A Kinetic Model for Xenon-Doped Liquid Argon Scintillation Light
D.E. Fields, R. Gibbons, M. Gold, J.L. Thomas, N. McFadden, S.R. Elliott, R. Massarczyk, K. Rielage
AA Kinetic Model for Xenon-Doped Liquid ArgonScintillation Light
D.E. Fields a , R. Gibbons a , M. Gold a , J.L. Thomas a , N. McFadden a ,S.R. Elliott b , R. Massarczyk b , K. Rielage b a Department of Physics and Astronomy MSC07 4220, 1 University of NewMexico,Albuquerque NM 87131-0001 b Physics Division, Los Alamos National Laboratory MS H803, P-23, Los Alamos, NM,87545, USA
Abstract
Scintillation from noble gases is an important technique in particle physicsincluding neutrino beam experiments, neutrino-less double beta-decay anddark matter searches. In liquid argon, the possibility of enhancing the lightyield by the addition of a small quantity of xenon (doping at ∼ − ∼ Keywords: liquid argon, scintillation, xenon doping
1. Introduction
The use of Liquid Noble Gases (LNG) as detectors and active vetoes inphysics experiments has become a mainstay, especially for low rate, large vol-ume/mass applications for direct dark matter detection [1], neutrino beamexperiments [2], and the neutrino-less double beta decay experiment LEG-END [3]. In particular, liquid argon (LAr) has become widely used because
Preprint submitted to Nuclear Instruments and Methods in Physics Research Section ASeptember 24, 2020 a r X i v : . [ phy s i c s . i n s - d e t ] S e p f its low cost. Due to the short wavelength of the argon scintillation light(128 nm), LAr experiments require the use of a wavelength shifter (typicallyTetraphenyl Butadiene, TPB) for the detection of the light. The possibil-ity of shifting the light to the xenon dimer emission wavelength (175 nm)is therefore tantalizing [4]. Previous work has demonstrated that a smalldopant concentration of ∼
10 ppm is sufficient to transfer a large portion ofthe scintillation to the xenon emission wavelength and to increase the totallight yield.[5],[6].
2. Model
LAr emission results from two argon excimer states, a singlet and a triplet.The singlet lifetime is short ( ∼ ∼ − → Ar + Ar ∗ → Ar ∗ → Ar + Ar + → Ar +2 → Ar ∗ (1)The argon excimer diffuses through the liquid and can, if there are im-purities (like oxygen, nitrogen, xenon, etc.) transfer its excitation energy toany of the impurities. If it is a nitrogen or oxygen atom, the excited impu-rity can de-excite through heat without giving off light. If the argon excimerinteracts with a xenon atom, it can form a mixed state (Ar-Xe) excimer. Ifthis mixed state excimer interacts with another xenon atom, it can create axenon excimer: Ar ∗ + 2Xe → Ar + ArXe ∗ + Xe → ∗ (2)The time evolution of these states can be described by coupled, timedependant differential equations. We label the number of molecules of acertain kind at a given time as: argon excimer singlet S ( t ), argon excimertriplet T ( t ) , mixed excimer M ( t ) , and xenon excimer X ( t ). The changein the number of states depends the exponential lifetimes: argon singlet τ s ,argon triplet τ t and xenon τ x (the xenon triplet and singlet times are takenP.2ogether as an average, since both are relatively short compared to the argontriplet lifetime and the diffusion time) and the collision energy transfer timecharacterized by a diffusion rate ( k ):˙ S = − S/τ s − k S ˙ T = − T /τ t − k T ˙ M = k ( S + T ) − k M ˙ X = k M − X/τ x Because LAr vessels are often not completely full, we must also take intoaccount emission from cold argon gas in the ullage,˙ G = − G/τ g where τ g is the argon triplet in the cold gas. From Henry’s law we deducethat a negligible amount of xenon is mixed into the argon gas at our xenondoping levels in the liquid (see Section 4.2). Additionally, we ignore thesinglet from the gas as in this work we do not fit the singlet light.We could, in principle, also take into account energy transfer to non-scintillating states, as occurs with contaminants such as oxygen and nitro-gen. This would simply add another diffusion rate dependent transfer outof the excimers. In this work, our argon was purified to ppb levels of thesecontaminants, so we neglect those terms here.As noted above, in our solution to these differential equations, we ignorethe singlet component as we did not have sufficient time resolution to resolveit. Furthermore, the simple exponential would have to be convoluted with thedetector time resolution as well as the spatial dependence of the ionizationdeposition in the detector. Thus, ignoring the singlet, these equations are eas-ily integrated analytically. Defining the time constants: 1 /τ t (cid:48) = 1 / ( τ t + k ),1 /t = (1 /τ x − k ) and 1 /t = (1 /τ x − /τ t (cid:48) ), then the solutions are: T ( t ) = T e − t/τ t (cid:48) M ( t ) = T τ t k (cid:0) e − k t − e − t/τ t (cid:48) (cid:1) X ( t ) = T τ t ( k ) (cid:2) t e − k t − t e − t/τ t (cid:48) + ( t − t ) e − t/τ x (cid:3) . (3)P.3or the gas component, G ( t ) = G e − t/τ G (4)and finally, the corresponding light emission L ( t ) is given by, L ( t ) = T ( t ) /τ t + X ( t ) /τ x + G ( t ) /τ g (5)We have not, as yet, included important experimental effects, which couldbe determined via simulation, including geometric effects, light transmissionand reflection, trigger effects, etc. We simply use this as an empirical modeland fit the data. Despite the lack of any attempt to model the detected light,the model fits the main features of our data. Moreover, we can extract avalue for the transfer constant k that is in good agreement with what weexpect theoretically.
3. Fit to Data
The data used in this paper has been previously described [6]. Our appa-ratus is a 100L liquid argon cryostat viewed by one 3 (cid:48)(cid:48)
Hamamatsu R11065PMT with a TPB coated acrylic disk fixed to the front of the tube. Weinserted xenon corresponding to added concentrations of 0, 1, 2, 5, and 10ppm with an uncertainty of 6%. The data was taken under two trigger con-ditions: a PMT trigger (referred to in [6] as a random trigger, RAN) and acosmic ray muon trigger (MU) derived from coincidence between scintillatorpanels placed above and below the cryostat. All the data was taken with theRAN trigger except for the 10 ppm (amount of added xenon) data which wastaken with both MU and RAN triggers. The light curves L ( T ) were derivedfrom pulses with integrated charge normalized to the single photon response(SPE). The six data sets were normalized to the number of triggers in eachset (see Figure 1). It can be seen that our PMT produced considerable after-pulsing, presumed to be from helium leaked into the PMT. No attempt wasmade here to correct for the after-pulsing, which limits our determinationof the shape of the time spectra at short times. However, the observationof the trend towards increasing light yield and decreased emission time withincreasing xenon concentration remains clear.For the samples with a visible gaseous tail (sets 4,5,6), we fit the tail in therange (7 − µs (where the spectra is simply exponential) to determine thegaseous triplet lifetime. For the sets 1,2,3 the large argon triplet componentprevents us from properly fitting the tail lifetime. The average triplet lifetimeP.4 -
10 110 y i e l d SPE / n s SPE versus Time all sets SPE versus Time all sets
Figure 1: The six data sets normalized to number of events: Set1: 0 ppm MU (darkorange), Set2: 1 ppm RAN (blue), Set3: 2 ppm RAN (red), Set4: 5 ppm RAN (green),Set5: 10 ppm RAN (cyan), Set6: 10 ppm MU (magneta).
P.5n the gas in these sets is 3 . ± . µs , consistent with previously measuredvalue 3 . ± . µs [9]. The average gaseous component in sets 4-6 is G /T =0 .
06, which is a factor of ∼
60 higher than GEANT simulations (see Section4.2 for a discussion).We then fit all sets to our model. In sets 1-3 we set the argon gas tripletlifetime to the average from sets 4-6 and allow the parameter G to float. Be-cause of the relatively strong correlation between several of the fit parametersand the after-pulsing at short times, we fix the liquid argon triplet lifetimeto the measured value in gas 3 . µ s and the xenon lifetime to 20 ns. Wechose the value of 3 . µ s rather then the standard value in liquid of 1 . µ sfor two reasons: 1) as we find xenon in our pure argon, the fundamentallifetime of the argon excimer must be larger than the apparent lifetime fromthe scintillation time distribution, and 2) we performed fits to all six datasets with the same τ t using several values from 1 . µs to 4 . µs and foundthat the best fit to the data corresponded to approximately 3 . µs .The remaining parameters allowed to vary in the fit to the data were T and k (and the component of light in the gas G in sets 1-3). The fit resultsare shown in Figure 2.X T SPE k ( µs ) − L Xe G /T ±
45 2044 ±
45 1 . ± .
04 0 . ± .
05 0 . ± . ±
178 3611 ±
60 0 . ± .
03 0 . ± .
04 0 . ± . ±
85 3907 ±
63 1 . ± .
03 0 . ± .
03 0 . ± . ±
63 4022 ±
63 2 . ± .
03 0 . ± .
03 0 . ± . ±
62 3983 ±
63 3 . ± .
05 0 . ± .
02 0 . ± . ±
67 4605 ±
68 3 . ± .
04 0 . ± .
02 0 . ± . Table 1: Fitted values T in SPE per event and k in ( µs ) − by dopant concentrationX [ppm] and trigger condition, together with the integral light yield in SPE and gaseouscomponent. The argon triplet lifetime was set to 3 . µ s (see text). The column L Xe isthe fraction of triplet light from Xe (175 nm). Note that the last 10 ppm set was takenwith the MU trigger. All other sets were taken with the RAN trigger.
4. Analysis
The self diffusion rate, k diff is given by k diff = 4 π × D × R × C P.6 / ndf c – – – -
10 110 y i e l d SPE / n s LifeFit set 1 Xe 00PPM-Ran / ndf c – – – LifeFit set 1 Xe 00PPM-Ran / ndf c – – – -
10 110 y i e l d SPE / n s LifeFit set 2 Xe 01PPM-Ran / ndf c – – – LifeFit set 2 Xe 01PPM-Ran / ndf c – – – -
10 110 y i e l d SPE / n s LifeFit set 3 Xe 02PPM-Ran / ndf c – – – LifeFit set 3 Xe 02PPM-Ran / ndf c – – -
10 110 y i e l d SPE / n s LifeFit set 4 Xe 05PPM-Ran / ndf c – – LifeFit set 4 Xe 05PPM-Ran / ndf c – – -
10 110 y i e l d SPE / n s LifeFit set 5 Xe 10PPM-Ran / ndf c – – LifeFit set 5 Xe 10PPM-Ran / ndf c – – -
10 110 y i e l d SPE / n s LifeFit set 6 Xe 10PPM-Mu / ndf c – – LifeFit set 6 Xe 10PPM-Mu
Figure 2: Fits of the data to our model (black line) with τ t fixed to 3 . µs as describedin the text. The components are: triplet argon (red line), xenon (green line), gas (yellowline). P.7here D = 2 . × − cm / s is the argon self-diffusion constant, R = 4 . × − cm is the xenon-argon dimer Van der Waals separation, and C is theconcentration of xenon in atoms per cm . Using the value for liquid argondensity (1 . / cm ), Avagadro’s number, and the molar atomic weight ofargon, we arrive at the diffusion-limited reaction rate k diff = 0 .
219 [ µ s − ] × Xwhere X here is the true Xe concentration in parts-per-million (ppm).The extracted values of k from our model versus dopant concentrationis shown in Figure 3. The fitted line is k = aX + b [ µs − ] where X is theadded Xe dopant concentration in ppm, a = 0 . ± . stat ) ± . sys )and b = 0 . ± . k diff . The intercept corresponds to xenonin our “pure” argon with a concentration of 3 . ± . stat ) ± . sys ) [ ppm ]The systematic error is due to the ∼
60% correlation between k and τ t inthe fit. This level of xenon in commercial argon is consistent with previousstudies of impurities in LAr [10], and may be expected since the atmosphericconcentration of argon is 0.934% by volume compared to xenon which is87 ± The light from the gaseous argon above our liquid is a complicating factorin this study. We first estimate the mole fraction of Xe in the ullage usingideal solution theory. The vapor pressure equation for Xe is P = P atm exp (cid:20) − LR (cid:18) T − T b (cid:19)(cid:21) , (6)where L is the latent heat of vaporization and T b is the boiling temperatureof pure Xe. The latent heat is 12.6 kJ/mol and the boiling temperature atatmospheric pressure is 165 K [12]. Thus, the Xe vapor pressure at the boilingpoint of Ar is 2 . × − atm. (The boiling point elevation of Ar by a fewppm Xe is negligible compared with their difference in boiling temperatures.)Raoults law states that the partial pressure is the vapor pressure of the puresubstance multiplied by the mole fraction in the liquid. Thus, at ppm Xedoping, the ullage contains a negligible concentration of Xe, i.e., < ∼ G /T is listed in thelast column of Table 1. Where the values of G are well determined by theP.8 k K By-PPM extrap -3.741 +/- 0.032 / ndf c - – – c - – – K By-PPM extrap -3.741 +/- 0.032
Figure 3: Fitted rate constant k for each of the run sets versus set doping concentration.The fitted line is k = aX + b [ µs − ] where X is the added Xe dopant in parts per million(ppm), a = 0 . ± . stat ) and b = 0 . ± . . ± . stat ) ± . sys ) [ ppm ]. P.9ong-time tail, the extracted ratios are a factor of 60 higher than determinedin the simulation.There are several possible explanations for this discrepancy. The mostmundane explanation is that the factor of the energy loss ratio between theullage and the liquid was underestimated, since some scintillation in the liq-uid occurs below the PMT, and will have a much lower likelihood of beingdetected. This is, at most, a factor of two. Another more intriguing possibil-ity is that the xenon is not fully mixed in the liquid argon, with more at thebottom of the cryostat (since it more massive). While this is something thathas worried those that have proposed xenon-doped liquid argon, we find thisextremely unlikely in this case, since the behavior of the time spectra withadded xenon is well characterized by the model, and a gravity-based grada-tion of the xenon concentration would lead to very different shapes (sumsof light from different concentrations) than what is seen in the data. In afollow-on experiment, we plan to minimize the ullage as much as possible (byfilling to a higher level) to better understand this component.
An empirical fit of our 0 ppm data to a single exponential gives a lifetimeof ∼ . µ s, a number consistent with the typically reported value for thetriplet lifetime of liquid argon. We have shown that this un-doped sampleactually has a xenon content of about 3 . ± . stat ) ± . sys ) ppm . Webelieve this short empirical lifetime is an artifact of the residual xenon intypically available argon. The current data, which is hampered at shorttimes by the after-pulsing, does not allow for a better determination of the“true” triplet lifetime, since, as can be seen in Figure 4, only the early times( < µs ) show a significantly different shape.Additionally, fits to the data where the liquid triplet lifetime is allowedto float, suggests that the argon triplet lifetime decreases with xenon dopantconcentration. While the quality of the data does not allow for this to beunambiguously determined, one could speculate that the presence of xenonmight reduce the real triplet lifetime as well as transferring the energy to thexenon dimer. One of the most important motivations for doping LAr with xenon is thereported increase in total light yield, as mentioned in the introduction. Ourresults are summarized in Figure 5 and Table 1. In Table 1, two measures ofP.10 igure 4: Model results with 3 ppm (left) and 13 ppm (right) of total xenon in LAr. Thesetwo values roughly correspond to set 1 and sets 5 and 6 of the data. Each plot shows twocurves corresponding to triplet lifetimes of 1.4 (black) and 3.5 (blue) µ s. One can see thatonly the shapes of the light curves at early times ( < . µ s) can easily differentiate thesetwo (quite different) triplet lifetimes. the total light from the scintillation are included. First, the value of T canbe used as a surrogate for the total light emission since this is the numberof triplet states initially created, the ratio of the initial triplet to the initialsinglet should be a fixed number, and we assume all the triplet plus singletstates eventually lead to scintillation. For the second measure of light yield,we integrate the actual light curves from just before the singlet light ( ∼ µs )to 10 µs in SPE. For the lowest doped sets, this will underestimate the lightbecause of the long time scale of light emission. Also, we note that the SPEvalues include the contribution from the ullage ( ∼ T exclude this light.The ratio of the T at 10 ppm to 0 ppm (both with the PMT (RAN)triggers, one finds a factor of more than two increase in the light yield. Fromsimulation (as has been previously reported for this data [6]), a factor of ap-proximately two is found. The reason given for this increase in reference [6])is the increase in the transparency of LAr to the 175 nm scintillation of xenoncompared to the 128 nm scintillation of argon. This increase in transparencyitself has been attributed to the xenon presence in commercial argon [13].However, by examining the fraction of the total light from xenon scintilla-tion, ( L Xe ), as a function of xenon added, the model fit finds that thereis only a ∼
15% increase in light from xenon scintillation (Figure 6). Themodel (red line in Figure 6) predicts that the xenon fraction of the total lightincreases non-linearly with dopant in agreement with the data. It should beP.11 T r i p l e t ( SPE ) Triplet 0Triplet 0
Figure 5: Fitted T and integrated light curves as a function of added xenon concentration.PMT (RAN) triggers are red and cosmic muon triggers are blue, while solid markers arethe fit values, T , and open markers are the light curve integral values. P.12oted that both the fitted data and the model curve are dependant on theargon triplet lifetime, with the curve rising less steeply for a shorter tripletlifetime. With a lifetime of τ t = 1 .
40 ns, the xenon fraction starts at about ∼
50% and increases to ∼
80% at the maximum absolute xenon concentra-tion. Therefore, it seems unlikely that better transparency is the only reasonfor the increase in total light if the model parameterization of this data givenhere is correct. x enon SPE f r a c t i on xenon light fraction xenon light fraction Figure 6: Ratio of xenon light (SPE) to total (SPE) versus absolute xenon concentrationusing our fitted extrapolation with τ t = 3 .
48 ns, where 0 ppm doped corresponds to 3.74ppm absolute xenon concentration. The red line is the model prediction, with the linethickness showing the model uncertainty due to the extrapolated value of k . With varia-tion of τ t the fitted values and curve remain consisent, but the shape varies considerably.See discussion in text.
5. Conclusion
We have shown that a simple model for the kinetics of excimer diffusionand light yield of liquid argon doped with small amounts of xenon is in goodagreement with our experimental data. Our result supports the conclusionP.13hat xenon doping at the small amount of the order of 10 ppm can signifi-cantly enhance the light yield of liquid argon.This model can be used to predict the light yields at both xenon andargon wavelengths in xenon-doped liquid argon for future LAr detector ex-periments. This may become important when determining the best detectordesign for a particular experimental application. In subsequent work we willseparately measure the 128 nm and 175 nm light. We hope to be able toachieve a better understanding the origin of the increased light yield seenwith xenon doping. P.14 eferences [1] R. Ajaj, et al. (DEAP), Search for dark matter with a 231-day exposureof liquid argon using DEAP-3600 at SNOLAB, Phys. Rev. D 100 (2019)022004. doi: . arXiv:1902.04048 .[2] W. C. Louis, R. G. V. de Water, Hidden neutrino particles may be alink to the dark sector, Scientific American 323 (2020) 46–53. doi: https://doi:10.1038/scientificamerican0720-46 .[3] N. Abgrall, et al. (LEGEND), The Large Enriched Germanium Experi-ment for Neutrinoless Double Beta Decay (LEGEND), AIP Conf. Proc.1894 (2017) 020027. doi: . arXiv:1709.01980 .[4] P. Peiffer, T. Pollmann, S. Schonert, A. Smolnikov, S. Vasiliev, Pulseshape analysis of scintillation signals from pure and xenon-doped liquidargon for radioactive background identification, JINST 3 (2008) P08007.doi: .[5] A. Neumeier, T. Dandl, T. Heindl, A. Himpsl, L. Oberauer, W. Potzel,S. Roth, S. Schnert, J. Wieser, A. Ulrich, Intense vacuum ultravi-olet and infrared scintillation of liquid ar-xe mixtures, EPL (Euro-physics Letters) 109 (2015) 12001. URL: http://dx.doi.org/10.1209/0295-5075/109/12001 . doi: .[6] N. McFadden, S. R. Elliott, M. Gold, D. E. Fields, K. Rielage, R. Mas-sarczyk, R. Gibbons, Large-scale, precision xenon doping of liquid argon,Thesis (2020). arXiv:2006.09780 .[7] E. Morikawa, R. Reininger, P. G¨urtler, V. Saile, P. Laporte, Argon,krypton, and xenon excimer luminescence: From the dilute gas to thecondensed phase, Journal of Chemical Physics 91 (1989) 1469–1477.doi: .[8] M. Kubota, S. Hishida, J. Himi, J. Suzuki, J. Ruan, The suppression ofthe slow component inxenon-doped liquid argon scintillation, NuclearInstruments and Methods in Physics ResearchSection A: Accelerators,Spectrometers, Detectors and Associated Equipment 327 (1993) 71–74.[9] M. Akashi-Ronquest, et al., Triplet Lifetime in Gaseous Argon,Eur. Phys. J. A 55 (2019) 176. doi: . arXiv:1903.06706 . P.1510] R. Acciarri, et al. (WArP), Effects of Nitrogen contamination in liquidArgon, JINST 5 (2010) P06003. doi: . arXiv:0804.1217 .[11] Huang, Lein, Morgan, Noble Gases,Kirk-Othmer Encyclopedia of Chem-ical Technology (5th ed.), Wiley, 2005.[12] J. Dean, N. Lange, Lange’s Handbook of Chemistry, number v. 15 inLange’s Handbook of Chemistry, McGraw-Hill, 1999.[13] J. Calvo, C. Cantini, P. Crivelli, M. Daniel, S. Di Luise, A. Gen-dotti, S. Horikawa, L. Molina-Bueno, B. Montes, W. Mu, S. Murphy,G. Natterer, K. Nguyen, L. Periale, Y. Quan, B. Radics, C. Regen-fus, L. Romero, A. Rubbia, R. Santorelli, F. Sergiampietri, T. Viant,S. Wu, Measurement of the attenuation length of argon scintillationlight in the ArDM LAr TPC, Astroparticle Physics 97 (2018) 186 – 196.doi: https://doi.org/10.1016/j.astropartphys.2017.11.009https://doi.org/10.1016/j.astropartphys.2017.11.009