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Neutrino-less double-βdecay ofCa48studied byCaF2(Eu) scintillators

We searched for the neutrino-less double beta decay(0nbb) of 48Ca by using CaF2(Eu) scintillators. Analysis of their pulse shapes was effective to reduce backgrounds. No events are observed in the Q-value region for the data of 3394 kg days. It gives a lower limit (90% confidence level) of T>2.7 x 10^22 year for the half life of 0nbb of 48Ca. Combined with our previous data for 1553 kg days, we obtained more stringent limit of T>5.8 x 10^22 year.

Among double beta decay nuclei, 48 Ca has an advantage of the highest Q ββ -value (4.27 MeV).
This large Q ββ -value gives a large phase-space factor to enhance the 0νββ rate and the least contribution from natural background radiations in the energy region of the Q ββ -value. Therefore good signal to background ratio is ensured in the measurement of 0νββ. However not many studies have been carried out so far [6,7,8,9,10], since the natural abundance of 48 Ca is only 0.187 %.
We carried out the measurements of 0νββ with CaF 2 (Eu) scintillators. We previously reported a lower limit (90 % confidence level) of 1.4 × 10 22 year for the half life of 0νββ of 48 Ca [1]. The measurement employed the ELEGANT VI system at Oto Cosmo Observatory. We observed 0 event in the Q ββ -value region although expected background exceeded 1 event which limits our experimental sensitivity. In what follows we describe characteristics of our measurement to achieve further background reduction. The ELEGANT VI system consists of three kinds of scintillation detectors. A CaF 2 (Eu) scintillator (45 mm cube) works as an active source-detector. We employed 23 CaF 2 (Eu) scintillators, which contained 7.6 g of 48 Ca. CaF 2 (pure) and CsI(Tl) scintillators work as veto counters for CaF 2 (Eu). Further details of the detector can be found in ref. [1].
A charge sensitive ADC (CSADC) and a flash ADC (FADC) recorded energy and pulse shape of CaF 2 (Eu) signals, respectively. The energy is obtained by summing the signals from two photomultiplier tubes (PMTs) for each CaF 2 (Eu). The two signals were used for effective background reduction.
Each CaF 2 (Eu) scintillator was calibrated by γ-rays from 137 Cs and β-and α-rays from 214 Bi and 216 Po as internal contaminations. A standard γ-ray source of 137 Cs was also used. Linearity has been confirmed in an energy range from 662 keV to 3.27 MeV and assumed to hold to up to the Q ββ -value. An energy resolution was measured by a peak width of the α-rays from 216 Po. The peak was clearly observed at 1.3 MeVee (electron equivalent energy). The energy resolution was assumed to be inversely proportional to square root of deposited energy in an energy region up to the Q ββ -value. This dependence has been confirmed up to 2.33 MeV by using 0 + → 0 + transition in 40 Ca for a CaF 2 (Eu) scintillator [1]. The extrapolated resolution was evaluated to be 4-6 % in FWHM depending on each CaF 2 (Eu) scintillator. The ELEGANT VI system is able to strongly suppress backgrounds by the 4π active shield and the large Q ββ -value of 48 Ca. Only a few processes are conceivable as backgrounds [1]. The main background processes are due to pile-up events from Bi and Po nuclei which are radioactive contaminations in the CaF 2 (Eu) scintillators.
The pile-up events come from the following sequential decays; A typical pulse shape of the pile-up event is shown in FIG. 1. In particular, the sequential decay (a) is serious because 212 Po has the half life of 0.3 µs which is much shorter than the CSADC gate width of 4 µs for the 1µs decay constant of CaF 2 (Eu) signal. As a consequence, the sequential decay (a) frequently becomes a pile-up event in the CSADC gate. The CSADC gives sum energy of β-and α-rays, which is occasionally close to the Q ββ -value.
The pile-up events can be rejected by using pulse shape information. The 100 MHz FADC recorded the pulse shape in a time window of 10 µsec, which is long enough for the CaF 2 (Eu) signal. In order to reduce data size, only a sum of 46 signals from 23 CaF 2 (Eu) scintillators was recorded. An energy threshold for the FADC was 500 keV. The criteria to select candidate events for 0νββ are given as follows.
(3) Pulse shape analysis(PSA) tells that the events are not the pile-up events.
The criteria (1) and (2) are the same as those in the previous analysis [1]. The new criterion (3) is to realize further background reduction in this analysis.
PSA can identify the pile-up event when time difference of the two pulses is longer than a certain value. Rejection of the pile-up events is carried out by the following three procedures.
(i) Preparation of reference pulse shape f ref (t).
(ii) Identification of the pile-up events.
(iii) Estimation of a rejection efficiency.
We describe each step in the followings.
(i) Reference pulse shape (f i ref (t)) was obtained for each CaF 2 (Eu) scintillator where i stands for the scintillator number. Eq.(1) represents the pulse shape where both decay and rise are represented by exponential functions with time constants τ i d and τ i r , respectively.
Here A is a normalization parameter corresponding to energy. We fitted the shapes generated by summing up pulse shapes of events in an energy region from 1 MeV to 2 MeV where we can safely take that almost all of the events are due to single-pulse events. Obtained τ i d ranged from 1230 to 1480 nsec for each scintillator. After fixing τ i d , τ i r was obtained by averaging that for each event, since time jitter between events deteriorated sharp rise time. τ i r was obtained as 6 -8 nsec for each scintillator.
(ii) A fitting function f (t) for the pile-up event has a delayed component represented by Here A 1 and A 2 correspond to energies of prompt and delayed components, respectively. We measured pulse shapes of β and α components and found that their difference is negligibly small for the present analysis. We evaluate χ 2 for a certain ∆t by fitting f (t) to events above 3 MeV.
We took ∆t that gave the least χ 2 .
An obtained ∆t distribution is shown in FIG. 2 a). The ∆t distribution is well represented by an exponential decay. An obtained half life of 296 ± 10 nsec is consistent with the half life of 299 nsec of 212 Bi. The energy spectra of prompt and delayed components are shown in FIG. 2 b) and  . 2 b)). A peak of α-rays from 212 Po is observed at 2.0 MeVee in   FIG. 2 c). These facts show that events above 3 MeV are due to the sequential decay (a).
(iii) We evaluated the rejection efficiency of the events from the sequential decay (a). The rejection efficiency depends on where a cut point on ∆t is set. We set the cut point at 30 nsec.
The rejection efficiency was obtained to be 90 % by analyzing software-generated events from the sequential decay (a). The rejection may introduce inefficiency for the single-pulse events due to misidentification. It is found to be negligible for the present cut point.
A selection of candidate events was made for 3394 kg·days of data as described above. The energy spectrum is shown in FIG. 3. One finds that the event rate is reduced by one order-ofmagnitude by requiring PSA. As the result, we observe no events in a 0νββ window of 4.17 -4.37 MeV.
Estimation of a background rate is needed to derive the half life of 0νββ. We know a contribution from the radioactive contaminations in the scintillators gives dominant background, which is estimated by a Monte Carlo simulation [11]. Radioactivities in the CaF 2 (Eu) scintillators were 0.11 mBq/kg and 1.20 mBq/kg on average for 220 Rn(Th-chain) and 214 Bi(U-chain), respectively.
The radioactivities in each CaF 2 (Eu) have been listed in ref. [1]. From the simulation using the measured radioactivities and the background rejection efficiency, we estimated the background rate in the 0νββ window to be 0.70 events/3394 kg·day as given in TABLE I. A contribution from two neutrino double beta decay (2νββ) is found to be negligible from the life time published elsewhere [9,10,12].
The detection efficiency which includes the acceptance efficiency of PSA was evaluated by a Monte Carlo simulation. The efficiency was estimated to be 53 % for the 0νββ window. It is dominantly determined by the probability that two electrons from 0νββ are fully contained in a single CaF 2 (Eu).
Here we discuss systematic errors. They are mainly from the uncertainties in the estimation of following three items. 1) Uncertainty on absolute energy calibration and gain stability may obscure the 0νββ window. We found it to be less than 1 %. 2) Uncertainty on PSA efficiencies was estimated to be 3 %. 3) Uncertainty on radioactivities in the CaF 2 (Eu) scintillators may change the estimation of backgrounds. It was estimated to be 3 %. Uncertainty 1) has no effect, since we still have no event even though we have the energy calibration off by 1 %. Uncertainties 2) and 3) are much smaller than statistical error. We thus do not take them into account in deriving the half life.
Following a procedure in ref. [13], One has to prepare large amount of source material to sense the mass region suggested by the oscillation experiments. Although the 4π active shield and the pulse shape analysis are shown to be effective to realize the background-free measurement, the ELEGANT VI system is not suitable to scale up. These techniques are applied to the detector system CANDLES [16,17,18,19,20,21,22], which realizes large scalability of the detector size.