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First search for double-beta decay of 184Os and 192Os

A search for double-beta decay of osmium has been realized for the first time with the help of an ultra-low background HPGe gamma detector at the underground Gran Sasso National Laboratories of the INFN (Italy). After 2741 h of data taking with a 173 g ultra-pure osmium sample limits on double-beta processes in 184Os have been established at the level of T_{1/2} about 10^{14}-10^{17} yr. Possible resonant double-electron captures in 184Os were searched for with a sensitivity T_{1/2} about 10^{16} yr. A half-life limit T_{1/2}>5.3 10^{19} yr was set for the double-beta decay of 192Os to the first excited level of 192Pt. The radiopurity of the osmium sample has been investigated and radionuclides 137Cs, 185Os and 207Bi were detected in the sample, while activities of 40K, 60Co, 226Ra and 232Th were limited at the mBq/kg level.


INTRODUCTION
Neutrinoless double-β decay (0ν2β) is one of the most promising probes for physics beyond the Standard Model. The process is sensitive to lepton number violation, the nature of the neutrino (Majorana or Dirac particle), the absolute neutrino mass and the neutrino mass hierarchy (see [1,2,3,4,5,6,7,8,9,10,11] and references therein). In particular, the investigation of neutrinoless double-electron capture (0ν2ε) and of electron capture with positron emission (0νεβ + ) could clarify the possible contribution of the right-handed currents to the 0ν2β − decay rate [8,12].
We have investigated the radiopurity of the osmium sample and realized the first search for double-β processes in 184 Os and 192 Os with the help of an ultra-low background HPGe γ spectrometer. Preliminary results of the experiment were presented in [19].

Experiment
An ultra-pure osmium sample (more than 99.999% purity grade [20]) with a mass of 173 g was used in the experiment. The material was obtained using electron-beam melting of osmium powder with further purification by electron-beam zone refining. The estimated density of the metal is 23 g/cm 3 (the tabulated value is 22.57 g/cm 3 [21]). The sample contains 1.1 × 10 20 nuclei of 184 Os and 2.2 × 10 23 nuclei of 192 Os assume the natural isotopic composition [14]. The experiment was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the ultra-low background HPGe detector GeCris with a volume of 465 cm 3 . The detector is shielded by lead (≈ 25 cm) and copper (≈ 10 cm). The FWHM energy resolution of the spectrometer is 2.0 keV for the 1333 keV γ quanta of 60 Co. The data with the sample were accumulated over 2741 h, while the background spectrum was taken over 1046 h. The spectra are presented in Fig. 3.

Radioactive contamination of the osmium sample
The peaks in the energy distributions can be ascribed to γ quanta of U/Th daughters, 40 K, 60 Co, 137 Cs, 185 Os and 207 Bi. The response functions of the detector to decays of these nuclides as well as to the double-β processes in the osmium isotopes were simulated by EGSnrc [22] and GEANT4 [23,24] packages with initial kinematics given by the DECAY0 event generator [25]. Both simulations gave consistent results 2 . Some excess of events in the 662 keV peak of 137 Cs was observed with an activity (1.9 ± 0.3) mBq/kg. The radioactive 185 Os (electron capture decay, T 1/2 = 93.6 d [26]) was also detected in the sample with an activity (3.0 ± 0.3) mBq/kg. We assume that this radionuclide was generated before the installation of the sample into the set-up by capture of neutrons by 184 Os and by spallation processes induced by cosmic rays on heavier osmium isotopes. The presence of 207 Bi at the level of (0.4 ± 0.1) mBq/kg can be explained by contamination of the sample. The activities of 137 Cs, 185 Os and 207 Bi, as well as upper limits of 40 K, 60 Co and U/Th daughters are presented in Table 1.

Search for εβ + and 2ε processes in 184 Os
We do not observe any peaks in the energy distribution accumulated with the osmium sample which could indicate double-β activity of 184 Os or 192 Os. Therefore only lower half-life limits (lim T 1/2 ) can be set according to the formula: where N is the number of potentially 2β unstable nuclei, η is the detection efficiency (in which the yields of the specific γ quanta in accordance with the scheme of the decay, Fig. 1, are included), t is the measuring time, and lim S is the upper limit on the number of events of the effect searched for which can be excluded at a given confidence level (CL). All the half-life limits and the values of lim S are presented in this paper at 90% CL.
One positron can be emitted in the εβ + decay of 184 Os with an energy up to (431.7 ± 0.6) keV. The annihilation of the positron should give two 511 keV γ's leading to an extra rate in the annihilation peak. To estimate lim S for the decay, the energy spectra were fitted in the energy interval (495 − 530) keV (see Fig. 4). There are (92 ± 24) events in the 511 keV peak in the data accumulated with the osmium sample. The area of the annihilation peak in the background spectrum is (24 ± 10) counts, corresponding to (63 ± 26) counts after normalising to the exposure of the osmium sample. The difference in the areas of the annihilation peak with and without sample [(29 ± 35) counts] gives no indication of the effect. In accordance with the Feldman-Cousins procedure [27] we should take lim S = 86 counts which can be excluded at 90% CL. Taking into account almost the same detection efficiency for 2ν (η=9.0%) and 0ν (8.9%) modes, we have obtained the following limit on the half-life of 184 Os for the 2ν and 0ν modes of εβ + decay (see also Table 2 where the energies of γ quanta used in the analysis, the detection efficiencies and the values of lim S are given): The εβ + decay of 184 Os is also allowed to the first excited level of 184 W with an energy of 111.2 keV. The strongest restrictions on the decay were obtained by analysis of the annihilation peak. Taking into account slightly different detection efficiencies for 2ν (9.0%) and 0ν (8.8%) modes, we have obtained the following limits: In the case of the 2ν2K capture in 184 Os, a cascade of X rays and Auger electrons with individual energies up to 69.5 keV is expected. The most intensive X ray lines of tungsten are [26]: 58.0 keV (the yield of the X ray quanta is 27.4%), 59.3 keV (47.0%), 67.0 keV (5.4%), 67.2 keV (10.3%) and 69.1 keV (3.6%). To derive a limit on the decay, the energy spectrum was fitted in the energy interval (47 − 72) keV by the model consisting of five Gaussians (to describe the expected X ray peaks) plus a polynomial function of the first degree (background). The fit provides the total area of the 2ν2K effect (21 ± 26) counts, which corresponds to lim S = 64 counts (see Fig. 5). The detection efficiency of the whole effect in this case is calculated as: η = Σ i η i , where η i are the efficiencies for the specific X lines with energies from 58.0 keV to 69.1 keV. Taking into account η = 0.05% 3 , one can calculate the following half-life limit:   The sensitivity of the experiment to the 2ν2ε decay of 184 Os to the 111.2 keV excited level of 184 W is estimated from the fit of the energy spectrum accumulated with the osmium sample in the vicinity of the energy 111.2 keV. The fit gives an area for the γ peak of (−4.8 ± 6.1) counts, that leads to lim S = 5.8 counts (see Fig. 5). The detection efficiency for the 111.2 keV γ quanta, taking into account the fact that the transition from the 111.2 keV excited level to the ground state of 184 W is efficiently converted to electrons (the experimental coefficient of conversion is α total = 2.57 [17]), was calculated to be 0.076%. Generally speaking, due to the large coefficient of conversion to electrons, the sensitivity of the experiment should be different for 2K, KL and 2L captures. For example, since both K electrons are already captured in the 2K process, the conversion from the K shell is prohibited in further 111.2 keV deexcitation process. The coefficients of conversion from different atomic shells can be calculated with the BrIcc program [28] 4 . However, the excited 111.2 keV level of 184 W has quite a long half-life of 1.251 ns [17] compared to the characteristic atomic relaxation time of ∼ 10 −15 s (see e.g. [29]). Thus, we consider that the relaxation processes in the W atomic shell after the initial 2ν2ε capture are finished before the 111.2 keV deexcitation and we can apply the value α = 2.57 for all 2ν2ε captures. This gives: The limits obtained for the 2ν2ε decay of 184 Os to the excited levels of 184 W are presented in Table 2.
In the neutrinoless double-electron capture in addition to X rays we suppose that only one bremsstrahlung γ quantum is emitted [30] to take away the rest of the energy, which in the 2ν process is taken by the neutrinos. In the case of the 0ν double-electron capture from K and L shells, the energy of the γ quanta is expected to be equal to E γ = Q 2β − E b1 − E b2 , where E bi are the binding energies of the captured electrons on the K and L atomic shells of tungsten [26]: E K = 69.5 keV, E L 1 = 12.1 keV, E L 2 = 11.5 keV, E L 3 = 10.2 keV. Therefore, the expected energies of the quanta for the 0ν2ε capture in 184 Os to the ground state of 184 W are: E γ = (1314.7 ± 0.6) keV for 2K, E γ = (1373.1 ± 1.6) keV for KL and E γ = (1431.4 ± 2.5) keV for 2L. There are no clear peaks in the data with these energies (see Fig. 6). We have estimated the values of lim S by fitting the data in the energy intervals with the simple model: a Gaussian function (to describe the peaks searched for) plus a polynomial function (continuous background). Taking into account the calculated efficiencies to detect γ quanta with energies of ≈ (1.31 − 1.43) MeV (≈ 4.1% − 4.2%), we set the following limits on the processes searched for: T 0ν2K 1/2 ( 184 Os, g.s. → g.s.) ≥ 2.0 × 10 17 yr, T 0νKL 1/2 ( 184 Os, g.s. → g.s.) ≥ 1.3 × 10 17 yr, T 0ν2L 1/2 ( 184 Os, g.s. → g.s.) ≥ 1.4 × 10 17 yr. The Q 2β energy of 184 Os allows also the population of several excited levels of 184 W. The limits obtained for the processes of 0ν2ε decay to the ground and to the excited levels of the daughter nuclei are presented in Table 2.  Table 2.

Double-β − decay of 192 Os
To set a limit on the 2β − transition of 192 Os to the 2 + 316.5 keV excited level of 192 Pt, the energy spectrum was fitted by a straight line (which represents the background model) and a Gaussian at 316.5 keV. The energy spectrum in the vicinity of the peak is presented in Fig. 7. Taking into account the detection efficiency (η = 3.0% both for the 2ν and 0ν modes of the decay), we have obtained the following limit:

CONCLUSIONS
The radiopurity of an osmium sample has been investigated and the first experiment to search for 2β processes in 184 Os and 192 Os was carried out by using ultra-low background HPGe γ spectrometry. After 2741 h of data taking with a 173 g ultra-pure osmium sample limits on double-beta processes in 184 Os have been established at the level of T The osmium sample has subsequently been placed in a well-type ultra low background HPGe detector especially designed for low energy γ rays spectrometry 6 . In such a way we expect to improve the sensitivity of the experiment at least to the 2ν2K decay, which is the most probable double-beta process in 184 Os. Further progress can be achieved by using osmium enriched in 184 Os, although this will require new enrichment techniques to be developed.

ACKNOWLEDGMENTS
The authors from the Institute for Nuclear Research (Kyiv, Ukraine) were supported in part by the Space Research Program of the National Academy of Sciences of Ukraine. 6 The main goal of this stage of the experiment is to search for α decay of 184 Os and 186 Os to the excited levels of their daughter nuclei (see [19] where an indication for α decay of 184 Os to the first excited level (103.5 keV) of 180 W with the half-life T 1/2 ∼ 5 × 10 14 yr was obtained).