Recent Developments and Results on Double Beta Decays with Crystal Scintillators and HPGe Spectrometry †

Recent developments, results, and perspectives arising from double beta decay experiments at the Gran Sasso National Laboratory (LNGS) of the INFN by using HPGe detectors and crystal scintillators and by exploiting various approaches and different isotopes are summarized. The measurements here presented have been performed in the experimental set-ups of the DAMA collaboration. These setups are optimized for low-background studies and operate deep underground Universe 2018, 4, 147; doi:10.3390/universe4120147 www.mdpi.com/journal/universe Universe 2018, 4, 147 2 of 14 at LNGS. The presented results are of significant value to the field, and the sensitivity achieved for some of the considered isotopes is one of the best available to date.


Introduction
DAMA is a pioneer project for the investigation of dark matter (DM), and it is also very active in the development of new highly radiopure crystal scintillators for their application to the search for rare processes. Many significant results have been obtained by investigating various rare processes in many experiments performed at the Gran Sasso National Laboratory (LNGS) by DAMA and its collaboration with researchers from INR-Kyiv and other institutions.
The most recent results obtained from the Large sodium Iodide Bulk for Rare processes DAMA/LIBRA-phase2 investigation of DM combined with those from the DAMA/NaI and DAMA/LIBRA-phase1 setups are presented elsewhere [1].
Here, some of the main results obtained from the search for rare processes with the DAMA setups 1 are briefly discussed; some details on the observation of 2ν2β decays from the meAsuReMent of twO-NeutrIno ββ decAy of 100 Mo to the first excited 0 + level of 100 Ru (ARMONIA) [2] and AURORA [3] experiments are given, and the latest activities on 106 Cd and 150 Nd [4] double beta decay are presented.
Many results have been obtained with the DAMA setups in experiments investigating the double beta decay of several candidate isotopes at LNGS; in particular, double beta decay processes in the following isotopes were investigated: 40 Ca, 46 Ca, 48 Ca, 64 Zn, 70 Zn, 100 Os,190 Pt,and 198 Pt. The sensitivities achieved for the half-life of the studied processes are competitive (between 10 20 and 10 24 year) due to the radiopurity of the detectors developed and the experimental approaches used. The results have improved (often by several orders of magnitude) the half-life limits obtained by previous experiments and have enabled new observations of two-neutrino double beta decay of 100 Mo [2], 116 Cd [3], and, preliminarily, 150 Nd [4]. Moreover, the obtained experimental sensitivities to decay modes with positron emission or double electron capture for some of the candidate isotopes are the best in the field.
As regards the rare α and β decays, we have obtained the first observation of 151 Eu α decay with T 1/2 = 5 × 10 18 year through the use of a CaF 2 (Eu) crystal scintillator [5]; we have also achieved the α decay of 190 Pt to the first excited level (E exc = 137.2 keV) of 186 Os with T 1/2 = 3 × 10 14 year [6]. The rare β decays of 113 Cd and 48 Ca have been investigated using CdWO 4 [7] and CaF 2 (Eu) [8] crystal scintillators, respectively. Moreover, pairs of NaI (Tl) detectors of the DAMA/LIBRA setup have been used to search for production of correlated e + e − pairs in the α decay of 241 Am [9]. Solar axions have been sought by studying their conversion to photons (inverse Primakoff effect) in NaI (Tl) crystals [10] and by investigating the resonance excitation of the 7 Li nuclei in a LiF crystal [11] and Li-containing powders [12]; the latter approach was based on the hypothetical axions emitted in the de-excitation of 7 Li nuclei in the Sun. Delayed coincidences have been investigated to search for such exotic particles as Q-balls [13] and SIMPs [14] using the DAMA/NaI detectors, and DAEMONs have been studied using the specially developed NEMESIS setup [15]. Electron stability has been investigated by searching for electron "disappearance" (i.e., decay into invisible channels as e − → ν eνe ν e ) [16,17] and by searching for the e − → ν e γ decay mode [17,18]. Finally, competitive limits have been obtained on the lifetime of several other possible nuclear processes. In particular, the following have been studied: (i) the spontaneous transition of 23 Na and 127 I nuclei to a superdense state [19]; (ii) cluster decays of 127 I [20] and of 138 La and 139 La [21]; (iii) nucleon, di-nucleon, and tri-nucleon decay into invisible channels [22,23]; (iv) Charge non-conserving (CNC) processes in 127 I [24]; (v) CNC β decay of 136 Xe [23], 100 Mo [2], and 139 La [25]; (vi) CNC electron capture with nuclear-level excitation in 127 I and 23 Na [26] and in 129 Xe [27]; (vii) nuclear processes violating the Pauli exclusion principle in sodium and iodine [28,29]; (viii) several rare nuclear decays in a BaF 2 crystal scintillator contaminated by radium [30]; (ix) long-lived superheavy ekatungsten with a radiopure ZnWO 4 crystal scintillator [31].

Observation of 2ν2β Decay of 100 Mo in the ARMONIA Experiment
To date, among the 35 naturally occurring 2β − candidates [32], more than 10 have been experimentally observed undergoing this process. One of the most interesting isotopes that has been the subject of 2β decay investigation is 100 Mo. The interest in this isotope is due to several aspects, including the following: (i) its natural abundance is rather high: δ = 9.744(65)% [33]; (ii) it has a high energy release, Q 2β = 3034.36 (17) keV [34], which yields a large phase space integral of the decay and thus a relatively high probability of the occurrence of 2β decay processes; moreover, this Q 2β value is even higher than the 2615 keV γ line from 208 Tl, which represents the highest-energy γ line from natural radioactivity (mostly 238 U, 232 Th, and 40 K), leading to lower achievable background; (iii) there is a possibility to obtain isotopically enriched material by using comparatively inexpensive ultra-speed centrifuge technology.
The half-life of the 100 Mo 2β decay isotope has been measured by a geochemical experiment [35] and by several direct experiments in which the 2ν2β decay to the ground state of 100 Ru was observed with T 1/2 values in the range of (3.3-11.5) × 10 18 year [32,36,37].
The aim of the ARMONIA experiment at LNGS's underground laboratories [2] was to remeasure 1 kg of Mo enriched in 100 Mo to 99.5%, used in [47], with more measurements and higher sensitivity in order to confirm the observations reported in [38][39][40][41][42][43][44][45][46] or to set an even more stringent T 1/2 limit. If the 0 + 1 excited level of 100 Ru (E exc = 1130.3 keV) is populated, two γs with energies of 590.8 keV and 539.5 keV will be emitted in cascade in the resulting de-excitation process. These γs have been searched for using the GeMulti setup. This setup is equipped with four low-background HPGe detectors mounted in one cryostat with a well in the center; the HPGe detectors have volumes of 225.2, 225.0, 225.0, and 220.7 cm 3 , respectively. The typical energy resolution (FWHM) of the detectors is 2.0 keV at the 1332 keV line of 60 Co. A lead and copper passive shield surrounds the experimental setup and has a nitrogen ventilation system to avoid radon near the detectors. A sample of metallic 100 Mo powder with a mass of 1009 g and a 99.5% enrichment in 100 Mo was measured at the first stage of the experiment. The collected data indicated the occurrence of the sought-after 2β decay [48]. Then, to reduce the background counting rate for the sample, it was further purified of radioactive residual contaminants. The 100 Mo metal was transformed into molybdenum oxide ( 100 MoO 3 ) with a mass of 1199 g. The purification procedure effectively removed 40 K and 137 Cs, and it also led to a reduction in the U/Th concentration [49]. The obtained sample of 100 MoO 3 was measured for 18120 h in the GeMulti setup. The background of the setup was collected under the same running conditions as the sample before (for 3211 h) and after (for 4500 h) the measurements with the sample to obtain consistent results; thus, in total, the background was measured over 7711 h.
The one-dimensional energy spectra measured with the 100 MoO 3 sample and the background in the (490-630) keV energy region are shown in Figure 1, left. Two peaks 540 keV and 591 keV (expected for 100 Mo → 100 Ru(0 + 1 ) 2ν2β decay) were observed in the experimental data collected with the 100 MoO 3 sample, while these peaks are absent in the background spectrum. The 100 MoO 3 had mass of 1199 g and 99.5% enrichment in 100 Mo; thus, it contained N = 4.85 × 10 24 100 Mo nuclei. The number of events in the 539.5 keV peak was determined by fitting the experimental energy spectrum to the energy interval (480-560) keV by the sum of the exponential distribution (which represents the background) and two Gaussians at 510.8 and 539.5 keV, respectively. This resulted in a value of S 540 = (319 ± 56) for the number of events, with a fit of χ 2 /n.d.f. = 0.76. In a similar manner, the number of events in the 590.8 keV peak was obtained by fitting the spectrum to the (560-625) keV energy region with the sum of the exponential with four Gaussians at 569.7, 583.2, 590.8, and 609.3 keV (χ 2 /n.d.f. = 1.4):S 591 = (278 ± 53). Thus, the peaks are observed with more than a 5σ significance level. The results of the fit are shown in Figure 1, left. Taking into account the detection efficiencies for the 539.5 keV and for the 590.8 keV γ lines (calculated by EGS4 [50] and GEANT4 [51] simulations), one obtains T 1/2 = 6.6 +1.4 −1.0 × 10 20 year for the 539.5 keV peak and 20 year for the 590.8 keV peak. Combining these results, we obtain the half-life: 10 20 year, where the systematic uncertainties are related to the uncertainty of the mass of the 100 MoO 3 sample (0.01%), the enrichment in 100 Mo (0.3%), and the calculation of the measurements' live time (0.5%), with a major contribution from the calculation of the efficiencies [2]. The two-dimensional energy spectrum of the events with multiplicity 2, accumulated in coincidence mode over a period of 17807 h, was also analyzed. Fixing the energy of one detector to the expected energy of a certain γ enables the observation of coincident signals in the other detectors with energies that correspond to γs emitted in cascade with the first one. By fixing the energy of one of the detectors to the expected energy of the γs emitted in the 2ν2β decay of 100 Mo to 100 Ru(0 + 1 ) (540 or 591 keV; width of the window: ±2 keV, in accordance with the energy resolution of the HPGe at these energies), the coincidence peak at the corresponding supplemental energy (591 or 540 keV) is observed. These coincidence spectra are shown in Figure 1, right. The bottom part of the figure shows the background events when the energy window is shifted to the neighboring value, (545 ± 2) keV. Taking into account the efficiency calculated for the 540 keV and 591 keV γs in cascade (8.0 × 10 −4 with GEANT4 [51]), the eight events detected in coincidence correspond to a half-life of T 1/2 = 6.8 +3.7 −1.8 × 10 20 year for the 2ν2β decay of 100 Mo → 100 Ru(0 + 1 ). This value is in agreement with the half-life derived from the one-dimensional spectrum (6.9 +1.2 −1.1 × 10 20 year). However, it has a much larger statistical uncertainty because of the small number of measurements (only eight events).
The data collected deep underground at the LNGS by the ARMONIA experiment allowed the observation of the 2ν2β decay of 100 Mo to the 0 + 1 excited level of 100 Ru (E exc = 1130.3 keV). The half-life values derived from the two-dimensional experimental spectrum of the coincidence events and from the one-dimensional spectrum are in perfect agreement. This observation does not confirm the negative result [47]; on the other hand, the measured half-life values are in agreement with the results of previous experiments [38,[41][42][43]46].

Search for Double Beta Decay in 116 Cd with the AURORA Experiment
The 116 Cd isotope is one of the best candidates to search for the 0ν2β occurrence owing to the high Q-value of Q 2β = 2813.49 (13) keV [34], the relatively large isotopic abundance of δ = 7.512(54)% [33], the possibility of enrichment by ultra-centrifugation in large amounts, and the promising estimations of the decay probability [52][53][54][55]. A new search for double-beta processes in 116 Cd was carried out by the AURORA experiment with two 116 CdWO 4 crystal scintillators (580 g and 582 g) enriched in 116 Cd to 82% [56,57]. Good optical and scintillation properties of the detectors were obtained due to the high purification of 116 Cd and W and to the advantage of the low-thermal-gradient Czochralski technique used to grow the crystals. The active source approach (high detection efficiency), the low levels of internal contamination in U, Th, and K, and the possibility of α/β pulse shape discrimination (PSD) were exploited to reach the best sensitivities to date in the search for several 2β decay modes of 116 Cd.
In the AURORA experiment [3], the two 116 CdWO 4 crystals were installed in the low-background DAMA/R&D setup at LNGS. The scintillators were fixed inside polytetrafluoroethylene containers filled with ultrapure liquid scintillator and viewed through low-radioactive quartz light-guides by two 3-inch low-radioactivity photomultiplier tubes (PMTs) (Hamamatsu R6233MOD, Hamamatsu, Japan). To reduce the external background, the passive shield was made of high-purity copper (10 cm), low-radioactivity lead (15 cm), cadmium (1.5 mm), and polyethylene/paraffin (4-10 cm). In order to remove environmental radon, the setup was enclosed inside a Plexiglas box continuously flushed by high-purity nitrogen gas. An event-by-event DAQ system based on a 1 GS/s 8-bit transient digitizer (Acqiris DC270, Plan-les-Ouates, Switzerland) recorded the amplitude, the arrival time, and the pulse shape of the events. The energy scale and resolution of the detector were checked periodically with 22 Na, 60 Co, 137 Cs, 133 Ba, and 228 Th sources. The energy resolution of the 116 CdWO 4 detector for 2615 keV quanta of 208 Tl was an FWHM of ≈ 6%.
The pulse profiles of the events were analyzed by using the optimal filter method [58,59] to discriminate γ(β) from α events. Thus, the PSD was applied to reduce the background and to estimate, by means of a time-amplitude analysis [60], the 228 Th contamination of the 116 CdWO 4 crystals. In order to reject the fast decay chain, 212 Bi → 212 Po, from the 232 Th family, a front-edge analysis was also performed. The 116 CdWO 4 crystal scintillators are highly radiopure, with 0.020(1) mBq/kg of 228 Th, <0.006 mBq/kg of 226 Ra, and 0.22(9) mBq/kg of 40 K, and the total U/Th α activity is 2.14(2) mBq/kg.
The energy spectrum of γ(β) events from the data, collected over 26831 h with the 116 CdWO 4 detectors, is shown in Figure 2, left. It was fitted in the (660-3300) keV energy region by the model built from the 2ν2β decay of 116 Cd; the internal contamination by 40 K, 232 Th, and 238 U; and the contribution from external γs. The model functions were simulated by the Monte Carlo code with the EGS4 package [50], and the initial kinematics of the particles emitted in the decays were given by the DECAY0 event generator [61]. The fit results in T 1/2 = 2.63 +0.11 −0.12 × 10 19 year for the half-life of 116 Cd relative to the 2ν2β decay to the ground state of 116 Sn; this result gives the highest accuracy to date for the half-life measurement of the 2ν2β decay of 116 Cd (with a signal-to-background ratio of 2.6 in the (1.1-2.8) MeV energy interval). To derive a limit on the 116 Cd 0ν2β decay, we also included in the analysis the data from the previous stage of the experiment with a similar background rate in the region of interest (ROI): ≈0.1 counts/keV/kg/year. In the (2.5-3.2) MeV energy interval, the measured energy spectrum was approximated by the background model built from the distributions of the 0ν2β (effect searched for) and 2ν2β decays of 116 Cd, the internal contamination of the crystals by 228 Th, and the contribution from external γs (mainly from the thorium contamination in the surrounding materials). The energy resolution at the Q 2β was extrapolated from calibrations with standard γ sources and is equal to an FWHM of ≈170 keV; for details, see Reference [57]. The fit gives an area of the expected peak of S = (−4.5 ± 14.2) counts, which means there is no evidence of the effect. In accordance with Reference [62], 19.1 counts can be excluded at 90% C.L., which leads to a new limit on the 0ν2β decay of 116 Cd to the ground state of 116 Sn: T 1/2 > 2.2 × 10 23 year. The half-life limit corresponds to the effective Majorana neutrino mass limit m ν < (1.0-1.7) eV, obtained by using the recent nuclear matrix elements reported in References [52][53][54][55], the phase space factor from Reference [63], and the value of the axial-vector coupling constant g A = 1.27. New improved limits on other 2β processes in 116 Cd (decays with Majoron emission, transitions to excited levels of 116 Sn) were set at a level of T 1/2 > (3.6-6.3) × 10 22 year.

Search for Double Beta Decay in 106 Cd with the DAMA/CRYS Setup
The experimental sensitivities for the search for double beta-plus processes (double electron capture 2ε, electron capture with positron emission εβ + , and emission of two positrons 2β + ) are substantially more modest with respect to 2β − processes, and only indications exist for the allowed 2ν2ε mode in 130 Ba [64,65] and 78 Kr [66,67] with the half-lives between 10 20 and 10 22 year.
One should note that a strong motivation to search for neutrinoless 2ε and εβ + decays is related to the possibility of refining the mechanism of the 0ν2β − decay: either it appears because of the neutrino Majorana mass or because of the contribution of right-handed admixtures in weak interactions [68].
The 106 Cd isotope is a very interesting nucleus in which to search for double beta-plus processes because of its high-energy release during decay, Q 2β = 2775.39(10) keV [34], and a relatively high natural isotopic abundance of δ = 1.245(22)% [33]. Moreover, it is also favored for possible resonant 0ν2ε transitions to excited levels of 106 Pd [69,70]. Thus, 106 Cd is one of the most investigated nuclei [69].
A new experiment to search for double beta decay in 106 Cd is being conducted in the DAMA/CRYS setup at LNGS using a 106 CdWO 4 crystal scintillator (215 g) that is enriched in 106 Cd to 66%. This is the third stage of DAMA experimentation with this crystal scintillator. In the first stage, in the low-background DAMA/R&D setup, the 106 CdWO 4 crystal was fixed inside a cavity filled with high-purity silicon oil and viewed by two low-radioactivity PMTs through ∼20 cm long light-guides. A sensitivity of T 1/2 ∼ (10 20 -10 21 ) year was reached for different channels of the double beta decay of 106 Cd [69]. In the second stage of the experiment, the 106 CdWO 4 crystal was viewed by a low-radioactivity PMT through a (archaeological) lead tungstate ( arch PbWO 4 ) crystal light-guide. It was installed in the central well of the ultralow-background GeMulti setup in the STELLA facility at LNGS. Limits on the 2ε, εβ + , and 2β + processes in 106 Cd were slightly improved [71] in comparison with the first stage [69].
The presently running experiment is being realized to increase the detection efficiencies of the coincidence events; thus, the 106 CdWO 4 was installed in coincidence with two large-volume low-background CdWO 4 crystal scintillators in close geometry. A scheme of the setup is given in Figure 3. The 106 CdWO 4 crystal scintillator is in a vertical position, as viewed through a arch PbWO 4 crystal light-guide by a low-radioactivity PMT (Hamamatsu R6233MOD). The arch PbWO 4 was developed from highly purified [72] archaeological lead [73]. The 106 CdWO 4 is almost entirely enclosed by two shaped CdWO 4 crystal scintillators, which are coupled to two low-radioactivity EMI9265-B53/FL PMTs through light-guides made by high-purity quartz and polystyrene. A copper structure maintains the detectors in a fixed position and also acts as a shield; the system was installed in the low-background DAMA/CRYS setup, which consists of a passive shield made of high-purity copper (11 cm), lead (10 cm), cadmium (2 mm), and polyethylene (10 cm). Moreover, to protect the detectors from environmental air, the setup is sealed and continuously flushed by high-purity nitrogen gas. The amplitude, the arrival time, and the pulse shape of the events are recorded by an event-by-event data acquisition system equipped with a 100 MSamples/s, 14-bit transient digitizer (DT5724 by CAEN, Viareggio, Italy) over a time window of 60 µs The β decay of 113 Cd and 113m Cd, which is not of interest for this measurement, dominate the low-energy part of the 106 CdWO 4 spectrum; thus, to considerably reduce the stored data, the scintillation events of 106 CdWO 4 with an energy ≤ 500 keV are recorded by the DAQ only if there is a coincidence signal in at least one of the two CdWO 4 crystal scintillators.
The measurements started in May 2016 and are still in progress. The 106 CdWO 4 and two large CdWO 4 scintillators are calibrated with 22 Na, 60 Co, 133 Ba, 137 Cs, and 228 Th γ sources. To discriminate γ(β) events from those induced by α particles, the difference in the pulse shapes in the CdWO 4 scintillators can be used. A preliminary data set was investigated in order to evaluate the PSD capability of the detectors in the present configuration by using various pulse shape analyses. Presently, the separation of the α and γ populations is worse than that obtained in the first stage of the experiment [69]; further analyses are in progress.
A preliminary time-amplitude analysis was performed on the data collected over 6935 h; in this way [60,74], by studying the arrival time and the energy of each event, it is possible to tag the fast α decay chain in the 232 Th family: 224 Ra (Q α = 5.79 MeV, T 1/2 = 3.66 d) → 220 Rn (Q α = 6.41 MeV, T 1/2 = 55.6 s) → 216 Po (Q α = 6.91 MeV, T 1/2 = 0.145 s) → 212 Pb. To select α events in the decay chain, the quenching of the scintillation output in the CdWO 4 scintillator was considered (the so-called α/β ratio, i.e., the ratio between the α peak position in the γ-calibrated scale of a detector and the energy of the alpha particles). From this preliminary analysis, the contamination of 228 Th in the 106 CdWO 4 crystal was estimated to be 5(1) µBq/kg.
Considering that, for some decay modes, the detection efficiencies (evaluated by Monte Carlo simulations) for coincidence events in the region of interest are 4-5 times larger with respect to the previous stage of the experiment, one can expect an improved experimental sensitivity to be obtained for the half-lives of some decay modes of 106 Cd to be in the range of (10 20 -10 22 ) year; this will allow us to explore the two-neutrino β + decay mode in the range of some theoretical predictions.
In this new measurement, a sample of high-purity Nd 2 O 3 (total mass of 2.381 kg), compressed into 20 cylindrical tablets ((56 ± 1) mm in diameter with a (16 ± 0.5) mm thickness), was installed in the GeMulti ultralow-background HPGe gamma-spectrometer (see Section 2). The energy scale and resolution of the HPGe detectors were measured at the beginning of the experiment with γ-sources. Then, the four spectra were equalized to the same energy scale by using background gamma peaks. As a result, the gamma peak positions in the cumulative spectrum deviate by less than 0.2 keV from the table values.
The radioactive contamination of the Nd 2 O 3 sample before and after the applied purification process was measured as reported in [4]. In particular, the Nd 2 O 3 sample was contaminated by 138 La and 176 Lu. The two-dimensional energy spectrum of coincidences between two detectors (events with multiplicity 2), accumulated over 16375 h with the Nd 2 O 3 sample, was analyzed. The 2β decay of 150 Nd to the first 0 + 1 excited level of 150 Sm is followed by the emission of γs in cascade with energies of 334.0 keV and 406.5 keV, respectively. By fixing the energy of the events in one of the detectors to the energy of the γ expected to be emitted in a cascade after the 2β decay of 150 Nd to the first 0 + 1 excited level of 150 Sm, a signal with energy corresponding to the other γs in cascade is expected. Fixing the energy of one of the detectors to the expected energy with the energy window ±1.4 × FWHM, the coincidence signals at the supplemental energy (406.5 or 334.0 keV, respectively) were observed (see Figure 4).
The area of each peak was estimated and, taking into account the detection efficiency, the half-life of the 2β decay 150 Nd → 150 Sm (0 + 1 , 740.5 keV) was preliminarily determined as T 1/2 = 4.7 +4.1 −1.9 × 10 19 year. This half-life is in agreement with the results of the previous experiments (see Reference [4] and references therein). The experiment is presently running to enhance the statistics in order to improve the half-life value accuracy.

Conclusions
In this report, the main results obtained with DAMA experimental setups in the search for rare processes and double beta decay are briefly summarized. Some further details are given about the main results of ARMONIA and AURORA experiments. Finally, a summary is provided of the status of (1) the new measurements of 106 Cd 2β decay using a 106 CdWO 4 detector and (2) the study of the 2ν2β decay of 150 Nd to the first 0 + 1 excited level of 150 Sm using a Nd 2 O 3 sample in the GeMulti HPGe γ setup. Data collection is in progress, and the study of further purification procedures for the samples of various compounds containing interesting isotopes for the purpose of establishing further improved sensitivities is ongoing.
Author Contributions: All the authors of this paper have been significantly contributing to the presented results working on the various aspects of the different phases of this experiment.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.