Search for alpha decay of naturally occurring osmium nuclides accompanied by gamma quanta
P.Belli, R.Bernabei, F.Cappella, V.Caracciolo, R.Cerulli, F.A.Danevich, A.Incicchitti, D.V.Kasperovych, V.V.Kobychev, G.P.Kovtun, N.G.Kovtun, M.Laubenstein, D.V.Poda, O.G.Polischuk, A.P.Shcherban, S.Tessalina, V.I.Tretyak
aa r X i v : . [ nu c l - e x ] S e p Search for alpha decay of naturally occurring osmiumnuclides accompanied by gamma quanta
P. Belli a,b , R. Bernabei a,b, , F. Cappella c,d , V. Caracciolo a,b,e , R. Cerulli a,b ,F.A. Danevich f , A. Incicchitti c,d , D.V. Kasperovych f , V.V. Kobychev f ,G.P. Kovtun g,h , N.G. Kovtun g , M. Laubenstein e , D.V. Poda i , O.G. Polischuk f ,A.P. Shcherban g , S. Tessalina j , V.I. Tretyak fa INFN, sezione Roma “Tor Vergata”, I-00133 Rome, Italy b Dipartimento di Fisica, Universita di Roma “Tor Vergata, I-00133 Rome, Italy” c INFN, sezione Roma “La Sapienza”, I-00185 Rome, Italy d Dipartimento di Fisica, Universita di Roma “La Sapienza”, I-00185 Rome, Italy e INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi (AQ), Italy f Institute for Nuclear Research of NASU, 03028 Kyiv, Ukraine g National Science Center “Kharkiv Institute of Physics and Technology”, 61108 Kharkiv,Ukraine h Karazin Kharkiv National University, 4, 61022 Kharkiv, Ukraine i Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France j John de Laeter Centre for Isotope Research, GPO Box U 1987, Curtin University, Bentley,WA, Australia
Abstract
A search for α decay of naturally occurring osmium isotopes to the lowest excitedlevels of daughter nuclei has been performed by using an ultra-low-background Broad-Energy Germanium γ -detector with a volume of 112 cm and an ultra-pure osmium samplewith a mass of 118 g at the Gran Sasso National Laboratory of the INFN (Italy). Theisotopic composition of the osmium sample has been measured with high precision usingNegative Thermal Ionisation Mass Spectrometry. After 15851 h of data taking with the γ -detector no effect has been detected, and lower limits on the α decays were set at level oflim T / ∼ − yr. The limits for the α decays of Os and
Os to the first excitedlevels of daughter nuclei, T / ( Os) ≥ . × yr and T / ( Os) ≥ . × yr (at90% C.L.), exceed the present theoretical estimates of the decays half-lives. For Osand
Os also decays to the ground states of the daughter nuclei were searched for dueto the instability of the daughter nuclides relative to β decay. Keywords : Alpha decay;
Os;
Os;
Os;
Os;
Os;
Os;
Os; Low-background HPGe γ spectrometry The interest to α decay, a phenomenon discovered more than 100 years ago [1], is still great, bothfrom the theoretical and the experimental sides. Various theoretical models are continuously Corresponding author at: Dipartimento di Fisica, Universit`a di Roma “Tor Vergata”, I-00133 Rome, Italy.E-mail address: [email protected] (R. Bernabei) α decays of naturally occurring osmium isotopes. J π is spin andparity of the nuclei, E is the energy of excited levels of the daughter nuclei, the Q α value isgiven for the g.s. to g.s. transitions. The g.s. of the parent nuclei is assumed. The limitsobtained in the present work are given at 90% confidence level (C.L.). Transition, J π , E (keV) Q α (keV) Partial T / (yr)[22] Theoretical Experimental[23] [24, 25] [5] [11] Os, 0 + → W, 0 + , g.s. 2958.7(16) 7 . × . × . × . × > . × [17] > . × [19]= (1 . ± . × [20] Os, 0 + → W, 2 + , 103.6 2 . × . × . × . × ≥ . × this work Os, 0 + → W, 4 + , 337.6 2 . × . × . × . × ≥ . × this work Os, 0 + → W, 0 + , g.s. 2821.2(9) 4 . × . × . × . × = (2 . ± . × [21] Os, 0 + → W, 2 + , 100.1 2 . × . × . × . × ≥ . × this work Os, 0 + → W, 4 + , 329.4 2 . × . × . × . × ≥ . × this work Os, 1 / − → W, 1 / − , g.s. 2721.7(9) 4 . × . × . × . × – Os, 1 / − → W, 3 / − , 46.5 4 . × . × . × . × ≥ . × this work Os, 1 / − → W, 5 / − , 99.1 2 . × . × . × . × ≥ . × this work Os, 0 + → W, 0 + , g.s. 2143.2(9) 6 . × . × . × . × – Os, 0 + → W, 2 + , 111.2 2 . × . × . × ≥ . × this work Os, 0 + → W, 4 + , 364.1 1 . × . × . × ≥ . × this work Os, 3 / − → W, 3 / − , g.s. 1976.1(9) 2 . × . × . × ≥ . × this work Os, 3 / − → W, 1 / − , 23.5 1 . × . × . × ≥ . × this work Os, 3 / − → W, 5 / − , 65.9 2 . × . × . × ≥ . × this work Os, 0 + → W, 0 + , g.s. 1375.8(12) 3 . × . × . × – Os, 0 + → W, 2 + , 122.6 1 . × . × . × ≥ . × this work Os, 0 + → W, 4 + , 396.5 5 . × . × . × ≥ . × this work Os, 0 + → W, 0 + , g.s. 361(4) 1 . × . × . × ≥ . × this work Os, 0 + → W, 2 + , 143.2 1 . × . × . × ≥ . × this work developed or improved (see e.g. [2, 3, 4, 5, 6, 7, 8, 9, 10, 11] and references therein), in particularmotivated by searches for stable or long-lived super-heavy isotopes [12, 13, 14] and predictionsof their half-lives.Improvements in the experimental sensitivity, especially related with the use of super-low-background set-ups located in underground laboratories, have led during the last decade to thediscovery of α decays which were not observed previously due to their extremely long half-lives.We refer the interested readers to [15] where the current status of the experimental searchesfor rare α and β decays is reviewed. The half-life of Hf was remeasured recently (afterpublication of the review [15]) with improved accuracy as T / = (7 . ± . × yr with thehelp of a Cs HfCl scintillator [16].All the seven naturally occurring osmium isotopes are potentially unstable relative to α decay (see Table 1), however, only for two of them (with the highest Q α values) indications ontheir existence were obtained. For Os, only limits were known previously: T / > . × yr [17, 18] set with nuclear emulsions, and T / > . × yr [19] with proportional countermeasurements of Os sample enriched in Os to 2.25%. However, recently an indication on α decay of Os was found in geochemical measurements [20] where an excess of daughter
Wwas measured in meteorites and terrestrial rocks; the half-life was determined as T / = (1 . ± . × yr, which is in contradictions with the results of the direct laboratory measurements.The decay of Os with T / = (2 . ± . × yr was observed in direct experiment with asemiconductor detector and an Os sample enriched in Os to 61.27% [21].2 + Os Q a + % ) + % ) W + + Os Q a + + % )229.3(83.6 % ) W + - Os Q a - % )52.6(7.5 % ) - % ) W - + Os Q a + + % )252.8(87.4 % ) W + Figure 1: (Color online) Expected schemes of
Os,
Os,
Os and Os α decay to thetwo first excited levels of daughter nuclei. The Q α values, energies of the levels and of thede-excitation γ quanta are given in keV; the probabilities of γ quanta emission are given inparentheses [28, 29, 30, 18].The process of α decay can be accompanied by the emission of γ quanta when the decaygoes to excited level(s) of a daughter nucleus. In this work, we look for γ quanta expectedin α decays of the naturally occurring osmium nuclides to the two lowest excited levels ofdaughter nuclei (see Figs. 1 and 2 where expected schemes of α decay of the osmium isotopesare shown). It should be noted that the Os and
Os also α decay to the ground state ofthe daughter nuclei can be searched for thanks to the β -instability of the daughter nuclideswhich is also accompanied by γ quanta. The experiment was realized with the help of ultra-lowbackground HPGe γ spectrometry of a highly purified osmium metal sample with the naturalisotopic composition. The isotopic composition of the osmium was measured precisely withthe help of Negative Thermal Ionization Mass Spectrometry. The results of the previous stageof the experiment, which was devoted mainly to search for 2 β processes in Os and
Os,were reported in [26, 27]. The main attention in the present study is focused on the search for α decays with emission of γ quanta in Os and
Os, taking into account the theoreticallyhighest decay probabilities for these nuclides (see Table 1).3 /2 - Os Q a - % )42.3(0.08 % ) - % ) W - Q b T Re % ) + + + Os Q a + % ) W + Q b T Re Q b T
17 h1 - Os + + % ) + Os Q a + + % )273.9(89.8 % ) W + Figure 2: (Color online) Expected schemes of
Os and Os α decay to the two first excitedlevels of daughter nuclei. The decay scheme of Os is also reported. The Q α values, energiesof the levels and of the de-excitation γ quanta are given in keV; the probabilities of γ quantaemission are given in parentheses [31, 32, 33]. 4 Experiment
Osmium in form of metal of at least 99.999% purity grade [34] was used in the present experi-ment. The material was obtained from osmium powder by electron-beam melting with furtherpurification by electron-beam zone refining at the National Science Center “Kharkiv Instituteof Physics and Technology” (Kharkiv, Ukraine). The osmium in form of four ingots with atotal mass of 173 g was used in the first low-background experiment aiming at the search fordouble beta processes in
Os and
Os [26, 27]. Preliminary results of the searches for α decay of Os and
Os to the first excited levels of daughter nuclei were reported too [27].The density of osmium metal is very high (in fact, osmium is the densest naturally occur-ring element: the sample density was estimated to be 23 g/cm , while the reference value is22.587 g/cm [35]). Thus, γ -ray quanta expected to be emitted in the α decays of the natu-rally occurring osmium isotopes are strongly absorbed in the sample. To increase the detectionefficiency the ingots were cut into thin slices with a thickness of (0 . − .
25) mm by using amethod of electroerosion cutting with brass wire in kerosene. The slices were then etched in asolution of nitric and hydrochloric acids and washed by ultra-pure water.
The Os isotopic composition was analysed in the John de Laeter Centre at Curtin University(Perth, Western Australia). In order to achieve a complete digestion of the pure Os metal, theCarius tube digestion method modified from Shirey and Walker [36] was applied. Approximately0.5 mg of Os metal was consumed for each of the two samples studied. The acid digestion wasdone using concentrated acids (3 mL of purged double-distilled HNO and 1 mL of triple-distilled HCl). This mixture was chilled and sealed in previously cleaned Pyrex TM borosilicateCarius Tubes and heated up to 220 ◦ C for 60 h. Osmium was extracted from the acid solutionby chloroform solvent extraction [37], then back-extracted into HBr, followed by purificationvia microdistillation [38]. The purified Os fraction of each of the two samples was loaded ontofive separate Pt filaments (ten in total), and measured using Negative Thermal Ionisation MassSpectrometry (N-TIMS) on a Thermo-Fisher Triton TM mass spectrometer using Faraday cupcollectors. The beam for samples studied was maintained at ∼ − A (for
Os) for extendedperiod of time for Os metal (100 blocks of 10 cycles were collected), allowing to obtain astandard error of the mean precision below 10 ppm level [39]. The measured oxide ion ratiosOsO − were corrected for isobaric oxygen interferences to obtain element ratios, which werecorrected for mass fractionation using a Os/
Os value of 3.08271 [40].The pure Os metal gave the average of
Os/
Os ratio 0 . ± . Os/
Os ratio 0 . ± . . ± . Os/
Os ratio for the blank was0 . ± .
020 ( n = 2).A summary of the osmium isotopic composition, as well as numbers of nuclei of the osmium5able 2: Isotopic composition ( δ ) of the osmium measured in the present work and the numbersof nuclei of each isotope in the sample calculated by using the measured isotopic concentrations.The representative isotopic abundances from [43] are given too.Isotope δ (%) Number of nucleiIUPAC [43] this work in the sample Os 0.02(2) 0.0170(7) 6 . × Os 1.59(64) 1.5908(6) 5 . × Os 1.96(17) 1.8794(6) 7 . × Os 13.24(27) 13.253(3) 4 . × Os 16.15(23) 16.152(4) 6 . × Os 26.26(20) 26.250(8) 9 . × Os 40.78(32) 40.86(5) 1 . × isotopes in the sample are given in Table 2. The accuracy of the Os measurement [0.0170(7)%]is similar to the accuracy of the “best measurement from a single terrestial source” [0.0197(5)%][42], and is definitely higher than the error scale recommended by IUPAC: 0.02(2)% [43]. The
Os isotopic concentration was measured with a much higher accuracy than the recommendedrepresentative isotopic abundance too. Also for other Os isotopes the errors in the present studyare much smaller than the ones given in [43] . The Os slices (see Sec. 2.1) with a total mass of 117.96(2) g were fixed on the inner surfaceof a plastic Petri dish (with a thickness of 0.8 mm) with the help of Scotch 811 removabletape. The Petri dish with the Os slices was installed directly on the aluminium end-cap ofthe cryostat of the ultra-low background Broad-Energy Germanium (BEGe) detector with avolume of 112.5 cm (Fig. 2.3). The detector, thanks to a very thin dead layer of 0.4 µ m, offersa high sensitivity to low-energy photons. The detector with the Os sample was shielded bylayers of ≈ ≈ γ sources in the beginning of the experiment. Then the data of each run werere-calibrated by using clear and intensive background γ peaks of K, Tl,
Pb,
Pb and
Bi to improve the energy resolution in the final sum spectrum. The dependence of energy Moreover, there is still a room for improvement of the Os isotopic composition accuracy as it was recentlydemonstrated in [44]. γ -ray quanta ( E γ , in keV) in thesum energy spectrum can be approximated by the following function:FWHM (keV) = 0 . . × q E γ . (1)The re-calibration procedure allowed to improve the detector energy resolution in the finalspectrum by 13% (at energy 100 keV) in comparison to the sum energy spectrum obtainedwithout the correction. The energy spectrum measured with the Os sample for 15851 h is shown in Fig. 4 togetherwith the background energy spectrum taken over 1660 h. One can see that the counting rate inthe spectrum measured with the Os sample below ≈ . γ -ray from Pb in the lead details of the shielding), and thus reducing thecount rate at low energies. 7
500 1000 1500 2000 2500 3000
Pb351.9,
Pb511Annihilation609.3,
Bi1120.3,
Bi1460.8, K1764.5,
Bi2204.1
Bi 2614.5 Tl Energy (keV) C oun t s / k e V Figure 4: Energy spectra accumulated for 15851 h with the Os sample (solid line, blue online)and background energy spectrum measured over 1660 h without sample (dots; red online). Thebackground data are normalized to the time of measurements with the Os sample. Energies of γ -ray peaks are in keV. 8he peaks in the energy spectra belong mainly to γ -ray quanta of naturally occurringprimordial radionuclides: K, and daughters of
Th, U, U. There are also weak peaks inboth the spectra that can be ascribed to Co and
Cs. Specific activities of the radionuclidesin the Os sample were calculated with the following formula: A = ( S sample /t sample − S bg /t bg ) / ( η · ε · m ) , (2)where S sample ( S bg ) is the area of a peak in the sample (background) spectrum; t sample ( t bg ) isthe time of the sample (background) measurement; η is the γ -ray emission intensity; ε is the fullenergy peak efficiency; m is the sample mass. The detection efficiencies to γ -ray quanta werecalculated using the GEANT4 simulation package [46, 47, 48], the decay events were generatedhomogeneously in the Os sample. If no statistically significant peak excess was observed (thecases of Co, daughters of
Th,
U and
U), only upper limits on the specific activitiesof the radioactive impurities in the sample were set. A summary of the Os sample radioactivecontamination is given in Table 3.Table 3: Radioactive contamination of the Os sample measured by the ultra-low-backgroundBEGe γ detector. Decay chain Radionuclide Specific activity (mBq/kg) K 11 ± Co ≤ . Cs 0 . ± . Th Ra ≤ . Th ≤ U U ≤ . Pa ≤ . Ac ≤ . U U ≤ Ra ≤ . Pb ≤ α decays of Os and
Os to the first excited levelsof daughter nuclei
There are no peaks in the energy spectrum measured with the Os sample that can be interpretedas α decay of naturally occurring osmium nuclides. Thus, by analysis of the data one can sethalf-life limits on the processes searched for with the help of the following formula:lim T / = N · ln 2 · η · ε · t lim S , (3)where N is the number of nuclei of the isotope of interest (given in Table 2), η is the γ quantaemission intensity (see Figs. 1 and 2), ε is the detection efficiency for γ quanta expected in thedecays, t is the time of measurement (15851 h), and lim S is the upper limit on the number ofevents of the effect searched for which can be excluded at a given C.L.9he detection efficiencies to γ -ray quanta expected in the decays searched for were MonteCarlo simulated with the GEANT4 [46, 47, 48] and the EGSnrc [49] packages in two geometries:with uniform and granulated source. In the “uniform geometry” the source was approximatedby a disc of 88 mm in diameter with a thickness of 0.88 mm, plus a ring with an inner diam-eter of 90 mm and a height of 8 mm, with the same thickness. The “granulated geometry”reproduces the actual geometry of the source in a more accurate way (separate objects withgaps between them). Both the GEANT4 and EGSnrc codes give compatible results with thestandard deviation of the relative difference 2 .
7% for γ quanta in the energy range from 46.5keV to 273.0 keV (for the “uniform geometry”). The main difference in the simulations re-sults is due to the different source geometries. The relative difference between the detectionefficiencies for the “uniform” and “granulated” geometries decreases from 11.9% to 4.5% withincrease of γ quanta energy from 46.5 keV to 273.0 keV, with a systematically higher efficiencyfor the granulated source. The higher efficiency for the “granulated geometry” can be explainedby the contribution of γ -quanta events emitted from the side parts of the osmium slices (incontrary to the uniform source geometry with no gaps in the Os material). The increase of thedifference with decrease of the γ -quanta energy can be explained by the “edge effect” that ismore significant at low energies. Taking into account that the “granulated geometry” describesthe sample in a more accurate way we use the detection efficiencies obtained with this geometryfor the further analysis. The full energy peak detection efficiencies for the α decays under studyare presented in Table 4.Table 4: Full energy peak detection efficiencies, ε , for signature γ -ray quanta with energy E γ , γ quanta emission intensity η , measured numbers of events ( S ), their standard deviations (∆ S )and estimated values of lim S (see discussions in the text) for α transitions with emission of γ quanta in naturally occurring osmium isotopes. The relative systematic uncertainties σ r andfactors a (see text below) to take into account the systematic uncertainties are given in the lasttwo columns. Transition E γ η ε S ∆ S lim S σ r a (keV) Os, 0 + → W, 2 + , 103.6 103.6 0.227 0.01382 − . Os, 0 + → W, 4 + , 337.6 234.0 0.845 0.05097 22.4 24.6 62.7 0.095 1.183 Os, 0 + → W, 2 + , 100.1 100.1 0.204 0.01274 8.6 21.8 44.4 0.135 1.325 Os, 0 + → W, 4 + , 329.4 229.3 0.836 0.05090 − . Os, 1 / − → W, 3 / − , 46.5 46.5 0.106 0.00695 1272 42 1341 0.120 1.493 Os, 1 / − → W, 5 / − , 99.1 99.1 0.0913 0.01219 2.9 22.8 40.3 0.117 1.254 Os, 0 + → W, 2 + , 111.2 111.2 0.280 0.01629 3.8 30.7 54.1 0.150 1.568 Os, 0 + → W, 4 + , 364.1 252.8 0.874 0.05200 − . Os, 3 / − → W, 3 / − , g.s. 125.4 0.00019 0.02098 − . Os, 3 / − → W, 5 / − , 65.9 65.9 0.061 0.01936 30.7 23.6 69.4 0.189 1.689 Os, 0 + → W, 2 + , 122.6 122.6 0.356 0.02085 17.3 24.4 57.3 0.122 1.296 Os, 0 + → W, 4 + , 396.5 273.9 0.898 0.05197 21.3 24.3 61.2 0.067 1.090 Os, 0 + → W, 0 + , g.s. 155.0 0.1549 0.03220 93.7 29.3 142 0.081 1.159 Os, 0 + → W, 2 + , 143.2 143.2 0.500 0.02898 42.5 27.0 86.8 0.090 1.180 Th100.1
Os 103.6
Os 106.7Unidentified
Energy (keV) C oun t s / . k e V Figure 5: Energy spectrum measured with the Os sample for 15851 h in the region where thepeaks with energies 100.1 keV and 103.6 keV after the α decay of the Os and of the
Os tothe first excited levels of daughter nuclei are expected. The fits of the data by the backgroundmodel (see text) are shown by solid lines (the fits for the 100.1 keV and 103.6 keV peaks arealmost indistinguishable). The peaks with energies 100.1 keV and 103.6 keV excluded at 90%C.L. are shown by dashed lines.To estimate the values of lim S , the energy spectrum taken with the Os sample was fitted inthe region of interest for a certain transition with the models accounting for the effect searchedfor and for the background. For instance, to estimate value of lim S for the decay of the Os to the first excited level of
W, the energy spectrum was fitted by a background modelconstructed from a linear function (to describe the continuous distribution), a peak with theenergy of 103.6 keV (the effect searched for), and an unidentified peak with energy ≈
107 keV.The data were fitted by the model with 5 free parameters: two parameters of the linear function,an area of the 103.6 keV peak, an area and a position of the unidentified peak. The peaks widthswere fixed according to the estimated energy dependence of the detector energy resolution (seeformula given in eq. (1)). The best fit was achieved in the energy interval (93 . − .
75) keVwith χ = 33 . α decay of Os to the firstexcited level of
W.The fits return the 100.1 keV and 103.6 keV peaks areas (8 . ± .
8) counts and ( − . ± .
3) counts, respectively, that is no evidence of the effects searched for . By using the recom-mendations [50] we get the following upper limits on the peaks areas: lim S = 44 . S = 28 . T / ( Os) > . × yr and T / ( Os) > . × yr, respectively. However, the limits include only statistical errors. The area of the unidentified peak is (60 ±
23) counts, the energy of the peak is (106 . ± .
15) keV. S depending on the fit interval were estimated by analysis of lim S distributions obtained from the fit of the data in the energy intervals within (93 . −
96) keVfor the starting point, and (110 − σ r were obtained by adding all thesystematic contributions in quadrature.Table 5: Estimated relative systematic uncertainties of the Os and
Os half-life limitsrelative to α decays to the first excited levels of the daughter nuclei.Source Nuclide Os OsDetection efficiency 0.098 0.118Interval of fit 0.076 0.065Isotopic abundance 0.041 0.0004Total relative systematic error ( σ r ) 0.131 0.135The systematic uncertainties σ r can be introduced into the obtained lower half-life limits bycorrection of the upper limits on the number of excluded events:lim S ′ = lim S × a, (4)where lim S ′ is a corrected upper limit, and the factor a is expressed by the formula proposedin [51]: a = [1 + (lim S − S ) × σ / . (5)After the correction the following half-life limits of Os and
Os relative to α decay tothe first excited levels of the daughter nuclei were obtained: T / ( Os) > . × yr, T / ( Os) > . × yr.It should be noted that the limits substantially exceed the present theoretical predictions(see Table 1). In particular, the limits are one order of magnitude higher than the estimatesobtained by using the empirical relationships based on the unified model for α decay and α capture (UMADAC) [5] and the half-life values calculated in the framework of a semi-empiricalmodel based on the quantum mechanical tunneling mechanism through a potential barrier [11]. α decays of osmium nuclides with emission of γ quanta Due to the smaller energy release, the theoretical predictions on half-lives of α decays of Osand
Os to the second excited levels of daughter nuclei, not to say for α decays of other12smium nuclides, are much longer. Thus, the sensitivity of the present experiment looks toolow to detect the processes. Nevertheless, the experimental data were used to analyze otherpossible decays of the osmium nuclides too.Examples of the energy spectrum fits in the regions of interest for the α decays of Osand
Os to the second excited levels of
W and
W, and for the α decays of Os to thefirst 46.5 keV excited level of
W are shown in Fig. 6. Unfortunately, the signature γ peakexpected in the decay of Os interferences strongly with the 46.5 keV γ -ray peak of Pb(daughter of
Rn from the
U family), typically present in low-background γ spectra. Thus,we accept the peak area (1272 counts) plus its standard error (42 counts) multiplied by 1.64 toget an estimation of lim S for this decay channel at 90% C.L. Os229.3,
Os 238.6,
Pb 242.0, Pb a Energy (keV) C oun t s / . k e V Os46.5,
Pb 61.5, 63.0, K X-ray Os63.2, Th b Energy (keV) C oun t s / . k e V Figure 6: Energy spectrum measured with the Os sample for 15851 h in the region where peakswith energies 234.0 keV ( α decay of Os to the 337.6 keV excited level of
W) and 229.3keV ( α decay of Os to the 329.4 keV excited level of
W) are expected (a). Low energypart of the spectrum, where a peak with an energy of 46.5 keV is expected ( α decay of Osto the 46.5 keV excited level of
W) (b). The existing peak with this energy can be explainedby γ quanta after β decay of Pb. Fits of the data by the background model are shown bysolid lines. The peaks searched for, excluded at 90% C.L., are shown by dashed lines.To estimate the lim S values for other possible decay channels the experimental spectrumwas analyzed in the different energy intervals in a similar way as described above. The detectionefficiencies and the emission intensities for the signature γ -ray quanta, the obtained values of S , ∆ S and lim S , the relative systematic errors σ r and the factors a to account systematicuncertainties of the limits are given in Table 4, while the half-life limits on the α decays of13aturally occurring osmium isotopes with emission of γ quanta are summarized in Table 1.It should be noted that for Os and
Os also decays to the ground states of the daughternuclei (in general, to any states of the daughter nuclei) were set due to the β -instability of thedaughter nuclides with lifetimes short enough to be in equilibrium with the parent nuclides.However, the theoretically estimated half-lives of the nuclides are very long to be observed ina realistic experiment. At the same time our experiment is not sensitive to the α decay of Os to the first 23.5 keV excited level of
W due to an approximately two times higherenergy threshold of the detector ≈
42 keV. Nevertheless, the limit obtained for the g.s. tog.s. transition (by using the β -instability of W) is valid for α decay to all levels, includingexcited ones (it should be stressed, however, that also this decay is expected to be too rare tobe observed).It should be also noted that a significant area (93 . ± .
3) counts of the 155.0 keV peak(expected in the decay sequence Os → W → Re → Os) was interpreted asabsence of the effect searched for. The peak can be explained by several sources: • γ -ray quanta with energy 154.0 keV of Ac (daughter of
Ra from the
Th family;emission probability 0.722%). • γ -ray quanta with energy 154.2 keV of Ra (daughter of
Ac from the
U family;emission probability 5.7%). • γ -ray quanta with energy 155.0 keV of Re (daughter of
W that can be cosmogenically-produced in osmium; emission probability 15.49%). • Thermal neutron capture γ -ray quanta with energy 155.0 keV emitted with an intensity65% after neutron-captures in Os that has a rather big thermal neutron cross section(320 ±
10 barn).Precise determination of the 155.0 keV peak area is difficult since the thermal neutrons flux inthe set-up, activity and localization of the
Ra and
Ac are unknown. Also estimation ofcosmogenic
W activity in the Os sample is not a trivial task. Here we conservatively ascribeall the counts in the 155 keV peak (with error bar) to the
Os alpha decay.
We calculated theoretical half-lives of Os nuclides relative to α decay using the semi-empiricalformulae [23] based on the liquid drop model and the description of α decay as a very asymmetricfission process. As well, the cluster model of Refs. [24, 25] was used. The approaches [23, 24,25] were tested with a set of experimental half-lives of almost four hundred α emitters anddemonstrated good agreement between calculated and experimental T / values, mainly insidea factor of 2 −
3. For Os α decays with a difference between spins and parities of the parent andthe daughter nuclei, which resulted in non-zero angular momentum l of the emitted α particle,we take into account the additional hindrance factor HF , calculated in accordance with [52](for the lowest possible l value). In particular, for the most important α decays of Os and
Os to the first excited levels of the daughter nuclei (0 + → + transitions), HF ≃ . α decays were observed at the first time:14 for W, the calculated values are T / = 2 . × yr [23] and T / = 8 . × yr[24, 25] while the experimental values are in the range of (1 . − . × yr [53, 54, 55, 56, 57];– for Eu, the calculated values are T / = 3 . × yr [23] and T / = 2 . × yr[24, 25] with the experimental half-life near 5 × yr [58, 59];– for α decay of Pt to the first excited level of
Os ( E exc = 137 . T / = 4 . × yr [23] and T / = 2 . × yr [24, 25] while the experimentalvalue is (2 . ± . × yr [60] ;– it is interesting to note that for Hf the calculated values T / = 7 . × yr [23]and T / = 3 . × yr [24, 25] were in strong contradiction with the old experimental valueof (2 . ± . × yr [61] (by factor of 17 − . ± . × yr [16] in a good agreement with calculations [23, 24, 25].The T / values calculated in accordance with [23, 24, 25] are presented in Table 1. Inaddition, we give the results obtained here with the semi-empirical formulae of Ref. [5] whichalso were successfully tested with about four hundred experimental α decays and which take intoaccount non-zero l explicitly. Also, recent calculations of Ref. [11] for Os isotopes, includingtransitions to the excited daughter levels, are presented in Table 1. A search for the alpha activity accompanied by the emission of γ -ray quanta in naturallyoccurring osmium isotopes was realized by an ultra-low background Broad-Energy Germanium γ detector located deep underground at the Gran Sasso National Laboratory of INFN (Italy).A sample of ultra-pure osmium with a mass of 118 g, composed of thin osmium slices with anaverage thickness of 0.88 mm, was used as a source of the decays. The isotopic compositionof osmium in the sample was precisely measured with the help of Negative Thermal IonisationMass Spectrometry, that is especially important for the isotope Os (theoretically the shortestliving candidate) whose representative isotopic abundance was given with a very big uncertaintyof ± γ -ray quanta expected in the decays searched for were observed but lower limits on theprocesses were set at level of lim T / ∼ − yr. The half-life limits for α decays of Osand
Os to the first excited levels of daughter nuclei have been set at 90% C.L. as T / ≥ . × yr and T / ≥ . × yr, respectively. The limits exceed substantially the presenttheoretical estimations of the decays probabilities that are within T / ∼ (0 . − × yr for Os and T / ∼ (0 . − × yr for Os.A new stage of the experiment is in progress by using an advanced geometry with theosmium sample placed directly on the BEGe detector inside its cryostat to increase the detectionefficiency to the low energy γ -ray quanta expected in the theoretically fastest decays of Osand
Os to the first excited levels of the daughter nuclei. Obviously, a further improvement ofthe experimental sensitivity to the decays with the highest decay probabilities can be achievedby using samples of osmium enriched in the
Os,
Os and
Os isotopes. Observation ofother Os isotopes α -instability looks practically problematic taking into account the very longtheoretically predicted half-lives. We use here for calculations the AME2016 Q α values from [22]. We corrected here the original value of T / = 2 . × yr [60] calculated for Pt natural abundance of δ = 0 . δ = 0 . Acknowledgments
D.V.K. and O.G.P. were supported in part by the project “Investigation of double beta decay,rare alpha and beta decays” of the program of the National Academy of Sciences of Ukraine“Laboratory of young scientists” (the grant number 0120U101838).
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