Mitigation of $^{42}$Ar/$^{42}$K background for the GERDA Phase II experiment

Background coming from the $^{42}$Ar decay chain is considered to be one of the most relevant for the GERDA experiment, which aims to search of the neutrinoless double beta decay of $^{76}$Ge. The sensitivity strongly relies on the absence of background around the Q-value of the decay. Background coming from $^{42}$K, a progeny of $^{42}$Ar, can contribute to that background via electrons from the continuous spectrum with an endpoint of 3.5 MeV. Research and development on the suppression methods targeting this source of background were performed at the low-background test facility LArGe. It was demonstrated that by reducing $^{42}$K ion collection on the surfaces of the broad energy germanium detectors in combination with pulse shape discrimination techniques and an argon scintillation veto, it is possible to suppress the $^{42}$K background by three orders of magnitude. This is sufficient for Phase II of the GERDA experiment.


Introduction
In Gerda bare germanium diodes immersed in liquid argon (LAr) are used both as the source and the detector of the neutrinoless double beta (0νββ) decay a e-mail: lav@nusun.jinr.ru of 76 Ge [1]. Broad Energy Germanium (BEGe) detectors [2] were introduced to Gerda in Phase I and dominate the Phase II detector inventory. BEGe detectors in Gerda have better energy resolution than semi-coaxial detectors and a significantly thinner dead layer [3]. The latter makes them prone to surface events, from the beta particles, which can penetrate the dead layer. This kind of background is considered to be one of the most dangerous background sources in Gerda Phase II.
LAr serves as a detector coolant and as passive shielding against external radiation. Background events can be additionally suppressed by a LAr veto, detecting scintillation light generated in the liquid argon. Cosmogenic 42 Ar, present in natural argon, decays into 42 K. 42 K is a beta emitter (Q β = 3525 keV) with a half-life of 12.3 h (see Fig. 1). The arXiv:1708.00226v1 [physics.ins-det] 1 Aug 2017 region of interest (ROI) of the 0νββ decay is centered around Q ββ = 2039 keV [4]. High energy electrons E ≥ Q ββ from 42 K beta decays occurring very close to the detector surface, can increase the background level in the ROI.
During the first commissioning runs of Gerda Phase I it was found that the intensity of the 1525 keV gamma line from 42 K is much higher than expected from homogeneous distribution of 42 Ar assuming a natural abundance of <43 μBq/kg [6]. A similar conclusion emerged from the measurements in the LArGe test facility [7], operated in the framework of Gerda. The measurements [3] show that the enhancement of 42 K background can be attributed to an accumulation effect: after the decay of their mother isotope, 42 K ions retain their positive charge long enough to move in the electric field of the germanium detectors [8]. Consequently, the 42 K distribution in liquid argon is not homogeneous.
Enclosing a detector string with a cylinder made from thin copper foil (called mini-shroud, MS) it is possible to considerably suppress the background contribution coming from the 42 Ar decay chain [1]. The mini-shroud screens the electric field of the germanium detectors and creates a mechanical barrier preventing the collection of the 42 K ions on detector surfaces and thus decreasing the 42 K background level. However, the copper MS could not be used in Phase II: the main reason is that argon scintillation light generated inside the copper MS would be blocked from detection by the LAr veto, thus the veto efficiency would be seriously impaired. Another reason is that the radiopurity of the copper MS used in Gerda Phase I does not suffice the more stringent radiopurity requirements of Phase II. Therefore, it was decided to develop a new mini-shroud. Results from this development and detailed tests of its 42 Ar mitigation capability are described here. BEGe detectors have powerful pulse shape discrimination (PSD) capability which allows to mitigate surface events from 42 K. The suppression capability of 42 K background events by the PSD has been tested in the current investigation. The suppression factors (SF) obtained with passive and active methods are presented.

Experimental
2.1 Development of a transparent mini-shroud 42 K background can be suppressed e.g. by modifying the electric field produced by the high voltage applied to detectors, or by a mechanical barrier. Several applications were tested for Gerda(mini-shroud made of copper mesh, copper plate, plastic scintillator, etc.) and proved to work well in liquid argon. The solution described here is the mini-shroud made from a transparent plastic foil. The MS does not screen the E-field of the detector, but as a mechanical barrier for 42 K ions prevents their drift towards the germanium detector. The mini-shroud encapsulates the detector, but is not tight to prevent liquid argon from pouring inside during the immersion. The collected 42 K atoms decay on the foil's surface at a distance of several millimeters from the detector, thus beta particles are attenuated by liquid argon.
A thin nylon film (thickness 125 μm) was chosen as the construction material. It is robust, durable and flexible. It has good transparency for the visible light and exhibits a very low intrinsic radioactivity. Several pieces of nylon film were provided by Princeton University. These are left-overs from the material used in Borexino to construct the Inner Vessel [14]. The radioactive impurities are only 2 ppt for 238 U and 4 ppt for 232 Th [15].
Scintillation light emitted by liquid argon (128 nm) must be converted to wavelengths suitable for scintillation light detectors (sensitive range is about 250 -500 nm). Thus the nylon mini-shroud (NMS) was covered with a wavelength shifter (WLS). It allows light to pass through the nylon film as it is opaque for deep ultraviolet radiation (below 300 nm). The performance of the WLS coating, its robustness and stability in time were also investigated in various tests. These studies include an optimization of the composition and thickness of the WLS coating.
The performance of the WLS coating was tested with a UV spectrophotometer (Cary Eclipse) at the Max-Planck-Institut für Kernphysik (MPIK) in Heidelberg. Direct investigation of the shifting of argon scintillation light at 128 nm was not possible since no light source in this far UV region was available. Instead, a qualitative comparison was made with the emission light of the spectrophotometer at 200 nm.
The initial WLS solution was prepared by dissolving tetra-phenyl-buthadiene (TPB) with polystyrene (PS) in a ratio of 1:10 in toluene (recipe previously used for coating of the VM2000 reflection foil in LArGe [16]). To improve the performance of the nylon mini-shroud we increased the concentration of TPB and replaced toluene by dichlormethane (DCM) as the latter is used for the production of the reflector foils in Gerda Phase II [17]. A higher concentration of TPB in the polystyrene matrix increases the intensity of emitted light (see Fig. 2). However, too high TPB concentration decreases the mechanical stability of the coating. Finally, a TPB concentration in the range of 30% -40% in the polystyrene matrix  proved to be a good balance between mechanical stability and light emission efficiency. The coating was applied by brushing both sides of nylon samples. The amount of deposited WLS (typically 0.3 mg per 1 cm 2 ) was estimated by weighting the nylon before and after coating.
Various tests were performed in order to understand the usability of such a foil in Gerda. Immersion of the nylon film in liquid nitrogen showed that it keeps flexibility at low temperatures and does not become brittle even after several weeks spent in cryogenic liquid. Long term stability of the coated nylon foils was checked in liquid nitrogen (five months) and liquid argon (two months in the LArGe cryostat). No visible deterioration of the coated surfaces was found. Changes in optical properties of the WLS were checked with a UV spectrophotometer. Fig. 3 shows a comparison of samples kept for five months in liquid nitrogen (blue dots) and in air (red dots). No significant difference between the two fluorescence spectra was observed.
To construct the NMS fully covering the detector (or a string of detectors) it is necessary to connect several nylon sheets together to form a cylindrical shape. Such connections should be radioactively clean and robust enough to survive manual handling and immersion into liquid argon. The first version of the mini-shroud was created by welding (see Fig. 4) not requiring any additional material, but the connections were brittle and easily damaged during handling. Finally, nylon pieces were glued using a solution of resorcinol in ethanol and water with sodium meta-bisulphite [18]. It was confirmed that the connections are very robust and suitable for cryogenic operations. The glued NMS was placed around a dummy detector string (aluminum dummies of detectors and holders) and it was submerged in liquid nitrogen, showing that it is robust enough and can keep its shape during the slow immersion process (∼1 hour) of the detector strings in Gerda. To minimize the risk of contamination, all preparations were performed in the clean room. Before the insertion into liquid argon, the NMS went through several outgassing cycles.

Contribution of the NMS to the Gerda background index
The content of radio-impurities of coated nylon films was checked by ICP-MS to verify that no significant background contribution is added to GERDA [19]. Results of the measurements are summarized in Tab. 1. The difference in the radioactive contamination of the starting foil material and the aggregated contamination of the final NMS may have been introduced during the preparation of the samples. The nylon cylinder for each Gerda Phase II detector string typically has a height of 430 mm and a diameter of 103 mm. The mass of the NMS is about 28 g. We expect about 6.1 μBq of 238 U and about 2.6 μBq of 232 Th reside in a single NMS. To prove that this radiopurity level is acceptable, a detailed simulation of the NMS background for the Gerda Phase II setup was performed. This Monte Carlo simulation is based on the MaGe framework [20] with the preliminary Gerda Phase II geometry, using 7 detectors strings with one NMS each, under the assumption of equilibrium in the U/Th chains [13]. The simulation code is validated with the Gerda calibration data. Radioactive isotopes were homogeneously distributed inside the NMS material. The simulated energy spectra of germanium detectors taken with 214 Bi and 208 Tl sources are shown in Fig. 5. Tracking of optical photons and the evaluation of the LAr veto suppression were only performed in the energy region of 1800-2300 keV, to save computation time. Suppression factors of 33±4 and ≥ 2000 are obtained for 214 Bi and 208 Tl respectively. The large suppression is due to the thinness of the NMS which allows the betas from 208 Tl and 214 Bi to escape the nylon and deposits a large fraction of their energy in the LAr. This creates a large scintillation signal which can be easily vetoed. The estimated contributions to the background index (BI) for 214 Bi are 1.8×10 −4 cts/(keV·kg·yr) before and 5.3×10 −6 cts/(keV·kg·yr) after applying the LAr veto. For 208 Tl these values are 2.7×10 −4 cts/(keV·kg·yr) and <1.4×10 −7 cts/(keV·kg·yr) before and after the LAr veto, respectively. The combination of these values gives the total contribution of the NMS to the BI in Gerda Phase II of about 4.6×10 −4 cts/(keV·kg·yr) and 5.3×10 −6 cts/(keV·kg·yr) before and after the LAr veto, respectively. These values are well below the Gerda Phase II requirements (total BI<1×10 −3 cts/(keV·kg·yr)). Simulated energy spectra of germanium detector taken with 214 Bi (top) and 208 Tl (bottom) sources. The simulated spectra before cuts are shown in black, after the detector anti-coincidence (AC) in blue and after applying the LAr scintillation veto cut in red [13]. Simulation of the anticoincidence spectrum was only performed near Q ββ , to save computation time.

Experimental setup
Detailed investigations of the 42 K background were performed in the LArGe test facility [7]. The setup allows to operate bare germanium detectors submerged in 1 m 3 of liquid argon. The cryostat is equipped with nine photomultiplier tubes (PMT) in order to suppress background events by detecting scintillation light in liquid argon, occurring in coincidence with germanium detector events (LAr veto). The LArGe setup is located at the Laboratori Nazionali del Gran Sasso (LNGS) Underground Laboratory at 3800 m w.e. depth. An achieved background index in LArGe [7] is close to to the level of Gerda Phase I. Hence, an investigation of low background sources is possible.
The measurements in LArGe were performed with a BEGe detector produced by Canberra [9]. The scheme of the detector and its dimensions are shown in Fig. 6. It is a p-type diode with the mass of 878 g. The thickness of the dead layer is estimated to be 0.6 mm. The detector mounting procedure and the holder design is the p-type germanium Φ 81 mm 32 mm 878 g n + electrode HV contact 0.6 mm dead layer p + electrode read-out contact Fig. 6 Schematic drawing of the bare BEGe detector used in the study [12].
same as in Gerda Phase I [1], i.e. usage of low-mass and radio-pure materials close to the detector is implied. A Gerda Phase I custom made charge-sensitive preamplifier (CC2) with integrated J-FET transistor and RC feedback components is used for the signal conditioning [10]. Signals are digitized with a Flash-ADC (Struck SIS3301 VME, 14 bit, 100 MHz) card.
In order to enhance the 42 K signal, two 42 Ar sources with activities of (5.18 ± 0.91) Bq and (79 ± 15) Bq were produced by irradiating a cell filled with gaseous nat Ar at the accelerator operated in the Maier-Leibnitz Laboratory (MLL) of the Technische Universität München (TUM). The sources were introduced into the LArGe cryostat and homogeniously distributed inside LAr. With the enhanced signal rate from 42 K it is possible to investigate the behavior of 42 K ions and to test different background suppression methods with better counting statistics. The long measurement without NMS and measurement with a first version of the NMS were performed after the insertion of the source with lower activity. Measurements with the second, final version of the NMS were done with both sources inside LAr. The 42 Ar activity of these sources increased the count rate of the 1525 keV gamma peak (with respect to the measurements with natural argon) by factors of about 40 and 200, respectively. The increase is not exactly proportional to the activity due to the evaporation of liquid argon during refilling of the cryostat.

Measurements of suppression factors
The energy region of 1540 -3000 keV ("beta region") contains predominantly surface events from beta particles (see the 42 K decay scheme in Fig. 1) and overlaps the Q ββ ±200 keV energy region. The energy region 1520-1530 keV mostly contains events from the 1525 keV gamma line.
The suppression factor in a certain energy region expresses the ratio of events in the unsuppressed (N 0 ) ver-  sus the suppressed (N S ) spectrum. For measurements with LAr veto in order to be independent of the source strength the LAr acceptance (ε LAr ) is taken into account, hense SF = (N 0 − B 0 ) · ε LAr /(N S − B S ), B 0 and B S are the background levels before and after suppression respectively.

Suppression of 42 K background by NMS
The BEGe detector inside the NMS (Fig. 7) was submerged into the LArGe cryostat. No deterioration of the detector's performance was found when operated with the NMS. A typical energy resolution of the detector is about 2.9 keV at the 2.6 MeV of the 208 Tl gamma line, similar to measurements without NMS. The energy spectra with and without NMS are shown in Figure 8.
The measurement without NMS was taken for a shorter time, therefore its spectrum is scaled to the NMS measurement time. Tab. 2 shows results from the calculation of the SF in the "beta region" using the ratio of count rates with and without NMS. The first two days of data taking are not taken into account in order to reduce the influence of previously accumulated  Fig. 9 Number of counts in the energy region 1520-1530 keV (blue) and 1540-3000 keV (green) in time for measurements of the detector without NMS in LArGe. The vertical red line indicates a period of the first two days which is not taken into account in the calculations. 42 K. An additional decrease of the 42 K count rate after first two days (see Figure 9) is also taken into account during calculation of the SF (henceforth referenced as "long-term correction"). Thus the SF is estimated to be 14.3(2.1).

Suppression of 42 K background by PSD and LAr veto
A strong weighting potential close to the read-out electrode in the BEGe-type detectors enables a powerful pulse shape discrimination (PSD) of the acquired signals [11]. The PSD used in this work is based on the method described in [12]. It was developed for the discrimination between single-site events (SSE) and multisite events (MSE) using differences in the amplitudes of current pulses with the same energy. The 0νββ events are expected to be SSE due to a rather short path length of beta particles in the germanium detectors. In contrast, photons will often undergo several scatterings and are mostly MSE. Surface events exhibit a slower rising edge of the pulse due to diffusion of the electric charge into the n + surface areas (n + contact surface pulses, NSP). In consequence, these events have smaller amplitude to energy (A/E) ratio compared to events in the bulk of the detector. The events that deposit energy near the p + contact of the detector (p + contact pulses, PCP) have higher amplitudes than SSE, and they can be rejected as well.
The PSD cut parameters were determined from calibration data taken with a 228 Th source. Events in the double escape peak (DEP) of the 2.6 MeV gamma line of 208 Tl are predominantly single-site with a shape similar to 0νββ events. The low cut is usually determined in order to keep 90% of the events in the DEP. Fig. 10 demonstrates such PSD cut obtained for the measurement with the BEGe detector in LArGe (rejected events are in the MSE region below the black line). The slope of the lines is determined from the distribution of the Compton scattering events. The p+ events are rejected by applying a high cut (these events are above the red line in Fig. 10). After applying low and high cuts 88% of the events are kept in the DEP.
The first tests of 42 K suppression by PSD were performed with the bare BEGe detector in LArGe without a mini-shroud with the smaller 42 Ar source. The A/E distribution is shown in Fig. 11. The majority of events coming from the beta decay of 42 K are located below the SSE band. They are predominantly NSP from electrons which deposit their energy in the n + surface of the germanium detector. Only a small amount of the events are located in the SSE band.
The LAr veto is not very efficient in suppressing events from 42 K in the ROI, because such electrons often do not deposit much energy in liquid argon. However, combined PSD and LAr veto work efficiently, helping to suppress different types of background. The LAr  veto acceptance measured by pulse generator is 96.5%. Part of the events in the SSE band are coming from other background sources (mostly from 228 Th). Such gamma background is removed with high probability by the scintillation veto [7]. After applying PSD and the LAr veto the events in the ROI are removed almost completely. Tab. 3 summarizes the SFs in different energy ranges. Only 2 events survive from the initial 610 events in the ±200 keV window around the ROI of 0νββ after applying PSD and LAr veto. For a precise estimation of the 42 K SFs the remaining background sources have to be taken into consideration. Unfortunately, no measurements prior to dissolving of 42 Ar are available for this detector to estimate the background level. So it is estimated with help of previous investigations with an encapsulated semi-coaxial germanium detector. The background level of that detector was (0.12 -4.6)×10 −2 cts/(keV·kg·yr) after LAr veto [7]. It was dominated by 208 Tl external to the cryostat, presumably from the PMTs [7], so we can expect to have this background with other detectors as well.
In addition to this background the contribution of cosmogenic background from 68 Ga in the BEGe detector is taken into account. The background index after applying the LAr veto and PSD is estimated with help of previous investigations in LArGe [7] and simulations [13]. The accumulated statistics is not enough to find precisely the suppression factor for the 42 K background in the ROI, but it is possible to obtain a lower limit of >121 at 90% C.I. for the combined LAr veto and PSD cuts. This value is obtained with help of TRolke class [22] assuming poisson statistics of the signal. This value can be improved by applying a stronger PSD cut: after applying 73% PSD cut (low 75% and high cuts) no events survive the PSD veto (see Fig. 11).
It is necessary to notice that the suppression factor of PSD depends on the detector performance: with worse A/E resolution some of the events can leak into the SSE band, reducing the efficiency of PSD cuts. That is why the SF achieved in LArGe may be slightly different than for the detectors in Gerda Phase II with different PSD performance.

42 K background suppression of NMS combined with PSD and LAr veto
The performance of the LAr veto with introduced NMS was investigated with a 228 Th source and with spiked 42 Ar in liquid argon. The suppression factors of the LAr veto are obtained with the two versions of the NMSs and without it (see Tab. 4). The LAr veto SFs improves when using the NMS, which is clearly seen in the suppression of the 42 K gamma line. The absorption length of light shifted by NMS is much longer compared to the 128 nm scintillation light, and thus more light can reach the LAr veto light instrumentation. This may be   Fig. 12. In this measurement the final, glued version of the NMS was implemented. Both 42 Ar sources were spiked into the LArGe cryostat. Similarly to the previous measurements without NMS, most of the events coming from 42 K are rejected by PSD. The remaining part is removed by the LAr veto. The LAr veto allows to suppress events located in the SSE band more efficiently than in the MSE band (see Fig. 12). This is an indication that most of the events in the SSE band are not electrons from 42 K. The number of events surviving PSD and LAr veto are shown in Tab. 5. From the initial 216 events in the ROI only 2 events survive after applying LAr veto and PSD cuts. The estimated number of background events is 0.4. After taking into account the pulser acceptance, the SF is greater than 38 (90% C.I.). By applying a stronger PSD cut (73%) it is possible to suppress all of the events. Fig. 13 shows the comparison of spectra with and without NMS and the effect of active 42 Ar suppression. The gray area shows the spectrum of the bare BEGe detector without NMS scaled to the measurement time with the NMS. Other spectra demonstrate the 42 K suppression by the NMS and different cuts. In the scaled energy spectrum registered without the NMS there are 4384 events in ROI. After applying the PSD cut and the LAr veto only 2 events survive, including an estimated background of 0.4 events. Taking into account other than 42 K background components, LAr veto and the NMS suppression factor, the resulting suppression factor is higher than 513 at 90% C.I. is obtained. (see Tab. 6).
The measurement with NMS has lower counting statistics compared to measurements without NMS. However, there is no indication that PSD performance in case of NMS is worse than in the measurements without NMS. The LAr veto works slightly better in case of NMS, but it almost does not suppress events from 42 K in the ROI, that is why it has little effect on the results. Therefore it is safe to assume SF > 121, obtained in the measurement without NMS and better statistics (see Tab. 6) instead of SF > 38. With the NMS suppression factor of 14.3(2.1) using SF > 121 for PSD and LAr veto a total SF of greater than 1476 is obtained.  Fig. 14. The setup was introduced into the Gerda cryostat and data taking successfully started. The achieved background rate in Gerda Phase II after all cuts is approximately 1×10 −3 cts/(keV·kg·yr), satisfying desired specifications [23]. So the described concept of 42 Ar background suppression has proven its effectiveness. Using SFs obtained in LArGe it is possible to estimate the 42 K background level in Gerda Phase II like setup. The expected 42 K background rate in Gerda is estimated by scaling the 42 Ar background in LArGe to Gerda using the ratio of the 1525 keV line intensi-ties. The dead layer thickness has a big influence on the 42 K count rate in the ROI. That is why this factor is taken into consideration with the help of simulations. From these calculations it is expected that a bare BEGe detector in Gerda without a mini-shroud and before applying any cuts has a 42 K BI in the range of [2.1..8]×10 −1 cts/(keV·kg·yr). The lower bound corresponds to a dead layer thickness of 1.0 mm with minimal expectation for the 42 K concentration in liquid argon, the higher value corresponds to 0.6 mm thickness and maximal expectation for the 42 K concentration. A typical value of the dead layer of a BEGe detector in Gerda is about 0.8 mm [3], so the limit for the 42 K background rate is expected to lay in the quoted range. By applying the SF derived in LArGe we obtain the background expectations in Gerda like setup after NMS, PSD and LAr veto (see Tab. 6).
However, it is necessary to note that obtained values just demonstrate possibility to suppress 42 Ar background to desired level, but can not be applied directly to Gerda setup. Gerda has 30 BEGe detectors and the LAr veto is rather different compared to LArGe. In principle, the difference in the LAr veto should not affect much the total suppression of the 42 K background, while its suppression is low (factor ∼ 1.2) compared to NMS and PSD (see Tab. 4). But some of the detectors in Gerda have a worse PSD performance than one tested in LArGe, so a worse suppression by PSD is expected for these detectors. One the other hand the suppression factors of NMS in Gerda should be higher due to the better design of the Gerda NMS with less inner volume for each detector.
However, all these differences should not be very big and current calculation gives a good estimate about possible 42 K background contribution for Gerda Phase II.

Conclusions
Our investigation shows that the NMS alone is an efficient tool to suppress the background caused by 42 K about 15 times. It is also demonstrated that PSD is a very good method to mitigate surface events from 42 K decays. Results of the measurements in LArGe with a combination of NMS show that the NMS together with the PSD and LAr veto can suppress 42 K background by more than 3 orders of magnitude.
The glued NMS is easy to construct and robust enough for handling and mounting. Moreover, there is a clear indication that NMS improves the performance of LAr veto. The NMS is made from radiopure material. The expected contribution to the background index from its contamination is only 4.6×10 −4 cts/(keV·kg·yr) and 5.3×10 −6 cts/(keV·kg·yr) before and after the LAr scintillation veto, respectively. These values are well below the requirements for Gerda Phase II and may also be acceptable for future experiments.
The NMSs were successfully mounted and immersed into the liquid argon cryostat of Gerda. The described concept of 42 Ar suppression proved its usability and performance. Taking into account the results obtained in LArGe and simulations we estimate the possible level of background from 42 K in Gerda Phase II. It is expected to be <[0.14..0.5]×10 −3 cts/(keV·kg·yr) with NMS and after applying PSD and LAr veto cuts in the ROI. This limit already meets the Phase II design criteria and can be further improved by a stronger PSD cut or by using the detectors with thicker dead layers.