Projected background and sensitivity of AMoRE-II

We used a Geant4-based simulation framework developed for modeling background spectra of the AMoRE-Pilot and AMoRE-I experiments, which adopted G4 version 10.4.2, implemented AMoRE-specific physics lists for both internal and external background simulations; the Physics list classes of G4EmLivermorePhysics for low energy electromagnetic process, G4RadioactiveDecay for radioactive decay process, QGSP_BERT_HP for high-energy physics process (above 10 GeV), and the precision of the neutron model for neutrons with energies below 20 MeV were used Agostinelli2003 ; Allison2006 ; Allison2016 . In addition, we used a full-elastic-scattering dataset for thermal neutrons with energies below 4 eV to precisely describe the shielding effect. Using the simulation framework, we perform simulations for the background contributions from the radioactive decay chains of ²³⁸U, ²³²Th, ²³⁵U, and ⁴⁰K.

We use the energy deposits in the crystals within a 5 ms window to simulate an event like that in the experimental data, considering the 1–2 ms rise times for crystal detectors used in the AMoRE-I experiment Hanbeom2022 . To simulate pileup events resulting from decays with short half-lives, followed by subsequent daughter decay within a few times the typical pulse width ($\sim$20–30 ms) in cryogenic measurements Hanbeom2022 , a time window of 100 ms is used. If the second decay happens within 5–100 ms of the first decay, it is excluded from the MC data, similar to the experimental data. In addition, pileup events can occur due to random coincidences between sources that contribute to the ROI. The LMO crystal is a major source of background events, particularly the random coincidence of background events from the two-neutrino double beta (2$\nu\beta\beta$) decay of ¹⁰⁰Mo. We also consider its impact on the background contribution to the ROI. More details about this can be found in the following section.

The energy distribution of simulated events was reconstructed by randomly smearing it in a Gaussian shape based on the resolution function obtained from the AMoRE-II R&D setup WTKim2022 .

Background caused by cosmic-ray muons is one of the most dangerous external radiation sources. To shield those external radiations, the AMoRE-II detector is positioned around 1000 meters deep under Yemi Mountain, which corresponds to $\sim$2700 meters water equivalent (m.w.e.), and is surrounded by robust shielding materials, as described in Sect. 2.

To investigate the impact of cosmic muons and the induced backgrounds resulting from their interaction with the rocky cavern, shield, and detector materials, we conducted simulations using the muon energy spectrum at the Yemilab underground. This spectrum was obtained by digitizing the contour map of the Mt. Yemi area, as detailed in Ref. Hanwook2020 . Due to various ambiguities from rock properties, different depths, etc., we used the total muon flux at the Yemilab for normalization, which is considered to be 8.2$\times$10^-8 muons/cm²/s. This value was derived by considering the measured flux at Y2L Prihtiadi2018muon and the fact that the Yemilab is approximately 1.5 times deeper than Y2L. The recent measurement at the Yemilab of around 10^-7 muons/cm²/s is consistent with this value; it represents a reduction by a factor of about 10⁵ compared to the sea level.

To account for all secondaries induced by muons traveling through the rocky cavern, we generated muons with the energy spectrum at the Yemilab from outside a 3-meter-thick rock shell surrounding the cavern. The thickness of the rock shell was optimized through additional simulations. We simulated muons with an energy of 236 GeV, the mean of the muon spectrum at the Yemilab, entering the rock with varying thicknesses from 0.5 to 10 meters. We measured the mean energy and event rates of neutron and gamma secondaries emerging from the rock as a function of thickness and determined the optimal thickness, 3 meters, at the points where the function saturated.

In order to estimate background rates for AMoRE-II, we analyzed the neutrons and gamma rays generated by muon interactions with materials in rock, shield, and detector components. The schematic view of the simulation geometry is presented in Fig. 3. Our study involved evaluating different shielding configurations, as described in Ref. Hanwook2020 . We compared heavy lead shielding with water shielding and ultimately decided to go for lead shielding due to the difficulty of implementing a cryostat in the water shielding. We compared the water Cherenkov detector with the plastic scintillation detector for the part above the cryogenic detector system. Based on simulation studies in Ref. Jeewon2022 , we opted for a 70-cm-thick water Cherenkov detector with an active muon veto capability. A thorough GEANT4 simulation was conducted to specify the thickness and layers of the various shielding materials. All of those parameters are reflected in the design of the AMoRE-II construction. As a result, we achieved a simulated background rate of 3.1$\times$10^-6 ckky in the (2.8–3.2) MeV energy region when the muon tagging efficiency with both PS and 70-cm-thick water tank is 93.9%.

The experimental enclosure is surrounded by a rock wall finished with shotcrete. Due to the presence of ²³⁸U, ²³²Th, ²³⁵U, and ⁴⁰K in the rock and shotcrete, this wall is a strong source of $\gamma$ rays. The rock sample, including shotcrete, is ground and measured by ICP-MS at the Korea Institute of Geoscience and Mineral Resource (KIGAM). The results of the activity measurements are utilized in this paper and will be published, along with measurements of the extensive detector and shielding materials for the AMoRE experiment, in a future publication. Since the estimation of the heavy shielding materials requires significant CPU time, we simulate high-energy gammas from the decay of ²¹⁴Bi larger than 3 MeV in order to estimate the background rate in the ROI.

Neutrons from ($\alpha$, n) natural radioactivity reactions in the rock and spontaneous fission, mainly of U atoms, in the rock are also possible background sources in underground environments. In particular, the thermal neutrons captured by copper or iron in the shield/structure materials generate high energy $\gamma$ rays around 7–8 MeV by (n,$\gamma$) reaction. To evaluate the background effect due to these neutrons, we use the neutron flux measured with a Bonner sphere spectrometer system at Y2L YSYoon2021 . We simulate neutrons by generating them from the rock surface based on the measured energy spectrum.

In addition, as a noble gas, radon is chemically not very reactive and can diffuse easily through many materials infiltrating into the active region of the detectors Next100:2016 . One of the most significant isotopes of radon for background considerations is ²²²Rn, generated from the ²³⁸U decay chain in rock walls. Even though its half-life is relatively short ($T_{1/2}$=3.82 d), its decay products form the long-living radioisotope ²¹⁰Pb ($T_{1/2}\approx 22$ yr). Moreover, several isotopes emitting high-energy gammas are fed by the subsequent decays of ²²²Rn, as stated in Ref. Formaggio2004 . Specifically, some emissions from decays ²¹⁴Bi, a descendant of ²²²Rn decays, have energies over 3 MeV and can produce backgrounds in the 0$\nu\beta\beta$ ROI. In order to minimize the effect of radon in the background, the Yemilab uses a radon reduction system (RRS) to supply air with radon levels reduced by at least 1000 times, resulting in 5 Bq/m³, the estimated maximum Rn level. Additionally, a vinyl curtain surrounds the shielding structure and is flushed with air containing 5 Bq/m³ radon. The radon concentration between the lead shield and cryostat is reduced by filling the space with urethane nitrogen-filled balloons. We simulated radon background events in the small amount of residual air between the OVC and the lead shielding to estimate the background rate in the ROI. This simulation resulted in a rate of 1.7$\times$10^-5 ckky.

It is potentially dangerous for the AMoRE experiment if there is nuclear beta decay with a Q-value over 3 MeV inside crystals. This can be caused by activation of radioisotopes in the crystal detectors due to cosmic rays.

At the AMoRE experimental site in the Yemilab, the rock overburden of approximately 1000 meters significantly reduces the muon flux. As a result, the effect of cosmogenic activation by muons and neutrons is negligible. However, during the crystal production process (including growing, polishing, cleaning, and gold deposition) at the Earth’s surface and during transportation to the Yemilab, the crystals are exposed to cosmic rays. This exposure may produce comparatively long-living radionuclides, contributing to the background.

To ensure the required radiopurity of the crystals, we used lithium carbonate and ¹⁰⁰MoO₃ powders with a purity better than 99.998%. We received about 180 kg of enriched molybdenum trioxide powder from Electrochemical Plant JSC ecp_hp . To prevent cosmogenic activation, the material was shipped to Korea by ground and sea. Upon arrival, the powder was stored in a desiccator at the Y2L, maintained at 23°C with a relative humidity of about 10%. A 1L/min flow of boil-off gas from a liquid nitrogen dewar was used to optimize the storage conditions. The molybdenum powder was purified at the Center for Underground Physics (CUP), and purification efficiency and final product radiopurity were checked with the High Purity Germanium (HPGe) array at CUP (CAGe) and the Inductively Coupled Plasma Mass-Spectroscopy (ICP-MS) SuyeonPark2019 ; SuyeonPark2020 ; HjYeon2023 ; Gileva2020 ; Gileva2017-qz . Lithium carbonate precursor was used from two different sources. One is old stock preserved decades ago at the Nikolaev Institute of Inorganic Chemistry (NIIC), named NRMP TU 6-09-3728-83 KAShin2024 and produced at CUP powder Olga2023 ; KAShin2024 .

We conducted simulations for all potential radionuclides meeting specific criteria, including origination by spallation from stable nuclides of Mo, Li, and O in the crystal, emission of beta/gamma-rays above 3 MeV, and having a half-live longer than 15 days. We used the ACTIVIA Back:2007kk code to calculate radionuclide production rates for 30 days of exposure and 90 days of cooling underground.

It found that the production of ⁸²Sr (EC, 180 keV, 25.6 d) / ⁸²Rb (EC, 4400 keV, 1.2 min) in Mo nuclides is most hazardous, with a background level of 10^-4 ckky. However, the half-life of ⁸²Sr is only 25.6 days. ⁵⁶Co (EC, 4566 keV, 77.3 d) in Mo is also dangerous, but most of these events are expected to occur within the first year. Hence, increasing the cooling time would help manage the risk associated with this radionuclide. The remaining cosmogenic nuclides are negligible, with a $\sim$10^-6 ckky background level.

Additionally, we considered the underground in-situ activation in detector modules, towers, cryostat, and shielding materials. Their impact on background contribution is negligible, below 10^-6 ckky.

As detailed in Sec. 2, the detector system consists of crystal detector modules, cryostat, and shielding materials. Radiations originating from the LMO crystals are known to be the dominant source of backgrounds. For internal contaminations, radioactive $\alpha$-decay can be recognized by high-energy peaks in the background spectrum. However, individual $\alpha$ peaks resulting from the decays of ²³⁵U, ²³⁸U, and ²³²Th partially overlap in the spectrum. Thus, the internal radioactivity of LMO crystals is evaluated using $\alpha-\alpha$ time-correlated events, as described in Ref. Alenkov2022 . In this study, we used the upper limit of internal activities obtained by analyzing $\alpha$ energy spectra measured cryogenically using LMO crystals in AMoRE-I at Y2L Hanbeom2022 . These crystals were produced by CUP and NIIC using the same procedure employed in the production of the AMoRE-II crystals.

Other possible sources are activities from radioisotopes in the ²³⁸U, ²³²Th, ²³⁵U, and ⁴⁰K decay chains from materials in the nearby crystal detectors, cryostat, and the shielding layers, which produce signals in the crystals. Therefore, this simulation considers all the materials used in the detector components and shielding layers. These materials are scanned with either the HPGe detectors at the Y2L or by the ICP–MS equipment Olga2023frontier . Several materials are measured in both methods. The activity measurements are listed in Table 1 and are used to normalize the simulation results.

To construct the energy spectra of $\beta$/$\gamma$ background events in the simulations, we applied the same selection cuts used to background data processing in AMoRE-Pilot and AMoRE-I for the selection of 0$\nu\beta\beta$ decay event candidates. We consider $\beta$/$\gamma$ events with an assumption of almost 100% $\alpha$ rejection power, based on a discrimination power (DP) of $\sim$10 $\sigma$ for energies around ROI WTKim2022 . It is followed by single-hit selection, $\alpha$-tagging, and rejection of muon coincidence, which are itemized in the following list.

• $\bullet$

  We select single-hit $\beta$/$\gamma$ events classified as those with hits in only one of the crystals and none in any of the other crystals, considering a 5 ms time window, to reject background signals resulting from energy deposits in multiple crystals.
  

• $\bullet$

  The $\beta$/$\gamma$ events from the decay of ²⁰⁸Tl in the ²³²Th chain can produce backgrounds in the ROI. However, they can be identified and rejected by using an $\alpha$-tagging method. This method involves checking for a time correlation with the $\alpha$ signal produced by the preceding ²¹²Bi$\rightarrow$²⁰⁸Tl $\alpha$ decay. We reject the events that occur within 30 minutes after an $\alpha$ event with 6207 $\pm$ 50 keV in the same crystal. This results in a 98% veto efficiency for beta events induced by ²⁰⁸Tl decay ($T_{1/2}$=3.05 min) in the crystals.
  

• $\bullet$

  In order to avoid counting muon coincidence events, we tag muon events with an energy deposit above a set threshold in the plastic scintillator(s) and water tank. Upon examining the time difference between veto hit and crystal hit from the simulation, we found that 99.5% of muon-tagged events occur within 2 ms. Therefore, we set the veto time window to 5 ms to reject any events occurring within 5 ms (in this case the detection efficiency of the muon-tagged events increases to 99.7%) following the appearance of a muon-tagged event in the muon veto detectors Jeewon2022 . As a result, the estimated background rate of cosmic muons is significantly reduced from 1.65$\times$10^-3 ckky to 2.75$\times$10^-6 ckky by implementing muon detectors.

The decay of surface $\alpha$ on crystals or nearby materials can deposit a range of energies, which can be as high as the Q-value of the decay. Sometimes, this energy falls in ROI. However, it can be distinguished from $\beta$/$\gamma$ signals through pulse shape discrimination (PSD) and the light/heat ratio, with a DP of more than 14 at around 4.785 MeV WTKim2022 . Nevertheless, events from the decay of radioactive contaminants in the crystal can pile up through subsequent daughter decay in the decay chains. When analyzing the real data, events that occur sequentially within approximately 2 ms for one crystal are considered indistinguishable. To assess the impact of such events on the background contribution, we carried out a study using beta-alpha pileup events considering a 5 ms time window. These $\beta$-$\alpha$ pileup events are from decays of (²¹²Bi+²¹²Po) in the ²³²Th decay chain, with a half-life of 294 ns, and decays of (²¹⁴Bi+²¹⁴Po) in the ²³⁸U decay chain, with a half-life of 164 $\mu$s. Our study found that these events contribute to the continuum down to the ROI region if they occur within the surface depth of the crystal, which is less than 50 $\mu$m. The estimated background level of these events is similar to that of $\beta$/$\gamma$ radiation of the crystal in ROI. However, the pileup events can be rejected by approximately 90% within 0.5 ms (as discussed in Sect. 4.3), reducing them to approximately 10^-6 ckky, which is considered in this study.

In addition, we considered the nearby materials directly facing the crystals, like the copper holder, which houses the crystal and the wafer. The Copper frames and posts are made of NOSV copper, with each post featuring two screw threads. Despite undergoing a surface etching process, the machining of the screw threads may have introduced contamination that became deeply embedded in the posts, resulting in radioactivity levels more than ten times higher than for bulk NOSV copper Olga2023frontier . This contamination likely occurred during the thread-making process. Subsequently, we identified a company capable of producing copper posts with screw threads that exhibited significantly lower contamination levels, measuring 0.97 ppt for ²³²Th, as listed in Table 1. This is considered post-surface contamination, and its background contribution is included in our simulations, as reflected in Table 3, where the post-surface contribution is estimated to be 1.59 $\times$ 10^-5 ckky.

Figure 4 shows simulated energy spectra with different colors for all possible background sources grouped in categories, which we obtained after applying event selection cuts to the simulated events and convolving them with energy resolution as a function of energy. We categorized the background sources from the detector system into two groups: components located near and far from the crystal. The near-crystal components (G1) include Araldite, bolts, clamps, Stycast, Kapton PCB, heaters, Pb-Sn solder, PTFE, Vikuiti reflector film, and copper materials used in the phonon/photon frame. The far-crystal components (G2) comprise OVC, Radon, SC-shield, lead shield, and other shielding materials.

In addition, there are other groups of background sources such as crystal internal background, 2$\nu\beta\beta$ decay, pileup events, neutrons, muons, and solar neutrinos. The background from interactions of solar neutrinos with the ¹⁰⁰Mo target is estimated to be 8.5$\times$10^-7 ckky at the energy of 3034 keV Bahcall2001 ; Ejiri2017 . This is mainly from single $\beta$ decay of ¹⁰⁰Tc. Electrons emitted in $\nu_{e}$ capture itself, and scattering of $\nu_{e}$, $\nu_{\mu}$, $\nu_{\tau}$ on electrons give much smaller contributions.

The energy spectrum summed over all simulations is shown in Fig. 5 by a solid black line with 1 $\sigma$ error bars. The background contribution below 3 MeV is mainly from 2$\nu\beta\beta$ decay, which is expected due to the use of purified materials.

The high-energy spectrum in the extended ROI ranging from 2.95 to 3.15 MeV is shown in Fig. 6 (a), where the main contributions are from the background sources of ²¹⁴Bi in the ²²⁶Ra–²¹⁰Pb decay sub-chain of ²³⁸U and ²⁰⁸Tl in the ²²⁸Th–²⁰⁸Pb decay sub-chain of ²³²Th.

The peaks at 2978.9, 3000., 3053.9, 3081.8, and 3142.6 keV are attributed to high-energy $\gamma$ emissions from the decay of ²¹⁴Bi in far-crystal components (G2), such as a 5-cm thick Boliden lead shield layer, OVC, and radon in the air between them.

To eliminate ²⁰⁸Tl decay events, a vetoing process is employed 30 minutes after the 6.2 MeV $\alpha$ precursor as the $\alpha$-tagging method. However, when dealing with backgrounds from ²⁰⁸Tl decay in materials located near-crystal components (G1), such as Pb-Sn solder and Kapton PCB, the precursor $\alpha$ may not provide an energy level of 6.2 MeV. It can lower veto efficiency and result in background contributions in ROI.

In addition, another background contribution to the ROI is pileup events due to the random coincidence of two ¹⁰⁰Mo 2$\nu\beta\beta$ decay events. We investigated the rate of this background using the DECAY0 program Ponkratenko2000 to produce ¹⁰⁰Mo 2$\nu\beta\beta$ decay events. The estimated background rate within the ROI, which occurred randomly within a 1 ms time window, was 1.2$\times$$10^{-4}$ ckky for 310 g of ⁴⁰Ca¹⁰⁰MoO₄ Luqman2017 . Furthermore, we found that a single 2$\nu\beta\beta$ decay that coincides randomly with other background sources has an upper limit of 1.1$\times$$10^{-4}$ ckky in ROI. To reduce the background level, we studied rejection efficiency for pileup events GBKim2017 and further developed it to meet the AMoRE-II background requirement in a separate work by utilizing various PSD parameters as input parameters for the Boosted Decision Tree (BDT) method. We found that it is possible to reject approximately 90% of pileup events within 0.5 ms, resulting in a background rate of 2.4$\times$$10^{-5}$ ckky for a 6 cm diameter LMO crystal, which includes a single 2$\nu\beta\beta$ decay that randomly coincides with other background sources. This information is used in this paper.

The background contribution in the (3024–3044) keV range (ROI) of each background source included in the group is shown in Fig. 6 (b). A bar graph represents the background rate based on a conservative detection limit for the impurity. Meanwhile, the filled circle with error bars is estimated based on the impurity measurement. One of the primary sources of background radioactivity is ²¹⁴Bi, which is found in the ²²⁶Ra–²¹⁰Pb decay sub-chain of ²³⁸U located in the lead shielding’s innermost layer. The inner 5 cm of current shielding with Boliden lead will be replaced by lead with a lower ²²⁶Ra contamination. This replacement aims to reduce the background level to approximately $10^{-5}$ ckky, which can be achieved using a purer lead with a radiopurity of less than 200 $\mu$Bq/kg for ²²⁶Ra.

The detailed results estimated in the ROI of the radioactive sources considered in this study for the background contributions from radioisotopes in the decay chains of the ²³⁸U and ²³²Th are summarized in Table 3. The summary table also includes evaluations of other background groups such as internal, 2$\nu\beta\beta$, neutrons, muons, and solar neutrinos. The total estimated background level is 2.01$\times$$10^{-4}$ ckky. Additionally, the study assessed the background effects of other radioisotopes, such as ²³⁵U, ⁴⁰K, and ²¹⁰Pb, and found that they have negligible contributions.