Search for 2\beta\ decays of 96Ru and 104Ru by ultra-low background HPGe gamma spectrometry at LNGS: final results

An experiment to search for double beta decay processes in 96Ru and 104Ru, which are accompanied by gamma rays, has been realized in the underground Gran Sasso National Laboratories of the I.N.F.N. (Italy). Ruthenium samples with masses of about (0.5-0.7) kg were measured with the help of ultra-low background high purity Ge gamma ray spectrometry. After 2162 h of data taking the samples were deeply purified to reduce the internal contamination of 40K. The last part of the data has been accumulated over 5479 h. New improved half life limits on 2\beta+/\epsilon \beta+/2\epsilon\ processes in 96Ru have been established on the level of 10^{20} yr, in particular for decays to the ground state of 96Mo: T1/2(2\nu 2\beta+)>1.4 10^{20} yr, T1/2(2\nu \epsilon\beta+)>8.0 10^{19} yr and T1/2(0\nu 2K)>1.0 10^{21} yr (all limits are at 90% C.L.). The resonant neutrinoless double electron captures to the 2700.2 keV and 2712.7 keV excited states of 96Mo are restricted as: T1/2(0\nu KL)>2.0 10^{20} yr and T1/2(0\nu 2L)>3.6 10^{20} yr, respectively. Various two neutrino and neutrinoless 2\beta\ half lives of 96Ru have been estimated in the framework of the QRPA approach. In addition, the T1/2 limit for 0\nu 2\beta- transitions of 104Ru to the first excited state of 104Pd has been set as>6.5 10^{20} yr.


Introduction
Double beta (2β) decay is a process of transformation of a nucleus (A, Z) either to (A, Z + 2) with simultaneous emission of two electrons (2β − decay) or to (A, Z − 2) through one of the following ways: emission of two positrons (2β + ), capture of electron and emission of positron (εβ + ) or double electron capture (2ε). The two neutrino (2ν) double β decay, in which two (anti)neutrinos are also emitted, is allowed in the Standard Model (SM); however, being a second order process in the weak interactions, it is characterized by very long half lives in the range of 10 18 − 10 24 yr [1]. There are 35 known nuclei candidates for 2β − and 34 candidates for 2β + /εβ + /2ε decays [2]. To-date, two neutrino 2β decays are observed for several 2β − decaying nuclei (see reviews [2,3] and recent original works [4,5]), while indications on double electron capture have been obtained for 130 Ba in geochemical experiments [6,7].
The neutrinoless (0ν) mode of the 2β decay is forbidden in the SM because it violates the lepton number by 2 units. It is, however, naturally expected in many SM extensions which describe the neutrino as a Majorana particle with non-zero mass. The neutrino oscillation experiments indicate that the neutrinos are massive. Nevertheless, since they are sensitive to the difference in ν masses, the absolute ν mass scale is unknown [8]. The 0ν2β decay is considered a powerful tool to check lepton number conservation, to determine the absolute ν masses and their hierarchy, to establish the nature of the neutrino (Majorana or Dirac particle), to find a possible contribution of right-handed admixtures to weak interaction and the existence of Nambu-Goldstone bosons (Majorons). A particular analysis of data on 76 Ge provided an evidence for 0ν2β decay [9]; several experiments with the aim to test it and to explore the inverted hierarchy of the Majorana neutrino mass region (m ν ∼ 0.1 − 0.05 eV) are now in progress or under development [1]. Studies of neutrinoless 2β − and 2β + /εβ + /2ε decays are mutually complementary, helping to distinguish contributions from the neutrino mass and righthanded admixture mechanisms [10]. 96 Ru is one of the only six isotopes where the decay with emission of two positrons is allowed [2] thanks to the high energy release: Q 2β = (2714.51 ± 0.13) keV [11]. It has also a quite big natural abundance: δ = 5.54% [12]. Moreover, in case of capture of two electrons from the K and L shells (the binding energies are E K = 20.0 keV, E L1 = 2.9 keV [13]) or both from the L shell, the decay energies (2691.61 ± 0.13) keV and (2708.71 ± 0.13) keV are close to the energy of the excited levels of 96 Mo (E exc = 2700.21 and 2712.68 keV [14]). Such a situation could give rise to a resonant enhancement of the neutrinoless KL and 2L capture to the corresponding level of the daughter nucleus as a result of the energy degeneracy [15] 2 .
Despite the high energy release and the high abundance, only one search for 2β + /εβ + processes in 96 Ru was performed in 1985, giving T 1/2 limits on the level of 10 16 yr [19]. The efforts were renewed only in 2009, when a Ru sample with a mass of 473 g was measured for 158 h with an HPGe detector (468 cm 3 ) in the underground conditions of the Gran Sasso National  Figure 1: Decay schemes of 96 Ru (a) and 104 Ru (b). Energies of the excited levels and emitted γ quanta are in keV. The relative intensities of γ quanta are given in parentheses [13,14,18].
Laboratories (Laboratori Nazionali del Gran Sasso, LNGS) of the I.N.F.N. (3600 m w.e.) [20] (an updated statistics of 2162 h was then reported in [21]). The achieved sensitivity for the 2β + /εβ + /2ε decays was 10 18 − 10 19 yr; for several modes of 2β decay of 96 Ru (and 104 Ru) T 1/2 limits were established for the first time. A search for 2β decays of Ru was also performed in the HADES underground laboratory (500 m w.e.) where a sample of Ru with mass of 149 g was measured during 2592 h; T 1/2 limits were obtained on the level of 10 19 yr [22]. Our previous measurements [20,21] showed that the used Ru sample was contaminated by 40 K at ≃ 3 Bq/kg, and better results are possible only with purified Ru. Here we report the final results of the search for 2β + /εβ + /2ε processes in 96 Ru and for 2β − decay in 104 Ru obtained with a purified sample of Ru (720 g) in measurements during 5479 h.

Purification of ruthenium and low background measurements
The ruthenium (with natural isotopic composition) of 99.99% grade produced by powder metallurgy was provided by Heraeus [23]. At the first stage [20,21], the Ru sample with total mass of 473 g was in form of pellets (50 tablets ⊘16 × 5 mm, density ≈ 8.7 g/cm 3 ). The analysis of the data showed a high level of 40 K contamination in the ruthenium (3.4 Bq/kg), and for further measurements the Ru sample with an increased total mass of 946 g was purified by an electron beam melting method.
The ruthenium was divided into five parts, each with a mass of almost 0.2 kg, which were slowly melted (to avoid intensive sprinkling) using an electron beam and kept in a liquid state under vacuum (0.01 -0.05 Pa) for ≃ 1.5 − 2 h. The purification occurs through the evaporation of the impurities from the melted ruthenium. More details about the purification process can be found in [24]. As a result, five Ru samples in form of oval disks (totally 719.5 g, density ≈ 10.0 g/cm 3 ) were obtained.
The purified ruthenium samples were measured over 5479 h in the GeMulti set-up (made of four HPGe detectors; ≃ 225 cm 3 each one) installed deep underground at the LNGS. The detectors are surrounded by a passive shield made of low radioactivity copper (≃ 5 cm thick) and low radioactivity lead (≃ 25 cm). The set-up was continuously flushed with high purity nitrogen to remove radon. The typical energy resolution of the detectors is 2.0 keV at the 1332.5 keV line of 60 Co. The energy spectra without samples were accumulated with the GeMulti spectrometer over 7862 h. The results of the measurements are presented in Fig. 2, where the effect of the purification is clearly visible (here and in the following, the spectra of the GeMulti set-up are the sum of the spectra of the 4 individual HPGe detectors). Table 1 gives a summary of the measured radioactive contaminations in the used Ru before and after the purification process. The purification allowed us to decrease the 40 K contamination of ≃ 20 times; the contamination by 226 Ra was also suppressed by ≃ 6 times, while the activity of 106 Ru was decreased by ≃ 5 times due to decay with the half life T 1/2 = 371.8 d [25].     [20] (473 g, 158 h) and of the purified Ru sample (720 g, 5479 h, measured here). For comparison, the results of the sample used in [22] (149 g, 2592 h) are also presented. The limits are given at 90% C.L. (95% C.L. for [22]). Activity of 103 Ru (T 1/2 = 39.26 d [13]) is quoted for the beginning of the present measurements.
Chain Nuclide Activity (mBq/kg) Ru [20] Purified Ru Ru [22] 3 New experimental T 1/2 limits on 2β decay of ruthenium We did not observe any peak in the spectra accumulated with the ruthenium sample which could be unambiguously attributed to the 2β processes in 96 Ru and 104 Ru. Therefore only lower half life limits are given using the formula: where N is the number of potentially 2β unstable nuclei in the Ru sample, η is the detection efficiency, t is the measuring time, 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 in the present study are given at 90% C.L.). The efficiency of the detectors for the double β processes in 96 Ru and 104 Ru has been calculated by using the EGS4 code [26] with initial kinematics given by the DECAY0 event generator [27]. The procedure of the analysis, in particular in determining the lim S values, is well described in [20].

Search for 2β + decay of 96 Ru
Only the ground state of 96 Mo can be populated in the 2β + decay of 96 Ru, and thus only annihilation γ quanta with energy 511.0 keV could be registered by our detectors. A possible extra rate in the annihilation peak in the spectrum accumulated with the purified Ru sample (see Fig. 3  The area of the annihilation peak in the measurements with the purified Ru during 5479 h is equal to (1461 ± 39) counts, while in the background spectrum it is (535 ± 27) counts during 3362 h 3 ; this gives (589 ± 58) counts of the extra events. The excess is explained by the following contributions: 1) the 511.8 keV γ line from 106 Rh which is the daughter radionuclide of the cosmogenic 106 Ru; this contribution is estimated to be (433 ± 52) counts using the supplementary 106 Rh peak at 621.9 keV with an area (197 ± 24) counts, taking into account the different yields of these γ quanta per decay (γ 512 = 20.4% and γ 622 = 9.93% [13]) and their detection efficiencies (η 512 = 3.0% and η 622 = 2.8%); 2) the 510.8 keV γ line from the 208 Tl contamination in the Ru sample; this contribution is estimated in a similar way as before to be (49 ± 11) counts using the area of the 583.2 keV peak of 208 Tl (with subtraction of the contribution from the corresponding background peak); 3) the e + e − pairs created by the 1460.8 keV γ quanta emitted in the 40 K decay; this contribution is estimated to be (165 ± 4) counts using the area of the 1460.8 keV peak, (5266 ± 132) counts (after subtraction of the corresponding background peak), and results of simulation with the EGS4, which give a ratio of 1:31.9 between the 511.0 keV and 1460.8 keV peaks from 40 K in our measurements.
The difference between the measured number of events in the 511.0 keV peak and the estimated contributions from the known sources, (−58±79) counts, could eventually be ascribed to the effect searched for. Obviously, there is no evidence of 2β + (and εβ + ) decay of 96 Ru to the ground state of 96 Mo. In accordance with the Feldman-Cousins procedure [28], it results in a limit lim S = 79 counts for the effect, which can be excluded at 90% C.L. Taking into account the calculated efficiency for 2β + processes (10.36% for 2ν mode and 10.31% for 0ν) and the number of the 96 Ru nuclei (N = 2.38 × 10 23 ), this gives: In case if the observed number of events is less than the expected background and thus the estimated effect is negative, G.J. Feldman and R.D. Cousins recommended [28] to give, in addition to the upper limit, also the so-called sensitivity of the experiment defined as "the average upper limit that would be obtained by an ensemble of experiments with the expected background and no true signal". Using the total number of events in the range of 509 −514 keV as the background (B = 2522 counts) and extrapolating Table XII of [28] (in terms of √ B), we obtain lim S s = 93 counts at 90% C.L. This gives the "sensitivity" T 1/2s value e.g. for the 0ν2β + decay as T 0ν2β + 1/2s (g.s. → g.s.) ≥ 1.1 × 10 20 yr, which is very close to the obtained above value of 1.3 × 10 20 yr. We accept the values (2) as the final ones (also to compare with results from other experiments where only the upper limits are given).
In addition to the analysis of the usual 1-dimensional spectrum, the GeMulti set-up with its 4 HPGe detectors has the possibility to use coincidences between different detectors for γ quanta emitted simultaneously (annihilation γ quanta in 2β + and εβ + decays, and γ's from cascades in the deexcitation of the excited 96 Mo levels). The set-up, with and without Ru sample, has been operated in coincidence mode over 5479 h and 2490 h, respectively. The procedure of the analysis is the same as described recently in [29], where a 2-dimensional spectrum was used to detect the 2ν2β − transition of 100 Mo to the first excited 0 + 1 state of 100 Ru. So, fixing the energy of one of the detectors to the expected 511±3 keV (in accordance with the energy resolution for the annihilation peak), we observe the coincidence peak at the corresponding energy 511±3 keV. There are 18(4) counts in both the spectra. The Monte Carlo simulations give the efficiencies to get coincidences of two γ quanta with energy 511.0 keV: 0.30% for 0ν2β + decay of 96 Ru and 8 × 10 −5 % for 40 K (which gives the biggest contribution of 2 counts during 5479 h). The difference between the observed and the expected number of counts (−24 ± 10) corresponds to lim S = 3.3 counts at 90% C.L. that results in T 0ν2β + 1/2 (g.s. → g.s.) ≥ 9.3 × 10 19 yr. This value is comparable but slightly lower than that obtained above from the analysis of the 1-dimensional spectrum. This concerns also other limits obtained from the analysis of coincidences: while they are comparable with those derived from the 1-dimensional spectrum, in general they are lower due to a lower detection efficiency.

εβ + processes in 96 Ru
The limit obtained above for the 2β + decay considering the 511.0 keV peak (lim S = 79 counts at 90% C.L.) can be used to estimate a half life limit on the εβ + decay to the ground state of 96 Mo. Taking into account the efficiencies for the εβ + decay of 96 Ru (6.12% for 2ν mode and 5.89% for 0ν), we obtain: In addition to the transition to the ground state, also few excited levels of 96 Mo can be populated in εβ + decay of 96 Ru (up to the level 2 + , 1625.9 keV). To estimate the number of events (lim S), the experimental energy spectrum was fitted in different energy intervals with the sum of components representing the background (internal 40 K, U/Th, external γ from the details of the set-up) and the EGS4-simulated models for 2β processes in 96 Ru. The used fitting approach is described in detail in Ref. [20].
For example, in the case of the transition to the 778.2 keV level of 96 Mo, a peak at 778.2 keV should be present in the energy spectrum accumulated with the Ru sample. To estimate an upper limit the spectrum was fitted in the energy interval (744 − 799) keV using a model made of four Gaussian functions at the energies of 768.4 keV (γ peak from 214 Bi), 786.0 keV ( 214 Pb), 794.9 keV ( 228 Ac) and 778.2 keV (the expected effect) with the energy resolution FWHM = 2.0 keV, and a linear function representing the background (see Fig. 4). The fit using the chi-square method (χ 2 /n.d.f. = 38.8/42 = 0.92, where n.d.f. is number of degrees of freedom) results in a peak area of S = (−16.9 ± 14.6) counts, which gives no evidence for the effect. In accordance with the procedure [28], one should take 10.5 counts which can be excluded at 90% C.L. (fits in other energy intervals give close results). Taking into account the detection efficiency (2.38%), we have obtained the following limit:  Similar fits allow us to set limits on possible transitions to other excited levels in the εβ + decay of 96 Ru; obtained results are listed in Table 2.

Double electron captures in 96 Ru
Double electron captures in 96 Ru lead to creation of holes in the atomic shells of 96 Mo. In the 2ν2ε process, all the energy release (except the part spent on atomic shell excitation) is taken away by two neutrinos. The energy threshold in the current measurements (around 50 keV) does not allow to search for the deexcitation processes in the atomic shell (which have energies less than 20 keV), thus we cannot derive limits for the g.s. to g.s. 2ν2ε capture.
In neutrinoless 2ε capture, we suppose (as also other articles on the subject) that the energy excess is taken away by (bremsstrahlung) γ quanta with energy where E bi is the binding energy of i-th captured electron on the atomic shell, and E exc is the energy of the populated (g.s. or excited) level of 96 Mo. In case of transition to an excited level, in addition to the initial γ quantum, other γ's will be emitted in the nuclear deexcitation process.
We did not observe peaks with energies expected in the 2ε decays of 96 Ru in the experimental data. Limits on the areas of the peaks were obtained using the fitting procedure as explained in the previous section. Fig. 5 shows an interval of the spectrum around 1921.8 keV and its fit by the sum of a straight line (representing the background) and the peak with energy of 1921.8 keV expected in the 96 Ru resonant decay to the 2700.2 keV level of 96 Mo.  All the obtained T 1/2 limits, together with the energies of the γ lines which were used to set the T 1/2 limits and corresponding detection efficiencies, are summarized in Table 2. Table 2: The half life limits on 2β processes in 96 Ru and 104 Ru isotopes together with theoretical predictions. The energies of the γ lines, which were used to set the T 1/2 limits, are listed in column 4 with the corresponding detection efficiencies (η) in column 5. The theoretical T 1/2 values for 0ν mode are given for m ν = 1 eV.  Fig. 1b). The peak at the energy 555.8 keV is absent in the experimental data (see Fig. 3). The fit of the spectrum accumulated over 5479 h was bounded within the (530 − 600) keV interval. The best fit (χ 2 /n.d.f. = 38.2/43 = 0.89) was achieved in the energy interval (540 − 590) keV. The derived area of the effect, (−17.4 ±18.8) counts, corresponds to lim S = 16.2 counts at 90% C.L. [28]. Using the number of 104 Ru nuclei in the purified ruthenium sample (N = 7.98 × 10 23 ) and the very close detection efficiencies for the 555.8 keV γ quanta in case of 2ν and 0ν mode (3.09% and 3.06%, respectively), the following half life limits were reached: (g.s. → 2 + , 555.8 keV) ≥ 6.6 × 10 20 yr, (g.s. → 2 + , 555.8 keV) ≥ 6.5 × 10 20 yr.

Theoretical estimates
The theoretical estimations of Table 2 were obtained by using a higher-QRPA framework [30,31] with detailed expressions given in [32,33]. For the neutrinoless modes of decay the UCOM short-range correlations [34] were used. All computational details are given in a recent article [35]. Estimates coming from other sources [36,37,38] are indicated in the table. In addition, a summary of other theoretical results can be found in our previous work [20].

Discussion
Experimental searches for 2β + /εβ + /2ε processes are not so popular as those for 2β − decays.
There are three reasons for such a situation: (1) These nuclei mostly have low natural abundance, usually less than 1%, with few exceptions [2] (and 96 Ru with δ = 5.54% is among them); (2) Energy available for positrons is related with the energy release Q 2β as Q 2β − 4m e c 2 (for 2β + decay) or Q 2β − 2m e c 2 − E b (for εβ + ), where m e c 2 is the electron rest mass, and E b is the binding energy of the captured electron on the atomic shell. This leads to smaller phase space factors in comparison with 2β − decay, and thus in lower probabilities for 2β + /εβ + processes; (3) In searches for X rays emitted in deexcitation of atomic shells in case of εβ + /2ε decays, detectors with low energy threshold (and good energy resolution) are needed; in addition, it is difficult to ensure high efficiency for detection of low energy X rays when external 2β sources are investigated.
As for resonance 0ν2ε capture, intensive high-precision measurements of Q 2β values during last few years (see reviews [52] and refs. therein) excluded many nuclei from the list of perspective candidates in searches for this exotic process, leaving in the list only 152 Gd and 156 Dy. While for 152 Gd experimental investigations were not performed to-date, for 156 Dy first experimental limits [53] were set on the level of only T 1/2 > 10 16 yr (this is related with 156 Dy low natural abundance δ = 0.056% [12]).
Comparing the above described T 1/2 limits for different isotopes with the values obtained in the present measurements, one could conclude that the latter are on the level of the best results achieved to-date in other experiments.

Conclusions
A low background experiment to search for 2β processes in 96 Ru and 104 Ru isotopes was carried out over more than 7.6 thousands hours in the underground Gran Sasso National Laboratories of the I.N.F.N. measuring ruthenium samples with ultra-low background HPGe detectors. The total exposure of the experiment is 0.56 kg × yr. Purification of the ruthenium using the electron beam melting method allowed to reduce the potassium contamination by more than 20 times; activities of 226 Ra and 106 Ru were decreased as well.
The new improved half life limits on double beta processes in 96 Ru have been set at the level of 10 20 − 10 21 yr. Moreover, the 2β − transition of 104 Ru to the excited 2 + level of 104 Pd has been investigated with the same sensitivity. All results give higher values than those recently published [20,21,22]. However, the limits are still far from the theoretical predictions, with the exception of the 2νεβ + channel for 96 Ru (g.s. to g.s. transition) and 2ν2ε decays with population of the 0 + levels (g.s. and the first 0 + level with E exc = 1148.1 keV), for which half lives T 1/2 ≃ 10 21 − 10 22 yr have been estimated.

Acknowledgments
The group from the Institute for Nuclear Research (Kyiv, Ukraine) was supported in part by the Space Research Program of the National Academy of Sciences of Ukraine. We thank anonymous referee for useful suggestions.