare thegoodness of the algorithm to the simulation is not as accurate as it can be with the biggersample.

5 Summary

As my fourth year honours project, i took a part in EXO project at Carleton Universitywhich ultimately seeks to find neutrino mass through observation of 0νββ decay in gaseousxenon. The first half of my involvement was spent mostly on simulation code development.Because of my minimal experience with computer programming and monte carlo methodbeforehand, this was a big challenge and a lot of time was spent on learning object orientedC++ programming. The second half of my involvement included improvement of the codedeveloped in the first term, analysis of the results and development of empirical reconstruc-tion algorithm.

The monte carlo simulation using GEANT4 was developed to estimate the scintillation pho-

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ton that would be collected by the PMTs in the scintillation counter that was specificallydesigned to assist in understanding of scintillation process for gaseous xenon. The empiricalmodel for reconstruction of initial energy and position was also developed and tested withthe simulation data. The algorithm seems to work well for particle with initial position alongthe central axis, but becomes a problem when the initial position is off-centre with respectto the z-axis. Also, it is found that the constants that were used for the algorithm dependssignificantly on the reflectivity (and other parameters) in the simulation code.

Even though my project term has ended, the EXO project is still in the development phase.Future plans include comparison of the actual scintillation data with the simulated data, andfurther simulation development with additional gas mixtures (xenon gas with various addi-tives) and time projection chamber (TPC) integrated system where the scintillation detectorsetup is integrated into TPC chamber.

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References

[1] Frauenfelder, H., Henley, E., Subatomic Physics, (NJ: Prentice-Hall, 1991).

[2] Giunti, C., Laveder, M., Neutrino Mixing hep-ph/0310238

[3] Akhmedov, E.K., Neutrino Oscillations hep-ph/0610064

[4] Zuber, K., Neutrinoless Double Beta Decay Experiments nucl-ex/0610007

[5] Breidenbach, M. et. al., EXO: an advanced Enriched Xenon double beta-decay Observatory(SLAC EPAC, 2001).

[6] Elliott, S.R., Vogel, P., Double Beta Decay Annu. Rev. Nucl. Part. Sci. 52 (2002)

[7] Geant4 Collaboration, Introduction to Geant4 , on WWW:http://geant4.cern.ch/support/about.shtml

[8] Kurt J. Lesker Company, on WWW: http://www.lesker.com/newweb/index.cfm

[9] Electron Tubes, on WWW: http://www.electrontubes.com

[10] Burton, W.M., Powell, B.A., Applied Optics 12 (1973) pp. 87

[11] ROOT Project, on WWW: http://root.cern.ch/

[12] K. Saito, et.al., IEEE Trans.Nucl.Sci. 49 (2002) pp1674-1680

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