Search for double beta decay processes in 106Cd with the help of 106CdWO4 crystal scintillator

A search for the double beta processes in 106Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the help of a 106CdWO4 crystal scintillator (215 g) enriched in 106Cd up to 66%. After 6590 h of data taking, new improved half-life limits on the double beta processes in 106Cd were established at the level of 10^{19}-10^{21} yr; in particular, T_{1/2}(2\nu \epsilon \beta^+)>2.1 10^{20} yr, T_{1/2}(2\nu 2\beta^+)>4.3 10^{20} yr, and T_{1/2}(0\nu 2\epsilon)>1.0 10^{21} yr. The resonant neutrinoless double electron captures to the 2718 keV, 2741 keV and 2748 keV excited states of 106Pd are restricted to T_{1/2}(0\nu 2K)>4.3 10^{20} yr, T_{1/2}(0\nu KL1)>9.5 10^{20} yr and T_{1/2}(0\nu KL3)>4.3 10^{20} yr, respectively (all limits at 90% C.L.). A possible resonant enhancement of the 0\nu 2\epsilon processes is estimated in the framework of the QRPA approach. The radioactive contamination of the 106CdWO4 crystal scintillator is reported.


INTRODUCTION
The neutrinoless double beta decay (0ν2β) is a powerful tool to investigate the properties of the neutrino and of the weak interactions. The study of this nuclear decay, forbidden in the framework of the Standard Model, can allow us to determine an absolute scale of the neutrino mass and its hierarchy, to establish the nature of the neutrino (Majorana or Dirac particle), and to check the lepton number conservation, the possible contribution of right-handed admixture to the weak interaction, and the existence of Nambu-Goldstone bosons (majorons) [1].
Experimental efforts over the last seventy years have concentrated mainly on the decay modes with emission of two electrons. Allowed in the Standard Model, the two neutrino (2ν) 2β − decay mode was observed in ten isotopes with half-lives in the range of 10 18 − 10 24 yr. For the 0ν2β − decay mode half-life limits at the level of 10 23 − 10 25 yr were set for several nuclei (see reviews [2,3] and original studies [4,5,6,7,8,9]), while positive evidence for 76 Ge has been published in [10] and new experiments are in progress to further investigate this latter isotope as well.
The isotope 106 Cd (the decay scheme is presented in Fig. 1) is among the most widely studied 2β + nuclides thanks to the large energy release (Q 2β = 2775.39 (10) keV [32]) and to the comparatively high natural abundance (1.25 ± 0.06% [33]). It should be stressed that 106 Cd is a rather promising isotope also according to the theoretical predictions [31,34,35,36,37,38]. In particular, the calculated half-lives for the two neutrino mode of the 2ε and εβ + processes are at the level of T 1/2 ∼ 10 20 − 10 22 yr [35,39,40,41,42], reachable with the present low counting technique.
Furthermore, in the case of the 0ν capture of two electrons from the K shell (or L and K shells), the energy releases of 2727 keV (2K capture), 2747 keV (KL 1 ) and 2748 keV (KL 3 ) are close to the energies of a few excited levels of 106 Pd (with E exc = 2718 keV, 2741 keV and 2748 keV). Such a coincidence could give a resonant enhancement of the 0ν2ε capture [43,44,45,46,47,48]. Therefore, it is not surprising that the study of 106 Cd has a rather long history. The half-life limits at the level of 10 15 yr could be extracted from the old (1952) underground measurements of a Cd sample with photographic emulsions [49], while a search for positrons emitted in 2β + decay was performed in 1955 with a Wilson cloud chamber in a magnetic field and with 30 g of cadmium foil; this gave a limit of 10 16 yr [50]. Measurements of a 153 g Cd sample during 72 h with two NaI(Tl) scintillators working in coincidence have been carried out in [51]; the half-life limits at the level of ∼ 10 17 yr were determined for 2β + , εβ + and 2ε processes.
The subsequent studies can be divided into two groups: experiments using samples of cadmium with external detectors for the detection of the emitted particles (with enriched 106 Cd [22,53] and natural cadmium [39]), and experiments with detectors containing cadmium, namely semiconductor CdTe and CdZnTe detectors [54,55] and CdWO 4 crystal scintillators [7,56,57]. Previous experiments on the searches for the 2β processes in 106 Cd are summarized in Table 1. Data from the experiment, performed in the Solotvina Underground Laboratory (1000 m w.e.), with a 15 cm 3 116 CdWO 4 crystal scintillator (enriched in 116 Cd to 83%, with 0.16% of 106 Cd), were used to set the limits on the 2β decay of 106 Cd at the level of 10 17 − 10 19 yr [56]. In experiment [39], 331 g of Cd foil were measured at the Frejus Underground Laboratory (4800 m w.e.) with a 120 cm 3 HPGe detector during 1137 h; γ quanta from the annihilations of the positrons and from the de-excitation of the daughter 106 Pd nucleus were searched for, giving rise to half-life limits at the level of 10 18 − 10 19 yr. In [57], a large (1.046 kg) CdWO 4 scintillator was measured at the Gran Sasso National Laboratories (3600 m w.e.) over 6701 h. The determined limits on the half-life for the 2β + and εβ + decays were at the level of ∼ 10 19 yr for 0ν, and ∼ 10 17 yr for 2ν processes. A small (0.5 g) CdTe crystal was tested as a cryogenic bolometer in 1997 [54]; the achieved sensitivity was ∼ 10 16 yr for 0ν2β + decay. An experiment [53] was performed in 1999 at the Gran Sasso National Laboratories using an enriched 106 Cd (to 68%) cadmium sample (154 g) and two low background NaI(Tl) scintillators installed in the low background DAMA/R&D set-up during 4321 h; these measurements reached a sensitivity level of more than 10 20 yr for 2β + , εβ + and 2ε processes. A long-term (14183 h) experiment in the Solotvina Underground Laboratory with enriched 116 CdWO 4 scintillators (total mass of 330 g) was completed in 2003 [7]; in addition, results of dedicated measurements during 433 h with a 454 g not-enriched CdWO 4 crystal were also considered [58]. In general, the experimental sensitivity was improved by approximately one order of magnitude in comparison with the older measurements [56].
There are two running experiments to search for 2β decay of 106 Cd: COBRA and TGV-II. The T 1/2 limits in the range of 10 17 − 10 18 yr were set in the COBRA experiment [55] using CdTe and CdZnTe crystals. In the TGV-II experiment [22,23], 32 planar HPGe detectors are used. Cadmium foils enriched in 106 Cd to 75% are inserted between neighbouring detectors. The main goal of the TGV experiment is the search for the two neutrino double electron capture in 106 Cd. After 8687 h plus 12900 h (in two phases of the experiment) of data taking, the limits on double β decay of 106 Cd to the ground state and to the excited levels of 106 Pd are around 10 20 yr. Table 1: Experiments on the searches for the 2β decay of 106 Cd. The range of the T 1/2 limits corresponds to values given for the transitions to the ground state or to the excited levels of 106 Pd. More detailed information can be found in the original papers (see also [2]). COBRA and TGV experiments are still running. We would like to mention two important advantages of the experiments using detectors containing cadmium: a higher detection efficiency for the different channels of the 106 Cd double β decay, and a possibility to resolve the two neutrino and the neutrinoless modes of the decay.
Thanks to their good scintillation characteristics, their low level of intrinsic radioactivity, and their pulse-shape discrimination ability (which allows an effective reduction of the background), cadmium tungstate crystal scintillators were successfully applied to low background experiments in order to search for the double β decay of the cadmium and tungsten isotopes [7,16,57], and in order to investigate rare α [59] and β [58,60] decays.
The aim of the present work was the search for the 2β processes in 106 Cd with the help of a low background cadmium tungstate crystal scintillator enriched in 106 Cd ( 106 CdWO 4 ).

EXPERIMENT
The cadmium tungstate crystal (27 mm in diameter by 50 mm in length; mass 215 g), used in the experiment, was developed [61] from deeply purified cadmium [62] enriched in 106 Cd to 66%. The scintillator was fixed inside a cavity (⊘47 × 59 mm) in the central part of a polystyrene light-guide, 66 mm in diameter by 312 mm in length. The cavity was filled with high purity silicon oil. Two high purity quartz light-guides, 66 mm in diameter by 100 mm in length, were optically connected to the opposite sides of the polystyrene light-guide. To collect the scintillation light the assembly was viewed by two low radioactive EMI9265-B53/FL, 3" diameter photomultiplier tubes (PMT). The detector was installed deep underground in the low background DAMA/R&D set-up at the Gran Sasso National Laboratories of the INFN (Italy). It was surrounded by copper bricks and sealed in a low radioactive, air-tight copper box continuously flushed with high purity nitrogen gas to avoid the presence of residual environmental radon. The copper box was surrounded by a passive shield made of high purity copper, 10 cm of thickness, 15 cm of low radioactive lead, 1.5 mm of cadmium and 4 to 10 cm of polyethylene/paraffin to reduce the external background. The shield was contained inside a Plexiglas box, also continuously flushed with high purity nitrogen gas.
An event-by-event data acquisition system recorded the amplitude, the arrival time, and the pulse shape of the events by means of a 1 GS/s 8 bit DC270 Transient Digitizer by Acqiris (adjusted to a sampling frequency of 20 MS/s) over a time window of 100 µs.
The energy resolution of the detector was measured with 22 Na, 60 Co, 133 Ba, 137 Cs, 228 Th, and 241 Am γ sources in the beginning of the experiment. For instance, the energy resolution (full width at half maximum, FWHM) of the 106 CdWO 4 detector for the γ quanta of 137 Cs (662 keV) and of 228 Th (2615 keV) was 14.2(3)% and 8.4(2)%, respectively. Two additional calibration measurements were performed: one approximately in the middle, and the second one at the end of the experiment with the help of 22 Na, 60 Co, 137 Cs, and 228 Th γ sources to test the detector stability. In addition, the energy scale of the detector was checked by using the peaks due to 207 Bi contamination of the 106 CdWO 4 crystal scintillator (see Section 3.4). The energy scale during the experiment was reasonably stable with a deviation in the range of (1 − 2)%. The data of the calibration measurements were used to estimate the dependence of the energy resolution on the energy. Below 500 keV the energy resolution of the detector to γ quanta with energy E γ can be described by the function: FWHM γ = 11.2 × E γ , while above 500 keV the data are fitted by FWHM γ = −4900 + 21 × E γ , where FWHM γ and E γ are given in keV.
The low background measurements were carried out in three runs listed in Table 2. The energy interval of the data taking was chosen as 0.05 − 4 MeV in Run 1 to investigate the background of the detector at low energy. Taking into account the rather high activity of β active 113 Cd m (see the next Section), the data acquisition was slightly modified in order to avoid the recording of the pulse shapes of all events with an energy lower than 0.4 MeV (Run 2); the upper energy threshold was ≈ 1.8 MeV. In a third run, after some improvement in the data acquisition system, the energy threshold was increased to ≈ 0.57 MeV and the upper energy threshold was set to 4 MeV (Run 3). The data accumulated in Run 2 were used to estimate the activity of 228 Th in the 106 CdWO 4 crystal by a time-amplitude analysis (see Section 3.1). The first 1320 h of data taking (Run 1 + part of Run 3) were already analyzed and presented in [63]. Table 2: The low background measurements with the 106 CdWO 4 crystal scintillator. Times of measurements (t), energy intervals of data taking (∆E), and background counting rates (BG) in different energy intervals are specified. Run

DATA ANALYSIS
The energy spectrum accumulated with the 106 CdWO 4 detector in Runs 1 and 3 over 6590 h is presented in Fig. 2. The counting rate ≈ 24 counts/s below the energy ≈ 0.65 MeV is mainly due to the β decay of 113 Cd m with activity 116(4) Bq/kg. Contamination of the enriched 106 Cd by the β active 113 Cd m has been found in the low background TGV experiment [64], where β particles and X rays from thin foils of the enriched 106 Cd were measured by planar Ge detectors; part of this material was used to produce the 106 CdWO 4 crystal.
Contributions to the background above the energy ≈ 0.6 MeV were analyzed by means of the time-amplitude and of the pulse-shape discrimination techniques, as well as by the fit of the data with Monte Carlo simulated models of the background. ratio of an α peak position in the γ scale of a detector to the energy of the alpha particles. The dependence of the α/β ratio on the energy of the α particles measured for 116 CdWO 4 scintillator [59]: α/β = 0.083(9) + 0.0168(13) × E α (where E α is in MeV), was used to estimate the positions of 224 Ra, 220 Rn, and 216 Po α peaks in the data accumulated with the 106 CdWO 4 detector. As a first step, all the events within an energy interval 0.6 − 1.8 MeV were used as triggers, while for the second events a time interval 0.026 − 1.45 s and the same energy window were required. Taking into account the efficiency of the events selection in this time interval (88.2% of 216 Po decays), the activity of 228 Th in the 106 CdWO 4 crystal was calculated to be 0.042(4) mBq/kg. As a next step, all the selected pairs ( 220 Rn -216 Po) were used as triggers in order to find the events of the decay of the mother α active 224 Ra. The positions of the three α peaks, selected by the time-amplitude analysis in the γ scale of the detector, were used to obtain the following dependence of the α/β ratio on the energy of the α particles, E α , in the range 5.8 − 6.9 MeV: α/β = 0.11 (2)

Time-amplitude analysis of 228 Th activity
The dependence is in agreement with the data obtained for the 116 CdWO 4 scintillation detector in [59].

Pulse-shape discrimination
As demonstrated in [68], the difference in pulse shapes in the CdWO 4 scintillator can be used to discriminate γ(β) events from those induced by α particles. The optimal filter method proposed by E. Gatti and F. De Martini in 1962 [69] was applied for this purpose. For each signal f (t), the numerical characteristic of its shape (shape indicator, SI) was defined as: . There the sum is over the time channels k, starting from the origin of signal and averaging up to 50 µs, and f (t k ) is the digitized amplitude (at the time t k ) of a given signal. The weight function P (t) was defined as: where f α (t) and f γ (t) are the reference pulse shapes for α particles and γ quanta measured in [70]. By using this approach, α events were clearly separated from γ(β) events as shown in Fig. 4 where the scatter plot of the shape indicator versus energy is depicted for the data of the low background measurements with the 106 CdWO 4 detector. The distribution of the shape indicators for events with energies in the range 0.7 −1.4 MeV (shown in Inset of Fig. 4) justifies reasonable pulse-shape discrimination between α particles and γ quanta (β particles), as well as a possibility to reject randomly overlapped pulses (mainly caused by the β decay of 113 Cd m ).
The energy spectrum of the α events selected with the help of the pulse-shape discrimination is shown in Fig. 5. As demonstrated in [59], the energy resolution for the α particles is worse than that for the γ quanta due to the dependence of the α/β ratio on the direction of the  Table 3. The total α activity of U/Th in the 106 CdWO 4 crystal is 2.1(2) mBq/kg. The pulse-shape analysis also allows us to distinguish the main part of the 212 Bi→ 212 Po→ 208 Pb events from the trace contamination of the crystal by 228 Th (see Fig. 4).

Identification of Bi-Po events
The  [59]). The energy spectrum of the selected 212 Bi -212 Po events and the time distribution of 212 Po decay are presented in Fig. 6. The approach gives the activity of 228 Th as 0.051(4) mBq/kg, in a reasonable agreement with the result of the time-amplitude analysis.
All the selected Bi-Po events were removed from the γ(β) spectrum of the 106 CdWO 4 detector.
3.4 Simulation of the γ(β) background, radioactive contamination of 106 CdWO 4 scintillator To reproduce the background of the 106 CdWO 4 detector, we consider the contribution of the primordial radioactive isotopes 40 K and 238 U/ 232 Th with their daughters, anthropogenic radionuclides 90 Sr-90 Y and 137 Cs, and cosmogenic 106 Ru and 110m Ag. Anthropogenic 90 Sr and 137 Cs are the most widespread radionuclides, in particular after the Chernobyl accident. Contamination of cadmium tungstate by 106 Ru and 110m Ag was estimated in [72], while presence of 110m Ag in 116 CdWO 4 crystal scintillators was observed in [73]. The radioactive contamination of the set-up (in particular the PMTs and the copper box) can contribute to the background, too. The energy distributions of the possible background components were simulated with the help of the EGS4 [74] and GEANT4 [75] codes. The initial kinematics of the particles emitted in the nuclear decays was given by the event generator DECAY0 [76]. The background energy spectrum of the γ and β events, selected by means of the pulseshape, of the front edge and of the double pulse analyses, was fitted by a model built from the simulated distributions. The activities of the U/Th daughters were bounded taking into account the results of the time-amplitude and of the pulse-shape analyses. The activities of the 40 K, 232 Th and 238 U in the PMTs were taken from [77]. The radioactive contaminations of the copper box have been assumed to be equal to those reported in [78]. In addition, we have added a model of the overlapped 113 Cd m β decays, which contribute to the background in the energy region up to ≈ 1 MeV.
Two clear peculiarities in the spectrum of the CdWO 4 detector at (1064 ± 3) keV and at (1631 ± 5) keV cannot be explained by the contribution from the external γ quanta. Indeed, no similar peaks were observed in the low background measurements with radiopure ZnWO 4 crystal scintillators [79] performed before the present experiment in the same experimental conditions.
To explain the peculiarities, we suppose a pollution of the crystal by 207 Bi (T 1/2 = 31.55 yr, Q EC = 2398 keV [67]). The presence of 207 Bi could be caused by the contamination of the facilities at the Nikolaev Institute of Inorganic Chemistry (Novosibirsk, Russia) where the 106 CdWO 4 crystal was grown. A large amount of BGO crystal scintillators is in production in that laboratory. BGO crystal scintillators are typically contaminated by 207 Bi at the level of 0.01 − 10 Bq/kg [80,81,82,83]. Moreover, we cannot also exclude the possibility of a 106 CdWO 4 crystal surface contamination in the laboratory of the Institute for Nuclear Research (Kyiv, Ukraine) where the scintillator was diffused and preliminary tested [61] with several gamma sources, including an open 207 Bi source. Therefore, two distributions of 207 Bi (uniformly distributed in the crystal volume and deposited on its surface) were also simulated and added to the background model.
A fit of the spectrum of γ(β) events in the energy region 0.66 − 4.0 MeV by the model described above, and by the main components of the background are shown in Fig. 7. The fit (χ 2 /n.d.f. = 111/108 = 1.03, where n.d.f. is number of degrees of freedom) confirmed more likely a surface contamination of the crystal scintillator by 207 Bi at level of 3 mBq (0.06 mBq/cm 2 ). We cannot distinguish the part of the activity due to bulk contamination and we give only a limit on the internal contamination of the crystal by 207 Bi as ≤ 0.7 mBq/kg.  There are no other clear peculiarities in the spectrum which could be ascribed to the internal trace radioactive contamination. Therefore, we just set limits on the activities of 40 K, 90 Sr-90 Y, cosmogenic 106 Ru and 110m Ag. A summary of radioactive contamination of the 106 CdWO 4 crystal scintillator is given in Table 3. We hope to clarify further the radioactive contamination of the scintillator at a next stage of the experiment by running the 106 CdWO 4 crystal scintillator in coincidence/anti-coincidence with an ultra-low background HPGe γ detector.

RESULTS AND DISCUSSION
There are no peculiarities in the data accumulated with the 106 CdWO 4 detector which could be ascribed to the double β decay of 106 Cd. Therefore only lower half-life limits can be set by using the formula: where N is the number of 106 Cd nuclei in the 106 CdWO 4 crystal (2.42 × 10 23 ), η is the detection efficiency, t is the time of measurements, and lim S is the number of events of the effect searched for, which can be excluded at a given confidence level (C.L.; all the limits on the double beta processes in 106 Cd are given at 90% C.L. in the present study).
The response functions of the 106 CdWO 4 detector to the 2β processes in 106 Cd were simulated with the help of the EGS4 [74] and the DECAY0 [76] packages (some examples of the simulated spectra are presented in Fig. 8). Energy (keV) Counts / keV

Double beta processes in 106 Cd with positron(s) emission
To estimate the value of lim S for the 2νεβ + decay of 106 Cd to the ground state of 106 Pd, the energy spectrum of the γ and β events accumulated over 6590 h with the 106 CdWO 4 detector was fitted by the model built from the components of the background (see Section 3.4) and the effect searched for. The activities of U/Th daughters in the crystals were constrained in the fit taking into account the results of the time-amplitude and pulse-shape analyses. The initial values of the 40 K, 232 Th and 238 U activities inside the PMTs were taken from [77], where the radioactive contaminations of PMTs of the same model were measured. The radioactive contaminations of the copper were constrained taking into account the data of the measurements [84] where copper of a similar quality was used. The best fit (achieved in the energy interval 780 − 2800 keV with χ 2 /n.d.f. = 93/81 = 1.15) gives an area of the 2νεβ + distribution in the interval of the fit: (26 ± 230) counts, thus with no evidence for the effect. In accordance with the Feldman-Cousins procedure [85], this corresponds to lim S = 403 counts at 90% C.L. Taking into account the detection efficiency within the fit window given by the Monte Carlo simulation (η = 0.700) and the 98% efficiency of the pulse-shape discrimination to select γ(β) events, we get the following limit on the decay: The excluded energy distribution expected for the two neutrino εβ + decay of 106 Cd is shown in Fig. 9.  One can prove this result by using the so called "one sigma" approach when a value of lim S can be estimated as the square root of the counts in the energy interval of interest. There are 5462 events in the energy interval 1140 − 2220 keV where the detection efficiency for the 2νεβ + decay is 36%. The method gives a limit T 2νεβ + 1/2 ≥ 6.0 × 10 20 yr at 68% C.L., similar to the result acquired by fitting the experimental data with the help of the Monte Carlo simulated models.
The sensitivity to the neutrinoless channel of the εβ + decay is better thanks to the shift of the energy distribution to higher energies. Moreover, there are clear peaks in the spectrum of the 0νεβ + process in the energy region 1.6 − 2.9 MeV, which make the effect much more distinguishable (see Fig. 9). A fit of the data in the energy interval 2000−3000 keV (χ 2 /n.d.f. = 23/25 = 0.92) gives an area of the effect (17 ± 13) events (lim S = 38 events, η = 0.675), which corresponds to the following limit on the 0νεβ + decay of 106 Cd to the ground state of 106 Pd: The "one sigma" approach gives for this decay the limit (there are 187 events in the energy interval 2140 − 2960 keV, where the detection efficiency for the 0νεβ + decay is 62%): T 0νεβ + 1/2 ≥ 5.6 × 10 21 yr at 68% C.L., proving the result obtained by fitting the experimental data.
A fit of the data in the energy interval 1200 − 3000 keV (χ 2 /n.d.f. = 71/65 = 1.09) gives S = (92 ± 52) events (lim S = 177 events, η = 0.616) of the 2ν2β + decay of 106 Cd to the ground level of 106 Pd. Therefore, we set the following limit: It should be stressed that the mass difference between 106 Cd and 106 Pd atoms also allows transitions to the excited levels of 106 Pd. Thus, we have given limits on the 2β + decay of 106 Cd to the first excited level of 106 Pd (2 + , 512 keV), and on the electron capture with positron emission to a few lowest excited levels of 106 Pd with the spin-parity 0 + and 2 + . The results are presented in Table 4.

Double electron capture in 106 Cd
In the case of 2ν double electron capture in 106 Cd from the K or/and L shells the total energy release in the 106 CdWO 4 detector is in the range from 2E L3 = 6.3 keV to 2E K = 48.8 keV (where E K and E L are the binding energies of the electrons on the K and L shells of the palladium atom, respectively). Detection of such an energy deposit requires a low enough energy threshold and low background conditions. In our measurements the energy threshold for the acquisition was set too high (because of the background due to the β decay of 113 Cd m ) to search for the two neutrino mode of double electron capture to the ground state and to the first excited level of 106 Pd.
In the case of the neutrinoless double electron capture, different particles can be emitted: X rays and Auger electrons from de-excitations in atomic shells, γ quanta and/or conversion electrons from de-excitation of daughter nucleus. We suppose here that only one γ quantum is emitted in the nuclear de-excitation process. It should be stressed that the electron captures from different shells (2K, KL, 2L and other modes) cannot be energetically resolved by our detector. The fit of the measured spectrum in the energy interval 1800 − 3200 keV (χ 2 /n.d.f. = 37/41 = 0.90, S = 7±10, lim S = 23, η = 0.194) gives the following limit on the 0ν2ε transition of 106 Cd to the ground state of 106 Pd: T 0ν2ε 1/2 (g.s. → g.s.) ≥ 1.0 × 10 21 yr at 90% C.L.
The limits on the double electron capture in 106 Cd to the lowest excited levels of 106 Pd were obtained by a fit of the data in different energy intervals (see Table 4).

Resonant neutrinoless double electron capture in 106 Cd
A resonant neutrinoless double electron capture in 106 Cd is possible on three excited levels of 106 Pd with energies 2718 keV, 2741 keV and 2748 keV.
The half-life of the 106 Cd resonant 2ε process was estimated [86] by using the general formalism of [87] and by calculating the associated nuclear matrix element in a realistic single-particle space with a microscopic nucleon-nucleon interaction. We have used a higher-RPA (randomphase approximation) framework called the multiple-commutator model (MCM) [88,89]. Using the UCOM short-range correlations [90], the half-life for the 0ν double electron capture in 106 Cd to the 2718 keV level of 106 Pd (assuming its spin-parity is 0 + ) can be written as: where x = |Q 2β − E|, and m ν (the effective Majorana neutrino mass) are in eV units. Here Q 2β is the difference in atomic masses between 106 Cd and 106 Pd, and E contains the nuclear excitation energy and the hole energies in the atomic s orbitals. The dependence of the half-life on x is plotted in Fig. 10 for several values of m ν . Use of the the recently remeasured (by the Penning-trap mass spectrometry [32]) value of Q 2β leads to a value x = 8390 eV for the degeneracy parameter, and thus to the 2ε half-life estimate: T 1/2 = (2.1 − 5.7) × 10 30 yr for m ν = 1 eV. We have estimated limits on the resonant 0ν2K and 0νKL processes in 106 Cd by using the data from our experiment. For instance, the fit of the energy spectrum of the γ and β events measured by the 106 CdWO 4 detector over 6590 h in the energy region 1280 − 3000 keV (η = 0.315) gives 35 ± 34 events for the 0ν double electron captures from two K shells to the excited level at 2718 keV. We should take lim S = 91 events, which leads to the following limit on the possible resonant process: However, one can expect that the 0νKL process is strongly suppressed due to the large spin (4 + ) of the level at 2741 keV. Finally, for the 0ν double electron capture of K and L 3 electrons to the 2, 3 − level at 2748 keV we have obtained the following limit (S = 35 ± 21, lim S = 69, η = 0.238): Despite the fact that the limits are far away from the theoretical predictions, they are higher than the existing limits and are at the level of the best restrictions on resonant processes reported for different isotopes. The limit for the 0ν double electron capture to the level at 2748 keV is obtained for the first time.
All the half-life limits on 2β decay of 106 Cd obtained in the present work are summarized in Table 4 where results of the most sensitive previous studies are given for comparison.
Although the obtained bounds are well below the existing theoretical predictions [31,34,35,36,37,38], most of the limits are about one order of magnitude higher than those previously established. Moreover, some channels of 106 Cd double β decay were investigated for the first time. It should be stressed that only two nuclides ( 78 Kr [21] and 130 Ba [28]) among six potentially 2β + active isotopes [2] were investigated at a comparable level of sensitivity T 1/2 ∼10 21 yr. A new phase of the experiment with the 106 CdWO 4 scintillation detector placed in the ultra-low background GeMulti set-up (four HPGe detectors of 225 cm 3 volume each, located at the Gran Sasso National Laboratories) is in preparation. We are going to record pulseprofiles and arrival time of the events from the 106 CdWO 4 scintillator both in coincidence and anti-coincidence modes. To suppress the background due to the radioactive contamination of the PMT, the development of a lead tungstate (PbWO 4 ) active light-guide from ultra-pure archaeological lead [91,62] has been completed. Our preliminary simulations show that such an experiment could investigate the 2ν mode of εβ + and of 2β + decays, and also 2ε transitions of 106 Cd to the excited states of 106 Pd, at a level of sensitivity near to the theoretical predictions: T 1/2 ∼ 10 20 − 10 22 yr [31,34,35,36,37,38].
Moreover, the development of a 106 CdWO 4 crystal scintillator depleted in the 113 Cd isotope by a factor 10 3 − 10 4 (to reduce the background caused by β decay of 113 Cd m ) is also possible [92]. Such a detector could be able to investigate two neutrino double electron capture, which is theoretically the most favorable process of 2β decay of 106 Cd.

CONCLUSIONS
A low background experiment using radiopure cadmium tungstate crystal scintillator (215 g) enriched in 106 Cd to 66% has been carried out at the underground Gran Sasso National Laboratories of the INFN. The background of the detector below 0.65 MeV is mainly due to the β active 113 Cd m (≈ 116 Bq/kg). We have found surface contamination of the crystal by 207 Bi at level of 3 mBq, which provides a considerable part of the background up to ≈ 2.5 MeV. The activities of U/Th in the scintillator are rather low: ≈ 0.04 mBq/kg of 228 Th and ≈ 0.01 mBq/kg of 226 Ra. The total α activity of U/Th is at level of ≈ 2 mBq/kg. A background counting rate of the detector in the vicinity of the 106 Cd double beta decay energy (2.7 − 2.9 MeV), after rejection of 212 Bi -212 Po events, is 0.4 counts/(yr×keV×kg).
After 6590 h of data taking, new improved limits on 2β decay of 106 Cd were set at level of 10 19 − 10 21 yr, in particular: T 2νεβ + A next stage of the experiment is in preparation. We are going to install a low background scintillation detector with the 106 CdWO 4 crystal into the GeMulti ultra-low background set-up with four 225 cm 3 HPGe detectors at the Gran Sasso National Laboratories. The sensitivity of the experiment, in particular to the two neutrino εβ + decay of 106 Cd, is expected to be enhanced thanks to the high energy resolution of the GeMulti detector and to the improvement of the background conditions in coincidence mode. In addition, we hope to reduce the surface contamination of the scintillator with 207 Bi, observed in the present study, by cleaning (removing) the crystal surface. We estimate the sensitivity of the experiment, in particular to the 2νεβ + decay of 106 Cd, to be at level of the theoretical predictions T 1/2 ∼ 10 20 − 10 22 yr.
Moreover, a further improvement of sensitivity can be reached by increasing the enrichment factor of 106 Cd, and by developing 106 CdWO 4 scintillators with lower level of radioactive contaminations, including depletion in 113 Cd. A 106 CdWO 4 scintillation detector with an activity of 113 Cd m reduced by a factor of 10 3 − 10 4 could be able to detect two neutrino double electron capture in 106 Cd, which is theoretically the most probable process.