Astroparticle Physics 114 (2020) 60–67 Contents lists available at ScienceDirect Astroparticle Physics journal homepage: www.elsevier.com/locate/astropartphys Neutron and muon-induced background studies for the AMoRE double-beta decay experiment H.W. Bae a , E.J. Jeon b , ∗, Y.D. Kim b , S.W. Lee a a Department of Physics, Kyungpook National University, Daegu 41566, Republic of Korea b Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea a r t i c l e i n f o Article history: Received 20 December 2018 Revised 31 May 2019 Accepted 22 June 2019 Available online 22 June 2019 Keywords: Geant4 simulation Neutron background Muon-induced background AMoRE Double-beta decay a b s t r a c t AMoRE (Advanced Mo-based Rare process Experiment) is an experiment to search a neutrinoless double- beta decay of 100 Mo in molybdate crystals. The neutron and muon-induced backgrounds are crucial to obtain the zero-background level ( < 10 −5 counts/(keV ·kg · yr)) for the AMoRE-II experiment, which is the second phase of the AMoRE project, planned to run at YEMI underground laboratory. To evaluate the effects of neutron and muon-induced backgrounds, we performed Geant4 Monte Carlo simulations and studied a shielding strategy for the AMORE-II experiment. Neutron-induced backgrounds were also in- cluded in the study. In this paper, we estimated the background level in the presence of possible shield- ing structures, which meet the background requirement for the AMoRE-II experiment. © 2019 Elsevier B.V. All rights reserved. t t e t t m b c m e s a p i t c o f a s u r g 1. Introduction AMoRE (Advanced Mo-based Rare process Experiment) [1] is an experiment to search for neutrinoless double-beta de- cays (0 νββ) of 100 Mo nuclei by using scintillating molybdate crys- tals, operating at milli-Kelvin temperatures. The second phase of the AMoRE project (AMoRE-II) is being planned to operate at the YEMI underground laboratory (YEMI), located at Handuk, an ac- tive iron mine in the region of Mt. Yemi, South Korea [2] . The AMoRE-II experiment will use a ∼200 kg array of molybdate crystals with the aim of achieving the zero-background level of < 10 −5 counts/(keV ·kg · yr) (ckky) in the region of interest (ROI), 3.034 ±0.010 MeV. The ROI is given by the Q value of 0 νββ of 100 Mo in molybdate crystals, which is at 3034.40(17) keV [3] , and the energy range based on the energy resolution of the detec- tor [4] . Therefore, it is important to precisely understand the effects of background sources on underground experiments of rare events such as 0 νββ for the suppression of backgrounds to the aimed level. Radiations from radioisotopes in the 238 U, 232 Th, 40 K, and 235 U decay chains in detectors, materials in the nearby detector system, shielding materials, and the rock walls surrounding the experimental enclosure are possible sources of backgrounds. We have studied the impact of backgrounds due to these sources for AMoRE-I that is the first phase of the AMoRE project and found∗ Corresponding author. E-mail address: ejjeon@ibs.re.kr (E.J. Jeon). f https://doi.org/10.1016/j.astropartphys.2019.06.006 0927-6505/© 2019 Elsevier B.V. All rights reserved. hat these backgrounds can be suppressed by the optimized de- ector design and specific analysis methods, as reported in refer- nce [5] . However there are backgrounds due to cosmic rays and neu- rons. Neutrons are generated by the natural radioactivity of ma- erials in underground environment or induced by cosmic-ray uons, as well as their secondaries. Gamma rays are also produced y neutrons and muons by (n, n ′ γ ), (n, γ ), and bremsstrahlung pro- esses. The electrons, positrons, and gamma rays produced when uons lose their energy by ionization and radiation, initiate an lectromagnetic shower, if they have high enough energy. This hower generates more gamma rays through bremsstrahlung . In this paper, we quantitatively studied the effects of neutron nd muon-induced backgrounds on the AMoRE underground ex- eriment by performing Geant4 Monte Carlo simulations. The text s structured as follows: Section 2 illustrates the detector geome- ry used for the AMoRE-II simulation. In Section 3 , we simulate the osmic-muon and muon-induced background to study their effects n the background level, using the Muon Veto system in two dif- erent shielding configurations. Neutron-induced backgrounds were lso included in the study. Section 4 describes the simulation re- ults used to quantify the effects of neutron backgrounds, from nderground environment, by considering the shielding configu- ations. Finally, in Section 5 , we conclude that the aimed back- round level could be achieved with the optimal shielding design or AMoRE-II experiment. H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 61 Fig. 1. (a) Cross-sectional view of the detector geometry used in the Geant4 simulations. The cryostat is located inside the external lead shield surrounded by 5-cm-thick plastic scintillator (green). It includes (b) 40 Ca 100 MoO 4 building and (c) 40 Ca 100 MoO 4 assembly. 2 w t m f o G m a Q f o n e 4 s f s 2 f n c f s a t s s i a s 6 t b i F 3 b t p w t 3 p c M t l ( l m i e 3 i c w 0 l a a d . Geant4 simulation For the background studies, we have performed simulations ith the Geant4 Toolkit [6] . We simulated both muons and neu- rons using the Geant4 version 4.9.6.p04, in which we imple- ented the AMoRE-specific physics list. The list was customized or improving the speed and precision of the hadron simulations, ver a wide energy range from a few eV to a few hundreds of eV. It should be highlighted that we also performed the same uon simulations using the higher Geant4 version (10.04.p02) nd little difference was found between them. We adopted the GSP −BERT −HP reference physics list, which is the appropriate one or high-energy physics simulations (above 10 GeV). The precision f the neutron model was also implemented in the physics list for eutrons with energies below 20 MeV. In addition, we used a full- lastic-scattering dataset for thermal neutrons with energies below eV in order to precisely examine the shielding effect. When a hit occurs, each simulated event included energy depo- itions in the crystals within a 100-ms event window, which is a ew times the typical pulse width ( ∼20–30 ms) in cryogenic mea- urements [7] . .1. The AMoRE-II detector geometry Fig. 1 (a) shows the simplified detector geometry that was used or this study. The cryostat is located inside a 30-cm-thick exter- al lead shield surrounded by 5-cm-thick plastic scintillator. It in- ludes 370 calcium molybdate ( 40 Ca 100 MoO 4 ) crystals enclosed by, rom the inside outward, a 2-mm-thick magnetic shielding layer of uperconducting lead, four copper shielding layers (50mK, 1K, 4K, nd 50K chambers) with total thickness of 10 mm, and a 5-mm- hick stainless-steel layer (outer vacuum chamber) of the cryo- tat. The 370 40 Ca 100 MoO 4 (CMO) crystals are arranged in thirty- even columns, each with ten crystals stacked coaxially, as shown n Fig. 1 (b). A 1-cm-thick copper plate and a 10-cm-thick lead plate re located above the CMO crystal array, inside the innermost Cu hield (50mK chamber). Each crystal has a cylindrical shape with cm of diameter, 6 cm of height, and mass of 538 g, resulting in a otal mass of 199 kg for all the 370 crystals. Each crystal is covered y a 65 μm-thick Vikuiti Enhanced Specular Reflector film [8] and s mounted in a copper frame. A crystal assembly is shown in ig. 1 (c). . Cosmic muon and muon-induced background To quantify the effects of all backgrounds not only from muons ut also from the secondary ones induced by muons, traveling hrough the rocky cavern, the shield, and detector materials, we erformed Geant4 Monte Carlo simulations by brute force, starting ith muons from the rocks surrounding the cavern. The details of he simulations are described in Sections 3.1 and 3.2 . .1. Muon energy spectrum at YEMI underground laboratory The AMoRE-II experiment is the second phase of the AMoRE roject planned to run at YEMI underground laboratory (YEMI), lo- ated at the Handuk mine, an active iron mine in the region of t. Yemi, South Korea. In order to obtain the muon’s energy spec- rum and the angular distribution at YEMI, we firstly used the sea- evel muon flux, parameterized by the modified Gaisser’s formula Section 3.1.1 ). Secondly, we estimated how much energy the muon oses when propagating through the mountain, and the resultant uon energy spectrum to be detected underground, by consider- ng the digitized contour map of the Mt. Yemi area and the param- terized average loss of muon energy within matter ( Section 3.1.2 ). .1.1. Modified Gaisser parameterization It is well known that the differential muon intensity at sea level s described by the modified Gaisser parameterization [9] , dN d Ed  = A 0 . 14 E −2 . 7 c m 2 · s · s r · G eV × ( 1 1 + 1 . 1 ˜ E cos θ ∗ 115 GeV + 0 . 054 1 + 1 . 1 ˜ E cos θ ∗ 850 GeV + r c ) , (1) os θ ∗ = √ ( cos θ ) 2 + P 2 1 + P 2 ( cos θ ) P 3 + P 4 ( cos θ ) P 5 1 + P 2 1 + P 2 + P 4 (2) here P 1 = 0.102573, P 2 = −0.068287, P 3 = 0.958633, P 4 = .0407253, and P 5 = 0.817285. We applied modifications of the parameters A, r c , and ˜ E for ow-energy muons ( E ≤100/cos θ ∗), as suggested in Ref. [9] , which re limited in the standard Gaisser parameterization [10,11] . We lso took the curvature of the earth into account by using cos θ ∗, escribing the muon flux for the full range of zenith angles. We 62 H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 Fig. 2. (a) Digitized contour map of the YEMI area on a meter scale; the detector is located at (0,0,0), (b) the muon energy spectrum at the YEMI underground laboratory; the mean muon energy is 236 GeV, and (c) the muon intensity in the units of muons/cm 2 /s/sr that depends on the azimuthal angle φ and the polar angle θ at YEMI. Fig. 3. Schematic view of the muon generated by brute-force simulations. p − w  i A g t t m s d o b m p s c i t b i generated muon events based on Eq. (1) with the adequate modi- fied parameters for both high- and low-energy muons. 3.1.2. YEMI underground laboratory YEMI has a vertical overburdened rock of 1005 meter in the re- gion of Mt. Yemi. A 3-dimensional profile of the mountain area is shown in Fig. 2 (a), generated by using a digitized contour map of Mt. Yemi area, from Korea Geodetic Datum 2002, based on ITRF20 0 0 [12] ; the (x,y) coordinates of digitized points indicate the location and z-axis is the altitude and the center of the bottom of the detector is located at (0,0,0). Hence, muons generated at sea level by Eq. (1) lose their energy when propagating through the mountain. We used the formula in Eq. (3) for the average energy loss of a muon traveling a distance X inside the matter, which is parameterized with Eq. (4) . The details of the calculation are re-orted in reference [13] . dE μ dX = a (E μ) + 3 ∑ n =1 b n (E μ) · E μ (3) here, a (E μ) = A 0 + (A 1 · log 10 E μ[ GeV ]) , b(E μ) = B 0 + (B 1 · log 10 E μ[ GeV ]) + { B 2 · ( log 10 E μ[ GeV ]) 2 } (4) We used the following coefficients for the average energy loss n standard rock with the density of 2.65 g/cm 3 : A 0 = 1.925 MeV, 1 = 0.252 cm 2 /g, and ( B 0 = 0.358, B 1 = 1.711, and B 2 = -0.17), iven in the unit of 10 −6 cm 2 /g. We first generated a muon based on the differential muon in- ensity given by Eq. (1) and then calculated the energy lost by he muon with a path length that starts at the point where the uon track intersects the mountain, expressed by Eq. (3) . We as- umed that the muon travels in the same direction of its inci- ence onto the mountain until it reaches the underground lab- ratory. Accordingly, we obtained the muon energy spectrum to e detected underground and the muon intensity in the units of uons/cm 2 /s/sr that depends on the azimuthal angle φ and the olar angle θ at the YEMI underground laboratory and the re- ults are shown in Fig. 2 (b),(c), respectively. It is difficult to cal- ulate the absolute muon flux underground due to many ambigu- ties from rock properties, different depths, etc. Therefore, the in- egrated muon intensity (through a horizontal area) at YEMI can e normalized by the measured flux. The total muon flux at YEMI s thus considered as 8.2 ×10 −8 muons/cm 2 /s, which is derived H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 63 Fig. 4. Muon-induced neutrons (a) and gamma rays (b) at the rock surface. The thick solid line of (a) includes the neutrons backscattered from the rock surface, as well as from shielding materials surrounding the detector that reenter the cavern. Neutrons entering the cavern for the first time are represented by the thin line of (a). Fig. 5. Shielding configurations: (a) lead shield ( d = 30 cm) (b) water shield ( d = 3 m). b s C t m c d b a t Y s 3 w t s f b r t u u t e e t i 3 o m s 3 g r S s b s 3 b t t a t s e t 2 y using the flux of 328 ±1(stat) ±10(syst) muons/m 2 /day, mea- ured at the Yangyang underground laboratory (Y2L) [14] by the OSINE-100 experiment [15] . YEMI is located ∼1.5 times deeper han Y2L and, thus, the integrated muon intensities in the units of uons/cm 2 /s for two sites, calculated from Eqs. (1)–(4) using both ontour maps of Mt. Yemi and Yangyang areas, are found to be as ifferent as 4.6 times. We used the measured muon flux at Y2L, y scaling it with 4.6, to derive the muon flux at YEMI with the ssumption that their rock properties are equal to each other for wo sites. The mean muon energy and the vertical muon intensity for EMI are 236 GeV and 4.0 ×10 −8 muons/cm 2 /s/sr, which are con- istent with the measured or simulated values reported in Ref. [16] . .1.3. Brute-force muon simulation To simulate all the primary and secondary particles induced hen the muons interact with rock, the shielding materials, and he detector components, we have performed Geant4 Monte Carlo imulations that start with muons, given by the underground dif- erential energy spectrum described in Sections 3.1.1 and 3.1.2 , y generating them from the outer surface of the rock shell sur- ounding the cavern, which is called a brute-force muon simula- ion. For the brute-force muon simulation, we added the rock vol- me with the thickness that was optimized based on another sim- lation; we simulated muons with the energy of 236 GeV that is he mean energy of the muon energy spectrum at YEMI by gen- rating it into the rock volume and estimated both of the mean nergy and event rate, as a function of the rock thickness, of neu-rons and gammas induced by muon interactions with materials n the rock that exited the rock volume. As a result, we added a -meter-thick rock shell outside the cavern. The schematic view f the simulation is shown in Fig. 3 and one hundred million uons corresponding to a 7-year period were simulated for this tudy. .2. Results We not only analyzed muons but also all the neutrons and amma rays induced by muon interactions with materials in the ock, in the shield, and in the detector components, as described in ection 3.1.3 . We evaluated the shielding effects with two different hielding configurations using the Muon Veto system to estimate ackground rates quantitatively. The details of the simulation re- ults are given in Sections 3.2.1–3.2.3 . .2.1. Muon-induced neutrons and gamma rays at the boundary etween rock and cavern Fig. 4 (a) and (b) show the neutron and gamma energy spec- ra at the rock surface, respectively, produced by the simula- ion of the muon propagation and its interaction with materi- ls in the rock, described in Section 3.1.3 . We also included neu- rons backscattered from the rock surface, as well as from the hielding materials surrounding the detector that reenter the cav- rn, represented by the thick solid line of Fig 4 (a). According to he simulation results, the muon-induced neutron flux at YEMI is .4 × 10 −9 n/cm 2 /s, for energies above 1 MeV. The muon-induced 64 H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 Fig. 6. Neutron ((a),(c)) and gamma rays ((b),(d)) energy spectra at the boundaries B1 (black), B2 (red), and B3 (green) with a 30-cm-thick lead shield in configuration 1. (a) and (b) represent the neutron and gamma energy spectra before vetoing muon-tagged events, respectively, and (c) and (d) represent the neutron and gamma energy spectra after vetoing muon-tagged events, respectively. Fig. 7. Energy spectra deposited in a single CMO crystal in configuration 1. It repre- sents the background contributions by (n, n’ γ ) in red and by (n, γ ) in green. Single- hit energy spectrum with 50-cm-thick polyethylene shielding installed outside the plastic scintillator in the cavern is shown in the inset. t b t m r a h r d t 3 b g m S g t d a s t t t t fi u neutron flux has a dependence on the rock composition and the depth of the underground laboratory and, thus, it is compared with other similar results. The vertical depth of YEMI (1005 m) is similar to that of Boulby (1070 m) and Boulby’s rock compo- sition ( < Z > = 11.7, < A > = 23.6) is similar to the standard rock ( < Z > = 11, < A > = 22), as reported in Refs [18] . It is in good agreement with the results of 1.34 × 10 −9 n/cm 2 /s (Mei and Hime’s prediction) and 8.7 × 10 −10 n/cm 2 /s (FLUKA predciton) at Boulby, values reported in Refs. [19,20] . There are features found in the muon-induced gamma-ray spec- rum of Fig. 4 (b): the peak and the absence of gammas for energies elow ∼100 keV. It occurred because photoelectric absorption that ransfers the energy from a gamma ray to an atomic electron of aterials in the rock is more common when the energy of gamma ay is of the same order of magnitude as the binding energy of the tomic electron that is relatively low energy and it interacts with igh atomic number materials. Gamma attenuation coefficient for ocks as a function of gamma energy shows strong energy depen- ence in the range 2–20 keV, dominated by photoelectric absorp- ion, as reported in Ref. [17] . .2.2. Shielding configurations and muon veto system There are three main sources of backgrounds, found from the rute-force muon simulation, in the cavern: muons, neutrons, and amma rays. The neutrons and gamma rays are produced by the uons traversing through the rock, as described in the previous ections. In order to reject the muons and muon-induced back- rounds from the rock surface, we consider the shield layer around he detector. However, neutrons and gamma rays can also be pro- uced by muon interactions with the shielding materials, as well s with the detector components. Thus, we install a Muon Veto ystem in addition to the shielding materials. In this study, we considered two different shielding configura- ions as shown in Fig. 5 : a 30-cm-thick lead shield ((a), configura- ion 1) and a 3-meter-thick water shield ((b), configuration 2). In he simulation, we installed 5-cm-thick plastic scintillator outside he lead shield as a Muon Veto system for configuration 1. For con- guration 2, we can measure the energy deposited in the water by sing photomultiplier Tubes (PMTs) installed in the water tank. Us- H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 65 Fig. 8. Background rates as a function of the thickness of the shielding materials in (a) configuration 1 and (b) configuration 2. i a b p t I i e g t t b n B t I v n i g T a i r s t s s t a f t m H e a d r c b t e s t t 3 b F t e F n i c ( F ( t t ∼ b t l g a t t h 9 t t a 3 m < i i 4 4 o h t ng the veto system, we can tag muon events that deposit at least s much energy as a minimum energy threshold, and reject all the ackgrounds induced by the muon, as muon-tagged events. We ap- lied the energy threshold of 7.5 MeV to the scintillating veto sys- em in shielding configuration 1 and 500 MeV in configuration 2. n water shielding configuration the energy threshold was changed n terms of the shield thickness. 500 MeV is corresponding to the nergy threshold of 3-meter-thick water shield. We tested the shielding effects by comparing the neutron and amma energy spectra, produced by muon interaction with rock, at he following boundaries: between the cavern and the plastic scin- illator (B1), between the plastic scintillator and the lead (B2), and etween the lead/water shields and the air (B3). Fig. 6 shows the eutron and gamma energy spectra at the boundaries B1, B2, and 3 with configuration 1. The black, red, and green colors represent he neutron/gamma energy spectra at B1, B2, and B3, respectively. n the simulation, we included a steel skeleton that supports the eto system and the shield layers, affecting the spectrum at B1. From the neutron spectrum at B3 of Fig. 6 (a), we found that the eutrons are built up in the lead shield, similar to results given n Refs. [20–22] . There is a small reduction in the neutron back- rounds at B1 and at B2 of Fig. 6 (a) by the plastic scintillator layer. hat occurred because the neutrons produced by the muon inter- ction in the scintillator were included. To exclude all the muon- nduced backgrounds, we vetoed the muon-tagged events and the esulting neutron/gamma backgrounds at several boundaries are hown in Fig. 6 (c) and (d). High-energy neutrons and gamma rays hat deposit as much energy as the energy threshold of the veto ystem, are also rejected as muon-tagged events. Fig. 6 (c) repre- ents the neutrons only from the rock or induced by neutrons in he shielding materials. As shown in the two neutron spectra at B1 nd at B2 of Fig. 6 (c), it is found to be effective to shield neutrons or energies below ∼1 MeV with even 5-cm-thick plastic scintilla- or [23] . According to the simulation results of gamma rays in Fig. 6 (b), ost of the low-energy gamma rays are blocked by the lead shield. owever, there is a little reduction for energies above ∼10 MeV, ven with a 30-cm-thick lead shield. This occurs because a large mount of gamma rays with a few hundreds of keV, to a few hun- reds of MeV energy, is formed at B3 (green dashed line). These ays are produced in the lead shield due to the bremsstrahlung pro- ess, which causes muon-induced electromagnetic showers, tagged y the Muon Veto system, and accordingly rejected as muon- agged events. The green dashed line of Fig. 6 (d) represents gamma nergy spectrum at B3 after vetoing muon-tagged events. As a re- ult, the gamma background inside the lead shield, originated at n he rock or induced by neutrons in the shielding materials, is found o be negligible in configuration 1. .2.3. Neutron-induced background In this section, we provided a quantitative understanding of ackgrounds induced by neutrons that are induced by muons. ig. 7 shows the energy spectrum deposited in a single CMO crys- al in configuration 1, called as single-hit events, when consid- ring the neutron flux at B3, shown in the green dotted line of ig. 6 (c), after vetoing the muon-tagged events. We examined how eutrons inside the lead shield make single-hit background events n a crystal. It was found that it occurred via two dominant pro- esses: neutron inelastic scattering (n, n ′ γ ) and neutron capture n, γ ). We showed their contributions in two different colors in ig. 7 : (n, n ′ γ ) in red and (n, γ ) in green. The γ -rays generated from thermal neutron capture by the n, γ ) process in the stainless-steel and copper shields composing he cryostat and the copper material around crystal detectors, con- ribute mainly to the high-energy backgrounds for energies above 1 MeV. This includes the 3.034 MeV region of interest (ROI). The ackground events resulting from (n, n ′ γ ) process give only a lit- le contribution for the high energies, contributing mainly to the ow-energy region, below ∼1 MeV. Thus, we tested the shielding effect of neutrons that lead to amma ray backgrounds by the neutron capture process, using 50-cm-thick polyethylene (PE) shielding layer installed outside he plastic scintillator in the cavern, and its result is shown in he inset of Fig. 7 . We estimated the background rates of single- it events with and without the PE shield and it resulted in .7 ×10 −7 counts/(keV · kg · yr) and 4.8 ×10 −6 counts/(keV ·kg · yr) in he (2–8) MeV energy region, respectively. Accordingly, we found hat the background is reduced to a level ∼5 times lower by dding the 50-cm-thick PE shield in configuration 1. .2.4. Single-hit background rates In order to find the thickness of the shielding material that eet the background requirement for the AMoRE-II experiment, 10 −5 counts/(keV · kg · yr), we estimated the single-hit event rate n the (2–8) MeV energy region with several shielding thicknesses n both configurations, 1 and 2: 5, 10, 15, 20, 25, 30, 35, and 0 cm for the lead shield and 100, 150, 200, 250, 300, 350, and 00 cm for the water shield. To understand the shielding effect f neutrons and gamma rays quantitatively, we tested the single- it background rate for both neutrons and gamma rays. The resul- ant single-hit background rates as a function of the shield thick- ess for both configurations are shown in Fig. 8 (a) and (b); if we 66 H.W. Bae, E.J. Jeon and Y.D. Kim et al. / Astroparticle Physics 114 (2020) 60–67 Fig. 9. Neutron background rates with and without 50-cm-thick PE shield in con- figuration 1. e n r r t g g fi l 9 e a b 1 g m c 5 a o e t b t l m t m e 5 s f c s p A e found no event in the 2–8 MeV energy region from the simula- tion we estimated an upper limit at the 90% C.L. [24] . In Fig. 8 (a), it is found that even a 10-cm-thick lead shield in configuration 1 is effective to shield muon-induced gamma rays, reducing them to the level of 10 −6 counts/(keV · kg · yr) (red solid line). It also shows the shielding effect of neutrons with respect to several thicknesses of the lead shield (blue dotted line). The background rate was re- duced to the aimed level by adding 50-cm-thick PE shield to the 30-cm-thick lead shield in configuration 1 (blue empty marker). Fig. 8 (b) shows the shielding effect of neutrons and gamma rays by the water shield in configuration 2. It is found that even a 100- cm-thick water shield is more effective to shield neutrons. It also shows that the aimed background level can be achieved with 200- cm-thick water shield in configuration 2. In addition, we tested the single-hit rate of muon-tagged events in the (2–4) MeV en- ergy region. The rate was found to be ∼ 10 −6 counts/(keV · kg · yr) for both shielding configurations with a 30-cm-thick lead and 3-m- thick water shield when the muon tagging efficiency is 99.9% that meets the background requirement for the AMoRE-II experiment ( < 10 −5 counts/(keV · kg · yr)). 4. Neutron background 4.1. Neutron flux at underground laboratory The neutron background at YEMI underground laboratory is mainly composed of two types of neutrons. The first contribu- tion is neutrons from the experimental environment, such as neu- trons from ( α, n) natural radioactivity reactions, and neutrons from spontaneous fission mainly of U atoms from the underground envi- ronment. The second is neutrons induced by muons. The dominant type of neutrons is the environment neutrons because its level is two or three orders of magnitude higher than the muon-induced neutrons [25] . Therefore, we need to test the effect of backgrounds not only from muon-induced neutrons but also from underground environment neutrons, although we evaluated quantitatively the background level of muon-induced neutrons by configuring shield- ing layers with the Muon Veto system in Section 3 . 4.2. Shielding effects and results We simulated neutrons by generating them from the rock sur- face with flat energy spectra over six different energy ranges: (1) 0.025 eV (2) 0.5 eV – 1 keV (3) 1 keV – 10 keV (4) 10 keV – 100 keV (5) 100 keV – 1 MeV (6) 1 MeV – 10 MeV We used the neutron flux measured by the Bonner sphere spec- trometer system at Y2L underground laboratory (Y2L) [26] as a ref- erence value, integrated in a large energy bin and measured in the six different energy binning itemized above. However, it needs a more detailed spectrum for some purposes due to the large energy bin width that results in a large uncertainty in the event rate. The total flux of neutrons at Y2L was measured twice by the Bonner spheres in 2012 [26] and by 3 He gas de- tector in 2018. The results of 6.6 × 10 −5 neutrons/cm 2 /s and 4.3 × 10 −5 neutrons/cm 2 /s, were found for energies below 10 MeV, respectively. They are consistent with each other, but they are about 10 ∼17 times higher than that found by Gran Sasso (3.78 × 10 −6 neutrons/cm 2 /s [27] ). We assumed that the neutron flux at YEMI is similar to that of Y2L where the neutron back- grounds for energies below 10 MeV are dominated by neutrons from the ( α, n) process. The simulation results with configuration 1 for the single-hit vent rate in the (2–8) MeV energy region at the six energy bin- ings are shown in red in Fig 9 . It shows the single-hit background ates in the level of 10 −3 counts/(keV · kg · yr) for the overall energy ange. We tested the shielding effects of neutrons using a 50-cm- hick PE shielding layer in the cavern and estimated the back- round rate for single-hit events in the (2–8) MeV energy re- ion, represented in blue in Fig 9 . The background rates of the rst four energy binnings (up to 100 keV) are reduced to the evel of < 10 −6 counts/(keV · kg · yr) that is an upper limit at the 0% C.L. with zero-entry; if we found no event in the 2–8 MeV nergy region from the simulation we estimated an upper limit t the 90% C.L. [24] . The background rate of the last energy inning of the 1–10 MeV energy interval is found to be about 0 −5 counts/(keV · kg · yr) with the PE. We found that the back- round level can be reduced by ∼20% with only an additional 4- m-thick silicone rubber sheet with 24% concentrations of boron arbide inside the PE shield from the simulation. . Conclusion In this study, we have simulated both the cosmic-ray muons nd the underground environment neutrons, as well as all the sec- ndary particles. Because these backgrounds depend strongly on an xperimental design, as reported in Refs. [28,29] , we quantitatively ested the effects of the neutron and muon-induced backgrounds y configuring different shielding layers with the active Veto sys- em. We studied the shielding effects with various thicknesses of ead in configuration 1 and found that it is good enough to shield uon-induced gamma rays with even a 10-cm-thick lead layer for he AMoRE-II experiment. However, there should be other gam- as from the radioisotopes in the rock, which should be consid- red with a lead layer as thick as 30 cm. In addition, an additional 0-cm-thick PE is needed to effectively shield neutrons. The water hield in configuration 2 is found to be more effective than lead or shielding neutrons. 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