1 Introduction

An ultralow-background environment is required in rare-event search experiments, because background events may cover the physical events of interest. Accordingly, most background-sensitive experiments are performed in underground laboratories to minimize the impact of cosmic rays. Among these underground laboratories, the China Jinping Underground Laboratory (CJPL) is the deepest currently in operation [1]. In addition, various types of passive or active shielding are applied to further reduce the background affecting these experiments. The shielding components and main detectors should be made of ultrapure materials to ensure that they do not additionally contribute to the background.

Germanium is a common detector material for direct dark matter detection and neutrinoless double-decay experiments, including the China Dark Matter Experiment (CDEX), Coherent Germanium Neutrino Technology experiment, Super Cryogenic Dark Matter Search, Edelweiss experiment, Germanium Detector Array experiment, and MAJORANA Demonstrator [1-6]. In these experiments, cosmogenic radionuclides in the germanium introduce a significant proportion of background signals. For example, the Edelweiss-III experiment reported a measurement of cosmogenic tritium and other nuclides in their germanium detectors [4]. The CDEX collaboration predicted the cosmogenic activation of germanium detectors manufactured at sea level for future ton-scale experiments [7]. In addition, copper, especially oxygen-free high thermal conductivity copper, is widely used as the shielding material closest to the active detectors in these experiments owing to its high chemical purity and mechanical strength. However, it has the same problem of cosmogenic activation.

One approach to eliminate the cosmogenic radionuclides in copper and germanium is to grow the crystals in underground laboratories, which are shielded from most cosmic rays. The second phase of CJPL (CJPL-II) is under construction, and the civil construction part of the project is almost complete. Dark matter detection and other experiments will soon be running in CJPL-II. The production of ultrapure copper and germanium directly in CJPL-II has been proposed. In this work, we develop a method of evaluating the cosmogenic background for copper and germanium in the underground laboratory using experimental measurements, Monte Carlo simulations, and theoretical calculations.

2 Methods

2.1 Muon source measurement and simulation

To simulate cosmogenic activation in an underground laboratory, it is necessary to know the flux and energy of cosmic rays at that depth. We combine experimental measurements and a Monte Carlo simulation to obtain this information for cosmic rays in CJPL-II.

Muons are the dominant component of cosmic rays in the underground laboratory [8]. High-energy, highly penetrating muons arrive at the underground laboratory through approximately 2400 m of rock. The method of measuring the muon flux in CJPL-I has also been applied in CJPL-II [9]. The system consists of six plastic scintillation detectors, which are divided into two groups. The length, width, and height of each detector are 1, 0.5, and 0.05 m, respectively, and the effective detection area is 0.5 m². As shown in Figure 1, each group consists of three stacked detectors, which form a triple-coincidence system that can distinguish cosmic muons from environmental radiation such as gamma-rays. The waveforms from the photomultiplier tubes in the plastic scintillators are also recorded to improve the background discrimination.

Fig. 1.Full-screen View

Photograph of the muon measurement system installed in CJPL-II.

After environmental radiation is rejected and the triple-coincidence events (N) are counted, the muon flux (Φμ) of the measurement can be estimated using Eq. 1.

${\Phi }_{\mu }=\frac{N}{\epsilon St}$ (1)

Here, ε is the total efficiency of the detection system, S is the detection area of the detector, and t is the acquisition time of the measurement. Efficiency corrections in our system include the dead time, detection efficiency of the plastic scintillator, edge effect, and solid-angle correction of the triple-coincidence system. Owing to the structure of Jinping mountain, muons approaching from directly above the mountain encounter the smallest rock thickness; thus, the majority of detected muons have zenith angles close to 0 [9]. Additionally, the dead time is negligible, and the detection efficiency of the system is close to 1. Thus, the total efficiency ε is set to 1 in our calculation.

However, the measurement system cannot measure the energy of incident muons. We have simulated the residual muon flux and spectrum in the CJPL using the MUSIC code [10, 11]. That simulation models the Jinping mountain as a semi-sphere of standard rock with a radius of 2400 m, and the laboratory is located at the center of the mountain. The energy and angular distribution of muons before they penetrate the mountain are calculated using the Gaisser formula [12]. The simulated muon flux is compared with our measurement for validation, and the energy distribution of residual muons is utilized to simulate cosmic activation in CJPL-II.

2.2 Secondary particles in the laboratory

The secondary particles from muons in the underground laboratory are simulated using CERN’s GEANT4 toolkit [13].

The experimental hall in CJPL-II is modeled as several boxes consisting of different materials (Figure 2). From the outside to the inside, these are standard rock (2 m thick), concrete (20 cm thick), and a 50 m × 10 m × 10 m experimental hall filled with air. We simulated a 25 m × 5 m × 0.4 m copper or germanium plate 1 m above the ground in the center of the experimental hall.

Fig. 2.Full-screen View

Model of the underground laboratory in the simulation (lateral view).

The incident particles in the simulation are residual muons from cosmic rays. The initial kinetic energy of the muons is set to the average energy found in the MUSIC simulation. Furthermore, the positions of the incident muons are randomly generated from the upper surface of the rock box with zero zenith angle, assuming that the residual muon trajectories are almost perpendicular to the outer rock.

GEANT4 uses different physics models and the corresponding cross sections to define the interactions between incident particles and target materials. For any Monte Carlo simulation, it is essential to choose a physics model that adequately describes the processes in the simulation. However, computational efficiency should also be considered to balance the time consumption and simulation precision. To improve the precision of secondary particles and the production of radionuclides, we choose the QGSP_BERT_HP physics list in GEANT4, which implements the Quark-Gluon String Precompound model and uses the data-driven high-precision neutron cross section for neutrons with energies lower than 20 MeV.

The track lengths and energies of secondary particles in the experimental hall, such as neutrons, protons, and gamma-rays, are recorded during the simulation. After the simulation results are normalized by the measured muon flux Φμ, the secondary particle flux at an energy E is expressed by Eq. 2.

${\Phi }_{\text{par}}(E)=\frac{l_{\text{par}}(E)}{V\times t_{\text{sim}}}=\frac{l_{\text{par}}(E)}{V\times \frac{N_{\text{sim}}}{\Phi \mu S_{\text{sim}}}}$ (2)

Here, l_par(E) is the accumulated track length of secondary particles at E, V is the total volume of the experimental hall, N_sim is the number of incident muons, t_sim is the time needed to produce N_sim muons when the flux is Φμ, and S_sim is the area of the rock box’s upper surface, where muons are randomly sampled.

3 Results

The results obtained after approximately 655 days of continuous operation of the muon detection system are listed in Table 1. The results from the two groups of detectors were combined, and the obtained flux of cosmic muons in CJPL-II was found to be (2.01± 0.19)× 10^-6 m^-2s^-1, or (63.5± 5.9) m^-2 year^-1. The system is still running to obtain more data and reduce the statistical uncertainty.

According to a previous calculation [10], the average energy of muons reaching the CJPL is 369 GeV. We used GEANT4 to simulate 10⁶ muons with that energy entering the CJPL-II model and obtained the cosmogenic neutron and proton flux spectra shown in Figure 3. On the basis of the measured muon flux of 2.01 × 10^-6 m^-2 s^-1, the total fluxes of cosmogenic neutrons and protons are 6.53 × 10^-7 m^-2 s^-1 and 5.33 × 10^-9 m^-2 s^-1, respectively. Thus, secondary neutrons dominate the incident particles according to the cosmogenic activation calculation.

Fig. 3.Full-screen View

Simulated secondary particle spectra (left: neutrons, right: protons) of experimental hall.

In comparison with the measured neutron background in CJPL-I [15] (Figure 4), the simulation result shows a neutron flux five to six orders of magnitude lower than the total neutron background, which suggests that cosmogenic neutrons are not the major component of the neutron background at an underground site at the depth of the CJPL depth.

Fig. 4.Full-screen View

Comparison of the measured total neutron spectrum and simulated cosmogenic neutron spectrum.

The simulated and calculated cosmogenic radionuclides affecting copper and germanium production in CJPL-II are listed in Tables 2 and 3, respectively. The yields at sea level calculated by ACTIVIA [14] are also presented for comparison. The yields from the simulation and calculation for CJPL agree within an order of magnitude for most nuclides, except for ⁶⁵Zn in copper, and ⁶³Ni and ⁶⁸Ge in germanium. The inconsistency may result from the differences between the cross sections in ACTIVIA and the physics models in GEANT4. For example, the cross section for ⁶⁵Zn activation in ⁶⁵Cu at 100 MeV is 9.8 mb in ACTIVIA, whereas the corresponding value is 0.7 mb in our simulation. A comparison of the yields of cosmogenic radionuclides at CJPL and sea level reveals that shielding by Jinping mountain can reduce the radionuclide production by six to eight orders of magnitude.

Using Eq.5 and the calculated yields in Tables 2 and 3, we calculated the radiation activities of cosmogenic radionuclides in copper and germanium grown in the CJPL after 30, 60, and 90 days. The results are presented in Tables 4 and 5, respectively.

4 Conclusion

To evaluate the advantages of growing copper and germanium in CJPL-II, we developed an estimation procedure based on experimental measurements, Monte Carlo simulations, and theoretical calculations. A triple-coincidence plastic scintillator detection system was used to measure the muon flux at CJPL-II. In addition, the energy of the muons was obtained from a previous simulation of muons penetrating Jinping mountain. The fluxes of secondary particles from muons in the experimental hall, as well as cosmogenic radionuclides in a simulated copper or germanium plate located in the experimental hall, were simulated using the GEANT4 toolkit. Additionally, the yields calculated from the simulated neutron flux and production cross sections were provided for validation.

The muon flux measurement indicates a significant reduction in cosmic rays due to shielding by Jinping mountain; the values are as low as (63.5± 5.9) m^-2 year^-1. Thus, the simulated fluxes of secondary particles from muons are negligible compared to the measured background neutrons in the CJPL, which are attributed mainly to environmental neutrons from the surrounding materials such as rock and concrete.

The simulated and calculated production of cosmogenic radionuclides in copper and germanium are in agreement. As expected, the radionuclide yields are approximately six to eight orders of magnitude lower than the yields at sea level. Moreover, the activities of most radionuclides after 90 days of exposure are less than 10^-6 μ Bq kg^-1. Our results demonstrated that the cosmogenic radionuclide background at the CJPL is negligible compared to other potential background sources.

The estimation method developed in this work can be adapted for different underground laboratories and materials to ensure that the cosmogenic radionuclides at the site are negligible. In the future, the cosmic muons and environmental neutrons should be measured in a broader energy region. However, the development of radioassay technology is essential for obtaining quantitative concentrations of cosmogenic radionuclides in crystals grown in underground laboratories.