The concern for radioactive contaminants in detector materials is from detector signals (backgrounds for a double beta decay experiment) generated by radioactivity, including gamma rays and alphas, emitted from the radioactive decays. The most direct way to measure these is to detect such emissions with a sensitive detector. High-purity germanium detectors are the most standard choice for observing long-ranged gamma emissions, especially owing to their high efficiencies, good resolutions, and, as the name implies, high purity. In particular, HPGe detectors measure gamma emissions from decays in the ⁴⁰K, ²³⁸U, and ²³²Th decay chains. In this work, we generally report measured results as the activities of the long-lived isotopes that support gamma-emitting sub-chains. Particularly, ²¹⁴Pb and ²¹⁴Bi peak rates are used to derive the ²²⁶Ra activities in the ²³⁸U chain, and ²⁰⁸Tl and ²¹²Pb are used to derive the ²²⁸Th activity in the ²³²Th chain. ²²⁸Ac activities are equivalent to ²²⁸Ra activities but are reported here as ²²⁸Ac since it is the only gamma-emitting decay in that sub-chain. For all HPGe analyses, gamma detection efficiencies are determined using GEANT4-based Monte Carlo simulation of whole decay chains for decays distributed uniformly within the samples. For HPGe assay of high-density samples such as lead, copper, solder, tin, stainless steel, and neutron shielding materials, a systematic error was included for potential background reduction from shielding effects of the sample as previously presented in Ref. [11] and using a similar method to the one described in Ref. [12]. An example of the general procedure used is described in more detail in Section 3.4.

Alpha counters of various types can also be used to measure alpha emissions directly from the surface layers of materials.

The whole radioassay landscape is complicated. Two of the main background-producing decay chains occur through a sequence of many radioactive decays, starting with ²³⁸U and ²³²Th. Most background-producing radioactivity is from long-ranged gamma emissions, which are not easily shielded. These gammas are generally supported by long-lived isotopes in the decay chains, specifically ²²⁸Ra and ²²⁸Th in the ²³²Th chain and by ²²⁶Ra in the ²³⁸U chain. However, some backgrounds are still generated by the upper-chain decays, particularly via alpha emissions from materials that face the detector material. For this reason it is still desirable to measure the ²³⁸U and ²³²Th concentrations directly to understand the complete background picture.

Furthermore, direct measurement of emissions from the gamma-emitting sub-chains is always challenging when selecting detector materials for a cutting-edge rare event experiment. By design, the background levels of interest should be barely detectable by the cutting-edge detector itself after it is built, even with years of data. As there are many construction materials to consider, counting times on assay detectors must generally be days or weeks, not years, and the detectors used for assay are often not as sensitive as the experiments themselves. This motivates alternative approaches.

In decay-chain-equilibrium, every isotope below ²³⁸U and ²³²Th decays at the same rate at which it is produced, which is the ²³⁸U or ²³²Th decay rate, respectively (otherwise, their concentrations would rise or fall until equilibrium is achieved). However, in that condition, the concentrations of the isotopes in the chain are proportional to their half-lives. Since the ²³⁸U and ²³²Th half-lives are billions of years, this would imply much higher concentrations and thus potentially easier detection relative to isotopes with shorter half-lives lower in the chains. Chain equilibrium is established on the time scales of the long-lived isotopes that support the lower chains (1,600 years for ²²⁶Ra) and is easily broken by geological or manufacturing processes. Still, using this relationship, concentrations or activities can be stated as equilibrium-equivalent concentrations of the other isotopes in the chain. If the equilibrium is assumed to be valid, measurements of the top-of-chain isotopes can result in much-enhanced sensitivity to the lower-chain concentrations. This assumption is questionable in many or most cases but has uses in some cases. The supporting isotopes of the lower ²³²Th decay chain have half-lives of a few years, so equilibrium assumptions can be informative for some scenarios. In other cases, it is simply the best that can be done before building and testing the final detector. While the value of this approach is limited, it can be another motivation for measuring isotopes from the top of the decay chains.

While alpha emissions from the upper chain can be directly measured as with the lower chain, two approaches to measuring ²³⁸U and ²³²Th concentrations with significantly higher sensitivity are inductively coupled plasma mass spectroscopy (ICP-MS) and neutron activation analysis (NAA).

The AMoRE-II experiment uses two types of scintillating crystals, CaMoO₄ and Li₂MoO₄. The internal contamination of the CaMoO₄ crystals is characterized by the AMoRE-Pilot and AMoRE-I detectors [19, 20]. Before growing the Li₂MoO₄ crystals, precursor materials (molybdenum trioxide and lithium carbonate powders) are tested to confirm the AMoRE-II purity requirements for precursors [16, 21]. The bulk contamination levels for ingots grown using preliminary purified and non-purified precursors are shown in Table 1. The internal contamination of all the enriched Li₂MoO₄ crystals grown from 2020 to 2023 by CUP and NIIC has been measured by ICP-MS to monitor the crystal production routine. For each crystal, about 1 g of sample is cut from the upper and bottom of the ingot after cutting the crystals and assayed with ICP-MS. For all recently tested 200 crystals, ²³⁸U and ²³²Th are found to be less than 10 pg/g.

After cutting the crystals from the original ingots, the crystal surfaces are lapped and polished. The SiO₂ abrasive powder is selected as the cleanest material for surface conditioning. The Admatechs SO-E (low-alpha beam grade) type powder is used. Powders with 8 μm and 1.5 μm particle sizes are used for lapping and final polishing of the crystal surface, respectively. Since lithium molybdate is highly hygroscopic, protection measures are required to save the crystal surface from moisture damage. The Lubriplate low-viscosity non-detergent mineral oil is selected as a lubricant to protect the crystal surfaces from moisture and smooth the polishing. The Ciegal 7355-000FE polyurethane polishing pads are used for buffing at the final polishing step.

We measured NOSV and OFE copper from Aurubis company in Germany and OFE copper from Mitsubishi company in Japan. Bulk contamination of the copper was studied and reported in Ref. [22]. For convenience, results are presented here in Table 2. Samples of about 1 cm³ were cut from the initially received stock plates. The cubic samples were etched twice in strong nitric acid with sonication to remove the contaminated surface. Cleaned samples were reconstituted within strong nitric acid, and Th and U were extracted with a 2 mL UTEVA resin cartridge. The extraction efficiency was controlled by analyzing a sample spiked with a known amount of Th and U standard solution. Bulk contamination levels of ²³²Th and ²³⁸U in the NOSV-Cu stock plate purchased in 2014 were found to be unacceptable for AMoRE-II, while levels in the plates purchased later in 2018 and 2021 were found to be suitable use as crystal holder material. Holder units, except for the screws, were machined from the original copper plates of NOSV-Cu purchased in 2018 and 2021. The screws were machined from the 2018 OFE-Cu. Each holder unit was degreased with kerosene and ethanol, and then a surface layer of about 1 μm was removed by etching with sonication in 5% nitric acid solution. The etched surface of the copper units was passivized and rinsed with deionized water.

After the surface etching procedure, the sensor plates, posts, and screws were measured with ICP-MS. Metal from the bodies of the pieces was digested in nitric acid and moved to the extraction procedure. Analysis of the sensor plates with simple flat surfaces showed efficient Th and U removal with this cleaning procedure. Each post has two screw threads, which, due to the machining process, may have more deeply-embedded contamination. The screws, like the posts, could not be etched deeper than 1 μm without compromising their functional integrity. The screws, which were made of OFE-Cu, showed about 10 pg/g of ²³²Th and 2 pg/g of ²³⁸U, while the bulk concentration of the stock OFE-Cu was about 1 pg/g for both.

While ICP-MS proved suitable levels for ²³²Th and ²³⁸U, proving sufficiently low levels of ²²⁶Ra and ²²⁸Th is a different challenge. To this end, we prepared a large sample of the 2014 NOSV copper reported in Ref. [22] to be counted on the CAGe array detector. The total sample mass was 145 kg, prepared as eleven plates, each 2 cm thick, with one 30 cm × 30 cm plate placed horizontally between the array halves, and the others (19.6 cm × 35 cm and 19.6 cm × 38 cm) placed on edge around the four sides of the detector elements. Before installation, the plates were all cleaned by scrubbing with Alconox, by a weak nitric, etch, and finally by rinsing in DI water. A supporter was designed to fill the space around the bottom array cryostat, thus supporting the outer copper plates at a height level with the bases of the cans housing the lower array detector elements. The supporter was machined from low-activity cast acrylic and made in four parts for assembly around the detector. Figure 2 shows the arrangement of the copper in the CAGe detector chamber with the acrylic supporter. The sample was counted for about 83 days with Rn-free air supplied to the room. Background data was taken in a similar condition for about 32 days with the supporter in place but with the sample removed.

For large samples, on any of the HPGe detectors, we often simulate potential background shielding of the sample [11, 12] and use the difference between the full background and the potentially shielded background as a systematic error. To be specific, backgrounds originating from sources near to or within the detector will not be shielded by the sample, while backgrounds originating from sources blocked by the sample could be significantly shielded. Since we do not know the distribution of background sources, this represents a systematic error. The simulation allows optional selection of a sample, as well as one of any pre-defined volumes for generating background decays, both as run-time configurations to the program. A batch submission script runs simulation jobs for events in the sample, in the background generation volume with the sample in place, and in the background generation volume without the sample, for any selected isotopes. A batch analysis determines detection efficiency for decays in the sample and compares background decay spectra with and without the sample to quantify the background-shielding effect of the sample. For the CAGe, we simulate background decays from the vicinity of two opposing copper shielding walls, specifically between the door shielding and the thin Vikuiti window sheets that seal the two detector openings. These volumes represent a realistic location for radon decays, and also represent a region where backgrounds are expected to be maximally shielded by the sample. In the case of the 2014 NOSV measurement, because of the unusually high density and thickness of the sample, the backgrounds from this simulation were attenuated to 20% of their un-shielded rates, or less, depending on the gamma energy. Since we do not know the true source of the backgrounds, or if they are shielded at all, we perform the analysis with full background subtraction, and again with subtraction of the attenuated background rates, treating the difference as a systematic error. For any decay sub-chain, if either scenario is consistent with zero, a 90% limit is derived from the higher result. In this case, because the potential background shielding is nearly absolute, the procedure is nearly equivalent to deriving upper limits from the sample data alone.

Peak rates from ²²⁸Th, ²²⁸Ac, and ⁴⁰K were conclusively positive but consistent with measured background levels. The ²²⁶Ra rates in the sample data were slightly below the background level. Results from the analysis are shown in Table 1. However, we note that the striking similarity between the sample and background rates, particularly in the ⁴⁰K and ²³²Th chains, leaves the likely possibility that the background sources are primarily internal to the detector and not shielded by the sample, such that full background subtraction would be appropriate. In particular, it was previously reported that o-rings in the detector construction contain high levels of ⁴⁰K [15]. A traditional background subtraction analysis, assuming no background shielding, implies stronger limits in the range of 19–26 μBq/kg for ²²⁸Th, ²²⁸Ac, and ²²⁶Ra, and <200 μBq/kg for ⁴⁰K, as limited by counting statistics, close to limits for earlier production batches of NOSV copper previously reported in Refs. [23, 24]. The ²²⁶Ra limits without background subtraction meet the requirements for AMoRE-II, while the ²²⁸Th results are also limits, but are close to our goals only if full background subtraction is assumed.

As copper is a material of particularly general interest for low-background experiments, in addition to the tabulated results, we report limits of <44 μBq/kg for ²³⁵U, <690 μBq/kg for ²³¹Pa, <32 μBq/kg for ²²⁷Ac, and <330 μBq/kg for ²³⁴Th. To handle interferences, particularly for ²³¹Pa and ²²³Ra, analysis was performed using an updated version of GDFIT [25], with a coupled fit of activities to the entire spectrum, where peak rates were modelled by the fitted activities and by efficiencies, branching rations, and intensities, with constrained background contributions to each peak. In the ²³⁵U chain, since the measurement was performed many months after production of the material, ²²⁷Ac was assumed to be in decay equilibrium with ²²³Ra and its daughters.

This measurement was prepared before ICP-MS measurements determined that the ²³⁸U and ²³²Th concentrations in the 2014 NOSV batch were not suitable for AMoRE. As reported in Ref. [22], the ²³²Th levels measured in the 2021 NOSV copper used for AMoRE-II were about 17 times lower than the levels in the 2014 copper measured on the CAGe. The combination of low ²²⁶Ra, ²²⁸Ra, and ²²⁸Th levels in the 2014 copper, and greatly reduced ²³²Th levels in the 2021 copper give reason for optimism that the ²²⁸Ra and ²²⁸Th activities in the 2021 copper may be significantly below the obtained limits.

In addition to the CAGe measurement of the 2014 NOSV copper, samples of the 2016 and 2021 NOSV coppers were assayed with the CC1 and CC2 100% HPGe detector. The results for all activities in the ²³⁸U, ²³²Th, and ⁴⁰K chains were limits for both, although with much worse sensitivities.

The detector crystals are cooled to low temperature via heat conduction through the copper holders to the thermal bath. However, the thermal conductivity between the crystals and the thermal bath should be low since the athermal phonons should be collected efficiently by the phonon collector. Therefore, the crystals are mechanically connected to the copper holders by small pieces of insulating PTFE. Specifically, the parts are machined from a product sold by the Maagtechnic company, listed as “ERIFLON Plastic plate PTFE pure virgin white,” and sold in various thicknesses.

ICP-MS measurement of PTFE and other fluorocarbon plastics is challenging because digestion requires particularly hazardous chemicals. However, as these have been found to be very clean materials, a number of high-sensitivity measurements have been performed [26–31]. Maagtechnic PTFE was selected largely because measurements have already been performed for other rare-event experiments and reported in Refs. [27, 29]. Both references report only limits for a range of naturally occurring radioactivies, with Ref. [29] reporting less than about 63 μBq/kg or better for all of ²²⁶Ra, ²²⁸Ra, and ²²⁸Th from direct HPGe assay and reporting corroborating limits inferred from ICP-MS measurements. At CUP, we prepared samples of the material (purchased as plates from the Eriflon product line) for measurement using neutron activation analysis (NAA). Samples were prepared as discs of 10 mm diameter by 5 mm height, machined from 15 mm stock, and cleaned along with irradiation vials via a procedure using ultrasonic cleaning and nitric acid etching. A total sample mass of 3.4 g was analyzed with NAA by the Korea Atomic Energy Research Institute using 4 h of sample irradiation at the HANARO reactor operated at a power of 15 MW. The resulting limits were <200 pg/g and <100 pg/g for ²³²Th and ²³⁸U, respectively, as tabulated in Table 2. This was the first attempt to use NAA at HANARO for sample analysis. Several factors can be optimized in the procedure, including reactor power, sample mass, counting time, and counting delay.

One of the most serious backgrounds to the 0νββ signal is from alpha decays from contaminants on or near the surfaces of the crystals. Because of energy loss in non-sensitive material, the resulting signals can be at any energy from zero to the alpha emission energy. To avoid this continuum of alpha signals, the scintillation from detector events is measured by photon sensors above the crystals. We positioned a Vikuiti reflective film around the sides of the crystals to improve photon transport. About 80 cm² is required for the 5 cm diameter crystals, and over 110 cm² is needed for the 6 cm diameter crystals. Since this film directly faces the detectors, it is critical that it has low levels of radioactive contaminants. Both a roll-type and sheet-type film were tested at CUP with a procedural detection limit of about 1 pg/g for ²³²Th and ²³⁸U [22].

The sample decomposition was performed without any preliminary cleaning, as in the real experiment. After a protection cover was peeled off, the Vikuiti film was cut into small pieces of about 0.5 g. Then the samples were ashed step-wise in quartz crucibles using microwave heat. The resulting ash was quantitatively dissolved in nitric acid, and thorium and uranium were directly measured with ICP-MS without any column separation. The roll-type Vikuiti film was found to have two times lower Th concentration and four times lower U concentration than the sheet-type film, and was selected for the detector assembly. Vikuitti is no longer manufactured, but we have enough supplies for AMoRE-II.

Energy depositions in the crystals are read by sensors composed of metallic magnetic calorimeters (MMCs) and superconducting quantum interference devices (SQUIDs). The sensors for each detector module are mounted on a copper sensor plate, with connections wire bonded to a printed circuit board (PCB) which is attached to the same plate, as shown in Figure 1. This arrangement serves to prevent strain on the connection to the sensors. Superconducting niobium wires from Supercon Inc. connect from this PCB to a connection board at the mixing chamber, above the lead shielding. This connection is about 2 m long. From there, bundled NOMEX ribbon cables make the connection to a junction box at room temperature. Ceramic or plastic PCBs have high radioactivity. The selected PCB board (sometimes called a flex cable) is model HGLS-D211EM made by Hanwha L&C, having copper foil (35 μm thick) glued with adhesive (10 μm thick) to both sides of a polyimide film (25 μm thick). One side is etched to make the circuit. The other side of the PCB board is attached to the copper plate by lead-tin solder. The PCBs were measured by ICP-MS and also by HPGe counting. The sample for HPGe counting had a mass of 1.16 kg and was measured with the detector for 20 days. This gave upper limits of 1.08 mBq/kg for ²¹⁴Bi and 1.07 mBq/kg for ²²⁸Th. The ICP-MS results were 893 ± 90 pg/g and <1.2 pg/g for U and Th, respectively.

The MMC and SQUID were attached to the copper sensor plate by Loctite brand Stycast glue. Both Stycast 2850 and Stycast 1266 were assayed with HPGe. We used Stycast 1266 for AMoRE-II as Stycast 2850 had high radioactivity. Stycast 1266 has two parts: resin and hardener. Both were measured individually, and the measurements gave upper limits, as shown in Table 1.

We use lead-tin solder to attach the PCB to the copper sensor plate and to attach the niobium wires to the PCB. The total mass of solder connecting this board to wires and the plate is nominally about 70 mg per board, and two boards are used (one for heat and one for light) for each detector module. Since the radiopurity of the lead solder is critical, we made this material in one of our chemical labs. The ratio of lead to tin is 6:4. We have measured different grades of tin material from the Alfa Aesar company. We started by measuring their 99.85% purity grade tin powder. The ²¹⁰Pb activity was observed to be about 500 Bq/kg, which was unacceptable for use in AMoRE-II. Zone-refining purification was implemented to reduce contamination of the lead. With 35 sequential zone melting cycles, the contamination level was still several hundred Bq/kg, so we then tested the tin bead samples with 5N and 6N purity grades from the same company. Upper limits of 2.1 Bq/kg for ²¹⁰Pb were found for both products using HPGe, and a 50 pg/g upper limit was found for both ²³⁸U and ²³²Th using ICP-MS. The 5N and 6N products were used for the solder production without any preliminary treatment. To be melted with the tin, lead pieces were cut from bulk plates of ancient lead [32] and were then cleaned with sonication using 10% nitric acid, rinsed with deionized water, and dried.

The low-background AMoRE physics run data is dominated by the 2νββ spectra and has few events in full-energy gamma peaks. For calibration, we need to have a steady source of events with well-defined energy and shape. For this purpose, we inject a thermal signal by flowing a small current with a resistance. The heater is made of a silicon wafer and is attached to the crystal surface by Araldite glue.

The outer vacuum chamber is made of 304-grade stainless steel. It is divided into two cylinders coupled with stainless screws M8. Therefore, it has three flanges in total. The flanges are made of stainless steel plate, bent and welded to make a hoop. The welding of flange ends to form the hoops is done with flux core welding rods (K-308LT from KISWEL Korea Welding company) with radioactivities found to be high, 48.4 ± 2.4 Bq/kg for ²²⁶Ra and 20.6 ± 1.0 Bq/kg for ²²⁸Th. The flux inside the welding rods may contribute strongly to the radioactivity of the rods, but the flux is not fully incorporated into the weld. It is thus necessary to evaluate the radioactivity contamination of the welded part after welding. We made a welding part similar to the flange structure by welding stainless steel with flux core welding with a similar weld geometry and applying a similar amount of weld material. We measured the resulting 1.77 kg sample part with the HPGe detector, and found activities of 16.4 ± 1.6 mBq/kg for ²²⁶Ra and 12.9 ± 1.5 mBq/kg for ²²⁸Th. The hoop-shaped flanges are welded to the cylinders with TIG welding using AWS AS.9 ER308L rod from Hyundai welding company. The cylinders themselves are also formed with a TIG-welded seam. Each part of the OVC is cleaned by electropolishing.

There are four copper plates and cans from outside to inside the plates at temperatures of 50 K and 4 K, the dilution refrigerator still, and the 50 mK stage. The inner vacuum can (IVC) is connected to the 4 K plate. The copper cans are made by bending the OFE copper plates of various thicknesses supplied by the Aurubis company. The size and thickness of the cans are listed in Table 3. The radioactivity is measured and is shown in Table 4. All cans are divided into two cylinders coupled with stainless screws M8 of 16 mm diameter. The surfaces were cleaned with 5% nitric acid before assembling. The welding is done by e-beam welding.

The inner lead is 26 cm thick, and the total mass of the shielding is about two tonnes. The outer 25 cm thick lead consists of lead bricks supplied by JL Goslar Gmbh in Germany. The lead bricks are in the size of 5 cm × 10 cm × 20 cm. The radioactivities of these bricks were measured with the CAGe [33]. The bricks were first sliced with a water jet cutting machine into 5 mm thick plates. The plates were cleaned with 10% nitric acids for 20 min. Then, six plates were located between the top and bottom arrays of the CAGe. This setup has a sensitivity to ²²⁶Ra of around 0.1 mBq/kg. The Goslar bricks samples were found to have ²²⁶Ra activity of 0.55 ± 0.17 mBq/kg and ²²⁸Th activity of 0.58 ± 0.17 mBq/kg. The ²¹⁰Pb content was 30 ± 1 Bq/kg. The ancient lead, forming the 1 cm inner layer and supplied by the Lemer Pax company, had ²¹⁰Pb activity of only 100 ± 10 mBq/kg. As this layer sits inside the Goslar lead, it shields the detector from the higher ²¹⁰Pb activity of the Goslar bricks. To increase the thermal conductivity between the mixing chamber plate and the detector assembly structure via the lead shielding, the lead bricks are divided into two sections and pressed by M20 (12 each) and M10 (9 each) copper rod-screws, with copper sheets between the lead blocks.

To remove the noise produced by the alternating and static magnetic fields in the detector environment, we installed the lead superconducting magnetic shield surrounding the detector towers. The lead sheet is made with ancient lead ingot imported from the Lemer Pax company in France. The ingot was melted to make a block about 1 cm thick and rolled with a drum to make plates with a thickness of about a millimeter. A cylindrical copper structure is made with a copper frame of 3 mm thickness and assembled with brass screws. The rolled lead sheets are welded to the structure with ultra-low radioactive lead-tin solder. The manufacturing process contaminated the surface of the lead sheets. A sample of 10 cm × 10 cm lead sheet is measured with the alpha counter, and the surface alpha emission rate was 2.53 ± 0.15 × 10⁻²/cm²/hour after 20 min in 10% nitric acid. Further cleaning with 40 min in 10% nitric acid reduced the rate to 1.25 ± 0.07 × 10⁻²/cm²/hour. The whole structure, including the lead sheets, is submerged in 10% nitric acid to remove surface contamination during the manufacturing processes. The superconducting shielding structure will be attached to the copper plate at the bottom of the inner lead shielding.

The outer lead shielding consists of 25 cm thick walls that surround the cryostat on five sides, with a total mass of about 60 tons. The outer 20 cm thick lead is made of normal lead supplied by a Korean company. It consists of lead bricks with dimensions of 5 cm × 10 cm × 20 cm.

As described in Section 4.3, we have assayed two batches of lead bricks with the CAGe detector at Y2L. The average radioactivities of these bricks used for the outer 20 cm of shielding are 0.38 ± 0.16 mBq/kg for ²²⁶Ra and <0.25 mBq/kg for ²²⁸Th. The inner 5 cm of shielding was filled with Boliden lead that was dismantled from the shielding of the KIMS experiment at Y2L. The average radioactivities measured with the CAGe detector are 0.48 ± 0.12 mBq/kg for ²²⁶Ra and 0.45 ± 0.11 mBq/kg for ²²⁸Th. This is similar to the activities of the JL Goslar lead as reported in Section 4.3. More details on lead measurements will be reported [33]. Since the 0.5 mBq/kg contamination level of ²²⁶Ra is about two times higher than the AMoRE-II requirement of an individual item, we will exchange this inner 5 cm of lead with lower background lead before we run the full-scale phase of the AMoRE-II experiment.

We considered placing a few centimeters thickness of additional copper inside the lead shielding to reduce the gamma rays from Bremsstrahlung produced by the decay of ²¹⁰Pb in the lead shield. However, the simulation shows that even with the neutron shielding layers described here, the background could increase due to thermal neutron capture in the copper plates.

Boron is a very effective material for absorbing thermal neutrons. The thermal neutrons are hazardous to the 0νββ experiment by way of generating high energy gammas from neutron capture reactions in the shielding materials. The effective cross-section of thermal neutrons in copper, iron, and lead are 3.78, 2.75, and 0.17 barn. We may put a few centimeter-thick additional copper layer inside the lead shielding to reduce the ²¹⁰Pb Bremsstrahlung gamma rays, but the simulation shows it could increase the background due to the thermal neutron capture in the copper plates. Therefore, we try to minimize the copper or iron inside the lead shielding. To minimize the thermal neutron contribution, we placed acrylic boxes containing ultra-pure boric acid powder. The boxes are 500 mm × 500 mm × 10 mm in size, with a wall thickness of 1 mm, so the boric acid is 8 mm thick. These boxes are attached to the lead shielding structure. Since the boric acid is inside the lead shielding, there are limits on its allowable radioactivity levels. We have measured the radioactivity levels of various grades of commercially available boric acid, as shown in Table 5. The radiopurity of boric acid of 99.99% purity supplied by Alpha Aesar company was assayed by HPGe counting with resulting activities of <0.46 mBq/kg for ²²⁶Ra and <0.5 mBq/kg for ²²⁸Th, though it has 97.9 ± 8.0 mBq/kg for ⁴⁰K. Another satisfactory boric acid powder, the one which will be used for AMoRE-II, is the 99.5% purity grade supplied by KANTO company with <1.4 mBq/kg for ²²⁶Ra and <0.95 mBq/kg for ²²⁸Th as shown in Table 5.

Since the lead shielding structure has a square cross-sectional footprint, and the cryostat cans are circular, there is a sizable volume of air inside the lead shielding (and inside the boric acid layer). We will surround the shielding structure with a vinyl curtain and flush the interior by injecting a constant flow of Rn-free air with an estimated maximum Rn level in the air of about 5 Bq/m³. At the same time, we will insert urethane balloons filled with nitrogen gas to fill the four corners. This further reduces the Rn level within the balloons and reduces the remaining flushing volume in the tent for more efficient removal of outside air from the tent. Two balloons made of urethane film will be installed inside the lead shielding for each half of the shielding structure. After 10 days of installing the balloons, the activity of ²¹⁴Bi inside the balloons should be less than 1 mBq in total if no radon penetrates the Urethane film. Two different film samples were assayed with an HPGe detector and found to have less than 1–2 mBq/kg for ²²⁶Ra and less than 1 mBq/kg for ²²⁸Th, implying a total activity level of less than 50 mBq for this film for all balloons combined.

The volume between the OVC and outer lead shielding is mainly filled by the nitrogen balloon, but some air remains outside of the balloon. The average radon level for the whole volume, including the air balloon, must be below 0.3 Bq/m³. The air in the balloons is expected to have negligible levels of radon activity. Therefore, the requirement for the remaining air is relaxed by a ratio of the total volume to the volume not filled by balloons.

To calibrate the energy and detector response, we will irradiate the detector with gammas emitted from a ²³²Th source. In particular, the 2614 keV gamma is useful since its energy is near the 0νββ Q-value, and since it penetrates the shielding better than low-energy gammas. The source will be attached outside of the OVC cans. The source material is ThO₂ powder with 602 Bq/kg of ²²⁸Th activity. The powder is mixed with silicone oil, injected inside a Urethane tube of 8 mm diameter, and cured at room temperature for about 24 h to be a flexible solid tube. The source tube is about 8.5 m long, looping the OVC two times, and can be moved within a tube with a larger diameter of 20 mm. A system of two driving motors located in the electronics room over the cryostat will position the source at different locations for calibration. Since the outer tube is fixed outside the OVC, the radioactivity of the tube will be assayed by the HPGe detector before installation to the OVC.