Cosmogenic production of $^{39}$Ar and $^{37}$Ar in argon
R. Saldanha, H.O. Back, R.H.M. Tsang, T. Alexander, S.R. Elliott, S., Ferrara, E. Mace, C. Overman, M.Zalavadia
TL;DR
This study measures the production rates of $^{39}$Ar and $^{37}$Ar isotopes in argon caused by cosmic ray neutrons at sea level, providing crucial data for dark matter experiments and atmospheric isotope analysis.
Contribution
It provides the first experimental determination of cosmogenic $^{39}$Ar and $^{37}$Ar production rates in argon at sea level using neutron beam irradiation and ultra-low background counting.
Findings
$^{39}$Ar production rate: 759 ± 128 atoms/kg/Ar/day
$^{37}$Ar production rate: 51.0 ± 7.4 atoms/kg/Ar/day
Total sea-level production rate for $^{39}$Ar: 1048 ± 133 atoms/kg/Ar/day
Abstract
We have experimentally determined the production rate of Ar and Ar from cosmic ray neutron interactions in argon at sea level. Understanding these production rates is important for argon-based dark matter experiments that plan to utilize argon extracted from deep underground because it is imperative to know what the ingrowth of Ar will be during the production, transport, and storage of the underground argon. These measurements also allow for the prediction of Ar and Ar concentrations in the atmosphere which can be used to determine the presence of other sources of these isotopes. Through controlled irradiation with a neutron beam that mimics the cosmic ray neutron spectrum, followed by direct counting of Ar and Ar decays with sensitive ultra-low background proportional counters, we determined that the production rate from cosmic ray…
| UAr cylinder II | AAr cylinder III | |||
| Value | Unc.[%] | Value | Unc.[%] | |
| Atomic Weight Böhlke (2014) | 7 | 3.8 | ||
| 40Ar Isotopic Abundance Böhlke (2014) | 0.07 | 4.2 | ||
| Mass [] | 2.3 | 2.3 | ||
| 40Ar Areal Density [] | 1.6 | 1.6 | ||
| Neutrons ( 10 MeV) through cylinder | 5.9 | 6.0 | ||
| ULBPC Sample Mass [] | 1.0 | 1.0 | ||
| ULBPC 39Ar Activity [] | 1.0 | 1.0 | ||
| ULBPC 37Ar Activity [] | 3.1 | 3.1 | ||
| 39Ar Half-life [yrs] Chen (2018) | 3 | 3 | ||
| Pre-existing 39Ar Activity [] | 9.5 | 8.5 | ||
| Beam-Averaged Cross-Section [cm2] | 7.2 | 7.3 | ||
| Beam Induced 39Ar Activity [] | 2.7 | 2.8 | ||
| 37Ar Half-life [days] Cameron et al. (2012) | 0.054 | 0.054 | ||
| 37Ar Decay Correction Factor | 0.22 | 0.26 | ||
| Pre-existing 37Ar Activity [] | 33 | 33 | ||
| Beam-Averaged Cross-Section [cm2] | 7.2 | 7.3 | ||
| Beam Induced 37Ar Activity [] | 4.0 | 4.0 | ||
| Cross-Section | Pred. LANSCE | Meas./Pred. LANSCE | Pred. Cosmogenic | Scaled Cosmogenic |
| Model | 39Ar Activity | 39Ar Activity | 39Ar Prod. Rate | 39Ar Prod. Rate |
| [mBq] | [] | [] | ||
| Silberberg & Tsao (ACTIVIA) | ||||
| MENDL-2P | ||||
| TENDL-2015 | ||||
| TALYS | ||||
| INCL++ (ABLA07) |
| Cross-Section | Pred. LANSCE | Meas./Pred. LANSCE | Pred. Cosmogenic | Scaled Cosmogenic |
| Model | 37Ar Activity | 37Ar Activity | 37Ar Prod. Rate | 37Ar Prod. Rate |
| [Bq] | [] | [] | ||
| Silberberg & Tsao (ACTIVIA) | ||||
| MENDL-2P | ||||
| TALYS | ||||
| INCL++ (ABLA07) |
| Reaction | Estimated 39Ar Production rate | Fraction of total |
| [] | AAr [%] | |
| 40Ar(n, 2n)39Ar + | 72.3 | |
| 40Ar(n, d)39Cl | ||
| 40Ar(, n)39Cl | 16.4 | |
| 40Ar(, n)39Ar | 8.5 | |
| 40Ar(, p)39Cl | 2.3 | |
| 40Ar(p, 2p)39Cl | ||
| 40Ar(p, pn)39Ar | 0.3 | |
| 38Ar(n, )39Ar | (UAr) | - |
| (AAr) | 0.1 | |
| Total | 100 |
| Reaction | Estimated 37Ar Production rate | Fraction of total UAr | Fraction of total AAr |
| [] | [%] | [%] | |
| 40Ar(n, 4n)37Ar | 90.0 | 55.5 | |
| 40Ar(, 3n)37Ar | 6.1 | 3.8 | |
| 40Ar(p, p3n)37Ar | 2.3 | 1.4 | |
| 36Ar (n, )37Ar | (UAr) | 1.6 | 38.9 |
| (AAr) | |||
| 38Ar(n, 2n)37Ar + | (UAr) | 0.5 | |
| 38Ar(, n)37Ar + | |||
| 38Ar(p, pn)37Ar | (AAr) | ||
| Total | (UAr) | 100 | 100 |
| (AAr) |
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Cosmogenic production of 39Ar and 37Ar in argon
R. Saldanha
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
H. O. Back
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
R. H. M. Tsang
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
T. Alexander
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
S. R. Elliott
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
S. Ferrara
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
E. Mace
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
C. Overman
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
M. Zalavadia
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
Abstract
We have experimentally determined the production rate of 39Ar and 37Ar from cosmic ray neutron interactions in argon at sea level. Understanding these production rates is important for argon-based dark matter experiments that plan to utilize argon extracted from deep underground because it is imperative to know what the ingrowth of 39Ar will be during the production, transport, and storage of the underground argon. These measurements also allow for the prediction of 39Ar and 37Ar concentrations in the atmosphere which can be used to determine the presence of other sources of these isotopes. Through controlled irradiation with a neutron beam that mimics the cosmic ray neutron spectrum, followed by direct counting of 39Ar and 37Ar decays with sensitive ultra-low background proportional counters, we determined that the production rate from cosmic ray neutrons at sea-level is expected to be for 39Ar, and for 37Ar. We also performed a survey of the alternate production mechanisms based on the state-of-knowledge of the associated cross-sections to obtain a total sea-level cosmic ray production rate of for 39Ar, for 37Ar in underground argon, and for 37Ar in atmospheric argon.
argon, cosmogenic, activation, 39Ar, 37Ar
I Introduction
Argon is a widely used medium for the detection of ionizing radiation. It has a high scintillation and ionization yield, allows for the propagation of scintillation photons and ionization electrons over large distances, and can be easily purified to remove non-noble impurities. Argon is therefore employed as the active medium for large neutrino detectors Rubbia et al. (2011); Abi et al. (2018), scintillation vetos Agostini et al. (2017), and direct-detection dark matter experiments Benetti et al. (2008); Agnes et al. (2018); Amaudruz et al. (2018). Argon is particularly attractive for dark matter detectors as the time profile of the scintillation light enables pulse-shape discrimination (PSD) of signal-like nuclear recoils from radiogenic electron recoils.
Argon is the third-most abundant gas in the Earth’s atmosphere, comprising roughly 0.93% of the atmosphere by volume. Argon extracted from the atmosphere consists primarily of the stable isotopes 40Ar, 36Ar, and 38Ar. However, due to interactions of cosmic rays, atmospheric argon also contains three long-lived radioactive isotopes: 39Ar, 37Ar, and 42Ar. The abundances and specific activity of the different isotopes in the atmosphere are given in Table 1. In this paper we will focus on the two radioisotopes that, due to their high specific activity, are most relevant for argon-based dark matter experiments: 37Ar and 39Ar.
39Ar is a pure -emitter with an end-point of 565 keV and a half-life of 268 years Chen (2018). For large or low background argon-based detectors 39Ar is often the dominant source of interactions at low energies. The decays of 39Ar limit the sensitivity to rare events and can also create difficulties through signal pileup and high data acquisition rates. In dark matter detectors PSD is extremely effective at reducing the 39Ar background at high energies, but at low energies the discrimination power is limited by the detected photon statistics and the energy threshold is often determined by the 39Ar rate Agnes et al. (2015); Amaudruz et al. (2018).
To mitigate the effects of 39Ar, the next generation of argon-based dark matter detectors propose to use argon extracted from deep underground. The DarkSide-50 collaboration has demonstrated that underground argon (UAr) they are using as their dark matter target has an 39Ar rate of Agnes et al. (2016), a factor below atmospheric levels. The use of UAr rather than atmospheric argon (AAr) has allowed for a reduction in energy threshold and increase in nuclear recoil acceptance while maintaining a background-free WIMP dark matter search Agnes et al. (2016, 2018). Additionally, the use of low radioactivity UAr is critical for low-mass dark matter searches which extend to lower energy thresholds than the standard WIMP search Agnes et al. (2018). The need for argon with low-levels of 39Ar grows as future dark matter experiments move towards tonne-scale target masses and beyond. The relative background contributions of radioactive contaminants in external components will decrease due to self-shielding of the argon and a decreasing surface-to-volume ratio, making 39Ar (which scales with the target mass) the likely dominant background.
Similar to the commercial production of argon from the atmosphere, UAr must be extracted from crude naturally occurring gases underground. In the case of the DarkSide-50 experiment this crude gas is primarily CO2, extracted from a gas well in Cortez, Colorado, USA Back et al. (2012). The processing, transport, and storage of the UAr on the surface of the Earth exposes the UAr to cosmic rays until it can be suitably shielded underground. Given the extremely stringent requirements on the levels of 39Ar for dark matter detectors, cosmogenic production of 39Ar in the UAr is an important concern.
37Ar decays purely through electron capture, producing low energy x-rays and Auger electrons, with a relatively short half-life of 35.01 days Cameron et al. (2012). Since low background experiments are typically operated deep underground, shielded from cosmic rays, the 37Ar activity typically decays below measurable levels within a few months, though the x-ray peak can be used as a low energy calibration source during early data-taking Agnes et al. (2018). 37Ar can also be produced by underground nuclear explosions through neutron reactions with calcium in the soil Aalseth et al. (2011). Elevated rates of 37Ar in the environment are a strong indicator of a nuclear explosion and can therefore be used to verify compliance with nuclear test ban treaties. Thus the natural cosmogenic production of 37Ar in the atmosphere and surface soil gas acts as a background to underground nuclear monitoring Riedmann and Purtschert (2011).
The cosmogenic production of both 37Ar and 39Ar in argon is expected to be dominated by neutron-induced reactions but there are no existing measurements of the total production cross-section or integrated cosmogenic production rate. Estimates for dark matter experiments have therefore had to rely on semi-empirical calculations, which as we show, significantly underestimate the production rates. In this paper we describe a measurement of the integrated production rate from a neutron beam at the Los Alamos Neutron Science Center (LANSCE) ICE HOUSE facility Lisowski and Schoenberg (2006); Takala (2006) which has a very similar energy spectrum to that of cosmic ray neutrons at sea-level (see Figure 1). While the spectral shape is similar, the neutron beam has a flux that is times higher above 10 MeV, which allows for the production of measurable amounts of 39Ar in short periods of time. We irradiated samples of underground and atmospheric argon for 3 days on the neutron beam and then measured the resulting activity in ultra-low background gas proportional counters (ULBPC) at Pacific Northwest National Laboratory (PNNL). The ULBPCs are custom-built to detect low levels of 39Ar and 37Ar in gas samples for the purpose of radiometric dating and support of future nuclear test ban treaty monitoring Aalseth et al. (2009), with a sensitivity to 39Ar at the level of Hall et al. (2016); Mace (2018) and to 37Ar at the level of Aalseth et al. (2011); Mace (2018). The high intensity of the LANSCE neutron beam and the sensitivity of the ULBPC detectors allow us to experimentally measure the 39Ar and 37Ar production rate and extrapolate them to estimate the sea-level cosmogenic neutron production rate.
II 39Ar Production Mechanisms
The production of 39Ar in the atmosphere is primarily due to cosmic rays. While several of the production channels do not have measured cross-sections, based on the known flux of the various cosmogenic particles and the general behavior of cross-sections for similar isotopes, it is estimated that interactions with fast neutrons account for more than 94% of the total 39Ar production in the atmosphere Loosli and Oeschger (1968). There are two111The neutron-induced production of 39S, which sequentially decays to 39Cl and 39Ar, is estimated to be 4 orders of magnitude smaller than the direct 39Ar production. For other possible production mechanisms see Section VII. primary fast neutron reactions that result in the production of 39Ar: 40Ar(n, 2n)39Ar and 40Ar[(n, np) + (n, pn) + (n, d)]39Cl. In the latter case, which we will henceforth abbreviate to 40Ar(n, d)39Cl, the short-lived 39Cl decays to 39Ar through decay with a 55.6 minute half-life. Since 39Ar is a pure emitter it is not possible to directly measure the total production cross-section by conventional methods that rely on -ray detectors to tag the reaction products. The only existing measurements are of the partial cross-sections 40Ar(n, 2n)39Ar to excited states of 39Ar MacMullin et al. (2012) and of 40Ar(n, d)39Cl through the detection of gamma rays from the 39Cl decay Rama and Honda (1961); Gray et al. (1965); Husain and Kuroda (1968); Ranakumar et al. (1969).
Estimates of the cosmogenic activation rates have therefore had to rely on either semi-empirical calculations such as the Silberberg and Tsao equations Silberberg and Tsao (1973a, b, 1977); Silberberg et al. (1985); Silberberg and Tsao (1990); Silberberg et al. (1998) that are employed by codes such as YIELDX Tsao et al. (1996), COSMO Martoff and Lewin (1992), and ACTIVIA Back and Ramachers (2008), Monte Carlo simulations of the hadronic interactions between nucleons and nuclei that are performed by codes such as INCL Boudard et al. (2013), ABLA Kelic and Schmidt (2008), TALYS Koning et al. (2008), etc., or compiled databases that combine calculations with experimental data such as ENDF Chadwick et al. (2011), MENDL-2P McLaughlin and Pronyaev (1998), and TENDL Koning and Rochman (2012). The 39Ar production cross-section estimates from some of these different methods222The Silberberg and Tsao, and MENDL-2P cross-sections were obtained from the ACTIVIA code package Back and Ramachers (2017), the INCLXX cross-sections were calculated using the INCL++ code (v6.0.1) with the ABLA07 de-excitation model Mancusi et al. (2014), and the TALYS cross-sections calculated using TALYS-1.9 Koning et al. (2017). The default parameters were used for all programs., along with the experimentally measured partial cross-sections, are shown in Figure 2. It can be seen that the estimates vary by up to an order of magnitude at certain energies, yielding similar sized variation in the predicted 39Ar production rate. It should be noted that previous estimates of the cosmogenic activation rate of underground argon Aalseth et al. (2018) have used the Silberberg and Tsao semi-empirical calculations as implemented in the COSMO and ACTIVIA codes, which have the lowest predicted cross-sections and are significantly below the experimentally measured partial cross-sections.
III 37Ar Production Mechanisms
The production of 37Ar in the atmosphere is also dominated by neutron interactions on argon. Previous calculations Loosli et al. (1970) estimate that 93% of the total production in the troposphere is due to fast neutrons through 40Ar(n, 4n)37Ar, with the remaining fraction333For other possible production mechanisms see Section VII. due to the capture of thermal and epithermal neutrons through 36Ar(n, )37Ar. The only detectable signal from 37Ar decays are the low-energy x-rays and Auger electrons following the electron capture, and thus the 40Ar(n, 4n)37Ar production cross-section cannot be measured with -ray detectors. To our knowledge there are no known experimental measurements of this cross-section. Examples of estimates from semi-empirical calculations, simulations, and evaluated databases are shown in Figure 3. As with the 39Ar production cross-sections, these estimates can vary by up to an order of magnitude.
IV Experiment
Three samples of argon gas were prepared for irradiation, two UAr samples and one AAr sample. The UAr samples were taken from the same source of gas that was used in the DarkSide-50 experiment and the AAr sample was commercial ultra high purity (99.999%) grade argon obtained from Oxarc. An AAr sample was used in addition to the UAr samples to investigate if the different isotopic composition of the gases would lead to significantly different 39Ar and 37Ar production. In addition to 40Ar, AAr contains 36Ar at 0.334% and 38Ar at 0.063% Böhlke (2014); Meija et al. (2016). UAr is composed almost solely of 40Ar with the 36Ar concentration measured by mass spectrometry to be less than 0.01% and the 38Ar concentration expected to be reduced by a similar factor compared to AAr, consistent with measurements of gas extracted from deep underground wells Loosli and Oeschger (1968). For the sake of clarity, all numbers and uncertainties related to the gas samples in the main body of this paper refer to one of the UAr samples (cylinder II). The corresponding numbers for the AAr sample (cylinder III) are included in Table 2, while the other UAr sample (cylinder I) was kept as contingency and not measured.
The gas samples were filled at and in three identical aluminum cylinders, each with an interior volume of (calculated through calibrated volume-ratio measurements), corresponding to of gas, where the uncertainty includes the uncertainties in pressure, temperature, and volume. The custom-designed cylinders had a nominal (3”) internal diameter and internal length and were fabricated from aluminum to minimize the attenuation of the neutron beam as well as activation of the cylinder material. The end caps of the cylinder, through which the neutron beam passed, had a thinned -thick central wall and were welded onto the cylindrical section. The gas was filled and emptied through a single diameter double-valved tube on each cylinder and the cylinders were evacuated to before being filled with the argon gas sample.
The samples were irradiated at the LANSCE WNR ICE-HOUSE II facility Takala (2006) on Target 4 Flight Path 30 Right (4FP30R). A broad-spectrum ( ) neutron beam was produced via spallation of 800 MeV protons on a tungsten target. A 50.8 mm (2”) diameter beam collimator was used to restrict the majority of the neutrons to within the diameter of the gas cylinder. The neutron fluence was measured with 238U foils by an in-beam fission chamber Wender et al. (1993) placed downstream of the collimator. The beam has a pulsed time structure which allows the incident neutron energies to be determined using a time-of-flight (TOF) measurement between the proton beam pulse and the fission chamber signals Lisowski and Schoenberg (2006); Wender et al. (1993). As shown in Figure 4, the three gas cylinders were placed end-to-end with the two UAr cylinders (I and II) closest to the fission chamber and AAr cylinder III furthest away. The closest end of the UAr cylinder I was located downstream from the fission chamber.
The beam exposure took place over three days between 11-14 December 2017. The fluence measured by the fission chamber is shown in Figure 1, with a total of neutrons above 10 MeV. The uncertainty is dominated by the systematic uncertainty in the 238U(n, f) cross-section which varies from 2% to 5% below 200 MeV Carlson et al. (1997) (which includes most of the production range) and we have conservatively assumed 5% across the whole spectrum. The uncertainty in the neutron energy spectrum due to the timing uncertainty in the TOF measurement (1.2 ns) is negligible for this measurement. While the nominal beam diameter was set by the 2” collimator, the cross-sectional beam profile has significant tails at larger radii, with roughly 10% falling outside the 3” diameter of the gas cylinders. Additionally the beam is slightly diverging, with an estimated cone opening angle of . A Geant4 Agostinelli et al. (2003); Allison et al. (2016) simulation that included the measured beam profile and beam divergence, the measured neutron spectrum, and the full geometry and materials of the gas cylinder, was used to calculate the neutron fluence through each cylinder. The estimated reduction factor of the neutron fluence through UAr cylinder II in the 10-200 MeV range, compared to the fluence measured by the fission chamber, is , where the uncertainty includes the uncertainty in the beam profile and a uncertainty in the alignment of the beam center with the cylinder axes.
Following the irradiation the cylinders were stored for a cool-down period of roughly a month before they were shipped to PNNL for counting. The measured pressure of the argon in the irradiated cylinders upon return to PNNL matched the initial fill pressures within uncertainties, indicating that no argon had leaked out during the transportation or irradiation. Activation calculations indicated that along with 39Ar and 37Ar, several other long-lived radioisotopes would also be produced by the irradiation, most notably 32P, 33P, 35S, 22Na, 3H, and 7Be. However previous experiments involving the irradiation of argon Brodzinski and Wogman (1970); Reyss et al. (1981) found that activation products remain in the irradiation canister when argon is transferred out. Since tritium is especially dangerous as it can introduce a long-lived radioactive background into the ULBPC, the argon gas was cryopumped through a hydrogen getter into a smaller cylinder for loading into the ULBPC. The irradiated gas was then mixed with 10% methane to form P-10 count gas.
A sample of the P-10 gas mixture from UAr cylinder II was loaded into the ULBPC at and , corresponding to an argon mass of . The irradiated UAr gas was counted for days at low gain to measure the 39Ar spectrum from and was also counted at high gain from for days to measure the 37Ar peak.
The 39Ar detection efficiency of the ULBPC detector was calibrated with a 39Ar source Williams et al. (2017), and a background run was also acquired. As shown in Figure 6, the extremely good agreement in spectral shape between the efficiency spectrum and the data indicate that no other -decaying activation products were present in the gas sample. After subtracting the measured background spectrum and accounting for the calibrated detection efficiency of , the measured 39Ar activity in the ULBPC was found to be .
For 37Ar, the spectrum was fit with a Gaussian to represent the Auger electrons and x-rays following a K-shell electron capture and an exponential decay for the underlying 39Ar spectrum (shown in Figure 6). The branching ratio for the K-shell electron capture is Cleveland et al. (1998); Cameron et al. (2012) and the combined ULBPC fiducial volume efficiency for both Auger electrons and x-rays is Williams et al. (2016). Including systematic uncertainties from the choice of fit range and response function we obtained a total measured 37Ar activity in the ULBPC of , scaled to the start of the counting time (accounting for the decay of 37Ar during the measurement period).
Scaling these activities by the fraction of the total irradiated gas measured and the radioactive decay between the start of the irradiation and the measurement, we found an 39Ar activity of and an 37Ar activity of for all the gas in the irradiated UAr cylinder II. Following the same procedure described above, for the gas from AAr cylinder III we found an 39Ar activity of and an 37Ar activity of .
One must also account for the cosmogenic 39Ar and 37Ar activity that is present in the samples even without the beam irradiation. Atmospheric argon was found to contain a specific activity of Benetti et al. (2007) of 39Ar, corresponding to an activity of in AAr cylinder III, which must be subtracted from the measured activity when calculating the beam activation rate. The UAr sample was obtained from the same source of gas used by DarkSide-50 that was found to have an 39Ar specific activity of . Compared to the DarkSide-50 target which was transported deep underground in February 2015, our UAr samples spent approximately 1170 additional days on the surface, exposed to cosmic-rays. Even assuming the highest considered cross-section, the total pre-existing rate of 39Ar in the irradiated gas sample is roughly , negligible compared to the measured activity.
For the short-lived 37Ar, both samples will have reached equilibrium activity from cosmogenic production at sea-level. Measurements of the 37Ar activity in the low troposphere (excluding variations due to in-flows of stratospheric air, outgassing of soil air, and emissions from nuclear installations) indicate an equilibrium value of () Purtschert et al. (3 O2). The equilibrium rate at sea-level is expected to be significantly lower than the rate averaged over the troposphere (in Section VII we estimate it to be ()), but we conservatively use the averaged tropospheric value as an upper limit, corresponding to total activity of , which is in any case negligible compared to the measured activity.
The final estimates for the beam-induced activity in the UAr [AAr] sample at the end of the irradiation are [] 39Ar and [] 37Ar. The specific input values used as well as the included statistical and systematic uncertainties are listed in Table 2. To compare the results between the UAr and AAr samples we can divide the measured activity by the total number of neutrons and target 40Ar atoms to obtain a beam-averaged cross-section (listed in Table 2). The ratio of the UAr to AAr beam-averaged cross-section, after eliminating common systematic uncertainties, is and for 39Ar and 37Ar respectively. The good agreement between the irradiated UAr and AAr activities indicate that, as expected, there was no appreciable contribution from neutron interactions with the small fractions of naturally occurring 36Ar and 38Ar isotopes present in the AAr sample. The agreement also verifies the accuracy of the simulations of the beam attenuation between the targets and the independent ULBPC activity measurements.
V Cross-Sections
If the neutron beam had an energy spectrum identical to that of the cosmic ray neutron flux we could simply estimate the cosmogenic production rate by scaling the measured activity by the ratio of the cosmic-ray neutrons to that of the neutron beam. However the beam spectrum falls off faster at higher energies than that of cosmic rays (see Figure 1). Thus we must rely on a model for the production cross-sections to extrapolate from the beam measurement to the cosmogenic production rate.
We can evaluate the accuracy of the different cross-section models by comparing the predicted 39Ar and 37Ar production rates from the LANSCE neutron beam irradiation to the measured rates. The number of isotopes atoms at a given time is governed by the equation
[TABLE]
where is the mean life [] of the isotope decay and is the isotope production rate []. Ignoring any existing isotope concentration (subtracted off from the measured experimental value), the measured decay rate at any time after the start of the beam irradiation is given by
[TABLE]
For a given cross-section model [cm2]
[TABLE]
where is the areal number density of the target argon atoms [] and is the energy spectrum of neutrons []. The second column of Table 3 shows the calculated values for the different 39Ar cross-section models considered, with the corresponding numbers for 37Ar shown in Table 4. We note that not all the cross-section models considered span the entire range of neutron energies. The TENDL 2015 and MENDL-2P cross-sections are only reported up to 200 MeV, while the TALYS cross-sections have been extended up to 1 GeV Koning et al. (2014). The INCL++ model can handle neutron-induced reactions up to 15-20 GeV, while the Silberberg & Tsao semi-empirical cross-section calculations implemented in ACTIVIA can be performed at any energy, though the cross-sections are assumed to be independent of energy above GeV.
From the ratio of the experimentally measured values to the predictions (shown in the third column of Table 3 and 4) it can be seen that the TENDL-2015, TALYS, and INCL++ models all predict 39Ar activities within 10% of the measured LANSCE activation value. However, the Silberberg and Tsao cross-section model used as the default by the ACTIVIA and COSMO codes, and previously used to estimate the cosmogenic production rate for argon dark matter experiments Aalseth et al. (2018), predict values more than a factor of 4 smaller than the experimental measurement. The predictions for the 37Ar production vary from the experimental measurements by roughly a factor three in both directions, with the TALYS and INCL++ models accurate to within about 50%.
If we assume that the shape of the cross-section model as a function of energy is correct, the ratio of the experimentally measured activity to the predicted activity represents the normalization factor that will need to be applied to each model to best match the experimental data. In the next section we will use this ratio to estimate the 37Ar and 39Ar production rates from cosmic ray neutrons.
VI Production Rates from Fast Cosmic Ray Neutrons
There have been several measurements and calculations of the cosmic ray neutron flux (for eg. Hess et al. (1959); Armstrong et al. (1973); Ziegler (1996)). The intensity of the neutron flux varies with altitude, location in the geomagnetic field, and solar magnetic activity (though the spectral shape does not vary as significantly) and correction factors must be applied to calculate the appropriate flux Desilets and Zreda (2001). The most commonly used reference spectrum for sea-level cosmic ray neutrons is the so-called ”Gordon” spectrum Gordon et al. (2004) (shown in Figure 1), which is based on measurements at five different sites in the United States, scaled to sea-level at the location of New York City during the mid-point of solar modulation. We have used the parameterization given in Gordon et al. (2004) which agrees with the data to within a few percent. The spectrum uncertainties at high energies are dominated by uncertainties in the spectrometer detector response function (% below 10 MeV and 10-15% above 150 MeV) and we have assigned an average uncertainty of 12.5%.
The production rate per unit target mass [] of isotopes from the interaction of cosmic ray neutrons can be written as
[TABLE]
where is the number of target atoms per kilogram of argon and is the cosmic neutron flux []. The integral is evaluated from 1 MeV to 10 GeV.
The predicted production rate per unit target mass for the cross-section models considered is shown in the fourth column of Table 3 and Table 4 for 39Ar and 37Ar respectively. Scaling these values by the ratio of the experimental to predicted activities for the LANSCE neutron beam, we obtain our best estimates for the cosmic neutron induced production rates per unit target mass, shown in the final columns. The spread in the values for the different cross-sections is an indication of the systematic uncertainty in the extrapolation from the LANSCE beam measurement to the cosmic neutron spectrum. If either the LANSCE neutron beam spectral shape was the same as that of the cosmic ray neutrons, or the cross-section models all agreed in shape, the central values in the final column would be identical. The estimated activation rate from cosmic ray neutrons is and , where the first uncertainty listed is due to experimental measurement uncertainties (represented by the average uncertainty on the ratio of the measured to predicted activity from the LANSCE beam irradiation for a specific cross-section model), the second is due to the uncertainty in the shape of the cross-section models (calculated as the standard deviation of the scaled cosmogenic production rates by the different models), and the third is due to the uncertainty in the sea-level cosmic neutron flux.
VII Alternate Production Mechanisms
In addition to activity induced by fast neutrons, interactions of gamma-rays, muons, protons, and thermal neutrons also contribute to the total production rate of 39Ar and 37Ar. Previous calculations estimated that interactions of fast neutrons account for 94% of the total 39Ar production in the atmosphere Loosli and Oeschger (1968) and 93% of the production of 37Ar in the troposphere Loosli et al. (1970). However, at the Earth’s surface the ratio of the fast neutron flux compared to other cosmogenic particles is significantly different due to different attenuation lengths in the atmosphere and the relative contributions must be re-evaluated. In the following two sub-sections we describe the methods we used to estimate the individual contributions using existing measurements and models.
VII.1 Alternate 39Ar Production Mechanisms
40Ar(, n)39Cl
The production rate from muon captures at sea-level, , can be estimated by
[TABLE]
where = is the rate of stopped muons at sea-level Charalambus (1971) and we have added a 10% uncertainty to account for the 10% difference in the (Z/A) value for argon compared to air, (40Ar) = is the capture rate of muons on argon Bertin et al. (1973), = is the decay rate of muons Tanabashi et al. (2018), and f^{*}(\text{{}^{39}{Cl}}) = is the effective probability of producing 39Cl or 39S Klinskikh et al. (2008); Pârvu et al. (2018). The sea-level production rate from muon captures is therefore estimated to be .
40Ar(, n)39Ar and 40Ar(, p)39Cl
The flux of high energy rays at the Earth’s surface was obtained using the PARMA analytical model Sato (2016) as implemented in the EXPACS software program Sato (2018). Similar to the neutron spectrum, we used New York city as our reference location for the spectrum, which is shown in Figure 8. We verified that the flux predicted by the model agreed with experimental measurements Ryan et al. (1979) to within 20% in the energy range of interest (10-30 MeV), which we used as our estimate of the systematic uncertainty. Experimental measurements of the 40Ar(, n)39Ar cross-section Ehhalt et al. (1965); Jury et al. (1973); Sutton et al. (1983) and the 40Ar(, p)39Cl cross-section Ehhalt et al. (1965); Sutton et al. (1983) are shown in Figure 8. Where multiple measurements exist we have used the mean and sample standard deviation of the calculated production rates as our estimates of the central value and uncertainty. The estimates for the individual processes are shown in Table 5 with the total sea-level production rate from rays estimated to be .
40Ar(p, 2p)39Cl and 40Ar(p, pn)39Ar
At sea-level the flux of 10-100 MeV cosmic ray protons is at least thirty times lower than that of cosmic ray neutrons due to the additional electromagnetic interactions of protons in the atmosphere. To estimate the production rate from protons we have used the proton spectra from Ziegler (1981) and Diggory et al. (1974) (scaled by the angular distribution from the EXPACS code) as shown in Figure 8. Measurements of the 40Ar(p, 2p)39Cl cross-section at low Nagatsu et al. (1999) and high Brodzinski and Wogman (1970) energies are shown in Figure 8 but, due to the low proton flux, the contribution to the overall production rate at sea-level is negligible. We are not aware of any measurements of the 40Ar(p, np)39Ar cross-section (again probably due to the difficulty of detecting 39Ar) and have therefore based our estimates on the 40Ar(n, d)39Ar cross-section from TALYS, scaled by the same factor used in Table 3. As before, we have used the mean and sample standard deviation of the calculated production rates with the different proton spectra and cross-sections as our estimates of the central value and uncertainty, yielding a sea-level production rate of .
38Ar(n, )39Ar
In atmospheric argon (AAr), 39Ar can also be produced through the capture of thermal and epi-thermal neutrons on 38Ar. For the low energy neutron flux we used the measurements taken in New York (see Figure 9 taken from Figure 4 in Gordon et al. (2004)). We note that even after correcting for altitude, location, and solar activity, the flux of low energy neutrons varies due to differences in the local environment Gordon et al. (2004) and we have therefore assumed a 30% uncertainty in the overall normalization of the flux. For the 38Ar(n, )39Ar cross-section we have used the ENDF/B-VIII.I values Chadwick et al. (2011) (shown in Figure 9) which agrees well with experimental data at thermal energies Katcoff (1952); Tessler et al. (2018). Due to the low abundance of 38Ar the contribution to the total production rate () is negligible.
The estimates for each of these alternate production mechanisms for 39Ar is summarized in Table 5, with fast neutrons contributing 73% of the total production rate of 39Ar at sea-level. As partial verification, one can compare the estimates of the total 39Cl production rate to an experimental measurement of the production rate of 39Cl in argon gas exposed at sea level Rama and Honda (1961). Summing up the contributions from fast neutrons ( through 40Ar(n, d)39Cl) with the alternate mechanisms listed in Table 5, one obtains a total production rate of which is in relatively good agreement with the experimentally measured .
Thus the total cosmic ray production rate at sea-level is expected to be for 39Ar, which corresponds to a cosmic ray activation rate of and a saturated equilibrium activity of . Note that the equilibrium activity at sea-level is lower than the measured level of 39Ar in the atmosphere because the total rate in the atmosphere is dominated by the production at high altitudes, where the neutron flux is significantly higher.
VII.2 Alternate 37Ar Production Mechanisms
40Ar(, 3n)37Ar and 40Ar(p, p3n)37Ar
We are not aware of any existing measurements of either the 40Ar(, 3n)37Ar or the 40Ar(p, p3n)37Ar cross-section. For the production rate from gammas we used the cross-section from TALYS (shown in Figure 8), while for proton induced reactions we have used the production rates obtained with the TALYS and INCL++ 40Ar(n, 4n)37Ar cross-sections. As above, where multiple flux or cross-section estimates exist we have used the mean and sample standard deviation of the calculated production rates as our estimates of the central value and uncertainty. We estimate a sea-level production rate of and from 40Ar(, 3n)37Ar and 40Ar(p, p3n)37Ar respecively.
36Ar (n, )37Ar
In AAr, 37Ar can also be produced through the capture of thermal and epi-thermal neutrons on 36Ar. For the 36Ar(n, )37Ar cross-section we have used the ENDF/B-VII.I values Chadwick et al. (2011) (shown in Figure 9) which agrees well with experimental data at thermal energies McMurtrie and Crawford (1950); Tessler et al. (2018), though recent measurements at higher energies (Maxwellian keV) indicate that the cross-sections could be significantly lower than previous estimates Tessler et al. (2018). This production channel produces a significant contribution to the total production rate of at sea-level. Note that the abundance of 36Ar in argon from underground sources is reduced by roughly a factor of 40, and hence the production of 37Ar from neutron captures in UAr is <$$1\text{\,}\mathrm{atom}\text{/}\text{(}\mathrm{kg_{\text{Ar}}}\text{\,}\mathrm{day}\text{)}.
38Ar(n, 2n)37Ar, 38Ar(, n)37Ar, and 38Ar(p, pn)37Ar
All of the direct production mechanisms of 39Ar from 40Ar also apply to the production of 37Ar from 38Ar in AAr. We are not aware of any experimental measurements of the cross-sections on 38Ar except for 38Ar(, n)37Ar Ehhalt et al. (1965) which is roughly the same as the 40Ar(, n)39Ar cross-section. We have therefore estimated the production rate from reactions on 38Ar by taking the sum of the production rates from all direct 40Ar(x, y)39Ar mechanisms () and scaling it by the abundance of 38Ar in AAr (0.000629). This is perhaps an overestimation due to the fact that 38Ar has a magic number of neutrons and may therefore be expected to have lower cross-sections for the ejection of a neutron than 40Ar, but the contribution is in any case negligible ().
The estimates for each of these alternate production mechanisms for 37Ar is summarized in Table 6. The total cosmic ray production rate at sea-level is expected to be for 37Ar in underground argon and for 37Ar in atmospheric argon. These numbers correspond to a cosmic ray activation rate of for UAr and for AAr, and a saturated equilibrium activity of , respectively.
VIII Summary and Discussion
We have made the first experimental measurement of the production rate of 39Ar and 37Ar due to fast neutron interactions in argon. This measurement was enabled by the ability to directly measure the and electron-capture decays that are not detectable with standard methods only sensitive to -rays from activation products. Including uncertainties in the cross-section models and the cosmogenic neutron flux we obtained a production rate of for 39Ar, and for 37Ar from cosmogenic neutrons at sea-level. Combined with calculated estimates of other production mechanisms, we obtain a total cosmic ray production rate at sea-level of for 39Ar, and for 37Ar in atmospheric argon ( for 37Ar in UAr).
These results are most relevant to argon-based dark matter detectors where 39Ar is the dominant background and lowering the rate of 39Ar can reduce energy thresholds and improve sensitivity. The argon extracted from underground and used as the target for the DarkSide-50 experiment was measured to have an 39Ar rate of Agnes et al. (2016), but it is thought that a large fraction of the residual 39Ar was due to an air infiltration during the purification of the underground gas. Thus it is possible that the measured activity is only an upper limit, and the true rate of 39Ar in UAr could be as low as Renshaw (2018). For future multi-ton dark matter detectors low levels of 39Ar are even more critical, and efforts will be made to avoid any contamination of the underground argon with the atmosphere Back (2018). At this possibly lower intrinsic 39Ar rate, cosmogenic activation of the underground argon (once it is extracted to the surface) is potentially a significant contributor to the overall background. The results from this paper, scaled by the cosmic ray flux at the relevant altitudes and locations, can be used to calculate the experiment-specific maximum duration UAr can spend above ground during extraction, purification, storage, and transportation. We note that the measured sea-level activation rate of 39Ar in this paper [] is nearly an order of magnitude larger than previous estimates based on semi-empirical calculations Aalseth et al. (2018).
Finally, these results can also be used to estimate the total equilibrium rate of 39Ar and 37Ar in the atmosphere. This is potentially useful for establishing baseline values for radioactive dating and nuclear activity monitoring, as well as evaluating the constancy of cosmic radiation Loosli et al. (1970).
IX Acknowledgements
This work was supported by the Laboratory Directed Research and Development Program at Pacific Northwest National Laboratory, a multiprogram national laboratory operated by Battelle for the U.S. Department of Energy under Contract No. DE-AC05-76RL01830, and also the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Los Alamos National Laboratory Award No. LANLE9BW. This work benefited from the use of the Los Alamos Neutron Science Center, funded by the US Department of Energy under Contract No. DE-AC52-06NA25396 and we would like to thank Steve Wender for his assistance with the beam exposure.
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