Astroparticle Physics 115 (2020) 102390 Contents lists available at ScienceDirect Astroparticle Physics journal homepage: www.elsevier.com/locate/astropartphys Study of cosmogenic radionuclides in the COSINE-100 NaI(Tl) detectors E. Barbosa de Souza a , B.J. Park b , ∗, G. Adhikari c , P. Adhikari c , 1 , N. Carlin d , J.J. Choi e , S. Choi e , M. Djamal f , A.C. Ezeribe g , C. Ha h , I.S. Hahn i , E.J. Jeon h , ∗, J.H. Jo a , W.G. Kang h , M. Kauer j , G.S. Kim k , H. Kim h , H.J. Kim k , K.W. Kim h , N.Y. Kim h , S.K. Kim e , Y.D. Kim h , c , b , Y.H. Kim h , l , b , Y.J. Ko h , V.A. Kudryavtsev g , E.K. Lee h , H.S. Lee h , b , J. Lee h , J.Y. Lee k , M.H. Lee h , b , S.H. Lee b , D.S. Leonard h , W.A. Lynch g , B.B. Manzato d , R.H. Maruyama a , R.J. Neal g , S.L. Olsen h , H.K. Park m , H.S. Park l , K.S. Park h , R.L.C. Pitta d , H. Prihtiadi f , h , S.J. Ra h , C. Rott n , K.A. Shin h , A. Scarff g , N.J.C. Spooner g , W.G. Thompson a , L. Yang o , G.H. Yu n , (COSINE-100 Collaboration) a Department of Physics, Yale University, New Haven, CT 06520, USA b IBS School, University of Science and Technology (UST), Daejeon 34113, Republic of Korea c Department of Physics, Sejong University, Seoul 05006, Republic of Korea d Physics Institute, University of São Paulo, São Paulo 05508-090, Brazil e Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea f Department of Physics, Bandung Institute of Technology, Bandung 40132, Indonesia g Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom h Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea i Department of Science Education, Ewha Womans University, Seoul 03760, Republic of Korea j Department of Physics and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin-Madison, Madison, WI 53706, USA k Department of Physics, Kyungpook National University, Daegu 41566, Republic of Korea l Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea m Department of Accelerator Science, Korea University, Sejong 30019, Republic of Korea n Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of Korea o Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA a r t i c l e i n f o Article history: Received 30 May 2019 Revised 10 September 2019 Accepted 15 September 2019 Available online 17 September 2019 Keywords: Cosmogenic radionuclide Activity Production rate COSINE-100 a b s t r a c t COSINE-100 is a direct detection dark matter search experiment that uses a 106 kg array of eight NaI(Tl) crystals that are kept underground at the Yangyang Underground Laboratory to avoid cosmogenic activa- tion of radioisotopes by cosmic rays. Even though the cosmogenic activity is declining with time, there are still significant background rates from the remnant nuclides. In this paper, we report measurements of cosmogenic isotope contaminations with less than one year half-lives that are based on extrapola- tions of the time dependent activities of their characteristic energy peaks to activity rates at the time the crystals were deployed underground. For longer-lived 109 Cd ( T 1 / 2 = 1 . 27 y) and 22 Na ( T 1 / 2 = 2 . 6 y), we investigate time correlations and coincidence events due to several emissions. The inferred sea-level pro- duction rates are compared with calculations based on the ACTIVIA and MENDL-2 model calculations and experimental data. The results from different approaches are in reasonable agreement with each other. For 3 H, which has a long, 12.3 year half-life, we evaluated the activity levels and the exposure times that are in reasonable agreement with the time period estimated for each crystal’s exposure. © 2019 Elsevier B.V. All rights reserved. 1 i K l i D v h 0. Introduction There are a number of experiments that search for direct ev- dence for dark matter particles in the halo of our Galaxy by∗ Corresponding authors. E-mail addresses: pbj7363@gmail.com (B.J. Park), ejjeon@ibs.re.kr (E.J. Jeon). 1 Present address: Department of Physics, Carleton University, Ottawa, Ontario 1S 5B6, Canada. p w A f c ttps://doi.org/10.1016/j.astropartphys.2019.102390 927-6505/© 2019 Elsevier B.V. All rights reserved. ooking for nuclei recoiling from dark matter nucleus scatter- ng [1,2] and report null results. One notable exception is the AMA/LIBRA experiment that has consistently reported the obser- ation of an annual event-rate modulation, that could be inter- reted as dark-matter signal, in an array of NaI(Tl) crystal detectors ith a statistical significance that is now more than 12.9 σ [3,4] . lthough this signal has persisted for over two decades and or three different configurations of the detector, it remainsontroversial because it is in conflict with the bounds from 2 E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 a u t h i s o h u m u 3 i t t s o p g i 1 1 f t t t c g l s a e s 1 g h s g t b s t t c H f 1 t b e s e n h c t i f other direct detection experiments using different tar get materials [5–10] and indirect searches [11] . However, since these conflicts depend on the details of the models for dark matter-nucleus scat- tering [12] and the properties of the galactic dark matter halo [13–15] , a conclusive statement about the DAMA/LIBRA signal can only be made by conducting an independent experiment using the same NaI(Tl) target material. This is the prime motivation of COSINE-100 and a number of other NaI(Tl)-crystal-based experi- ments [16–20] . COSINE-100 is a dark matter direct detection experi- ment [21,22] that uses a 106 kg array of eight low-background NaI(Tl) crystals situated in a 20 0 0 l liquid scintillator veto counter. The experiment is located 700 m underground at the Yangyang Underground Laboratory (Y2L), where it has been operating since September 2016. The search for an annual modulation signal requires a complete understanding of background sources and their time dependence. To accomplish this, a complete simulation that accurately models the background energy spectra measured in the detector is required [23] . In addition to backgrounds from long-lived radioactive contaminations in the crystal bulk and surfaces, we have to deal with time-dependent backgrounds from short-lived cosmogenically activated radionuclides. These are iso- topes that are created by interactions of cosmic rays with stable nuclides in the detector material. In COSINE-100, almost all of the cosmogenic isotopes come from cosmic ray interactions with either Na or I nuclei. This paper is organized as follows. The COSINE-100 detector is described in Section 2 . In Section 3 , the cosmogenic isotopes that are produced in NaI(Tl) are listed and the determination of the ac- tivity levels at the time of their initial deployment underground at Y2L is described. The use of these initial activity levels to in- fer production rates for cosmogenic isotopes at sea level and their comparison with ACTIVIA and MENDL-2 calculations [24,25] and with experimental data are discussed in Section 4 . The fitted activ- ities of 3 H and 129 I from the background modeling are evaluated in Section 5 and conclusions are provided in Section 6 . 2. The COSINE-100 experimental setup The experimental setup of COSINE-100, shown in Fig. 1 (a), is described in detail in Ref. [21] . Eight NaI(Tl) crystals, arranged in two layers, are located in the middle of a four-layer shielding structure. From outside inward, this comprises plastic scintillator panels, a lead-brick castle, a copper box, and a tank of scintillating liquid. The eight encapsulated NaI(Tl) crystal assemblies and their support table are immersed in the scintillating liquid that serves both as an active veto and a passive shield. The eight NaI(Tl) crys- tals were grown from powder provided by Alpha Spectra (AS). Two crystals (Crystal-5 and Crystal-8) are not considered in this paper because their low light yields result in poorer energy resolution and because of their relatively high background contamination lev- els, especially at low energies. Since the detailed cosmic ray exposure history of each crystal is unknown, we estimated the time period for each crystal’s expo- sure, listed in Table 1 , from the time between the powder produc- tion by Alpha Spectra at Grand Junction, Colorado, to the date de- livered to Y2L. We considered that the preparation of the NaI pow- der precedes the crystal growth date by 2 months. It includes 30 days as the duration of transportation to Y2L. Since Crystal-3 has a complicated exposure history, having been repaired once before deployment at Y2L, we can only be certain that the corresponding period is more than 9 months. The radioactivity cooling time for each crystal between delivery to Y2L and the start of data-taking is also listed in Table 1 . The six crystals that are considered in this analysis have light yields of about 15 photoelectrons/keV; the energy threshold for anccepted signal from a crystal is 2 keV. Selection criteria that are sed to isolate scintillation-light generated signals from photomul- iplier tube noise are described in detail in Ref. [21] . Events that ave above-threshold signals in only one of the crystals and none n any of the other crystals or the liquid scintillator are classified as ingle-hit events. Those with above-threshold signals in more than ne crystal and/or the liquid scintillator are classified as multiple- it events. Monte Carlo simulations based on the Geant4 toolkit [26] are sed to better understand the background spectra from the cos- ogenic isotopes in the crystals; the geometry used for these sim- lations is shown in Fig. 1 (b). . Cosmogenic radionuclides and initial activities Although the eight NaI(Tl) crystals had underground radioactiv- ty cooling times that range from several months to three years, here are still backgrounds from the long-lived cosmogenic iso- opes that were activated by cosmic rays while they were on the urface. To understand these backgrounds, we first considered the list f cosmogenic radioactive isotopes that are produced in NaI(Tl) re- orted in Refs. [30–33] . In Table 2 , we list the contributing cosmo- enic isotopes with their half lives and decay modes; short-lived sotopes, for which half lives are less than a year, are 125 I, 121 Te, 21 m Te, 123 m Te, 125 m Te, 127 m Te, and 113 Sn and long-lived isotopes are 09 Cd, 22 Na, 3 H, and 129 I. Since there are no characteristic peaks rom the decay of 123 m Te/ 125 m Te in the low energy below 100 keV heir contributions are negligible in all crystals in Table 1 and, thus, hey are not further considered in the analysis. The short-lived ( T 1/2 < 1 year) isotopes are not expected to con- ribute significantly to either Crystal-1 or Crystal-2 because their ooling times are long enough to reduce these activities to a negli- ible level. However, we expect some backgrounds from the short- ived isotopes in other crystals because their production rates at ea level, as estimated in [30–33] , are high and their cooling times re less than or equal to a year. Data points in Fig. 2 show the energy spectra for the six consid- red NaI(Tl) crystals during the first (blue) and last (green) 25 day egments of the dataset taken between October 21, 2016 and July 8, 2018. A significant reduction of peaks from short-lived cosmo- enic isotopes in Crystals 4, 6, and 7 for both single- and multiple- it events is evident, while the differences for Crystals 1 and 2 are mall, as expected. To associate the specific peaks with its cosmo- enic nuclide, we simulated each isotope in Table 2 as a radioac- ive contaminant randomly distributed inside the NaI(Tl) crystal ulk. Fig. 3 shows the differences between the initial and final data egments for Crystal-4. The subtracted spectrum is well fitted by he simulated cosmogenic components that are treated as parame- ers floating in the fit, thereby validating our selection of the main osmogenic contributors to the low-energy single-hit distribution. owever, the derived weight of each isotope from the fit are not urther considered in the analysis. Those two structures at about 2 and 48 keV in Fig. 3 are characteristic of 210 Pb. It decays over ime with the half-life of 22.3 year and there is a little difference etween the first and last 25 day spectra of the 1.7 year data. Four long-lived nuclides, 109 Cd, 22 Na, 3 H, and 129 I have low en- rgy deposits and are, therefore, potentially troublesome. It is es- ential to understand their background contributions to the low nergy spectra regions, especially in the (2–6) keV dark matter sig- al region of interest (ROI). The beta-decay spectrum of tritium as an endpoint energy of 18 keV and the electron capture de- ay of 22 Na produces 0.87 keV emissions. The beta decay of 129 I o 129 Xe ∗ is followed by 129 Xe ∗ transitioning to the stable 129 Xe sotope via the emission of a 39.6 keV γ -ray. Its spectral feature rom this process has a distribution with a peak around ∼45 keV. E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 3 Table 1 Mass, dimensions, powder, surface exposure, and underground radioactivity cooling times for each one of the analyzed crystals (see text). Crystal Mass Size Powder type Exposure time Radioactivity (kg) (diameter × length) (years) cooling time at Y2L (inches) (years) Crystal-1 8.3 5.0 × 7.0 AS-B 2.17 3 Crystal-2 9.2 4.2 ×11.0 AS-C 0.92 2.75 Crystal-3 9.2 4.2 ×11.0 AS-WSII > 0.92 1.2 Crystal-4 18.0 5.0 × 15.3 AS-WSII 1.83 0.5 Crystal-6 12.5 4.8 ×11.8 AS-WSIII 0.5 0.6 Crystal-7 12.5 4.8 ×11.8 AS-WSIII 0.5 0.6 Table 2 Cosmogenic radionuclides in the NaI(Tl) crystals identified in other studies and taken into consideration here. Cosmogenic Half-life [27–29] Decay type isotopes (days) and emissions energy 125 I 59.4 EC, 35.5 + 31.7 = 67.2 keV 121 Te 19.17 EC, 4.1–4.7 and 30.5 keV 121 m Te 164.2 EC, 4.1–4.7 and 30.5 keV 123 m Te 119.3 IT, 247 keV 125 m Te 57.4 IT, 145 keV 127 m Te 106.1 IT, 88 keV 113 Sn 115.1 EC, 3.7–4.2 and 28 keV 109 Cd 462 EC, 25.5 and 88 keV 22 Na 950 β+ , 511 and 1274.6 keV 3 H 4494 β− 129 I 1.57 × 10 7 year β− T a t k l t t m i a t 3 t o b s a i t b m r e D d f A w B s d F che electron capture decay of 109 Cd contribute peaks at 25.5 and round 3.5 keV. Because it is impossible to compute the initial activities of he cosmogenic radioisotopes from the production rates without nowing their detailed cosmic ray exposure conditions: i.e., time, ocation, altitude, etc. [30] , we, when possible, extrapolated the ime-dependent reduction of characteristic peaks from their decays o determine their activity levels at the time of their initial deploy- ent at Y2L. For the activities of the long-lived 22 Na and 109 Cd sotopes we investigated temporal and spatial correlations of char-ig. 1. (a) The COSINE-100 detector. From outside inward, the four shielding layers includ opper box (orange), and liquid scintillator (light blue). (b) A side view of the detector gecteristic γ /X-rays peaks produced in their decays. The details of hese technique are discussed in the following sections. .1. Measurement of decay rates One way to measure the activities of the cosmogenic isotopes is hrough their decay rates. This measurement requires a selection f events of the specific decays studied, which can be identified y investigating the main contributions of the decay to our data pectra. Therefore, we first simulate each of the cosmogenically ctivated isotopes with the COSINE-100 GEANT4 package, study- ng their generated spectra and selecting the energy regions where hey can have a significant contribution in comparison to the flat ackground. Once the regions where the main contributions from each cos- ogenically activated isotope are identified, we look into the decay ates for each of them, integrating the rates over the specific en- rgy ranges. We fit the decay rate over time for each component. epending on the energy region selected for each cosmogenic, the ecay rate can be fitted by a constant and one or more exponential unctions, as following: + B · e −ln (2)(t−t 0 ) C (1) here t 0 is the initial time, A is the expected flat background rate, is the rate in t 0 , and C is the half-life, a constant of the fit. Fig. 4 hows an example of decay rate modeling with the units given in ru (counts/day/kg/keV). e: 3 cm thick plastic scintillator panels (green), 20 cm of lead (khaki), a 3 cm thick ometry used in the Geant4 simulations. 4 E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 C1 Energy (keV)0 20 40 60 80 co u n ts /k eV /k g/ da y 0 5 10 15 20 25 C2 Energy (keV)20 40 60 80 C3 Energy (keV)20 40 60 80 C4 Energy (keV)20 40 60 80 C6 Energy (keV)20 40 60 80 C7 Energy (keV)20 40 60 80 C1 Energy (keV)0 20 40 60 80 co u n ts /k eV /k g/ da y 0 0.5 1 1.5 2 2.5 3 C2 Energy (keV)20 40 60 80 C3 Energy (keV)20 40 60 80 C4 Energy (keV)20 40 60 80 C6 Energy (keV)20 40 60 80 C7 Energy (keV)20 40 60 80 Fig. 2. Background spectra for six NaI(Tl) crystals during the first (blue points) and the last (green points) 25 days of the dataset taken from October 21, 2016 to July 18, 2018. The upper plots show single-hit events and the lower ones show multiple-hit events. Energy (keV) 0 10 20 30 40 50 60 70 80 90 100 co u n ts /k eV /k g/ da y 0 0.5 1 1.5 2 2.5 3 3.5 Data Cd109 I125 Te121m Te127m Sn113 Fit Fig. 3. Difference between the first and last 25 day spectra of the 1.7 year data for Crystal-4 (in black) together with the fitted spectrum (in red) from several simulated individual contributions (in several colors). The subtracted spectra in Crystals-4, 6, and 7 are similar to each other due to their relatively short cooling times underground. However, the short-lived isotopes are not expected to contribute to either Crystal-1 or Crystal-2 due to their relatively long cooling times underground. i r t b t r t a f r r c 1 r The amplitude of the exponential ( B ) can be used to calculate the activity (in Bq/kg) of the cosmogenic isotope at the indicated initial time: A 0 = E × B 86400 × f E (2) where f E is the fraction of the events from that cosmogenic de- positing energy in the specified integration region, which can be calculated from the simulated spectra. E s for each isotope are 60–70 keV in single hit for 125 I, 20–40 keV in multiple hit for 121 m Te, 80–94 keV in single hit for 127 m Te, and 20–30 keV in single hit for 113 Sn. 3.1.1. Iodine 125 I Since iodine is one of the main components in the crystal, a sig- nificant amount of 125 I is activated. However, the half-life of thissotope is short with T 1/2 = 59.4 days. We define the integration egion for this isotope as 60 and 70 keV of the single-hit spec- rum, as shown in Fig. 4 ; it decays to an isomeric state of 125 m Te y electron capture, producing 31.7 keV emissions for K-shell elec- rons, which is followed by the emission of an 35.5 keV gamma ay from the isomer transition of 125 m Te. Although there is a con- ribution from 121 m Te in this region, it is very small due to the low ctivity of this isotope and more importantly, due to the very small raction of total 121 m Te events that actually deposit energy in this egion. Therefore, the contribution of 121 m Te in the 60 to 70 keV egion is insignificant, and the amounts of activated 125 I in the rystals during their deployment at Y2L can be found in Table 3 . Fig. 5 shows the difference between the measured activities of 25 I for the six crystals analyzed. The different amounts of 125 I are elated to the cooling time of the crystals before the start of data E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 5 Date (mm/dd/yy) 10/31/16 12/31/16 03/02/17 05/02/17 07/02/17 08/31/17 10/31/17 co u n ts /k eV /k g/ da y 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Data Fit Flat Background I Decay125 Fig. 4. Average rate in 60–70 keV region of Crystal-4’s single-hit spectrum over time. The rate shows a clear decrease, which can be modeled with an exponential decay, for 125 I in this case, in addition to a flat background component. The data is divided in bins of 15 days. However, down times between runs can result in some bins having less statistics than others. It is not expected to contribute to either Crystal-1 or Crystal-2 due to their relatively long cooling times underground. Fig. 5. Average activities of 125 I during the first 60 days of data. The values measured through the decay fit method, described in the text, are plotted in green, while the ones measured through the background modeling [23] are shown in red. Table 3 Initial activity A 0 (mBq/kg) of 125 I in each crystal as measured by the decay rate method. This includes the statistical uncertainty. Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 125 I – – 9.0 ± 0.9 3.4 ±0.1 5.1 ± 0.2 5.4 ±0.2 t fi 3 aking. We also compare the activities calculated in the background t [23] to those measured through this method. .1.2. Tellurium 121m Te, 127m Te and Tin 113 Sn • The line chosen to investigate 121 m Te is the one between 20 and 40 keV in the multiple-hit spectrum, contributed by 30 keV emissions from the 121 m Te decay via electron capture. This line is dominant in that region, unlike the 121 m Te lines in the single- hit spectra. The method used is the same as described above. • As we can see from the simulated spectra, 127 m Te has only one peak at 88.3 keV in the single-hit spectrum, contributed by the de-excitation of 127 m Te. However, there are other com- ponents that can have significant contributions in that energy region as well, such as 109 Cd and 121 m Te: a 88 keV emis- sion from the isomer transition of 109 m Ag and another one at 81.8 keV from the de-excitation of 121 m Te. The contribution coming from 121 m Te can be calculated based on the measure- ment from the multiple-hit spectrum, as described above. The contribution from 109 Cd, however, is calculated based on an- other study, which will be described in Section 3.2.2 . Both of these are added to the fitting function, allowing the measure- ment of 127 m Te, activity. • The electron capture decay of 113 Sn produces 28 keV emissions. The method used is the same as described above. The peaks at 25.5 keV and 30 keV contributed by 109 Cd and 121 m Te can be 6 E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 Table 4 Initial activity A 0 (mBq/kg) of 121 m Te, 127 m Te, and 113 Sn in each crystal as measured by the decay rate method. This includes the statistical uncertainty. Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 121 m Te – – 0.90 ±0.16 0.89 ± 0.06 0.44 ± 0.07 0.41 ± 0.07 127 m Te – – 0.87 ± 0.16 0.48 ± 0.03 0.38 ± 0.04 0.35 ± 0.04 113 Sn – – 0.16 ± 0.05 0.15 ± 0.06 0.16 ± 0.01 0.12 ± 0.01 w t c a m t 3 i t a h t G l d 1 2 l s t m s t t T 4 m u o a o p mcalculated, as described above, and added to the fitting func- tion, allowing the measurement of 113 Sn. Fig. 6 (a) and (b) shows the differences between the measured ac- tivities of 121 m Te and 127 m Te for the six crystals analyzed. We also compare the activities calculated in the background fit to those measured through this method. As listed in Tables 3 and 4 , the initial activities when crystals were deployed at Y2L were derived for 125 I, 121 m Te, 127 m Te, and 113 Sn in each crystal. 3.2. Long-lived isotopes 3.2.1. Sodium 22 Na The decays of 22 Na ( Q -value = 2.84 MeV) to 22 Ne ∗ proceed via β+ emission (90.3%) or electron capture (9.6%) with 3.75 year mean lifetime, followed by 22 Ne ∗ transitioning to the stable 22 Ne isotope via the emission of a 1274.6 keV γ -ray with a 5.3 ps mean lifetime. The electron capture of 22 Na from K-shell produces 0.87 keV emissions. As a result, ∼10% of the 22 Na decay will si- multaneously produce a 1274.6 keV γ -ray and 0.9 keV emissions. In the case of β+ decay, the final-state positron immediately anni- hilates to two 511 keV γ -rays. If one of the two 511 γ -rays es- capes the crystal, the remaining energy deposited in the crystal will be substantially greater than 650 keV. Fig. 7 (a) shows the en- ergy spectrum in another crystal in coincidence with a signal in the (650–10 0 0) keV energy interval in Crystal-3, which are called double coincidence events. The 22 Na β+ decay events show up as the peak at 511 keV (red color). Since the eight NaI(Tl) crystal assemblies are immersed in the scintillating liquid (LS), as described in Section 2 , we can also iden- tify 22 Na decay events in which the 1274.6 keV gamma-ray con- verts in the LS in coincidence with two 511 keV signals in two crystals. These are referred to as triple coincidence events. Fig. 7 (b) shows the peak at 511 keV (red color) in another crystal, con- tributed by triple coincidence events, while a signal is in the (650– 10 0 0) keV energy interval in Crystal-3. We used the time-dependent reduction of the peak at 511 keV, contributed by the double/triple coincidences of the 1.7 year data divided in bins of 60 days, to extrapolate the activity at the indi- cated initial time with the relation: A 0 = N m · t ·  (3)Fig. 6. Average activities of (a) 121 m Te, (b) 127 m Te, and (c) 113 Sn during the first 60 days of in the text, are plotted in green, while the ones measured through the background modehere N is the number of events,  is the detection efficiency ob- ained from a Monte Carlo simulation, m is the mass of the NaI(Tl) rystal, and t is the time of the measurement. Fig. 8 shows the measured activities of 22 Na for the six crystals nalyzed by these methods, compared with the activities deter- ined from the global background fit. The initial activities, when he crystals were first deployed at Y2L, are listed in Table 5 . .2.2. Cadmium 109 Cd The cosmogenic isotope 109 Cd decays via electron capture to an someric state of 109 m Ag, with a prompt energy deposit of 25.5 keV, he binding energy of the Ag K-shell electron. This is followed by n emission of 88 keV from the isomer transition of 109 m Ag that as a mean lifetime of 57.4 s. From the time interval distribu- ion between 25.5 keV and 88 keV signals, selected within three aussian width of the peaks in the same crystal, we extract the evel of 109 Cd from a fit with two exponential decay functions. As iscussed in Section 3.1.2 there are significant contributions from 27 m Te and 121 m Te around 88 keV and 113 Sn and 121 m Te around 5 keV, which dominate the blue curve in Fig. 9 . The fitted mean ifetime, 56 ±14 s, from the exponential curve in red, as can be een in Fig. 9 , is consistent with the mean lifetime of 57.4 s from he isomer transition of 109 m Ag. We determined the 109 Cd activity rates in mBq/kg from these easurements: Fig. 10 shows the measured activity levels for the ix crystals analyzed through this method, compared with the ac- ivities determined from the global background fit. The crystal ac- ivity levels when they were first deployed at Y2L are listed in able 6 . . Results and comparisons for production rates In Section 3 we describe the determination of the crystals’ cos- ogenic isotope activities at the time they were first deployed nderground at Y2L. However, since we do not know the details f their previous exposure conditions, such as times, locations, nd altitudes, these cannot be directly related to production rates r saturation activity levels. But an attempt to extract sea level roduction rates has been made from a simplified mathematical odel for production and decay of radionuclides. data in six crystals. The values measured through the decay fit method, described ling [23] are shown in red. E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 7 Fig. 7. (a) Energy spectrum in another crystal in coincidence with a signal in the (650–10 0 0) keV energy interval in Crystal-3. In the fitting, it represents the peak at 609 keV from 214 Bi in green and the peak at 511 keV from 22 Na, activated in Crystal-3, in red. (b) Energy spectrum in another crystal contributed by triple coincidence events. The red line represents the peak at 511 keV from 22 Na in Crystal-3. The same plots for all the other crystals are similar to each other. Ac tiv ity (m Bq /kg ) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Double coincidence Triple coincidence Background modeling Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 Fig. 8. Average activities of 22 Na during the first 60 days of data in six crystals. The values measured through the double/triple coincidence methods, described in the text, are plotted in green/pink, while the ones measured through the background modeling [23] are shown in red. Table 5 Initial activity A 0 (mBq/kg) of 22 Na as measured by double and triple coincidences in each crystal. This includes the statistical uncertainty. Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 Double coincidence 2.59 ± 0.27 1.46 ±0.27 0.99 ± 0.07 1.20 ± 0.09 0.73 ± 0.09 0.93 ±0.08 Triple coincidence 2.0 ±0.4 1.52 ±0.37 0.84 ± 0.18 1.17 ± 0.19 0.65 ± 0.14 0.87 ±0.23 p R w r t l R R T c r w T N The production rate R for activation of an isotope can be ex- ressed as ∝ ∫ σ (E) · (E) · dE (4) here σ is the neutron capture cross section and  is the cosmic- ay neutron flux. Since cosmic-ray neutron flux  depends on al- itude, location, and time the production rate R at any arbitrary ocation can be calculated by scaling the reference production rate s at sea level, = f · R s (5) he produced nuclide then decays according to the standard de- ay law, and the net rate of change for the number of existing adioactive nuclei N is by the differential equation dN dt = −λ · N + R (6) here λ is the decay constant: λ = ln 2 T 1 / 2 ( T 1/2 is the decay half-life). he solution of Eq. (6) is = R (1 − e −λt ) , (7) λ 8 E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 Std Dev 288.4 / ndf 2 270.8 / 296 Prob 0.8506 p0 14.2 711.7 p1 2.8 293.6 Const 18.1 164.5 Mean lifetime 13.51 56.29 Time difference (s) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Co un ts /d ay /k g/ ke V 0 100 200 300 400 500 600 700 800 900 Data Fit(Exponential+Exponential) Exponential Component Cd)109Exponential Component( Fig. 9. Distribution of the time difference between 25.5 keV and an 88 keV signals, selected within three Gaussian width of the peaks in Crystal-3, fitted with the sum of two exponential decay functions. The 109 Cd contribution with lifetime 56 s is shown in red. The parameter Const is an amplitude of the exponential decay of 109 Cd. The parameters p0 and p1 are an amplitude and a mean lifetime of the exponential decay of the background contribution. The same plots for all the other crystals are similar to each other. Fig. 10. Average activities of 109 Cd during the first 60 days of data in six crystals. The values measured through this method, described in the text, are plotted in blue, while the ones measured through the background modeling [23] are shown in red. Table 6 Initial activity A 0 (mBq/kg) of 109 Cd in each crystal. This includes the statistical uncertainty. Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 109 Cd ( ×10 −2 ) 4.6 ±3.0 0.9 ±1.8 7.5 ±0.9 9.2 ± 0.7 1.5 ±0.7 1.5 ± 0.5 T fl i t m l t A and the activity A ( t ) is related to the number of existing nuclei N by A (t) = λ · N (8) = R (1 − e −λt ) (9) When the time t is sufficiently large, then a saturation activity A s is reached at a given place, A s = f · R s (10)he ANAIS experiment [31] realized that the cosmic-ray neutron ux  can be scaled from its sea level reference flux, as reported n Ref. [30] , to the NaI(Tl) crystal production point in Grand Junc- ion, Colorado (altitude = 1400 m), by a factor of f = 3 . 6 . Using the easured A 0 activity levels reported here and the exposure times isted in Table 1 , we compute a production rate R s at sea level from he relation, 0 = R s [1 + ( f (1 − e −λt 1 ) − 1) · e −λt 2 ] (11) E. Barbosa de Souza, B.J. Park and G. Adhikari et al. / Astroparticle Physics 115 (2020) 102390 9 Table 7 Production rate R s [kg −1 d −1 ] at sea level. 22 Na 109 Cd 125 I 121 m Te 127 m Te 113 Sn Crystal-1 132.0 ± 24.0 1.7 ±1.1 Crystal-2 148.5 ± 44.9 0.6 ± 1.2 Crystal-3 114.5 ± 19.7 4.7 ±0.6 280.1 ± 29.3 31.1 ± 5.5 26.9 ± 4.8 5.1 ± 1.6 Crystal-4 81.0 ± 12.7 3.7 ±0.3 104.2 ± 3.7 24.9 ± 1.6 13.5 ± 0.7 4.1 ± 1.6 Crystal-6 144.0 ± 31.2 1.8 ±0.8 184.7 ±6.3 23.5 ± 3.5 16.3 ± 1.5 7.1 ± 0.5 Crystal-7 151.0 ± 52.1 1.8 ± 0.6 194.0 ± 6.3 22.3 ± 3.5 15.0 ± 1.5 5.3 ± 0.5 ACTIVIA 66 4.8 221 93 93 9 MENDL-2 4.8 208 102 ANAIS measurement [31,32,34] 45.1 ±1.9 2.38 ±0.20 220 ± 10 23.5 ± 0.8 10.2 ± 0.4 4.53 ± 0.40 DM-Ice17 measurement [30] 230 25 < 9 16 Table 8 Initial activity (A 0 ) of 3 H in the NaI(Tl) crystals derived from background fitting and the derived estimated exposure times. Crystal-1 Crystal-2 Crystal-3 Crystal-4 Crystal-6 Crystal-7 A 0 [mBq/kg] 0.38 ± 0.04 0.20 ± 0.04 0.25 ±0.04 0.26 ±0.04 0.11 ±0.04 0.09 ± 0.04 Exposure time [year] 2.19 1.11 1.37 1.44 0.66 0.52 w T p a t t A T r n t c C 1 t c t d a u 5 c l γ g t k u f w t 3 A g i s b 1 i N a v 6 i u s i t t o p p t a s t d l 1 A f o m f p l b m e b t t A p here the exposure time t exp , listed in Table 1 , is t exp = t 1 + t 2 . he crystals are exposed at Alpha Spectra for a time t 1 and ex- osed at sea level for a time t 2 . We considered t 2 = 30 days s transportation duration to Y2L. Table 7 shows the produc- ion rate of cosmogenic isotopes in each NaI(Tl) crystal used for he COSINE-100 experiment compared with measurements from NAIS [31,32,34] and DM-Ice17 [30] , and calculations using AC- IVIA and MENDL-2; we used v1.3 of ACTIVIA that follows the pa- ameterization of Gordon [35] , valid from 1 MeV to 10 GeV, for the eutron flux spectrum and MENDL-2 that contains neutron reac- ion data up to 100 MeV. The results obtained with the six NaI(Tl) rystals are in reasonable agreement with each other, except for rystal-3 that has a complicated exposure history; we considered year exposure time for Crystal-3 for calculation of the produc- ion rates listed in Table 7 . The production rates of 22 Na in the six rystals are compatible with each other although they are larger han other measurement and calculation. For Crystal-4, since we o not know clearly the month and day of the powder production nd the crystal delivery to Y2L it is possible to have about 60 days ncertainty for the exposure and the cooling times, respectively. . Discussion on tritium 3 H and iodine 129 I It is generally difficult to measure activity levels of long-lived osmogenic isotopes, directly from the data due to their long half- ives. This is especially the case for 3 H, which has no distinguishing /X-ray peak that can be exploited. Therefore, we simulated back- round spectra from 3 H in the six NaI(Tl) crystals and used the ex- racted spectral shapes in the data fitting, while floating their un- nown fractions [23] . We determine the initial activity A 0 of 3 H by sing the average activity during the first 60 days of data, obtained rom the global background fitting model [23] described above, ith results shown in Table 8 . From these we computed exposures ime t exp from Eq. (11) . We assumed that the production rate of H at sea level is R s = (83 ±27) kg −1 d −1 , which was reported by NAIS [33] . The resultant exposure times, listed in Table 8 , are in ood agreement with the time period during which they were be- ng produced at Alpha Spectra and undergoing delivery to Y2L, as hown in Table 1 . The presence of cosmogenic 129 I was introduced y DAMA/LIBRA with the estimated concentration of 29 I/ nat I = (1.7 ±0 . 1) × 10 −13 [36] . It is used as a floating parameter n the global background fitting modeling for the COSINE-100aI(Tl) crystals, with resulting values of 1.01, 1.08, 0.75, 0.72, 0.91, nd 0.94 mBq/kg for Crystal-1, 2, 3, 4, 6, and 7, respectively. These alues agree well with the ANAIS result: 0.96 ±0.06 mBq/kg [37] . . Conclusion We have studied background contributions from cosmogenic sotopes activated by cosmic rays in the COSINE-100 detectors. To nderstand their time-dependent energy spectra we simulated re- ponses to decays of the most abundantly produced cosmogenic sotopes in NaI(Tl) crystals and identified the energy regions where hey make strong contributions to the crystals’ background spec- ra. Based on these simulation studies we measured decay rates f the cosmogenic isotopes using the time-dependent decrease of eaks from characteristic decays of these isotopes. We also ex- loited the correlations of characteristic emissions in terms of ime differences between sequential decays of 109 Cd and double- nd triple-coincidences for 22 Na-decay-induced multi-gamma final tates. From these measurements, we extrapolated the various iso- opes’ activity levels to the times that they were first deployed un- erground at Y2L. With these data we estimated production rates (at sea evel) for the cosmogenic isotopes that are relevant for COSINE- 00 and compared them with other experimental data and CTIVIA/MENDL-2 calculations. As listed in Table 7 , the results rom different approaches are in reasonable agreement with each ther. We extracted exposure times using initial 3 H activities deter- ined from the COSINE-100 global background fitting model and ound results that are in reasonable agreement with the times re- orted in Table 2 (b). We also quantified the unknown 129 I activity evel by including it as a free-floating parameter in the the global ackground fit model and found consistency with an ANAIS result. This study has given us a quantitative understanding of the cos- ogenic isotopes in the NaI(Tl) crystals used for the COSINE-100 xperiment. It provides important constraints on time-dependent ackgrounds in our search for a time-dependent modulation hat would be a characteristic signal for dark matter interac- ions [38,39] . cknowledgments We thank the Korea Hydro and Nuclear Power (KHNP) Com- any for providing underground laboratory space at Yangyang. This 10 E. Barbosa de Souza, B.J. Park and G. 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