Search for rare processes with DAMA experimental set-ups

Profiting of the favourable conditions offered by the Gran Sasso underground laboratory and of the several low-background DAMA set-ups, many and competitive results have been obtained for rare processes. Here the main results will be briefly resumed and some more details about the latest activities will be given. In particular, the searches on ββ decays of 106Cd and 116Cd and the perspectives of a complementary investigation on those Dark Matter (DM) candidates inducing just nuclear recoils, by exploiting the directionality approach with the anisotropic ZnWO4 scintillators, will be underlined.


Introduction
DAMA (DArk MAtter) is a pioneer project for the investigation of DM, but it is also very active in the search for many other rare processes and in the development of new highly radiopure crystal scintillators. Many important results or competitive limits have also been obtained in the investigation of various rare processes in many experiments performed at the Gran Sasso National Laboratory (LNGS) of the INFN in collaboration with researchers from INR-Kyiv and other institutions.
The important results obtained in the investigation of DM with the DAMA/NaI and DAMA/LIBRA set-ups are discussed in another article of this volume. Here the main results obtained in the searches for rare nuclear processes with all the DAMA set-ups 1 will be briefly summarized and some more details about the latest activities will be given: the searches for ββ decays in 106 Cd and 116 Cd and the perspectives for the investigation of the directionality approach with the ZnWO 4 detectors.

Brief review of the main results
Many important results have been obtained with the DAMA set-ups in experiments studying double beta decay of several candidate isotopes at LNGS. In particular, double beta decay processes of 28 candidate isotopes have been investigated: 40 Ca, 46 Ca, 48 Ca, 64 Os,190 Pt and 198 Pt. The sensitivities reached on the lifetime of the studied processes are competitive (between 10 20 and 10 24 yr), thanks to the radiopurity of the developed detectors and to the used experimental approaches. The obtained results have improved (often by several orders of magnitude) the limits on lifetime obtained by previous experiments and have allowed new observations of two-neutrino double beta decays of 100 Mo [1] and 116 Cd [2]. Moreover, in the study of decay modes with positron emission or double electron capture, we have obtained ones of the best experimental sensitivities of the field for all the candidate isotopes to these decay modes.
As regards rare α and β decays, we have obtained the first observation of the 151 Eu α decay with T 1/2 = 5 × 10 18 yr using a CaF 2 (Eu) crystal scintillator [3] and of 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 yr [4]. Rare β decays of 113 Cd and 48 Ca have been investigated with CdWO 4 [5] and CaF 2 (Eu) [6] crystal scintillators, respectively. Pairs of NaI(Tl) detectors of the DAMA/LIBRA set-up have been used to search for production of correlated e + e − pairs in the α decay of 241 Am [7]. We measured an excess of double coincidences events with energy around 511 keV in faced pairs of detectors that cannot be explained by known side reactions. Therefore, the relative activity for the Internal Pair Production (IPP) with respect to the α decay of 241 Am has been determined to be: (4.70 ± 0.63) × 10 −9 . This value is of the same order of magnitude as previous determinations and is independent of the livetime estimate. Solar axions have been searched for studying the conversion of axion to photon (inverse Primakoff effect) in NaI(Tl) crystals [8] and the resonant absorption of axions emitted in the Sun by 7 Li in a LiF crystal [9] and powders [10].
Delayed coincidences have been investigated to search for exotic particles as Q-balls [11] and SIMPs [12] using the DAMA/NaI detectors and DAEMONs using the specially developed NEMESIS set-up [13].
The electron stability has been investigated searching for electron "disappearance" (i.e. decay into invisible channels as e − → ν eνe ν e ) with the DAMA/NaI set-up [14] and with the DAMA/LXe set-up [15] and searching for the e − → ν e γ decay mode with the DAMA/LXe set-up [15,16].

Search for double beta decay in 106 Cd with the DAMA/CRYS set-up
Experimental sensitivities for the search for double beta plus processes (double electrons 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 [30,31] and 78 Kr [32,33] with the half-lives of the order 10 20 − 10 22 yr. At the same time a strong motivation to search for neutrinoless 2ε and εβ + decays are related with the possibility to refine the mechanism of the 0ν2β − decay: either it appears due to the Majorana mass of neutrino or due to the contribution of the right-handed admixtures in the weak interaction [34]. The 106 Cd isotope is one of the most suitable nuclei to search for the double beta plus processes having a high-energy release in the decay, Q 2β = 2775.39(10) keV [35], and relatively high natural isotopic abundance, δ = 1.245(22)% [36]. In addition the 106 Cd is also favored for the possible resonant 0ν2ε transitions to excited levels of 106 Pd [37,38]. The 106 Cd is, in fact, one of the most studied nuclei [37].
A new experiment to search for double beta decay in 106 Cd is running in the DAMA/CRYS set-up at LNGS using a 106 CdWO 4 crystal scintillator (215 g), enriched in 106 Cd to 66%. It is the third stage of the DAMA activity with this crystal scintillator. In the first stage the 106 CdWO 4 crystal was fixed inside a cavity filled with high purity silicon oil and viewed by two low radioactive photomultiplier tubes (PMT) throughout ∼ 20 cm long light-guides. After 6590 h of data taking in the low background DAMA/R&D set-up, a sensitivity at the level of T 1/2 ∼ 10 20 − 10 21 yr was reached for different channels of double beta decay of 106 Cd [37]. In the second stage, the 106 CdWO 4 crystal was viewed through a lead tungstate (PbWO 4 ) crystal light-guide by a low radioactive PMT and installed in the central well of the ultra-low background GeMulti set-up in the STELLA facility at LNGS. This set-up is equipped with four HPGe detectors (225 cm 3 each) and was used to search for coincidence events induced, e.g., by the 511 keV gamma(s) produced by the positron annihilations in the εβ + or 2β + processes. After 13085 h of data taking, limits on 2ε, εβ + and 2β + processes in 106 Cd were few times improved [39] in comparison with the first stage [37].
The new experiment, now running, was realized in order to increase the detection efficiencies of the coincidence events. For this reason the 106 CdWO 4 has been installed in coincidence with two large volume low background CdWO 4 crystal scintillators in close geometry. A scheme of the set-up is depicted in Fig. 1. The 106 CdWO 4 crystal scintillator is in vertical position, viewed through a PbWO 4 crystal light-guide by a 3 inches low-radioactive PMT (Hamamatsu R6233MOD). The PbWO 4 crystal ( 40 × 83 mm) was the one used for the previous stage of the experiment and was developed from deeply purified [40] archaeological lead [41]. The 106 CdWO 4 is almost entirely enclosed by two shaped CdWO 4 crystal scintillators. These two crystals are coupled to two low radioactive EMI9265-B53/FL PMTs (3 inches diameter) through light-guides made by high purity quartz and polystyrene (both are 66 mm in diameter and 100 mm in length). A copper structure keeps the detectors in a fixed position also acting as a shield for the scintillators. The detectors system is installed in the lowbackground DAMA/CRYS set-up. This set-up consists of a passive shield made of high purity copper (11 cm), lead (10 cm), cadmium (2 mm), and polyethylene (10 cm); it is sealed and continuously flushed by high purity nitrogen gas to prevent the detector to be in contact with the environmental air. In Fig. 2 some pictures of the 106 CdWO 4 set-up during the assembling are shown.
An event-by-event data acquisition system records the amplitude, the arrival time, and the pulse shape of the events by means of a 100 MSamples/s, 14 bit Transient Digitizer DT5724 by CAEN, over a time window of 60 µs. The low energy part of the 106 CdWO 4 spectrum is dominated by the β decay of 113 Cd and 113m Cd, not of interest in this measurement. For this reason, the scintillation events of the 106 CdWO 4 with energy below about 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. In this way the stored data are considerably reduced. For scintillation events in 106 CdWO 4 with energy above 500 keV the signals of the three detectors are always recorded whether or not a coincidence event is present. The difference in pulse shapes in the CdWO 4 scintillators can be used to discriminate γ(β) events from those induced by α particles. With a preliminary set of data the pulse shape discrimination (PSD) capability of the detectors in the present configuration has been evaluated by using different pulse shape analyses. The separation of the populations of α and γ is presently worse than the one obtained in the first stage of the experiment [37]; further analysis is in progress.
With the data collected over 6935 h a preliminary Time-Amplitude analysis has been performed. With this technique [42,43], 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 crystal scintillator, the so-called α/β ratio, defined as the ratio between the α peak position in the γ calibrated scale of a detector and the energy of the alpha particles, has been considered. From this preliminary analysis the contamination of 228 Th in 106 CdWO 4 crystal was estimated as: 5(1) µBq/kg.
Considering that for some decay modes the detection efficiencies for coincidence events in the region of interest, evaluated by Monte Carlo simulations, is 4-5 times larger with respect to the previous stage, we expect to improve the experimental sensitivity reaching, for some decay modes in 106 Cd, the half-life level of (10 20 -10 22 ) years. This will allow us to explore for the two neutrino β + decay mode the range of some theoretical predictions.

Search for double beta decay in 116 Cd with the AURORA experiment
The isotope 116 Cd is one of the best candidates for 0ν2β experiments thanks to the high Q-value Q 2β = 2813.49(13) keV [35], relatively large isotopic abundance δ = 7.512(54)% [36], possibility of enrichment by ultra-centrifugation in large amount and promising estimations of the decay probability [44][45][46][47]. A new search for double beta processes in 116 Cd has been carried out by the AURORA experiment, with two 116 CdWO 4 crystal scintillators (580 g and 582 g) enriched in 116 Cd to 82% [48]. Good optical and scintillation properties of the detectors were obtained thanks to the deep purification of 116 Cd and W and the advantage of the low-thermal-gradient Czochralski technique to grow the crystal. The active source approach (high detection efficiency), the low levels of internal contamination in U, Th and K and the possibility of α/β PSD have been exploited to reach the best up-to-date sensitivities in the search for several double beta decay modes of 116 Cd.
In the AURORA experiment, the two 116 CdWO 4 crystals were installed in the low background DAMA/R&D set-up at LNGS. The scintillators were fixed inside polytetrafluoroethylene containers filled with ultra-pure liquid scintillator and viewed, through low-radioactive quartz light-guides ( 7 × 40 cm), by two 3 inches low radioactive PMTs (Hamamatsu R6233MOD). The passive shield was made of high purity copper (10 cm), low radioactive lead (15 cm), cadmium (1.5 mm) and polyethylene/paraffin (4 to 10 cm) to reduce the external background. The whole set-up was contained inside a plexiglas box and continuously flushed by high purity nitrogen gas to remove environmental radon. An event-by-event DAQ system based on a 1 GS/s 8 bit transient digitizer (Acqiris DC270) 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 FWHM ≈ 5%.
The pulse profiles of the events were analyzed by using the optimal filter method [49,50] to discriminate γ(β) from α events. The PSD was applied to reduce background and to estimate, with the Time-Amplitude analysis [43], the 228 Th contamination of the 116 CdWO 4 crystals. The front edge analysis was also used to reject the fast chains of decays 212 Bi → 212 Po from the 232 Th family. The γ" or "ext. Th."). The peak of the 0ν2β decay of 116 Cd excluded at 90% C.L. is also shown.
The energy spectrum of γ(β) events selected from the data accumulated over 25037 h with the 116 CdWO 4 detectors is shown in Fig. 3. The spectrum was fitted in the energy interval 660 − 3300 keV by the model built from the 2ν2β of 116 Cd, the internal contamination by 40 K, 232 Th and 238 U, and the contribution from external γ quanta. The model functions were Monte Carlo simulated with the EGS4 package [51], the initial kinematics of the particles emitted in the decays was given by an event generator DECAY0 [52]. The fit gives the half-life of 116 Cd relatively to the 2ν2β decay to the ground state of 116 Sn as T 1/2 = [2.69 ± 0.02(stat.) ± 0.14(syst.)] × 10 19 yr. The main contribution to the systematic error comes from the ambiguity of the radioactive contamination of the 116 CdWO 4 crystals by 238 U, since the β spectrum of 234m Pa (daughter of 238 U) competes with the 2ν2β spectrum of 116 Cd. The obtained result gives the highest up-to-date accuracy for the half-life measurement of the 2ν2β decay of 116 Cd (with a signal to background ratio 2.6 in the 1.1 −2.8 MeV energy interval).
To estimate a limit on the 0ν2β decay of 116 Cd we also included in the analysis the data from the previous stage of the experiment with a similar background counting rate of ≈ 0.1 counts/keV/kg/yr in the region of interest (ROI). Furthermore, the background in the ROI was reduced to ≈ 0.07 counts/keV/kg/yr by selection of the following chain of decays: 212 Bi (Q α = 6207 keV) → 208 Tl (Q β = 4999 keV, T 1/2 = 3.053 min). The obtained energy spectrum was approximated in the energy interval 2.5 − 3.2 MeV by the background model constructed 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 γ quanta (mainly from the 228 Th contamination in the surrounding materials). The fit gives an area of the expected peak S = −3.2 ± 10.7 counts, that is no evidence of the effect. In accordance with ref. [53] 14.6 counts can be excluded at 90% confidence level (C.L.), that leads to the new limit on the 0ν2β decay of 116 Cd to the ground state of 116 Sn: T 1/2 > 2.4 × 10 23 yr. The half-life limit corresponds to the effective neutrino mass limit m ν < (1.1 − 1.6) eV, obtained by using the recent nuclear matrix elements reported in refs. [44][45][46][47], the phase space factor from ref. [54] 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 the level of T 1/2 > (0.09 − 6.3) × 10 22 yr.

Exploring the directionality approach with ZnWO 4 anisotropic detectors
In DM direct experiments, in order to point out the presence of a signal of Galactic origin, it is mandatory to pursue a signature for signal identification. The most important one is the model independent DM annual modulation that has been successfully exploited by the DAMA/NaI and DAMA/LIBRA experiments [55]. An independent evidence could be obtained in case of DM candidates inducing just nuclear recoils by pursuing the so-called directionality approach [56]. This strategy is based on the study of the correlation between the arrival direction of the DM particles able to induce nuclear recoils and the Earth motion in the Galactic rest frame. In fact, the solar system moves through the halo of DM and therefore a wind of DM particles apparently flows along a direction opposite to that of solar motion. For an earthly observer the average direction of DM particles changes during the sidereal day because of the rotation of the Earth. Since the directions of the induced nuclear recoils are expected to be strongly correlated with the impinging direction of the DM particles, in principle an experiment able to measure the nuclear track might be suitable to investigate the directionality.
One possibility is to use low pressure gas detector (such as Time Projection Chambers, TPC) where the range of recoiling nuclei is of the order of mm. However, a realistic experiment with low pressure TPC can be limited e.g. by the necessity of an extreme operational stability, of large detector size and of a great spatial resolution in order to reach a significant sensitivity. On the other hand, in solid detectors the range of recoiling nuclei is typically of the order of µm. The solution can be offered by anisotropic scintillation detectors [57,58], that does not require the detection and recognition of the track. In these detectors the response for heavy particles depends on the incoming direction of the heavy particles relatively to the crystal axes and the presence of DM induced nuclear recoils can be highlighted by a peculiar variation of the measured counting rate during the sidereal day [59].

Advantages of the ZnWO 4 anisotropic scintillator
Recently, measurements and R&D works have shown that the ZnWO 4 scintillators can offer suitable features for a DM experiment based on the directionality. In this crystal the light output and the scintillation decay time for heavy particles (p, α, nuclear recoils) depend on the direction of such particles with respect to the crystal axes while the response to γ/β radiation is isotropic. In Fig. 4 le f t the behaviour of the light output ratio for α and β (α/β ratio) is reported as a function of the energy and of the direction of the α beam in a ZnWO 4 crystal [60]. The response of the detector for  α particles measured along direction 1 is about 1.5 times larger than that measured along direction 2, and about 1.4 times larger than that measured along direction 3. On the contrary, the anisotropy of the light response of the ZnWO 4 scintillator disappears in case of electron excitation. The same behaviour has been reported also for the anthracene in Ref. [57,62]. Measurements with a neutron beam to study the anisotropy of the ZnWO 4 crystal for recoils at keV energy range are now under way with a neutron generator producing 14 MeV neutrons at ENEA-CASACCIA [63].
In addition to the anisotropy, the recently developed ZnWO 4 scintillators have also other important characteristics for a DM experiment: i) very good level of radiopurity [64]; ii) high light output that is to say energy threshold at level of few keV feasible [65]; iii) high stability of the running conditions; iv) sensitivity to both small and large mass DM candidates inducing nuclear recoils thanks to three target nuclei with very different masses; v) possibility to realize crystals with masses of some kg [66].
As regards the measured radioactive contamination in radiopure ZnWO 4 scintillators, it is: < 0.002 mBq/kg for 228 Th and 226 Ra (∼ 0.5 ppt for 232 Th and ∼ 0.2 ppt for 238 U, assuming the secular equilibrium of the 232 Th and 238 U chains), < 0.02 mBq/kg for 40 K; the total α activity is 0.18 mBq/kg [64]. Moreover, for ZnWO 4 the shape of the scintillation pulse depends on the type of irradiation [60]; this feature allows one to discriminate γ(β) events from those induced by α particles. This PSD capability is of general interest.
Another feature of this scintillator is the relatively high light output ≈ 13 − 20% of Na(Tl). It has been observed that the light output largely increases when the crystal scintillator working temperature is decreased [61] (see Fig. 4 right). A cryostat for low temperature measurement has been recently realized at LNGS for the purpose to determine the behaviour and the low energy threshold reachable for ZnWO 4 detectors when operated at low temperature.

The expected signal for a directionality experiment with anisotropic detectors
Taking into account the mean DM arrival directions during the sidereal day 2 , it is very convenient to consider a directionality experiment performed at the LNGS latitude: 42 • 27 N (see Fig. 5 le f t). In fact, in this case, at 21 h LST the DM particles come mainly from the top, while 12 h later they come from the North and parallel to the horizon line. Thus, the optimal performance for an anisotropic detector is obtained when arranging the crystal axis that corresponds to the largest light output in the vertical direction and the axis that gives the smallest light output towards the North. With this configuration the range of variability of the anisotropic detector response during a sidereal day is at maximum. As a consequence of time-varying detector response, the counting rate measured in a fixed low energy interval by an anisotropic scintillator is expected to vary during a sidereal day. As an example, Fig. 5 right shows the effect achievable in the [2][3] keV energy window with a ZnWO 4 detector when considering a DM candidate with spin independent interaction, mass 10 GeV and cross section on nucleon σ p = 5 × 10 −5 pb. We also assume isothermal halo model, Maxwellian velocity distribution, 0.3 GeV/cm 3 local density and the same form factor, scaling law, energy resolution and detector response to Zn, W and O recoils as that considered in ref. [59]. The absolute maximum rate is at day 152 and at 21 h LST when the DM flux is at maximum and the DM preferential arrival direction is near the zenith, that is near the crystal axis with the largest light output.

Conclusions
The main results obtained with DAMA experimental set-ups in the search for rare processes have been briefly resumed. Some further details have been given about the latest activities: the searches on ββ decays of 106 Cd and 116 Cd with enriched CdWO 4 scintillators and the feasibility study for a possible future investigation on DM with the directionality approach using anisotropic ZnWO 4 scintillators.