Using 220Rn to calibrate liquid noble gas detectors

In this paper, we describe 220Rn calibration source that was developed for liquid noble gas detectors. The key advantage of this source is that it can provide 212Bi-212Po consecutive events, which enables us to evaluate the vertex resolution of a detector at low energy by comparing low-energy events of 212Bi and corresponding higher-energy alpha-rays from 212Po. Since 220Rn is a noble gas, a hot metal getter can be used when introduced using xenon as the carrier gas. In addition, no long-life radioactive isotopes are left behind in the detector after the calibration is complete; this has clear advantage over the use of 222Rn which leaves long- life radioactivity, i.e., 210Pb. Using a small liquid xenon test chamber, we developed a system to introduce 220Rn via the xenon carrier gas; we demonstrated the successful introduction of 6 times 10^2 220Rn atoms in our test environment.


Introduction
In recent years liquid noble gases, such as liquid xenon (LXe) or liquid argon (LAr), have been increasingly used for particle detectors. Many sensitive searches for dark matter particles, axions, and particles beyond the standard model were conducted using such LXe and LAr detectors [1,2,3,4]. These studies require a sufficient understanding of detector response from ∼O(100)keV down to the detector threshold caused by nuclear and electron recoils. In particular, an energy calibration and evaluation of vertex reconstruction of the detector are an important means to interpreting experimental results. To evaluate the energy response of a detector, neutron sources and small accelerators are commonly used for nuclear recoil events, whereas the direct introduction of radio-active sources (e.g., 83m Kr and tritiated ethane) into detectors is typically performed via electron recoil events. Conversely, methods for evaluating reconstruction performance of vertex determination for low-energy events region are not wellestablished, because true vertices of diffused radioactive decay are not given independently. To overcome this problem, Kim el al. proposed the use of low-energy events whose event vertices are accurately determined by accompanying higher-energy events [5]. In this paper, we report on the development of a calibration source based on 220 Rn for liquid-noble-gas detectors. Here, 220 Rn is one of the isotopes of Rn located at the middle of the Thorium series. There are several advantages of using 220 Rn calibration as a source, including the following: Both 212 Bi and 212 Po are daughter nuclei of 220 Rn and provide β-α consecutive decays. Since the lifetime of 212 Po is short, the difference between decay vertices of 212 Po and 212 Bi is negligible, though they freely move in a liquid medium. Further, 212 Po provide an accurate determination of the decay vertex by reconstruction because of a large number of scintillation photons. Thus enabling us to use the difference of reconstructed vertices of low-energy β and α-rays to evaluate the performance of reconstruction at low energy. Since they are expected to uniformly distribute in the detector, an elevation of position dependence of vertex resolution is possible as well.
(ii) No long-life radioactivity downstream of 220 Rn The second advantage is that there are no long-life radioisotopes downstream of 220 Rn. Because of this, radioactivity that is introduced can decay out rather quickly. Though 212 Bi and 212 Po in a Uranium chain also cause consecutive decays with a half-life of 164 µs, decaying out of all radioactivity takes a longer amount of time; more specifically, 222 Rn and 210 Pb have half-lives of 3.8 days and 20 years, respectively, which is undesirable since it will cause an increase in background levels. (iii) Existence of 220 Rn as a noble gas The third advantage is that 220 Rn is a noble gas, which is useful for suppressing other impurities since 220 Rn can go through a hot metal getter typically used to purify a noble gas. Here, the getter removes impurities such as O 2 , H 2 O, and oily molecules that may impact the performance of the detector.

Source
We first note that there are publicly available thorium sources. In our calibration system, we used 50 pieces of lantern mantle containing thorium, as shown in Fig. 2, CAPTAIN STAG M-7911. Thorium is useful for generating strong light. Direct measurements using a Ge detector show 220 Rn activity with 1.2 kBq per one piece of lantern mantle. Emanating gas from some of these pieces of lantern mantle was measured and found to contain ∼30 Bq of 220 Rn per one piece when in radioactive-decay equilibrium.

Detector and 220 Rn injection system
The key issue to introduce 220 Rn is its short half-life of 56 s. For our system, we used a small LXe chamber located in the Kamioka mine. Its inner cylindrical chamber was filled by LXe while its outer chamber was used for vacuum insulation. The detector used 1.7 kg LXe and two photomultiplier tubes (PMTs) HAMAMATSU R10789; the PMTs were set face-to-face using an aluminum holder and a polytetrafluoroethylene (PTFE) cylinder, as illustrated in Fig. 1. The detector was connected to a large Xe gas bottle containing ∼6 kg of xenon gas, with xenon introduced into the chamber from the bottle. The gaseous xenon were liquefied and refrigerated using temperature feedback; here, its cold head was located above the top of the PMTs. A container with a thorium source emanating 220 Rn was then connected between the gas bottle and LXe chamber. The diameter of the source container was 4 cm, and its length was 40 cm; the container had a volume of 502 cm 3 . The 50 pieces of lantern mantle were kept in the source container. To introduce 220 Rn gas, xenon gas from the gas bottle was used as the carrier. The xenon carrier gas introduced the emanated 220 Rn gas into the detector through a getter. Here, the getter was necessary to remove impurities from the pieces of lantern mantle. At the cold head, the mixture of carrier gas and 220 Rn gas was liquefied. To avoid a sudden change of pressure or temperature of the detector, the flow rate of the gas mixture was set to two liters per minute and maintained for two min. In total, four liters of xenon carrier gas were introduced with 220 Rn. This quick operation is important for realizing the successful introduction of 220 Rn.

Data acquisition trigger and energy calibration for LXe chamber
The detector was equipped with a flash analog-to-digital converter (FADC) with 1 ns sampling and a 1 V dynamic range. The output of the two PMTs was amplified and fed into the FADC. Another output of the amplified signal was used to make a coincidence signal to trigger data acquisition. The discrimination for each PMT signal was ∼30 keV, and coincidence was issued when two discriminator signals existed within 150 ns of each other.
To calibrate an energy scale of the detector and monitor its stability, we used a 137 Cs external γ-ray source. This source was located at the bottom of the detector, outside of the outer chamber. Because there is position dependence of the light yield in the inner chamber, events happening around the center were extracted based on the balance of observed photoelectrons from the two PMTs to form a photoelectric peak caused by 667 keV γ-rays, as shown in Fig. 3. The peak was then fitted by Gaussian and linear functions, as shown in Fig. 4, and the light yield was evaluated as the mean of the Gaussian. Figure 3. Contour plot of observed events with a 137 Cs source; here, the data shown within the black line (i.e., 0.9 < Top/Bottom < 1.1) are shown in the red histograms of Fig. 4. Figure 4. ADC count distribution with a 137 Cs source; here, the black histogram shows all events, whereas the red histogram shows events within the black lines of Fig. 3; red, blue, and green curves depict the fitting function, Gaussian component, and linear component, respectively.

Identification of 212
Bi-212 Po consecutive events and evaluation for number of 220 Rn atoms 3.1. Data collection After introducing four liters of carrier xenon gas with 220 Rn from the source, data collection was conducted for 61 h. The first hour of data was found to be useless because the recorded FADC range was not appropriate and rejected.

Search for 212 Bi-212 Po consecutive events
To identify 212 Bi-212 Po consecutive events, we required the following two conditions: (1) the peak with the maximum height in a waveform must be alpha-like; and (2) the events must have been triggered by another lower peak with the timing difference between the peak at the trigger position and peak position with the maximum height larger than 30 ns but smaller than 900 ns. Condition (1) utilizes the fact that α particles have a shorter decay constant of scintillation lights than that of β and γ-ray particles. To discriminate α and β / γ, the ratio between two integrated areas of the FADC waveform was used to provide a comparison. The ratio of the pulse shape discrimination (PSD) parameter is defined as the blue area of Fig. 5 divided by the sum of the blue and red areas shown in the figure. The energy of an event was obtained by summing the area observed in waveforms from the top and bottom PMTs, and calibration data was calculated via the 137 Cs source, assuming linearity of the energy response. Figure 6 shows the PSD parameter versus the observed energy. In the figure, the events within the black box were selected as alpha-like events. Condition (2) requires the presence of a peak at the trigger position that differs from the maximum peak identified as α-like. If the timing of the α-like peak is within the range of 30 to 900 ns after the trigger timing, it was selected as the final 212 Bi-212 Po consecutive events. As a result of our analysis here, we found 292 events in our data over 60 h. The expected number of events due to chance coincidence was evaluated as 0.5 and was not subtracted. The black dots in Fig. 6 show the 212 Po events of our final data sample, while Fig. 7 shows the energy distribution of the α-ray events. From this data sample, a distribution of the timing differences between 212 Bi and 212 Po was obtained and is shown in Fig. 8. The distribution was fitted by a single exponential function; as a result of this fit, the decay constant of 212 Po candidates was 297 ± 34 ns, which is consistent with the expectation of 299 ns. Therefore, this supports the claim that the observed consecutive events are due to 212 Bi-212 Po decays.  Figure 5. Integration was performed only for the maximum peak; more specifically, integration within the blue timing period (with short arrow, i.e., a maximum time−30 ns +35 ns) and blue-and-red timing period (with long arrow, i.e., a maximum time−30 +300 ns) was used for pulse shape discrimination. Figure 6. Distribution of energy and the PSD parameter (see text), with green contours showing all events, events within the black box were selected as α-ray events, with black dots showing 212 Bi-212 Po candidates. Figure 7. Energy of the maximum peak of each event, with the green dotted line respecting all events, the green dashed line respecting α-like events, and the black solid lines respecting 212 Po candidates. Figure 8. Distribution of the timing difference between 212 Bi-212 Po candidates; here, the histogram with error bars shows the observed data, while the red line shows a fitted exponential curve with the decay constant of the fitted curve observed to be consistent with that of 212 Po.

Evaluation of 220 Rn atoms
There are two methods for evaluating the number of 220 Rn atoms introduced. One method is based on the number of observed 212 Bi-212 Po consecutive events, while the other method is based on the number of α-rays due to 220 Rn and 216 Po just after the introduction of 220 Rn. Table 1 shows a summary of our analysis here. In short, 6 × 10 2 pairs of 212 Bi-212 Po consecutive events were observed in this data-set though a small discrepancy between the two methods was also observed. A more detailed description of our two analysis follows.
• The first method yielded a total of 608.3 ± 35.6 atoms after taking into account several factors, i.e., the branching ratio of the consecutive decay (0.64), the efficiency caused by the cut on the timing difference between the trigger and α-like event (0.81), and the hour of "dead time" just after the introduction (0.93).
• The second method yielded a total of 700.5 ± 19.0 atoms. Since the event rate was high (i.e., ∼10 Hz, as shown in Fig. 9) just after introduction of 220 Rn, tagging each 220 Rn and 216 Po event was not possible, because the half-life of 216 Po is 0.145 seconds; however, α-like events were separated from β and γ-ray events using the difference of scintillation decay constants. As a result, the number of observed α-like events was 1427 in 15 min after the injection of 220 Rn. The number of expected background atoms was evaluated to be 26.5 using data after the first hour and should therefore be subtracted from the observed number of events. The final number was obtained by taking into account two α-like events observed from a single 220 Rn atom. The energy spectrum of the observed α-like event is shown in Fig. 10.

Summary
In this paper, we presented our work in developing a 220 Rn calibration source for liquid noble gas detectors. The key advantage of using this source is that it can provide 212 Bi-212 Po consecutive events, thus enabling us to evaluate vertex resolution of a detector at low-energy by comparing low energy events of 212 Bi and corresponding higher-energy α-rays from 212 Po. Since 220 Rn is a noble gas, a hot metal getter can be used when 220 Rn is introduced using xenon as the  carrier gas. In addition, no long-life radioactive isotopes are left behind in the detector after the calibration; this is substantially more advantageous than the method using 222 Rn which leaves long-life radioactivity in the term of 210 Pb. Using a small LXe test chamber, we developed a system to introduce 220 Rn with a xenon carrier gas and demonstrated the successful introduction of 6 × 10 2 220 Rn atoms.