A study on energy resolution of CANDLES detector
B. T. Khai, S. Ajimura, W. M. Chan, K. Fushimi, R. Hazama, H. Hiraoka, T. Iida, K. Kanagawa, H. Kino, T. Kishimoto, T. Maeda, K. Nakajima, M. Nomachi, I. Ogawa, T. Ohata, K. Suzuki, Y. Takemoto, Y. Takihira, Y. Tamagawa, M. Tozawa, M. Tsuzuki, S. Umehara, S. Yoshida
AA study on energy resolution of CANDLES detector
B. T. Khai,
Member, IEEE,
S. Ajimura,
Member, IEEE,
W. M. Chan, K. Fushimi, R. Hazama, H. Hiraoka, T. Iida,K. Kanagawa, H. Kino, T. Kishimoto, T. Maeda, K. Nakajima, M. Nomachi,
Senior Member, IEEE,
I. Ogawa,T. Ohata, K. Suzuki, Y. Takemoto, Y. Takihira, Y. Tamagawa, M. Tozawa, M. Tsuzuki, S. Umehara,and S. Yoshida
Abstract —In a neutrino-less double-beta-decay ( νββ ) exper-iment, an irremovable two-neutrino double-beta-decay ( νββ )background surrounds the Q-value of the double beta decayisotope. The energy resolution must be improved to differentiatebetween νββ and νββ events. CAlcium fluoride for studiesof Neutrino and Dark matters by Low Energy Spectrometer(CANDLES) discerns the νββ of Ca using a CaF scintillatoras the detector and source. Photomultiplier tubes (PMTs) collectscintillation photons. Ideally, the energy resolution should equalthe statistical fluctuation of the number of photoelectrons. At theQ-value of Ca, the current energy resolution (2.6 % ) exceedsthis fluctuation (1.6 % ). Because of CaF ’s long decay constant of1000 ns, a signal integration in 4000 ns is used to calculate theenergy. The baseline fluctuation ( σ baseline ) is accumulated in thesignal integration, degrading the energy resolution. Therefore,this paper studies σ baseline in the CANDLES detector, whichhas a severe effect (1 % ) at the Q-value of Ca. To avoid σ baseline , photon counting can be used to obtain the number ofphotoelectrons in each PMT; however, a significant photoelectronsignal overlapping probability in each PMT causes missing photo-electrons in counting and reduces the energy resolution. “Partialphoton counting” reduces σ baseline and minimizes photoelectronloss. We thus obtain improved energy resolutions of 4.5–4.0 % at1460.8 keV ( γ -ray of K), and 3.3–2.9 % at 2614.5 keV ( γ -ray of Tl). The energy resolution at the Q-value shows an estimatedimprovement of 2.2 % , with improved detector sensitivity byfactor 1.09 for the νββ half-life of Ca.
Index Terms —CaF , photon counting, energy resolution Manuscript received MM DD, YYYY; accepted MM DD, YYYY. Date ofpublication: MM DD, YYYY; date of current version, MM DD, YYYY. Thiswork was supported by JSPS/MEXT KAKENHI Grant Number 19H05804,19H05809, 26104003, 16H00870, 24224007, and 26105513. This workwas supported by the research project of Research Center for NuclearPhysics (RCNP), Osaka University. This work was also supported by thejoint research program of the Institute of Cosmic Ray Research (ICRR),the University of Tokyo. The Kamioka Mining and Smelting Company hasprovided service for activities in the mine.B. T. Khai, W. M. Chan, K. Kanagawa, H. Kino, T. Maeda, T. Ohata, M.Tsuzuki, and S. Yoshida are with the Graduate School of Science, OsakaUniversity, Toyonaka, Osaka 560-0043, Japan.S. Ajimura, T. Kishimoto, M. Nomachi, Y. Takemoto, Y. Takihira, and S.Umehara are with the Research Center for Nuclear Physics, Osaka University,Ibaraki, Osaka 567-0047, Japan.K. Fushimi is with the Faculty of Integrated Arts and Science, Universityof Tokushima, Tokushima 770-8502, Japan.R. Hazama is with the Faculty of Human Environment, Osaka SangyoUniversity, Daito, Osaka 574-8530, Japan.T. Iida is with the Faculty of Pure and Applied Sciences, University ofTsukuba, Ibaraki 305-8571, Japan.H. Hiraoka, K. Nakajima, I. Ogawa, Y. Tamagawa, and M. Tozawa arewith the Graduate School of Engineering, University of Fukui, Fukui 910-8507, Japan.K. Suzuki is with the Wakasa Wan Energy Research Center, 64-52-1Nagatani, Tsuruga, Fukui 914-0192, Japan.
I. I
NTRODUCTION
A. Double Beta Decay D OUBLE beta decay (DBD) is a transition between twoisobaric nuclei (A, Z) and (A, Z + 2) with two decaymodes. For two-neutrino DBD ( νββ ) mode, two electronsand two electron-type anti-neutrinos are emitted. However, analternative decay mode can occur without anti-neutrino emis-sion, and this is called neutrino-less DBD ( νββ ). The νββ mode is forbidden in the Standard Model of particle physics(SM) due to its violation of lepton number conservation, but itcan probe new physics beyond the SM [1]. The discovery ofneutrino oscillation indicates that a neutrino has non-zero mass[2], [3]. The remaining questions related to the neutrino massand whether neutrinos are Majorana or Dirac fermions areattracting the interest of physicists, and the νββ experimentis a useful tool for these purposes [1]. The νββ mode hasbeen experimentally observed (e.g. the νββ half-lives of 10DBD isotopes are summarized in [4]), but the νββ modehas not been observed yet. Ca has the highest DBD Q-value ( Q ββ = 4272 keV), but its natural abundance is very low(0.187 % ). The highest Q ββ gives a large phase-space factorto enhance the DBD rate and has the least contribution fromthe natural background. B. CANDLES experiment
The CAlcium fluoride for studies of Neutrino and Darkmatters by Low Energy Spectrometer (CANDLES) experi-ment aims to obtain νββ from Ca. The experiment isvery challenging owing to the extremely low decay rateof νββ from Ca ( T ν / > . × years with 90 % confidence level [5]). To obtain νββ , a massive amount ofthe source and a low background measurement are required.The current CANDLES III experiment is constructed in theKamioka Underground Observatory (2700 m water equivalentdepth) to reduce the cosmic-ray background [6]. We setup an experiment with 96 CaF (un-doped, non-enriched) × × cm crystals used as both the detector and source.We are developing low-cost enrichment techniques [7], [8], [9]to increase the amount of Ca in our detector in the future.All crystals are submerged inside a 2 m vessel of liquidscintillator (LS). The scintillation decay constants of CaF andLS are 1000 ns and 10 ns, respectively, and the LS is used as4 π active shielding. Scintillation photons are collected by 62photomultiplier tubes (PMTs) surrounding the vessel, of which12 are 10-inch (R7081-100), 36 are 13-inch (R8055), and 14are 20-inch (R7250), all manufactured by Hamamatsu [10].Light pipes are installed between the LS vessel and PMTs1 a r X i v : . [ phy s i c s . i n s - d e t ] S e p o increase the efficiency of photon collection. Everything ismounted inside a cylindrical water tank, with a height of 4m and a diameter of 3 m. To reduce the ( n, γ ) background inthe detector materials and rocks, a passive shield consisting oflead blocks and silicon rubber sheets containing boron carbide(B C) is installed both inside and outside the tank [11]. Moredetails of the detector setup can be found in [5].The data acquisition (DAQ) system consists of 74 channelsof 500 MHz-8 bits-8 buffers flash analog-to-digital converters(FADCs), of which 62 are recording PMT waveforms and 12are used for trigger purposes [12]. Trigger logics implementedin the global trigger control of our DAQ system include adual-gate trigger to select the CaF signal, and other triggerlogics for monitoring purposes (a clock trigger of 3 Hz, aminimum bias trigger to select LS signals, a low-thresholddual-gate trigger to select CaF signals at a lower threshold,and a cosmic-ray trigger) [13]. The clock trigger of 3 Hz isused to study single photoelectron charges in dark current andbaseline fluctuation, which are discussed in Section II. C. νββ and energy resolution In νββ experiments, νββ is an irremovable backgroundproportional to the mass of Ca. We plan to develop aton-scale and highly-enriched- Ca detector to improve thesensitivity of νββ study, so that νββ will provide a high-contrast background compared to the νββ . The energy distri-butions of νββ and νββ of Ca are a continuous spectrumand a mono-energetic peak at Q ββ , respectively. Figure 1shows simulation energy spectra of νββ and νββ withdifferent energy resolutions. In this simulation, the νββ half-life ( T ν / ) is 4.2 × years [4] and νββ half-life ( T ν / ) isassumed to be 10 years, which is equivalent to an effectiveneutrino mass (m ββ ) of 80 meV because T ν / is proportionalto the inverse square of m ββ [1]. In this simulation, m ββ is close to the world-best upper limit of m ββ reported bythe Kamioka Liquid-scintillator Anti-Neutrino Detector - Zeroneutrino double beta decay search (KamLAND-Zen) [14].Improving the resolution from 2.6 % to 1.6 % increases theratio of νββ to νββ from 0.2 to 1.0 within the region ofinterest (ROI); hence, a better energy resolution is required toreduce the νββ background.The CaF signal consists of many photoelectrons (p.e.). Inan ideal case, the energy resolution should be equal to thestatistical fluctuation of the number of p.e. ( N p . e . ). At the Q ββ of Ca, the current energy resolution of the CANDLES IIIdetector is 2.6 % [15] and, with a p.e. yield of 0.91 p.e./keV,the statistical fluctuation of N p . e . is 1.6 % . The resolution islarger than the statistical fluctuation, and other fluctuationsare likely to be present that degrade the resolution further. Thefluctuations affecting the CANDLES energy resolution includestatistical fluctuation, detector stability, crystal position, andcharge measurement. Statistical fluctuation is mainly influ-enced by N p . e . ; hence, we cool the CaF crystals at approx-imately 5 ◦ C to increase the scintillation light output, installlight pipes to increase the photo-coverage [16], and introducea magnetic cancellation coil to increase the efficiency of p.e.collection [17]. The detector stability and crystal position were
Energy (keV) - · C oun t s / k e V / / y ea r yr · =1 n » bb m ROI =1.0 n bb /R n bb R =0.2 n bb /R n bb R1.6%2.6% bbn bbn Fig. 1: Simulation histograms of νββ and νββ of Ca withenergy resolutions of 2.6 % (red) and 1.6 % (blue). The ROI tocompare the ratio of νββ to νββ ( R ββ ν / R ββ ν ) is marked withdashed black lines.studied in previous research [15], [17], and were found to havea small contribution to the energy resolution of CANDLES.In this paper, the uncertainty in charge measurement of theCANDLES III detector is discussed (Section II), and a methodto reduce the uncertainty is introduced (Section III).II. E RROR IN CHARGE MEASUREMENT
In the current analysis, we sum the waveforms of62 PMTs and calculate the charge using signal integration= Σ i (Pedestal − Signal[ i ]) , where i is the waveform’s timebin, with each time bin equivalent to 2 ns. Because of CaF ’slong decay constant of 1000 ns, each signal is integrated in4000 ns; hence, the baseline fluctuations are accumulated. Inthis study, we examined possible fluctuations over a long inter-val, including dark current in the PMTs, noise in the baseline,digitization error (related to the resolution of the FADCs), andpedestal uncertainty. In the following subsections, these long-interval fluctuations at a γ -peak of K (1460.8 keV), a γ -peakof Tl (2614.5 MeV), and Q ββ of Ca are estimated.
A. Dark current
Dark current (DC) can be accidentally obtained in a CaF waveform, affecting the energy resolution statistically. For DCanalysis, we use the clock trigger events to avoid the p.e. fromthe scintillator, but the p.e. signals from scintillation photonsof low energy radiations may be accidentally collected. To es-timate the DC rate in each PMT, a threshold is individually setfor each PMT to count the p.e. signals. Details of the thresholdsetting are described in Section III. Figure 2 shows the DCrates of 62 PMTs, all of which are in the order of 10 p.e./s.From summing the DC rates of 62 PMTs, the DC rate inthe sum waveform is approximately µ DC =6.2 × p.e./s.Thus, the DC accumulated in an integration interval T INT is calculated as N DC = µ DC × T INT , and the fluctuation ofDC is σ DC = √ N DC . In 4000 ns of the summed waveform,the average amount of DC is 2.5 p.e., and the fluctuation ofDC is σ DC =1.6 p.e. The relative uncertainties induced by DC2 PMT Number · D a r k C u rr en t r a t e ( p . e ./ s ) Fig. 2: Dark current rates of 10-inch (12, blue circles), 13-inch(36, black squares), and 20-inch PMTs (14, red triangles).( σ DC / N p . e . ) at K, Tl, and Q ββ ( Ca) are 0.1 % , 0.06 % ,and 0.04 % , respectively. The N p . e . at the K peak,
Tl peak,and Q ββ ( Ca) can be calculated from the p.e. yield.
B. Noise in baseline
The sine-wave noise of 62 PMTs is analyzed using a clocktrigger, with visible noise found in the baseline of the 10-inchPMTs, whereas the noise amplitudes of the 13-inch and 20-inch PMTs are not visible. We sum the 12 baselines of 10-inchPMTs for noise analysis and estimate the effect of noise onthe energy resolution. Figure 3 shows a sinusoidal shape ofthe sum baseline of the 12 10-inch PMTs in one clock event.For every clock event, the sum baseline is fitted with a sinefunction to estimate the noise amplitude and cycle: A ( t ) = A n sin (cid:18) π t − ϕ n T n (cid:19) , (1)where A n is the noise amplitude, T n is the noise cycle, and ϕ n is the phase factor. From analyzing more than 10 clockevents, the mean values of the noise amplitude and cycle arefound to be 0.73 ADC, equivalent to approximately 3 mV inthe FADC input, and 730 ns, respectively. The noise amplitudeis small, although we sum the noise of the 12 10-inch PMTs.Each PMT signal is amplified by 10 times before being fedinto an FADC, meaning the noise amplitude is approximately Time bin (ns) - - - - A m p li t ude ( A DC ) n T n j t- p · n + A n A(t) = Offset – : 0.73 n A 1.81 ns – : 727.96 n T Sum baseline of 12 10-inch PMTsFig. 3: Sine fitting on the sum baseline of 12 10-inch PMTsin one clock event of CANDLES III. 0.3 mV before amplification. The impedance of each PMTis 50 Ω ; therefore, the power of the sine-wave noise is only1.8 nW, which is extremely small. The fluctuation induced bysinusoidal noise in the signal integration in T INT ns is: σ noise = (cid:90) T INT A ( t ) dt = A n T n π ¯ µ p . e . sin (cid:18) π T INT T n (cid:19) sin (cid:18) π T INT − ϕ n T n (cid:19) , (2)where ¯ µ p . e . , which is the average charge of single-p.e. (1 p.e.)signals of the 62 PMTs in the ADC unit, is used to convert σ noise into p.e. units. The noise effect is clearly a sinefunction of phase ϕ n , which is random in every CaF eventand difficult to estimate. Thus, we estimate the maximumfluctuation induced by the 730-ns-cycle sine noise in thisresearch. The maximum fluctuation, as the root mean squareof the sine function in equation 2, is a function of T INT : σ maxnoise ( T INT ) = A n T n √ π ¯ µ p . e . (cid:12)(cid:12)(cid:12)(cid:12) sin (cid:18) π T INT T n (cid:19)(cid:12)(cid:12)(cid:12)(cid:12) . (3)For the integration interval of 4000 ns, the maximum effectof the 730-ns-cycle noise is 2 p.e.; hence, the maximumrelative uncertainties of noise ( σ maxnoise /N p . e . ) at K, Tl, and Q ββ ( Ca) are 0.15 % , 0.08 % , and 0.05 % , respectively. C. Digitization error
We record the PMT waveform using a 500 MHz—8 bitsADC08DL502 from Texas Instruments with 7.5 effectivenumber of bits [18]. The probability of recording a digitizedvalue “ n ” is the integral within the range n ± . of a Gaussianfunction P n ( µ A , σ A ) , where µ A and σ A are the mean andstandard deviation values, respectively, of the analog input. Inthis study, the pedestal is calculated as the average value ofthe first 40 data points, equivalent to 80 ns, in the waveform.The measured pedestal, which is theoretically calculated as Σ n (n × P n ) . Figure 4 shows the measured pedestal as afunction of true pedestal, or µ A , in one PMT. To perform - M ea s u r ed P ed ( A DC ) Ped-vs-DAC | Etc010-036 | PMT04
True Ped. (ADC) M ea s u r ed P ed . ( A DC ) Meas. Ped. (fit)True Ped.Meas. Ped. (data)
DAC's division 0.2 ADC »
243 243.5 244 244.5 245 245.5 246True Ped (ADC)0.4 - - D i g i t i z a t i on E rr o r ( A DC ) DigitErr-vs-TruePed | Etc010-036 | PMT04
243 244 245 246
Measured Ped. (ADC) - - D i g i t i z a t i on E rr o r ( A DC )
243 243.5 244 244.5 245 245.5 246True Ped (ADC)5055606570758085 M ean ( A DC ) Mean1pe-vs-TruePed | Etc010-036 | PMT04
243 243.5 244 244.5 245 245.5 246Measured Ped (ADC)5055606570758085 M ean ( A DC ) Mean1pe-vs-MeasuredPed | Etc010-036 | PMT04Mean1pe-vs-MeasuredPed | Etc010-036 | PMT04
Fig. 4: Measured pedestal plotted as a function of true pedestalwith three σ A values.3he test, we adjust the true pedestal using a 12-bit digital-to-analog converter (DAC), which is installed in each FADCmodule, with its voltage division equivalent to approximately0.2 ADC units. The black points depict experimental dataobtained at different true pedestal values, the solid red lineis the fitting function, and the blue dashed line is the expectedtrue pedestal. Because of the least significant bit (LSB), themeasured pedestal is different from the true pedestal, and thisdifference is called the digitization error (DE). The DE causesa fluctuation in the measured pedestal, which accumulateswhen calculating the signal integration. In a 1 p.e. signal, theDE accumulates at the non-pedestal points in the width of the1 p.e. signal. At the pedestal of 244.5 ADC, the DE is zero;thus, the 1 p.e. charge at this pedestal value is not affected bythe DE. Because the measured pedestal of each PMT is set atnearly 244.5 ADC, the DE fluctuation on the 1 p.e. charge ofone PMT can be assumed to be linearly correlated with themeasured pedestal: ∆ iPMT1 p . e . = Slope iPMT × ∆ iPMTPed . , (4)where Slope iPMT is the linear coefficient and ∆ iPMTPed . is equalto Pedestal iPMT − . . The DE is accumulated atnon-pedestal points; if the 1 p.e. signals do not overlap in high- N p . e . events, the number of non-pedestal points is N p . e . w/δ ,where w is the width of the 1 p.e. signal, and δ is theFADC sampling interval (2 ns). In contrast, if many 1 p.e.signals overlap each other, the number of non-pedestal pointsis reduced. In this study, we estimate the reduction factorusing the following mathematical model. The CaF waveformfollows an exponential function: µ ( t ) = µ (0) e − t/τ = N p . e . τ e − t/τ , (5)where µ ( t ) is the signal amplitude at time t , and τ is the decayconstant of CaF , which is 1000 ns. The expectation numberof p.e. within the width of the 1 p.e. signal is µ ( t ) w , and theprobability of obtaining the pedestal point is q ( t ) = e − µ ( t ) w .The number of non-pedestal points can be deduced as follows: N signal = 1 δ (cid:90) T INT (1 − q ( t )) dt, (6)and the reduced factor is estimated as R = N signal N p . e . w/δ . (7)Each CaF waveform contains up to several thousands 1 p.e.signals from the 62 PMTs. Because the pedestals and numbersof p.e. are not the same in every PMT, the DE is estimatedindividually for each PMT using the corresponding n iPMTp . e . andmeasured pedestal in that PMT: ω iPMT = n iPMTp . e . × ∆ iPMT1p . e . × R iPMT , (8)and the DE of the whole detector is the sum of DEs in the62 PMTs: Ω = (cid:80) ω iPMT . In Figure 5, the distributionsof estimated summed DEs of 62 PMTs on the γ -peaks of K and
Tl with the Gaussian fitting functions are plottedin blue and red, respectively. The standard deviation of eachdistribution is due to the fluctuation of the measured pedestal. For the DE distribution of each energy peak, the mean valueof DE ( µ DE ) causes a shift in the mean peak, and the standarddeviation ( σ DE ) influences the energy resolution. The DEfluctuation depends on the measured pedestal and N p . e . , whichcorresponds to the energy and integration interval. With anintegration interval of 4000 ns, the σ DE at the γ -peaks of K and
Tl are 7.3 p.e. and 10.4 p.e., respectively, andthe relative fluctuation of DE ( σ DE /N p . e . ) on these γ -peaksare 0.55 % and 0.44 % , respectively. According to the obtainedfluctuations, the relative fluctuation induced by DE on the Q ββ ( Ca) should be small. - - - - Estimated Digit. Err. (p.e.) -
10 110 c oun t s / p . e . K Tl
208 DE m DE s Fig. 5: Distributions of estimated DEs in 62 PMTs withGaussian fitting at the γ -peaks of K (blue) and
Tl (red).
D. Pedestal uncertainty
In this study, the pedestal of each PMT is calculated bytaking the average of the first 40 sampling points in thewaveform. Because the pedestal of each PMT is adjusted toapproximately 244.5 ADC, it follows a binomial distributionof 40 trials with the obtained value in each trial either 244 or245 ADC. Taking p as the probability of obtaining 245 ADCin a single trial in one PMT, the statistical uncertainty of thepedestal in that PMT is σ iPMTPedStat = (cid:112) p (1 − p ) / , (9)which is plotted as a solid red line in Figure 6. σ iPMTPedStat isthe ideal pedestal uncertainty, and the experimental pedestaluncertainty ( σ iPMTPed ) in each PMT is obtained by taking theroot mean square of the measured pedestal distribution of eachPMT. The magenta circles in Figure 6 are the experimentalpedestal uncertainties of the 62 PMTs. Because our PMTsare affected by noise, σ iPMTPed is approximately twice as largeas σ iPMTPedStat . In signal integration, the pedestal uncertaintyis accumulated at every data point, and the accumulatedfluctuations ( σ iPMTPedErr ) are linearly proportional to the numberof sampling points ( N ): σ iPMTPedErr = N × σ iPMTPed . The pedestalsof the 62 PMTs are summed in the sum waveform, and the4uctuation induced by the pedestal uncertainty of the 62 PMTsis amplified by several times: σ PedErr = (cid:118)(cid:117)(cid:117)(cid:116) (cid:88) iPMT=1 (cid:0) σ iPMTPedErr (cid:1) , (10)and σ PedErr is also linearly proportional to the number ofsampling points. In this analysis, we make distributions ofintegration of the baseline for each PMT, and the root meansquare (RMS) of the distribution is σ iPMTPedErr . For σ PedErr , wemake the distribution of integration of the sum baseline ofthe 62 PMTs, and obtain the RMS value. σ PedErr with thecurrent signal integration calculation can be estimated usingan integration interval of 4000 ns (or 2000 sampling points). Inthe current analysis, σ PedErr in each 4000 ns integration of theCaF waveform is 38.6 p.e. The relative fluctuations inducedby the pedestal uncertainty of the 62 PMTs, or σ PedErr /N p . e . ,at the K peak,
Tl peak, and Q ββ ( Ca) are 2.8 % , 1.6 % ,and 1 % , respectively. Measured Pedestal (ADC) P ede s t a l F l u c t ua t i on ( A DC ) Fig. 6: Standard deviations of measured pedestal distributionsplotted with magenta points as a function of measured pedestalof the 62 PMTs. The solid red line is the expected binomialfluctuation.
E. Summary of baseline fluctuations
The baseline fluctuations are accumulated in the long in-tegration interval of 4000 ns for the CaF signal and reducethe energy resolution. In this report, we study the baselinefluctuations including DC, sinusoidal noise, DE, and pedestaluncertainty. These fluctuations are plotted as functions ofthe integration interval, 500–4000 ns, in Figure 7. The DCfluctuation ( σ DC ), which is proportional to √ T INT , is plottedwith a solid blue line. The maximum noise fluctuation ( σ maxnoise ),which is calculated using equation 3, is plotted with a solidred line. The estimated DE fluctuations ( σ DE ) as functionsof the integration interval at the γ -peaks of K and
Tlare plotted with magenta dashed and solid lines, respectively. σ DE is proportional to N p . e . ; therefore, when the integrationinterval is shrunk, N p . e . is reduced, leading to a reductionin σ DE . Because N p . e . ( K) is smaller than N p . e . ( Tl), σ DE ( K) is smaller than σ DE ( Tl). The fluctuation inducedby pedestal uncertainty ( σ PedErr ) in the sum waveform of the 62 PMTs is calculated with different integration intervals,and plotted as a function of integration interval with a solidblack line. σ PedErr is the most severe, the DE fluctuationis small, and the fluctuations induced by DC and 730-ns-cycle sinusoidal noise are both negligible. The baseline andstatistical fluctuations ( σ stat ) at the K peak,
Tl peak,and Q ββ ( Ca) with an integration interval of 4000 ns arelisted in Table I. The DE at Q ββ is not estimated, but therelative DE fluctuation should be small. σ PedErr is a severefluctuation compared with σ stat at Q ββ . Because σ PedErr isproportional to the integration interval, the signal integration ispoor. An alternative method in CANDLES III is recommendedto obtain the energy information with the least effect ofbaseline fluctuation on the energy.
Integration Interval (ns) B a s e li ne F l u c t ua t i on ( p . e . ) DC s P e d E r r s Tl on DE s K on DE s noisemax s Fig. 7: Baseline fluctuations as a function of integration inter-val. Fluctuations induced by DC (blue), maximum fluctuationof 730-ns-cycle noise (red), DE at γ -peaks of K (magentadashed) and
Tl (solid magenta), and error in pedestalmeasurement (black).TABLE I: All baseline fluctuations ( σ DC , σ noise , σ DE , and σ PedErr ) and statistical fluctuation ( σ stat ) at the K peak,
Tl peak, and Q ββ ( Ca) with an integration interval of4000 ns. K γ -peak Tl γ -peak Q ββ ( Ca)1460.8 keV 2614.5 keV 4272 keV σ DC ( σ DC / N p.e. ) (0.1 % ) (0.06 % ) (0.04 % ) σ noise ≤ ≤ ≤ σ noise / N p.e. ) ( ≤ % ) ( ≤ % ) ( ≤ % ) σ DE ( σ DE / N p.e. ) (0.6 % ) (0.4 % ) (small) σ PedErr ( σ PedErr / N p.e. ) (2.9 % ) (1.6 % ) (1.0 % ) σ stat = (cid:112) N p.e. σ stat / N p.e. ) (2.7 % ) (2.0 % ) (1.6 % ) III. P
HOTON COUNTING IN
CANDLES III
A. DAQ for photon counting
The unavoidable fluctuation induced by the pedestal uncer-tainty is accumulated in the signal integration. The photoncounting method is widely used in scintillator experiments toreduce baseline fluctuations. The sum waveform of the CaF signal is formed by up to several thousands of p.e. signals,5nd each PMT waveform contains less N p . e . . The overlapof 1 p.e. signals results in inefficiency in photon counting,as mentioned in III-B; hence, we should count N p . e . in eachPMT of CANDLES. Currently, the first 768 ns of each PMTwaveform is digitized by an FADC every 2 ns and recorded as8-bit data; thereafter, digitized values in every 64 ns is summedand recorded as 16-bit data [12]. The waveform interval ofeach FADC is 8960 ns, and the data size is 640 B/FADC/event[12]. The 1 p.e. width of each PMT is less than 50 ns; thus, theshape of the 1 p.e. signal is difficult to see if the signal risesafter 768 ns. The DAQ software is modified to record the first4088 ns of the waveform at a speed of 2 ns/sample, and records128 ns by summing the digitized values for every 64 ns.After DAQ modification, the waveform interval is reduced to4216 ns, and the data size is increased to 2048 B/FADC/event,which is the limit of buffer size in each FADC. Using datafrom a previous study [12], the readout time per event forphoton counting measurement is 20 ms/event, which is twiceas long as the current readout time in the physics run ofCANDLES [12]. Owing to the development of the DAQ witheight buffers acting as derandomizers [12] in each FADC,the data-taking efficiency with the increased data size is stillalmost 100 % . B. Overlap of single p.e. signals
The threshold for photon counting should not be set toolow to avoid baseline noise, or too high to avoid losingp.e. in counting. In this study, the threshold for each PMTis Pedestal − ( µ p − σ p ), where µ p and σ p are the meanand standard deviation, respectively, of 1 p.e. pulse heightdistribution of the corresponding PMT. This threshold is setfor every PMT because it provides a good separation betweenthe baseline and non-baseline signals. For every time binin 4088 ns of the waveform, if the signal crosses over thethreshold, it is counted as 1 p.e. With simple photon counting,a multi-p.e. signal is counted as a single p.e. signal, whichleads to missing p.e. in counting.If the time interval between the two 1 p.e. signals is tooshort, it is impossible to distinguish them in photon counting.We use a simple mathematical model to estimate the numberof counted p.e. from the number of true p.e. We assume thatthere are two adjacent 1 p.e. signals in one PMT, named “A”and “B”, respectively, and thus define signal interval ( w s ) asthe shortest interval to distinguish these two signals. The w s value is related to the 1 p.e. signal width of the PMT. To avoidmissing signal B in counting, there should be no signal in the w s ns preceding signal A. The probability of counting signalB is the probability of no signal in the w s ns preceding signalA: e − µ ( t ) w s , where µ ( t ) is defined in equation 5. The numberof counted p.e. ( N c ) is dN c = µ ( t )e − µ ( t ) w s dt ⇒ N c = (cid:90) ∞ dN c = τw s (cid:16) − e − N p . e . w s /τ (cid:17) . (11)The counting efficiency in a PMT is evaluated in Figure 8by checking the correlation of the counted p.e. and the signalintegration. The green dashed line indicates the expected 100 % counting efficiency, and the solid red line is the fitting functionusing equation 11. At Q ββ ( Ca), the number of p.e. is approx-imately 63 p.e./PMT, whereas the number of counted p.e. inthis PMT is approximately 40 p.e. Two histograms constructedusing signal integration in 4000 ns and photon counting in4000 ns are plotted in black and magenta, respectively, inFigure 9. It is very clear that the histogram using 4000 nsphoton counting has a worse energy resolution due to missingmany p.e. in counting.
Signal Integral (p.e.)0 20 40 60 80 100 C oun t ed P ho t on s ( p . e . ) Fig. 8: Counting efficiency in a PMT. The green dashed lineis the expected linearity, and the solid red line is the fittingfunction.
C. Partial photon counting
The severe baseline fluctuations are accumulated in the4000 ns integration interval (Section II); therefore, it is en-couraged to use photon counting instead of signal integra-tion in CANDLES III. However, the spectrum constructedusing 4000 ns photon counting has a poor energy resolution(Section III) because the overlap of 1 p.e. signals leads tomissing p.e. in counting. In this section, we introduce a methodnamed “partial photon counting” (PPC) to reduce the baselinefluctuation with the fewest possible missed p.e. in photoncounting. The multi-p.e. signals are found predominantly nearthe rising edge of the CaF waveform. Thus, each PMTwaveform is divided into two regions: in the prompt regionnear the rising edge, where many multi-p.e. signals are found,signal integration is used to avoid missing p.e.; and in the latterregion near the tail, where only a few multi-p.e. signals arefound, photon counting is performed to reduce the baselinefluctuation. The sum of the integration and photon-countingintervals is fixed at 4000 ns. From summing the waveforms of62 PMTs, we can get the energy of CaF signal. The detailsof the PPC method for the CANDLES detector and somepreliminary results of improved energy resolutions obtainedwith a Gaussian-plus-exponential fitting function are intro-duced in reference [19]. Energy histograms are constructedwith different mixtures of integration and photon-counting in-tervals to evaluate the performance of PPC. Several histograms6onstructed using the PPC method are shown in Figure 9 withdifferent mixtures including 4000 ns (integration), 3000 ns(integration) + 1000 ns (counting), 2000 ns (integration) +2000 ns (counting), 1000 ns (integration) + 3000 ns (counting),and 4000 ns (counting), plotted in black, red, green, blue,and magenta, respectively. Because the counting efficiency isnot 100 % , the energy peaks are left-shifted when the photon-counting interval is increased. Therefore, all energy histogramsin Figure 9 are calibrated using γ -peaks of K and
Tl inthis research for ease of further analysis.
Energy (keV) c oun t s / k e V COUNT + 0
INT
COUNT + 1000
INT
COUNT + 2000
INT
COUNT + 3000
INT
COUNT + 4000
INT Fig. 9: Energy histograms constructed using the PPC methodafter calibration. Histograms using different mixtures of inte-gration and photon-counting intervals are shown.Each energy histogram obtained in PPC is fitted with afunction, which is a sum of Gaussian functions, including the γ -peaks emitted from K (1.46 MeV [20]),
Bi (1.76 MeVand 2.2 MeV [20]), and
Tl (2.6 MeV [20]), and an errorfunction, as the Compton and other background. Figure 10shows the energy spectrum constructed with a 4000 ns integra-tion interval with the fitting function. The energy resolutionsat K and
Tl peaks in each histogram are checked. Toevaluate the performance of the PPC method, the resolutionsare plotted as a function of the integration interval in Figure 11.The estimated resolutions at the K and
Tl peaks are
Energy (keV) c oun t s / k e V K . M e V B i . M e V B i . M e V T l . M e V Compton&other BKG
Fig. 10: Fitting function (solid red line) applied to every energyspectrum to obtain the energy resolutions of the K and
Tlpeaks. The fitting function contains Gaussian peaks ( γ -peaksof Tl,
Bi, and K) and an error function as the Comptonand other background.
Interval of Integration (ns) K ( k e V ) o f E s - Interval of Photon Count (ns) T l ( k e V ) o f E s K Tl Fig. 11: Obtained energy resolution at K (blue circles) and
Tl (red squares) peaks as a function of integration interval.The estimated resolutions at the K and
Tl peaks areplotted with blue and red dashed lines, respectively. The linesare plotted using equation 15.plotted using blue and red dashed lines, respectively. Theestimated resolutions are calculated using equation 15, whichis the root sum square of all fluctuations examined in thisstudy. The differences between the experimental and estimatedvalues at both energy peaks may be caused by imperfectestimation of the statistical fluctuation, which is discussed inthe next paragraph, and the assumption of remaining fluctu-ation, which is discussed in IV-A. The differences betweenthe experimental and estimated values are small (less than4 keV) at both energy peaks. For each γ -peak, the errorsof adjacent data points are correlated; therefore, only oneerror bar at one integration interval is shown. Owing to thesmall number of events at the Tl peak, we found deviationof the obtained resolutions at this energy peak as well as awide error bar. The energy resolutions at the two energies areimproved owing to the reduction of baseline fluctuation whenthe integration interval is decreased. Near the rising edge, theenergy resolutions degrade because more p.e. are missed, dueto the high overlapping probability of 1 p.e. signals. Becausethere are more p.e. obtained at the
Tl peak compared tothe K peak, the overlapping probability of 1 p.e. signals atthe
Tl peak is higher compared to that at the K peak.The integration interval to obtain the best energy resolution atthe
Tl peak should be longer than that at the K peak tolimit the p.e. missed in counting. From the results, we obtainthe energy deviation ( σ E ) improved from 66.8 to 59.3 keV,or energy resolution ( σ E /E) improved from 4.5 % to 4.0 % ,at the K peak when reducing the integration interval from4000 to 1600 ns; and σ E improved from 86.7 to 75.3 keV, or σ E /E improved from 3.3 % to 2.9 % at the Tl peak whenreducing the integration interval from 4000 to 1700 ns. Withthe results at the K and
Tl peaks, it is expected to obtainan improved resolution at Q ββ ( Ca).The overlap of 1 p.e. signals degrades the energy resolutionbecause of the increment in the statistical fluctuation. Thestatistical fluctuation in PPC is estimated using the followingmathematical model. The regions in PPC include the promptregion for integration and the latter region for photon counting.7ith the predefined parameters in equation 5, the number ofp.e. in the prompt region ( N P ) is N P = (cid:90) T INT µ ( t ) dt = N p . e . (cid:16) − e − t/τ (cid:17) . (12)The number of p.e. in the latter region is N D = N p . e . e − t/τ ,and the number of counted p.e. in the latter region of a PMTwaveform, M D , is calculated using equation 11: M D = τw s (cid:16) − e − N D w s /τ (cid:17) . (13)The obtained number of p.e. ( N T ) is the sum of N P and M D . Because N T is normalized to N p . e . in the analysis, thestatistical fluctuation after calibration is ∆ N T = (cid:115) ∆ N + ∆ M (cid:18) dN D dM D (cid:19) . (14)Applying equation 14 with different mixtures of integrationand photon-counting intervals, the statistical fluctuations inthe PPC method at the K and
Tl peaks are estimated.The statistical fluctuations at these two peaks are plotted asfunctions of the integration interval with the two solid blacklines in Figure 12.IV. R
ESULTS AND DISCUSSION
A. Discussion of the fluctuations
In Figure 12, we summarize the fluctuations at the Kand Tl γ -peaks, and plot them as a function of integrationinterval. The statistical fluctuations estimated by equation 14are shown as solid black lines. Extending the photon-countinginterval increases the number of 1 p.e. signals overlappingeach other; hence, those p.e. are missed in counting, and thestatistical fluctuation becomes worse. The root sum squares ofthe statistical and baseline fluctuations, (cid:112) σ + σ , atthe two energy peaks are plotted as solid red lines. The base-line fluctuations include the pedestal uncertainty, σ PedErr , andthe DE, σ DE . Because the fluctuations induced by DC , σ DC ,and sinusoidal noise, σ noise , are negligibly small, they are notaccounted for in the baseline fluctuations. Additionally, photoncounting cannot remove the DC 1 p.e. signals in the CaF waveform, so the DC fluctuation cannot be reduced by the PPCmethod. In addition to the baseline fluctuation and estimatedstatistical fluctuation, we study the remaining fluctuation asa function of integration interval. The remaining fluctuations, σ Remain = (cid:112) σ − σ − σ , of the two energy peaksare plotted as magenta points. The remaining fluctuation atthe Tl peak is almost unchanged for T INT of 600–4000 ns.At the K peak, we obtain some uncertainties of remainingfluctuation at T INT > T INT < K peak. In general, the remaining fluctuation can be assumedto be independent of the integration interval, and its source isnot determined in this study.Because the remaining fluctuation can be assumed to beindependent of the integration interval, the tendency of im-proved resolution by the PPC method can be explained by R e s o l u t i on ( k e V ) - Interval of Photon Count (ns) K ) ( s t a t + b a s e li n e s K) ( stat s K) ( Remain s Interval of Integration (ns) R e s o l u t i on ( k e V ) T l ) ( s t a t + b a s e l i n e s Tl) ( stat s Tl) ( Remain s Fig. 12: The statistical fluctuations, statistical+baseline fluctu-ations, and remaining fluctuations at K and Tl γ -peaksare plotted as a function of the integration interval.the reduction of baseline fluctuation. In Figure 12, for eachenergy peak, the average value of remaining fluctuation isclose to the statistical fluctuation at a 4000 ns integrationinterval. Assuming that the remaining fluctuation is zero withno incident p.e., the function Remain (E) = a × √ E canexplain the remaining fluctuations at 0 keV, 1460 keV ( K),and 2614 keV (
Tl). By fitting the remaining fluctuationsat the K and
Tl peaks in all the PPC histograms, theobtained parameters a fluctuate around 1. Using this functionfor each combination of integration and photon- countingintervals allows the remaining fluctuation at Q ββ ( Ca) to beextrapolated from the remaining fluctuations at the K and
Tl peaks. Figure 13 shows the remaining fluctuations atthe K peak,
Tl peak, and Q ββ ( Ca). The remainingfluctuation at each energy is the average of all remainingfluctuations obtained with a 600–4000 ns integration interval,and its error bar is the standard deviation. The function y = √ E , plotted with a solid line, can explain the dependenceof the remaining fluctuation on the energy.In summary, the energy resolution can be calculated usingthe following function: σ E = (cid:113) σ + σ + σ + σ , (15)where σ stat is the statistical fluctuation, σ DE is the DEfluctuation, σ Remain is the remaining fluctuation, and σ PedErr is the accumulated fluctuation induced by pedestal uncer-tainty. The estimated DE corresponds to N p . e . , so the σ DE fluctuation depends on √ E . From the above discussion,8
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Energy (keV) R e m a i n F l u c . ( k e V ) K Tl Ca (extrapolated) E y = Fig. 13: Remaining fluctuation as a function of energy. The cir-cles represent the remaining fluctuations at γ -peaks of K and
Tl, and at the Q-value of Ca. The remaining fluctuationat the Q-value is estimated assuming
Remain (E) = a × √ E ,where a fluctuates around 1.0, so y = √ E is plotted in thisfigure.the fluctuations studied in this research can be categorizedinto two groups: energy-dependent fluctuations ( σ stat , σ DE ,and σ Remain ), which are proportional to √ E , and energy-independent fluctuation ( σ PedErr ). We assume that the energyresolution can be estimated by the following fitting function: σ E E = (cid:114) p E + p E . (16)The goodness of the above fitting function is evaluated byapplying it to the energy resolutions taken from [21] obtainedat different energies. In Figure 14, the energy peaks consistof γ -peaks from radioisotopes ( K, Tl, and Y), and γ -peaks from ( n , γ ) reactions on H, Si, Fe, and Ni. Thedetails of ( n , γ ) calibration for the CANDLES III detector andthe emitted γ -peaks can be found in [21]. Energy (keV) / E ) s E ne r g y R e s o l u t i on ( Ep1 + Ep0f(E) = Y K H Tl Y Si Si Fe Ni Fig. 14: Application of the fitting function in equation 16 onthe obtained resolutions in Run010 of CANDLES. The datapoints are referred from [21].
B. Estimating the improved sensitivity of CANDLES III
For each mixture of integration and photon-counting inter-vals, equation 16 is used to fit the energy resolutions at the Kand
Tl peaks. The energy resolution at Q ββ ( Ca) is then extrapolated. The estimated results are plotted as a functionof integration interval with blue circles in Figure 15. Theuncertainty of the blue circles at the 1200–2600 ns integrationinterval, shown in Figure 15, is due to the uncertainty ofthe resolutions obtained at the K and
Tl peaks plottedin Figure 11. The energy resolutions at Q ββ ( Ca) reportedby Ohata [15] and Iida [21] are obtained with the 4000 nsintegration method, and plotted with black triangles and redsquares, respectively. With an integration interval of 4000 ns,there is an agreement between the estimated resolution at Q ββ ( Ca) in this study and those obtained in previous studies.From the figure, the energy resolution at Q ββ ( Ca) can beimproved from 2.6 % to 2.2 % by using the PPC method whenthe integration interval is reduced from 4000 to 2300 ns. Interval of Signal Integration (ns) E ne r g y R e s o l u t i on a t Q - v a l ue Interval of Photon Count (ns) [IIDA][OHATA] t h i s r e s ea r c h Fig. 15: Estimated energy resolutions at the Q-value using thePPC method. The blue circles represent the σ E ( Q ββ ) estimatedin this study. The black triangle and red square indicate the σ E ( Q ββ ) obtained in previous studies by Ohata [15] and Iida[21], respectively.The sensitivity of T ν / is related to the background rateand energy resolution. In the current CANDLES III, the2 νββ background is not dominant compared to the naturalbackground, and the sensitivity of T ν / is proportional to theinverse square root of the energy resolution at Q ββ [1]. Theenergy resolution at Q ββ ( Ca) is estimated to be improvedfrom 2.6 % , by using a 4000 ns integration, to approximately2.2 % , by using PPC. Therefore, using the PPC method canimprove the sensitivity of the CANDLES III detector for T ν / of Ca by (cid:112) . / .
2% = 1 . times.V. S UMMARY
CANDLES aims to obtain the 0 νββ of Ca using CaF crystals. The 2 νββ mode is an irremovable background inCANDLES, and it can be a high-contrast background in ourfuture ton-scale detector with CaF (un-doped, Ca-enriched)crystals. To reduce the 2 νββ , it is necessary to improvethe energy resolution. At Q ββ ( Ca), the energy resolution,2.6 % , is larger than the ideal statistical fluctuation of thenumber of p.e., 1.6 % , and there are other fluctuations thatworsen the energy resolution. The baseline fluctuations areaccumulated in the 4000 ns signal integration, which is usedto calculate the energy of CaF . In this study, the baselinefluctuations are investigated, and the fluctuation induced by9edestal uncertainty is found to be the most severe fluctuationof 1 % at Q ββ ( Ca). Photon counting is useful for removingthe baseline fluctuations, but it results in missing p.e. incounting for each PMT and, consequently, a worse energyresolution. We introduce a method named “partial photoncounting”, in which the signal integration is carried out inthe prompt region and the photon counting is carried out inthe tail region, to improve the energy resolution. Using thismethod, we obtain an improvement in the energy resolutionsat γ -peaks of K and
Tl, and the energy resolution at Q ββ is estimated to be improved to 2.2 % . With this improvement,we expect the sensitivity of T ν / of Ca to be improved by1.09 times using the same detector status as that reported in[15]. VI. A
CKNOWLEDGMENT
The authors thank Mr. Keita Mizukoshi from Kobe Univer-sity for his helpful discussions and comments.R
EFERENCES[1] M. J. Dolinski et al. , “Neutrinoless Double-Beta Decay: Status andProspects,”
Annu. Rev. Part. Sci. , vol. 69, no. 1, pp. 219–251, 2019.DOI: 10.1146/annurev-nucl-101918-023407.[2] S. Fukuda et al. (Super-Kamiokande Collaboration), “Solar B and hepNeutrino Measurements from 1258 Days of Super-Kamiokande Data,”
Phys. Rev. Lett. , vol. 86, pp. 5651–5655, 2001. DOI: 10.1103/Phys-RevLett.86.5651.[3] Q. R. Ahmad et al. (SNO Collaboration), “Direct Evidence for NeutrinoFlavor Transformation from Neutral-Current Interactions in the SudburyNeutrino Observatory,”
Phys. Rev. Lett. , vol. 89, p. 011301, 2002. DOI:10.1103/PhysRevLett.89.011301.[4] A. Barabash, “Average (Recommended) Half-Life Values for Two-Neutrino Double-Beta Decay,”
Czechoslovak Journal of Physics , vol. 52,no. 4, pp. 567–573, 2002. DOI: 10.1023/A:1015369612904.[5] S. Ajimura et al. (CANDLES Collaboration), “Low background mea-surement in CANDLES-III for studying the neutrino-less double betadecay of Ca,” arXiv:2008.09288 [hep-ex], 2020.[6] Y. Suzuki et al. , “Kamioka Underground Observatories,”
The Eur. Phys.J. Plus , vol. 127, no. 9, p. 111, 2012. DOI: 10.1140/epjp/i2012-12111-2.[7] T. Kishimoto et al. , “Calcium isotope enrichment by means of multi-channel counter-current electrophoresis for the study of particle andnuclear physics,”
Prog. Theor. Exp. Phys. , vol. 2015, no. 3, 2015. DOI:10.1093/ptep/ptv020.[8] S. Umehara et al. , “A basic study on the production of enriched isotope Ca by using crown-ether resin,”
Prog. Theor. Exp. Phys. , vol. 2015,no. 5, 2015. DOI: 10.1093/ptep/ptv063.[9] K. Matsuoka et al. , “The laser Isotope separation (LIS) methodsfor the enrichment of Ca,” in
The 16th International Conferenceon Topics in Astroparticle and Underground Physics (TAUP 2019) et al. , “Performance of updated shielding system inCANDLES,” in
The 6th International Workshop on Low Radioac-tivity Techniques (LRT 2017) , vol. 1921, p. 060003, 2018. DOI:10.1063/1.5018999.[12] B. T. Khai et al. , “ µ TCA DAQ system and parallel reading in CANDLESexperiment,”
IEEE Trans. Nucl. Sci. , vol. 66, no. 7, pp. 1174 – 1181,2019. DOI:10.1109/TNS.2019.2900984.[13] T. Maeda et al. , “The CANDLES Trigger System for the Study ofDouble Beta Decay of Ca,”
IEEE Trans. Nucl. Sci. , vol. 62, no. 3,pp. 1128–1134, 2015. DOI: 10.1109/TNS.2015.2423275.[14] A. Gando et al. (KamLAND-Zen Collaboration), “Search for MajoranaNeutrinos Near the Inverted Mass Hierarchy Region with KamLAND-Zen,”
Phys. Rev. Lett. , vol. 117, p. 082503, 2016. DOI: 10.1103/Phys-RevLett.117.082503. [15] T. Ohata, “Search for Neutrinoless Double Beta Decay in Ca with theCANDLES III experiment,” Doctor Thesis, Osaka University, section4.2, p. 42, 2018. DOI: 10.18910/69325.[16] S. Umehara et al. , “CANDLES - Search for neutrino-less double beta de-cay of Ca,” in
The International Nuclear Physics Conference (INPC)2013 , vol. 66, p. 08008, 2014. DOI: 10.1051/epjconf/20146608008.[17] T. Iida et al. , “Status and future prospect of Ca double beta decaysearch in CANDLES,” in
The 16th International Conference on Topicsin Astroparticle and Underground Physics (TAUP 2015) et al. , “Photon counting method for improvement of energyresolution in CANDLES experiment,” in et al. , “The energy calibration system for CANDLES using (n, γ )reaction,” arXiv:2003.13404 [physics.ins-det], 2020.)reaction,” arXiv:2003.13404 [physics.ins-det], 2020.