Characterization of SABRE crystal NaI-33 with direct underground counting

Ultra-pure NaI(Tl) crystals are the key element for a model-independent verification of the long standing DAMA result and a powerful means to search for the annual modulation signature of dark matter interactions. The SABRE collaboration has been developing cutting-edge techniques for the reduction of intrinsic backgrounds over several years. In this paper, we report the first characterization of a 3.4 kg crystal, named NaI-33, performed in an underground passive shielding setup at Gran Sasso National Laboratory. NaI-33 has a record low $^{39}$K contamination of 4.3$\pm$0.2 ppb as previously determined by Inductively Coupled Plasma Mass Spectrometry. We measured a light yield of 11.1$\pm$0.2 photoelectrons/keV and an energy resolution of 13.2% (FWHM/E) at 59.5 keV. From the measurement of the $\alpha$ rate due to $^{210}$Po decays, we evaluated a $^{210}$Pb activity at equilibrium of 0.53$\pm$0.04 mBq/kg and an $\alpha$ quenching factor of 0.63$\pm$0.01 at 5304 keV. This paper also illustrates the analyses techniques developed to reject electronic noise in the lower part of the energy spectrum: a traditional cut-based strategy and an innovative Boosted Decision Tree approach. Both of these indicated a signal attributed to the intrinsic radioactivity of the crystal with a rate of $\sim$1 count/day/kg/keV in the [5-20] keV region.


Introduction
The SABRE experiment seeks to detect the annual modulation of the dark matter interaction rate in NaI(Tl) crystals with sufficient sensitivity to test the long standing DAMA result in a model independent way. Among the best-motivated candidates to solve the dark matter puzzle [1], Weakly Interacting Massive Particles (WIMPs) [2] are thought to exist as a halo within which our Galaxy resides. Despite the decades-long effort of direct detection experiment searches for interactions of such dark matter candidates with different target materials, the DAMA experiment (short for DAMA/NaI and DAMA/LIBRA) [3] is the only one reporting a positive observation. The DAMA evidence of a clear annual modulation, which satisfies the criteria for a model-independent WIMP-induced signal [4], has reached a strong statistical significance of 12.9 σ [5], after 20 years of data taking at the Gran Sasso National Laboratory (LNGS), in Italy. While the null result of experiments based on different target materials and other direct detection techniques [6][7][8][9][10][11][12][13] cannot be reconciled with such modulation in the simplest scenario of WIMP-nucleon elastic scattering, a NaI(Tl) annual modulation search similar to DAMA is still crucial to shed light on the origin of the positive signal [14].
Currently running NaI(Tl) dark matter experiments are COSINE-100 [15] at the YangYang Laboratory in South Korea, and ANAIS-112 [16] at the Canfranc Laboratory in Spain. They both feature a mass of about 100 kg of NaI(Tl) scintillating crystals in an underground setup and have so far neither confirmed nor fully disproved the DAMA observation [17,18]. Given the very low count rate and energy featured in dark matter nuclear recoils, its detection is challenged by background from radioactive decays, where the dominating component arises from impurities in the crystals themselves. One key feature of DAMA that has never been rivalled by competing experiments is the background rate which is as low as ∼ 0.7 count/day/kg/keV in the energy range where the modulation is observed: [1][2][3][4][5][6] keV [5]. The amplitude of the observed modulation is at the level 0.01 count/day/kg/keV. Consequently, background levels about two or three times higher than those of DAMA/LIBRA, such as achieved by the ANAIS and COSINE experiments, negatively affect their sensitivity. Indeed these experiments, even after several years of operation, might not be able to resolve all possible scenarios in interpreting the DAMA signal as a dark matter signature.
The SABRE concept and ambitious goal is to obtain an ultra-low background rate in the energy region of interest, namely of the order of 0.1 count/day/kg/keV, that is several times lower than the DAMA/LIBRA level. This challenging goal is achievable by developing high-purity crystals and operating them inside a liquid scintillator veto for active background rejection. This SABRE veto concept has also been adopted by the COSINE experiment.
The SABRE scientific program is currently in a Proofof-Principle (PoP) phase at LNGS, to assess the radio-purity of the crystals, as well as the acceptance of the liquid scintillator veto. In the longer term, twin detectors of at least 50 kg of NaI(Tl) will be located in the northern and southern hemispheres, namely at LNGS and at the Stawell Underground Physics Laboratory (SUPL) in Australia, located 240 km north-west of Melbourne, where a section of an active gold mine is being converted into a laboratory. The twin locations will help to identify any possible contribution to the modulation from seasonal or site-related effects. The SABRE concept and the PoP setup are described in more detail in Ref. [19].
In this paper we focus on the initial characterization of a relatively large crystal, named NaI-33, that marks a breakthrough after a technical effort of several years. In Sec. 2 we recall the SABRE production strategy for high purity crystals; in Sec. 2.1 we give more details about the production of the crystal NaI-33; in Sec. 3 we describe the underground facility used for the measurements and we detail the data taking campaign; in Sec. 4 we show the main results on the crystal parameters and backgrounds and we also outline the analysis strategy we developed.

SABRE high purity NaI(Tl) crystals
For many years, the quest for high-purity NaI(Tl) crystals has focused on removing common impurities such as 238 U, 232 Th, 40 K and 87 Rb. One of the 40 K decay channels includes an Auger/X-ray cascade with a total energy of ∼3 keV, which happens to be in the energy region where the DAMA modulation is observed. Consequently, a large effort was devoted to reduce, or being able to identify, the 40 K background. Eventually, the potassium content in the NaI(Tl) powder and crystals was progressively lowered to the point where the background is now dominated by 210 Pb and cosmogenic-activated isotopes [20], in particular 3 H.
To keep the intrinsic contaminants at a very low level, SABRE developed a method to obtain ultra-pure NaI powder and a clean procedure to grow crystals. More details on this method can be found in Ref. [19,21]. Princeton University and industrial partner Sigma-Aldrich produced ultrahigh purity NaI powder, so-called Astro Grade powder, with 39 K levels consistently lower than 10 ppb. The NaI(Tl) crystals were then grown by Radiation Monitoring Devices, Inc. (RMD), using the vertical Bridgman technique [22]. In this method, the powder is placed inside a sealed ampule, reducing the possibility of contamination during the growth phase. In 2015, we successfully grew at RMD a 2 kg crystal with an average 39 K level of 9 ± 1 ppb [23, 24] and with 87 Rb upper limit of 0.1 ppb measured by Inductively Coupled Plasma Mass Spectrometry (ICP-MS) [25]. Based on these results, a simulation study of the background contributions expected for the SABRE PoP phase can be found in Ref. [26]. The study demonstrates the importance of reducing the background contributions from radioactive decays inside the crystal. The same conclusion can be drawn from the background model presented by COSINE and ANAIS experiments in [27,28], verified against experimental data. However ICP-MS only permits testing for a subset of the backgrounds, namely primordial parents such as U, Th, K and Rb. Cosmogenic isotopes produced after the crystal growth, 210 Pb and other non-primordial parents, if present, can only be measured by direct counting of the crystal as a scintillator in an underground setup. Consequently, the focus in the past years has shifted to the growth of a NaI(Tl) crystal with a sufficient mass to perform a physics run. We have started to acquire signals with a SABRE grade NaI(Tl) crystal for a preliminary background characterization reported in this paper. In the next few months we aim at a more comprehensive characterization with the PoP setup.

SABRE crystal NaI-33
At the end of October 2018, a new NaI(Tl) crystal, named NaI-33, was grown. The powder and the crucible were prepared by the Princeton group, and the crystal was grown in an oven at RMD. The crystal was then cut into an octagon and polished, obtaining a final mass of 3.4 kg. In order to determine the concentration of 39 K, and consequently of 40 K, in the final crystal, samples from the tip and the tail of the ingot were analyzed using ICP-MS at Seastar Chemicals. The average 39 K concentration within the crystal volume was extrapolated to be 4.3±0.2 ppb, several times lower than 20 ppb, the upper limit reported for the DAMA/LIBRA crystals [29]. Further details on the powder preparation, the crystal growth and the results on internal radioactivity can be found in Ref. [21].
During May 2019, the crystal NaI-33 was assembled in the SABRE detector module, developed for the PoP phase and described in Ref. [19]. Two Photomultiplier Tubes (PMTs) were directly coupled to each end of the crystal, while its lateral surface was wrapped with reflector, for higher light collection acceptance. For NaI-33, we used Polytetrafluoroethylene (PTFE) as a reflector and 3-inch Hamamatsu R11065-20 PMTs, which have been specifically developed to have a low intrinsic radioactivity [30]. We purchased selected units with a quantum efficiency as high as ∼ 35% at 420 nm. The detector assembly was placed inside an air-and lighttight copper enclosure. The cylinder, end-caps, and support rods are made out of low-radioactivity copper. The holders of the crystal and of the PMTs are made out of high-purity Delrin. Being that NaI is highly hygroscopic, all parts were thermally treated prior to assembly, to remove any residual moisture. For the same reason, the assembly procedure was performed entirely under dry nitrogen atmosphere inside a glove box. After sealing, the detector module was flushed with high purity N 2 gas to avoid humidity and radon. The detector module before the sealing of the copper enclosure can be seen in Fig. 1. In order to limit cosmogenic activation, the crystal was then shipped by surface transportation and delivered on 6 Aug 2019 at LNGS, where it was immediately stored underground.

Experimental setup at LNGS
The experimental SABRE setup at LNGS consists of two facilities: a shielded counting system in Hall B and the PoP facility in Hall C. Upon arrival of the NaI-33 crystal, the PoP was not yet ready for operations: consequently, for the first crystal characterization reported in this paper, we used our facility in Hall B. The facility consists of a passive shielding to reduce the γ environmental background, made of low radioactivity copper and lead. The shielding is enclosed in a plexiglass box that can be sealed and flushed with highpurity nitrogen. In August 2019, we commenced data taking with detector NaI-33 and continued for approximately a year. This time was divided into two periods denoted as Run 1 and Run 2, interleaved by the refurbishment of the shielding performed at the end of February 2020. Shielding during Run 1 featured 5 cm of copper and a layer of lead at least 17.5 cm thick on all sides. The experimental volume inside the shielding allowed for the insertion of two detector modules, which was useful to acquire data with a radioactive source (see Sec.4.4). During Run 2, the thickness of low radioactivity copper was increased to 10 cm, effectively reducing the background due to the surrounding lead layer. However, this was done at the expense of the experimental volume, that then could only host one detector module. Fig. 2 shows the two setups.
We define the presence of a PMT pulse by discriminating the signal over a threshold corresponding to approximately one photoelectron. Data acquisition is triggered by the logical AND of the two PMT pulses occurring within a window of 125 ns. For each event, we acquire the waveforms of each PMT, together with their amplified (× 10) copies. Amplified signals are used for the low energy analysis and saturate above 500 keV energy. The PMT signals without amplification instead provide sensitivity to α decays. Waveforms are digitized at 12 bit and 250 MS/s by CAEN v1720 modules. The acquisition window was set at 5 µs, including a 1.5 µs pre-trigger for baseline evaluation. The trigger rate was ∼ 0.48 s −1 .
An offline reconstruction program processes each event and computes physical quantities. PMT pulses are isolated within the acquisition window; the baseline is computed on the pre-trigger samples and subtracted; and the pulse integral is computed. The same operations are performed for each channel, amplified and not, and for the software sum of the two PMT pulses. The event energy estimator is the integral of the sum channel. Pulse Shape parameters are also computed during this phase and are useful to separate scintillation events in the crystal from PMT noise, as well as to distinguish α from β /γ interactions. Pulse Shape parameters are discussed in detail in Sec. 4.3.

Data Analysis and results
Data acquired during Run 1 were used to measure light yield and energy resolution (Sec. 4.1), and to determine the α rate (Sec. 4.2); however, for the analysis of its evolution over time, Run 2 data were also used. Run 1 included a campaign with a 108m Ag source (see Sec. 4.4). Run 2 data were used  for the background study. In order to build the low energy spectrum, we selected a subset of Run 2 data, denoted as Run 2-lowRn. These data were acquired while flushing the setup with high-purity nitrogen and, consequently, with a reduced background contribution from Rn and its daughters. A small fraction of the dataset was not included in the analysis due to noisy experimental conditions related to activity in the laboratory. The live time for each of the two runs is reported in Table 1.
The characterization of the NaI-33 will proceed within the PoP setup in Hall C, which has recently been commissioned, and it will be the subject of a separate publication.

Light yield and energy resolution
To characterize the crystal performance, we initially used a 241 Am calibration source positioned on the copper enclosure, longitudinally aligned with the crystal centre. The spectrum acquired with the source is shown in Fig. 3, including where µ and σ are the mean and standard deviation from the gaussian fit. The low tail of the Am peak is longer than its high tail due to a small contamination of 210 Pb (46 keV γ). In order to avoid this bias, we evaluate the energy resolution fit-ting in an asymmetric interval around the peak of [629,734] photoelectrons (phe). The resulting values are 13.2% for the energy resolution and 11.1 ± 0.2 phe/keV for the light yield. The error takes into account the systematic uncertainty due to the imperfect reproducibility of the source position across several calibrations.

Measurement of the α rate
The identification and counting of α particles has two main aims: (1) a measurement of the internal radioactivity of the crystal in terms of U/Th contamination and 210 Pb contamination out of secular equilibrium; (2) a measurement of the α quenching factor in NaI. Identification of α particles exploits the Pulse Shape discrimination capability of NaI(Tl) crystals, where signals induced by α decays are faster than β /γ ones. In particular, the amplitude-weighted mean time t 600 (defined in Sec 4.3), gives a good separation between α particles and β /γ particles, as seen in Fig. 4.
In order to evaluate the content of primordial radioactive chains in the crystal, we searched for fast β -α sequences, called Bismuth-Polonium (Bi-Po). These are present in Th and U chains with atomic mass numbers of 212 and 214, respectively, each with a characteristic decay time. The Bi-Po-212 sequences can be identified in the same digitization windows, because of the very short lifetime of 212 Po (431 ns). Since the lifetime of 214 Po is 237 µs, correlated Bi-Po-214 decays are instead found in event pairs occurring in close succession. Considering the rate of single β and α decays of 0.02 s −1 and 0.002 s −1 respectively, we compute the probability of accidental coincidences to be ∼ 5·10 −3 (∼ 5·10 −6 ) for the Bi-Po-214 (Bi-Po-212) selection.
By counting the number of Bi-Po events and correcting for event selection acceptance, we estimated the activ- ity of 226 Ra and 228 Th inside the crystal. These are 5.9 ± 0.6 µBq/kg and 1.6 ± 0.3 µBq/kg, respectively. These uncertainties are statistical only, and are dominant due to the very low number of coincident counts. If the assumption of secular equilibrium for 238 U and 232 Th held, such values would correspond to a part-per-trillion (ppt) level contamination, which is very close to our target [26].
With very few counts ascribed to long-lived radioactive chains, the α spectrum is dominated by the decay of 210 Po. Generally, this originates from an out-of-equilibrium contamination of 210 Pb, accidentally introduced sometime during the manufacture of the crystal (e.g. due to an exposure to radon). We applied a loose energy selection around the 210 Po peak in the α spectrum and measured its activity over a period of a several months with results shown in Fig. 5. We observe an increase well described by a build-up function with the half-life of 210 Po (138.4 days). The fit also includes a constant contribution due to other α decays that satisfy the selection requirement on the energy. This contribution is computed from the result of the two Bi-Po analyses to be 0.03 mBq/kg, including also 210 Po in equilibrium with 226 Ra, and fixed in the fit. The date of the initial 210 Pb contamination is freely determined by the fit to be 9 September 2018 with an uncertainty of 10 days. This date corresponds to the last days before the beginning of the growth process. The activity of out-of-equilibrium 210 Po, and hence of 210 Pb, reaches a plateau of 0.51 ± 0.02 mBq/kg (statistical uncertainty). While such activity is still higher than our target, it is amongst the lowest ever reported after DAMA/LIBRA [27,28].
Measuring the ratio of the 210 Po peak position in the βcalibrated spectrum over the nominal α energy of 5304 keV, we can estimate the quenching factor for α particles as 0.63± 0.01. To this end, the calibration of the β spectrum was performed using the 2615 keV line of a 228 Th source.

Pulse shape parameters
As reported by all NaI(Tl) experiments, the low energy spectrum is populated by events that do not show the correct pulse shape of scintillation light in the crystal, and must be efficiently discarded as noise. We developed a twofold selection strategy for this purpose, detailed in the next sections. More specifically, we report a cut-based method (Sec. 4.4) and a more sophisticated Boosted Decision Tree approach (Sec. 4.5). The results of these analyses are given in section 4.6.
We introduce here several variables common to both approaches. In the definitions of the variables, h i and t i are the pulse amplitude in mV and the time of the i−th sample (starting from the trigger, t 0 ), respectively. h max is the absolute value of the maximum pulse amplitude in mV. C (t i ,t f ) is defined as the pulse area between t i and t f in nanoseconds. E 0 and E 1 correspond to the energy measured using the two PMTs in the 1000 ns following the trigger.
In addition to the variables defined above, we define a Kolmogorov-Smirnov distance from an 241 Am reference pulse, and the number of clusters (NC). A cluster is defined by the waveform exceeding a threshold corresponding to ∼2.5 phe. Accepting only events with NC > 2 in each of the PMTs, we eliminate accidental coincidences of single photo-electrons in opposing PMTs and events originated in the PMTs due to their intrinsic radioactivity.

Cut-based analysis
We define here the selection criteria adopted for low energy noise rejection, tuned on data acquired with a 108m Ag source.
The 108m Ag source produces three γ rays of 434 keV, 614 keV, and 723 keV. We exploit these simultaneous emissions by placing a commercial NaI detector along NaI-33 inside the shielding (see Fig. 6). Requiring coincidence between the two detectors within 125 ns and using a copper layer as energy degrader between the source and the NaI-33 crystal, we obtain a continuum of low energy scintillation events. We have evaluated the contamination of the sample by accidental coincidences and found it to be negligible. Fig. 7 shows the distributions of the shape parameters in the source data, with the indication of the values corresponding to the selection criteria as red lines. We choose to cut on each variable conserving at least 95% of signal events with energy within (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) keV (with the exception of SK, where we preserve only 68% of events).
The combined acceptance of all the cuts as a function of energy and the resulting low-energy spectrum will be presented below (Sec. 4.6) in comparison with those obtained Fig. 6 Schematic view of the experimental setup used for the 108m Ag source campaign. It is shown the passive shielding of lead and copper, with the NaI-33 detector module and the commercial NaI detector. γ rays emitted from the 108m Ag source, identified by a red circle, are degraded via a copper layer.
with the boosted decision tree analysis which will now be described.

Boosted decision tree analysis
In order to improve the separation between noise and scintillation events, we implemented a multivariate analysis using Boosted Decision Trees (BDT) [31], with a focus on low energy events up to 100 keV.
The BDT algorithm has to be trained using a sample of true scintillation events as "signal" and a sample of noise event as "background". For the signal training we used the 108m Ag data, selecting the events in coincidence with the commercial crystal, weighted in order to match the energy distribution expected for the crystal background.
For the background training we used NaI-33 data in the 1-10 keV energy region, which is dominated by noise. We evaluate from the cut-based analysis that the contamination of signal events in the background training set is about 5% and consider this bias reasonably small. As cross-check, we also trained the BDT with a background set obtained by inverting the selection described in Sec. 4.4, achieving comparable results.
The analysis wass performed by training two separate BDTs, which we refer to as BDT 1 and BDT 2 . The input variables are those described in Sec.4.3, aside from Skewness and Kurtosis, which are only included in BDT 2 . As for the cut-based analysis, we evaluate the selection on the BDT variables using the data with the 108m Ag source.
The BDT classifier output is defined in the range [−1, 1] where lower scores are assigned to noise-like events and higher scores to signal-like events. Fig. 8, shows the output as a function of the energy for the source data.
We define an energy-dependent threshold for the two BDTs defined as following: (2) : if E ≥ 20 keV where a i , b i and c i are chosen in order to ensure an acceptance for each BDT of ∼50% (99.8%) in the energy range [1][2][3] keV ([20-100] keV). We then combine the two BTD algorithms by selecting as scintillation events only those passing both thresholds, with the results described in the next section.

Comparison of analysis procedures
The results of the cut-based analysis and the BDT analysis are shown in Fig. 9 and Fig. 10. Fig. 9 compares the acceptance as a function of energy below 60 keV. The acceptance is measured using the 108m Ag data, by computing the proportion of events passing the selection. Fig. 10 shows the low energy spectrum before and after noise rejection. This spectrum corresponds to a live time of 58 days. After noise rejection the average count rate in the 5-20 keV energy range is close to 1 count/day/kg/keV.
The multivariate analysis shows a promising performance: the acceptance is significantly higher with respect to the cutbased approach. At the same time, the energy spectra of events selected with the two methods, after being corrected for the acceptance, compare well above 8 keV whereas at lower energies the BDT approach grants a slightly higher noise rejection.

Conclusions
The NaI-33 crystal is the most radiopure crystal produced so far by the SABRE collaboration, with a size suitable for the PoP phase and close to the target of 5 kg for the fullscale experiment. The 39 K content measured with ICP-MS is 4.3 ± 0.2 ppb, significantly lower than all values reported by experiments DAMA, which quotes a 20 ppb upper limit [29], COSINE-100 and ANAIS-112, which have both 17 ppb at best [27,28]. We reported here the results from a first characterization performed using the SABRE passive shielding setup in Hall B of LNGS.
The crystal scintillation properties were measured with the 59.5 keV line of an 241 Am source. Our detector shows a very competitive light yield, as high as 11.1 ± 0.2 phe/keV, and an energy resolution of 13.2% (FWHM/E). The presence of trace elements from primordial radioactive chains was evaluated using Bi-Po delayed coincidence analysis and found to be at the part-per-trillion (ppt) level. However, 210 Pb out of secular equilibrium is observed, and is one of the major sources of background at low energy for all NaI(Tl) experiments. We measured its activity by studying the evolution of the 210 Po α rate over time. An increase of this rate due to the build-up from 210 Pb decays was observed, allowing us to estimate an activity at equilibrium of 0.53 ± 0.04 mBq/kg. We also measured an α quenching factor of 0.63 ± 0.01 at the 210 Po decay energy E α = 5304 keV.
We employed two pulse-shape-driven analysis techniques to reject noise at low energy: a cut-based analysis and a multivariate Boosted Decision Tree. The latter shows a significantly higher acceptance. The acceptance-corrected energy spectra obtained with the two methods are found to be compatible above ∼8 keV. Below this energy, the spectra are similar though the multivariate analysis shows a slightly better noise rejection. Part of the rate can be attributed to residual noise events, leaving room for improvements in the rejection in the region around and below 5 keV. In order to perform direct counting of 40 K decays and to build a complete background model we will continue the characterization in the PoP setup, equipped with the active veto system. The commissioning was successfully completed in July 2020 and the measurement of crystal NaI-33 inside the liquid scintillator has started in August.
The results already achieved in the passive shielding and presented in this work show that the average interaction rate in the 5-20 keV energy range is close to 1 count/day/kg/keV. This, and other results presented in this paper show, a breakthrough achievement for the SABRE project. The PoP setup is expected to further improve the current understanding of the NaI-33 background toward the SABRE full scale experiment design.