Search for 2β decays of 96Ru and 104Ru by ultra-low background HPGe gamma spectrometry at LNGS: final results
P. Belli, R. Bernabei, F. Cappella, R. Cerulli, F. A. Danevich, S. d'Angelo, A. Incicchitti, G. P. Kovtun, N. G. Kovtun, M. Laubenstein, D. V. Poda, O. G. Polischuk, A. P. Shcherban, D. A. Solopikhin, J. Suhonen, V. I. Tretyak
aa r X i v : . [ nu c l - e x ] F e b Search for β decays of Ru and
Ru by ultra-lowbackground HPGe γ spectrometry at LNGS: final results P. Belli a , R. Bernabei a,b, , F. Cappella c,d , R. Cerulli e , F.A. Danevich f ,S. d’Angelo a,b , A. Incicchitti c,d , G.P. Kovtun g , N.G. Kovtun g , M. Laubenstein e ,D.V. Poda f , O.G. Polischuk c,f , A.P. Shcherban g , D.A. Solopikhin g , J. Suhonen h ,V.I. Tretyak fa INFN, sezione Roma “Tor Vergata”, I-00133 Rome, Italy b Dipartimento di Fisica, Universit`a di Roma “Tor Vergata”, I-00133 Rome, Italy c INFN, sezione Roma “La Sapienza”, I-00185 Rome, Italy d Dipartimento di Fisica, Universit`a di Roma “La Sapienza”, I-00185 Rome, Italy e INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi (AQ), Italy f Institute for Nuclear Research, MSP 03680 Kyiv, Ukraine g National Science Center “Kharkiv Institute of Physics and Technology”, 61108 Kharkiv,Ukraine h Department of Physics, University of Jyv¨askyl¨a, P.O. Box 35 (YFL), FI-40014 Finland
Abstract
An experiment to search for double β decay processes in Ru and
Ru, which areaccompanied by γ rays, has been realized in the underground Gran Sasso National Labo-ratories of the I.N.F.N. (Italy). Ruthenium samples with masses of ≈ (0 . − .
7) kg weremeasured with the help of ultra-low background high purity Ge γ ray spectrometry. After2162 h of data taking the samples were deeply purified to reduce the internal contamina-tion of K. The last part of the data has been accumulated over 5479 h. New improvedhalf life limits on 2 β + /εβ + / ε processes in Ru have been established on the level of10 yr, in particular for decays to the ground state of Mo: T ν β + / ≥ . × yr, T νεβ + / ≥ . × yr and T ν K / ≥ . × yr (all limits are at 90% C.L.). The resonantneutrinoless double electron captures to the 2700.2 keV and 2712.7 keV excited states of Mo are restricted as: T νKL / ≥ . × yr and T ν L / ≥ . × yr, respectively.Various two neutrino and neutrinoless 2 β half lives of Ru have been estimated in theframework of the QRPA approach. In addition, the T / limit for 0 ν β − transitions of Ru to the first excited state of
Pd has been set as ≥ . × yr. PACS : 23.40.-s, 27.60.+j, 29.30.Kv
Keywords : Double beta decay, Double electron capture, Ru, Ru Corresponding author.
E-mail address: [email protected] (R. Bernabei). Introduction
Double beta (2 β ) decay is a process of transformation of a nucleus ( A, Z ) either to (
A, Z + 2)with simultaneous emission of two electrons (2 β − decay) or to ( A, Z −
2) through one of thefollowing ways: emission of two positrons (2 β + ), capture of electron and emission of positron( εβ + ) or double electron capture (2 ε ). The two neutrino (2 ν ) double β decay, in which two(anti)neutrinos are also emitted, is allowed in the Standard Model (SM); however, being asecond order process in the weak interactions, it is characterized by very long half lives in therange of 10 − yr [1]. There are 35 known nuclei candidates for 2 β − and 34 candidates for2 β + /εβ + / ε decays [2]. To-date, two neutrino 2 β decays are observed for several 2 β − decayingnuclei (see reviews [2, 3] and recent original works [4, 5]), while indications on double electroncapture have been obtained for Ba in geochemical experiments [6, 7].The neutrinoless (0 ν ) mode of the 2 β decay is forbidden in the SM because it violates thelepton number by 2 units. It is, however, naturally expected in many SM extensions whichdescribe the neutrino as a Majorana particle with non-zero mass. The neutrino oscillationexperiments indicate that the neutrinos are massive. Nevertheless, since they are sensitiveto the difference in ν masses, the absolute ν mass scale is unknown [8]. The 0 ν β decay isconsidered 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 existenceof Nambu-Goldstone bosons (Majorons). A particular analysis of data on Ge provided anevidence for 0 ν β decay [9]; several experiments with the aim to test it and to explore theinverted hierarchy of the Majorana neutrino mass region ( m ν ∼ . − .
05 eV) are now inprogress or under development [1]. Studies of neutrinoless 2 β − and 2 β + /εβ + / ε decays aremutually complementary, helping to distinguish contributions from the neutrino mass and right-handed admixture mechanisms [10]. 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 β = (2714 . ± .
13) keV [11]. It has also a quite bignatural 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 . E L = 2 . L shell, the decay energies (2691 . ± .
13) keV and (2708 . ± .
13) keV are close to the energyof the excited levels of Mo ( E exc = 2700 .
21 and 2712.68 keV [14]). Such a situation could giverise to a resonant enhancement of the neutrinoless KL and 2 L capture to the correspondinglevel of the daughter nucleus as a result of the energy degeneracy [15] .In addition, another isotope of ruthenium, Ru, is potentially unstable with respect to the2 β − decay ( Q β = (1301 . ± .
7) keV [17], δ = 18 . Ru and
Ruare shown in Fig. 1.Despite the high energy release and the high abundance, only one search for 2 β + /εβ + processes in Ru was performed in 1985, giving T / limits on the level of 10 yr [19]. Theefforts were renewed only in 2009, when a Ru sample with a mass of 473 g was measured for 158h with an HPGe detector (468 cm ) in the underground conditions of the Gran Sasso National In accordance with older atomic masses [16], the energy release Q β = (2718 ±
8) keV gave the decay energiesfor KL and 2 L captures as (2695 ±
8) keV and (2712 ±
8) keV, respectively, compatible within uncertainties tothe energies of the Mo excited levels (2700.2 and 2712.7 keV), and Ru was considered as a very promisingcandidate in looking for resonant 0 ν ε captures. After the recent high-precision measurement of Ref. [11]: Ruis no more considered a promising candidate to search for this process. + (0) + (3 + ) 2540.5 + + + + + + + + + Mo + + Tc
43 96 Ru + e , eb + , 2 b + Q = b (a) Ru + b - + Rh + Pd + Q = 1301.2(2.7) keV b (b) Figure 1: Decay schemes of Ru (a) and
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 the2 β + /εβ + / ε decays was 10 − yr; for several modes of 2 β decay of Ru (and
Ru) T / limits were established for the first time. A search for 2 β decays of Ru was also performed inthe HADES underground laboratory (500 m w.e.) where a sample of Ru with mass of 149 gwas measured during 2592 h; T / limits were obtained on the level of 10 yr [22].Our previous measurements [20, 21] showed that the used Ru sample was contaminatedby K at ≃ β + /εβ + / ε processes in Ru and for 2 β − decay in Ruobtained with a purified sample of Ru (720 g) in measurements during 5479 h.
The ruthenium (with natural isotopic composition) of 99.99% grade produced by powder met-allurgy was provided by Heraeus [23]. At the first stage [20, 21], the Ru sample with total massof 473 g was in form of pellets (50 tablets ⊘ × ≈ . ). The analysisof the data showed a high level of K contamination in the ruthenium (3.4 Bq/kg), and forfurther measurements the Ru sample with an increased total mass of 946 g was purified by anelectron beam melting method. 3he ruthenium was divided into five parts, each with a mass of almost 0.2 kg, which wereslowly melted (to avoid intensive sprinkling) using an electron beam and kept in a liquid stateunder vacuum (0.01 – 0.05 Pa) for ≃ . − ≈ . ) were obtained.The purified ruthenium samples were measured over 5479 h in the GeMulti set-up (madeof four HPGe detectors; ≃
225 cm each one) installed deep underground at the LNGS. Thedetectors are surrounded by a passive shield made of low radioactivity copper ( ≃ ≃
25 cm). The set-up was continuously flushed with high puritynitrogen to remove radon. The typical energy resolution of the detectors is 2.0 keV at the1332.5 keV line of Co. The energy spectra without samples were accumulated with theGeMulti 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 ofthe GeMulti set-up are the sum of the spectra of the 4 individual HPGe detectors). Table 1gives a summary of the measured radioactive contaminations in the used Ru before and afterthe purification process. The purification allowed us to decrease the K contamination of ≃ Ra was also suppressed by ≃ Ruwas decreased by ≃ T / = 371 . -3 -2 -1
110 500 1000 1500 2000 2500
Pb351.9
Tl, 510.8Annihil., 511.0
Rh, 511.8
Bi, 609.3
Rh, 621.9
Ac911.2 K, singleescape K, 1460.8
Bi, 1764.5
Bi, 2204.2
Tl, 2614.5Ru, 1153 hRu-pur, 5479 hBg, 7862 h
Energy (keV) C oun t s / ( h k e V ) Figure 2: (Color on-line) The energy spectra above 20 keV accumulated with the initial Rusample over 1153 h (Ru) and with the purified Ru over 5479 h (Ru-pur) in comparison with thebackground (Bg) of the GeMulti ultra-low background HPGe γ spectrometer measured over7862 h. The energies of γ lines are in keV. 4able 1: Radioactive contamination of the Ru sample used in [20] (473 g, 158 h) and of thepurified Ru sample (720 g, 5479 h, measured here). For comparison, the results of the sampleused in [22] (149 g, 2592 h) are also presented. The limits are given at 90% C.L. (95% C.L.for [22]). Activity of Ru ( T / = 39 .
26 d [13]) is quoted for the beginning of the presentmeasurements. Chain Nuclide Activity (mBq/kg)Ru [20] Purified Ru Ru [22] Th Ra ≤ . ≤ . . ± . Th ≤ . . ± . . ± . U U ≤ . ≤ . U Th ≤
390 – ≤ Pa m ≤ ≤
23 –
Ra 6 . ± . . ± . . ± . Pb – – ≤ K 3400 ±
600 153 ± ± Co ≤ . ≤ . ≤ . Cs ≤ . ≤ . ≤ . Ru – 3 . ± . Ru 24 ± . ± . ≤ . T / limits on β decay of ruthenium We did not observe any peak in the spectra accumulated with the ruthenium sample whichcould be unambiguously attributed to the 2 β processes in Ru and
Ru. Therefore onlylower half life limits are given using the formula:lim T / = N · η · t · ln 2 / lim S, (1)where N is the number of potentially 2 β unstable nuclei in the Ru sample, η is the detectionefficiency, t is the measuring time, and lim S is the number of events of the effect searched forwhich can be excluded at a given confidence level (C.L.; all the limits in the present study aregiven at 90% C.L.). The efficiency of the detectors for the double β processes in Ru and
Ru has been calculated by using the EGS4 code [26] with initial kinematics given by theDECAY0 event generator [27]. The procedure of the analysis, in particular in determining thelim S values, is well described in [20]. β + decay of Ru Only the ground state of Mo can be populated in the 2 β + decay of Ru, and thus onlyannihilation γ quanta with energy 511.0 keV could be registered by our detectors. A possible5xtra rate in the annihilation peak in the spectrum accumulated with the purified Ru sample(see Fig. 3) could be related to the 2 β + (and εβ + ) decay of Ru. C oun t s / ( h k e V ) Ru sampleBackground
Ac463.0
Ru497.1
Tl, 510.8Annihil., 511.0
Rh, 511.8
Tl, 583.2
Bi, 609.3
Rh621.9
Ru, 555.8
Figure 3: (Color on-line) Fragment of the energy spectra accumulated with the rutheniumsample over 5479 h (Ru sample) and without the sample over 3362 h (Background; see footnote ) in the vicinity of the annihilation peak.The area of the annihilation peak in the measurements with the purified Ru during 5479h is equal to (1461 ±
39) counts, while in the background spectrum it is (535 ±
27) countsduring 3362 h ; this gives (589 ±
58) counts of the extra events. The excess is explained by thefollowing contributions:1) the 511.8 keV γ line from Rh which is the daughter radionuclide of the cosmogenic
Ru; this contribution is estimated to be (433 ±
52) counts using the supplementary
Rhpeak at 621.9 keV with an area (197 ±
24) counts, taking into account the different yields ofthese γ quanta per decay ( γ = 20 .
4% and γ = 9 .
93% [13]) and their detection efficiencies( η = 3 .
0% and η = 2 . γ line from the Tl contamination in the Ru sample; this contributionis estimated in a similar way as before to be (49 ±
11) counts using the area of the 583.2 keVpeak of
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 K decay; thiscontribution is estimated to be (165 ±
4) counts using the area of the 1460.8 keV peak, (5266 ± K in our measurements. We use here the last series of the background measurements with the GeMulti set-up close to the dataaccumulated with the purified Ru sample. − ±
79) counts, could eventually be ascribedto the effect searched for. Obviously, there is no evidence of 2 β + (and εβ + ) decay of Ru tothe ground state of Mo. In accordance with the Feldman-Cousins procedure [28], it results ina limit lim S = 79 counts for the effect, which can be excluded at 90% C.L. Taking into accountthe calculated efficiency for 2 β + processes (10.36% for 2 ν mode and 10.31% for 0 ν ) and thenumber of the Ru nuclei ( N = 2 . × ), this gives: T ν β + / (g . s . → g . s . ) ≥ . × yr , (2) T ν β + / (g.s. → g.s.) ≥ . × yr.In case if the observed number of events is less than the expected background and thusthe 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 “theaverage upper limit that would be obtained by an ensemble of experiments with the expectedbackground and no true signal”. Using the total number of events in the range of 509 −
514 keVas 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 / s value e.g. for the0 ν β + decay as T ν β + / s (g.s. → g.s.) ≥ . × yr, which is very close to the obtained abovevalue of 1 . × yr. We accept the values (2) as the final ones (also to compare with resultsfrom 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 its4 HPGe detectors has the possibility to use coincidences between different detectors for γ quantaemitted simultaneously (annihilation γ quanta in 2 β + and εβ + decays, and γ ’s from cascadesin the deexcitation of the excited Mo levels). The set-up, with and without Ru sample, hasbeen operated in coincidence mode over 5479 h and 2490 h, respectively. The procedure of theanalysis is the same as described recently in [29], where a 2-dimensional spectrum was used todetect the 2 ν β − transition of Mo to the first excited 0 +1 state of Ru. So, fixing the energyof one of the detectors to the expected 511 ± ± γ quanta with energy 511.0 keV: 0.30% for 0 ν β + decay of Ruand 8 × − % for K (which gives the biggest contribution of 2 counts during 5479 h). Thedifference between the observed and the expected number of counts ( − ±
10) corresponds tolim S = 3.3 counts at 90% C.L. that results in T ν β + / (g.s. → g.s.) ≥ . × yr. This value iscomparable but slightly lower than that obtained above from the analysis of the 1-dimensionalspectrum. This concerns also other limits obtained from the analysis of coincidences: whilethey are comparable with those derived from the 1-dimensional spectrum, in general they arelower due to a lower detection efficiency. εβ + processes in Ru The limit obtained above for the 2 β + decay considering the 511.0 keV peak (lim S = 79 countsat 90% C.L.) can be used to estimate a half life limit on the εβ + decay to the ground state of Mo. Taking into account the efficiencies for the εβ + decay of Ru (6.12% for 2 ν mode and5.89% for 0 ν ), we obtain: 7 νεβ + / (g.s. → g.s.) ≥ . × yr, T νεβ + / (g.s. → g.s.) ≥ . × yr.In addition to the transition to the ground state, also few excited levels of Mo can bepopulated in εβ + decay of Ru (up to the level 2 + , 1625.9 keV). To estimate the number ofevents (lim S ), the experimental energy spectrum was fitted in different energy intervals withthe sum of components representing the background (internal K, U/Th, external γ from thedetails of the set-up) and the EGS4-simulated models for 2 β processes in Ru. The used fittingapproach is described in detail in Ref. [20].For example, in the case of the transition to the 778.2 keV level of Mo, a peak at 778.2 keVshould be present in the energy spectrum accumulated with the Ru sample. To estimate anupper limit the spectrum was fitted in the energy interval (744 − γ peak from Bi), 786.0 keV (
Pb),794.9 keV (
Ac) and 778.2 keV (the expected effect) with the energy resolution FWHM = 2.0keV, and a linear function representing the background (see Fig. 4). The fit using the chi-squaremethod ( χ /n.d.f. = 38.8/42 = 0.92, where n.d.f. is number of degrees of freedom) results in apeak area of S = ( − . ± .
6) counts, which gives no evidence for the effect. In accordancewith the procedure [28], one should take 10.5 counts which can be excluded at 90% C.L. (fits inother energy intervals give close results). Taking into account the detection efficiency (2.38%),we have obtained the following limit: T (2 ν +0 ν ) εβ + / (g.s. → + , 778.2 keV) ≥ . × yr. Bi, 768.4 2 e , eb + , Ru → Mo * Pb786.0
Ac794.9
Energy (keV) C oun t s / k e V Figure 4: (Color on-line) Fragment of the energy spectrum accumulated with the purifiedruthenium sample over 5479 h with the ultra-low background HPGe γ spectrometer. The fit isshown by solid line. The arrow shows the energy of the peak expected in decay of Ru throughthe 2 + , . Mo. The energies of γ lines are in keV.8imilar fits allow us to set limits on possible transitions to other excited levels in the εβ + decay of Ru; obtained results are listed in Table 2. Ru Double electron captures in Ru lead to creation of holes in the atomic shells of Mo. In the2 ν ε process, all the energy release (except the part spent on atomic shell excitation) is takenaway 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 energiesless than 20 keV), thus we cannot derive limits for the g.s. to g.s. 2 ν ε capture.In neutrinoless 2 ε capture, we suppose (as also other articles on the subject) that the energyexcess is taken away by (bremsstrahlung) γ quanta with energy E γ = Q β − E b − E b − E exc ,where E bi is the binding energy of i -th captured electron on the atomic shell, and E exc is theenergy of the populated (g.s. or excited) level of Mo. In case of transition to an excitedlevel, in addition to the initial γ quantum, other γ ’s will be emitted in the nuclear deexcitationprocess.We did not observe peaks with energies expected in the 2 ε decays of Ru in the experimentaldata. Limits on the areas of the peaks were obtained using the fitting procedure as explainedin the previous section. Fig. 5 shows an interval of the spectrum around 1921.8 keV and its fitby the sum of a straight line (representing the background) and the peak with energy of 1921.8keV expected in the Ru resonant decay to the 2700.2 keV level of Mo. res 0 n KL , Ru → Mo * Energy (keV) C oun t s / k e V Figure 5: (Color on-line) Fragment of the energy spectrum accumulated with the purified Rusample over 5479 h by the ultra-low background HPGe γ spectrometer. The fit is shown bysolid line. The arrow shows the energy of a peak at 1921.8 keV due to possible resonant 0 νKL capture in Ru and further de-excitation of the 2 + , 2700.2 keV level of Mo.All the obtained T / limits, together with the energies of the γ lines which were used to setthe T / limits and corresponding detection efficiencies, are summarized in Table 2.9able 2: The half life limits on 2 β processes in Ru and
Ru isotopes together with theoreticalpredictions. The energies of the γ lines, which were used to set the T / limits, are listed incolumn 4 with the corresponding detection efficiencies ( η ) in column 5. The theoretical T / values for 0 ν mode are given for m ν = 1 eV. Level of Experimental limits,Process of decay daughter E γ η T / (yr) at 90% C.L. Theoretical estimations,nucleus (keV) (%) Present Ref. [22] T / (yr)(keV) work Ru → Mo2 β + ν g.s. 511.0 10.36 ≥ . × ≥ . × . × − . × ν g.s. 511.0 10.31 ≥ . × ≥ . × . × − . × εβ + ν g.s. 511.0 6.12 ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × > . × ν g.s. 511.0 5.89 ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × –0 + ≥ . × ≥ . × (1 . − . × + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –2 ε ν g.s. – – – – 4 . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × . × − . × + ≥ . × ≥ . × > . × + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –(0) + ≥ . × ≥ . × –2 ε ν + ≥ . × ≥ . × –0 + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –2 + ≥ . × ≥ . × –(0) + ≥ . × ≥ . × –2 K ν g.s. 2674.5 1.56 ≥ . × ≥ . × . × [37] KL ν g.s. 2691.6 1.58 ≥ . × ≥ . × –2 L ν g.s. 2708.7 1.55 ≥ . × ≥ . × –Resonant KL ν + ≥ . × ≥ . × . × − . × [38]Resonant 2 L ν ≥ . × ≥ . × . × − . × Ru → Pd2 β − ν + ≥ . × ≥ . × > . × [36]0 ν + ≥ . × ≥ . × – .4 β − decay Ru → Pd ∗ In case of 2 β − decay of Ru, only one excited level (2 + , 555.8 keV) can be populated (seeFig. 1b). The peak at the energy 555.8 keV is absent in the experimental data (see Fig. 3). Thefit of the spectrum accumulated over 5479 h was bounded within the (530 − χ /n.d.f. = 38.2/43 = 0.89) was achieved in the energy interval (540 − − . ± .
8) counts, corresponds to lim S = 16.2 counts at 90%C.L. [28]. Using the number of Ru nuclei in the purified ruthenium sample ( N = 7 . × )and the very close detection efficiencies for the 555.8 keV γ quanta in case of 2 ν and 0 ν mode(3.09% and 3.06%, respectively), the following half life limits were reached: T ν β − / (g.s. → + , 555.8 keV) ≥ . × yr, T ν β − / (g.s. → + , 555.8 keV) ≥ . × yr. 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 UCOMshort-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].
Experimental searches for 2 β + /εβ + / ε processes are not so popular as those for 2 β − decays.There are three reasons for such a situation:(1) These nuclei mostly have low natural abundance, usually less than 1%, with few excep-tions [2] (and Ru with δ = 5 .
54% is among them);(2) Energy available for positrons is related with the energy release Q β as Q β − m e c (for2 β + decay) or Q β − m e c − E b (for εβ + ), where m e c is the electron rest mass, and E b is thebinding energy of the captured electron on the atomic shell. This leads to smaller phase spacefactors in comparison with 2 β − decay, and thus in lower probabilities for 2 β + /εβ + processes;(3) In searches for X rays emitted in deexcitation of atomic shells in case of εβ + / ε decays,detectors with low energy threshold (and good energy resolution) are needed; in addition, it isdifficult to ensure high efficiency for detection of low energy X rays when external 2 β sourcesare investigated.In result, while in searches for neutrinoless 2 β − decay the sensitivity of T / > yr wasachieved (for Ge [39] and
Xe [40]), the best T / limits achieved in 2 β + /εβ + / ε experimentsare much more modest. Sensitivity T / > yr was reached in direct experiments for Fe[41], Ni [42], Zn [43], Mo [44], and limits T / > yr were obtained for Ca [45], Kr [46],
Cd [47],
Sn [48],
Te [49],
Ba [6]. Geochemical experiments currently givean indication on 2 ν ε capture in Ba with T / = (2 . ± . × yr [6] and T / =(6 . ± . × yr [7] (also limit > . × yr is known [50]). In addition, an observationof 2 ν K capture in Kr was recently claimed; the obtained half life is T / = 1 . +2 . − . × yr(however, also cautious limit is given as T / > . × yr at 90% C.L.) [51].11s for resonance 0 ν ε capture, intensive high-precision measurements of Q β values dur-ing last few years (see reviews [52] and refs. therein) excluded many nuclei from the list ofperspective candidates in searches for this exotic process, leaving in the list only Gd and
Dy. While for
Gd experimental investigations were not performed to-date, for
Dy firstexperimental limits [53] were set on the level of only T / > yr (this is related with Dylow natural abundance δ = 0 . T / limits for different isotopes with the values obtainedin the present measurements, one could conclude that the latter are on the level of the bestresults achieved to-date in other experiments. A low background experiment to search for 2 β processes in Ru and
Ru isotopes was carriedout over more than 7.6 thousands hours in the underground Gran Sasso National Laboratoriesof the I.N.F.N. measuring ruthenium samples with ultra-low background HPGe detectors. Thetotal exposure of the experiment is 0.56 kg × yr. Purification of the ruthenium using theelectron beam melting method allowed to reduce the potassium contamination by more than20 times; activities of Ra and
Ru were decreased as well.The new improved half life limits on double beta processes in Ru have been set at the levelof 10 − yr. Moreover, the 2 β − transition of Ru to the excited 2 + level of Pd hasbeen investigated with the same sensitivity. All results give higher values than those recentlypublished [20, 21, 22]. However, the limits are still far from the theoretical predictions, withthe exception of the 2 νεβ + channel for Ru (g.s. to g.s. transition) and 2 ν ε decays withpopulation of the 0 + levels (g.s. and the first 0 + level with E exc = 1148 . T / ≃ − yr have been estimated. The group from the Institute for Nuclear Research (Kyiv, Ukraine) was supported in partby the Space Research Program of the National Academy of Sciences of Ukraine. We thankanonymous referee for useful suggestions.
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