New limits on double-beta decay of $^{190}$Pt and $^{198}$Pt

A search for double-beta decay of $^{190}$Pt and $^{198}$Pt with emission of $\gamma$-ray quanta was realized at the HADES underground laboratory with a 148 g platinum sample measured by two ultralow-background HPGe detectors over 8946 h. The isotopic composition of the platinum sample has been measured with high precision using inductively coupled plasma mass spectrometry. New lower limits for the half-lives of $^{190}$Pt relative to different channels and modes of the decays were set on the level of $\lim T_{1/2}\sim 10^{14}-10^{16}$ yr. A possible exact resonant $0\nu KN$ transition to the 1,2 1326.9 keV level of $^{190}$Os is limited for the first time as $T_{1/2} \geq 2.5 \times10^{16}$ yr. A new lower limit on the double-beta decay of $^{198}$Pt to the first excited level of $^{198}$Hg was set as $T_{1/2} \geq 3.2\times10^{19}$ yr, one order of magnitude higher than the limit obtained in the previous experiment.


Introduction
Double-beta decay was considered for the first time by Goeppert-Mayer in 1935 [1]. The neutrino accompanied mode of the decay with emission of electrons (two-neutrino double-beta decay, 2ν2β − ) is allowed in the Standard Model of particles and interactions (SM) and is already observed in eleven nuclei with measured half-lives in the range T 1/2 ∼ (10 19 − 10 24 ) yr [2]. Another possibility could be 2β − decay without neutrino emission, neutrinoless doublebeta decay (0ν2β − ). However, this process violates the lepton number conservation and is only possible if neutrinos are massive Majorana particles [3]. Thus, the 0ν2β − decay is the most sensitive test of the lepton number conservation law and one of the most promising tools to study properties of the neutrino and the weak interaction. In general, the neutrinoless process can be mediated by many effects beyond the SM and is considered as one of the most powerful probes of the SM [4,5,6,7]. Despite the attempts, the 0ν2β − decay is still not observed: the most sensitive experiments give upper half-life limits in the range lim T 1/2 ∼ (10 24 − 10 26 ) yr.
where Γ f = Γ 1 + Γ 2 is the de-excitation width of the electron shell of the daughter nuclide. The degeneracy parameter ∆ is equal to Q 2β − E exc − E b1 − E b2 , where E exc is the energy of the daughter nucleus excited level, E bi are the binding energies of the captured electrons on the atomic shells of the daughter atom. Taking into account the presently recommended Q 2β value [25] the resonance parameter for 190 Pt (normalized on the value for the 0ν2ε decay 54 Fe → 54 Cr) can reach one of the biggest values ≈ 7.0 × 10 8 among the possible resonant transitions [24] 2 . The method of ultralow-background HPGe γ-ray spectrometry was applied in the present study to search for different channels and modes of 2ε and εβ + processes in 190 Pt, including the possible resonant transitions in the nuclide. A simplified decay scheme of another possible 2β unstable isotope of platinum, 198 Pt, is presented in Fig. 2. The 2β − transition of 198 Pt to the first 2 + 411.8 keV excited level of 198 Hg is expected to be accompanied by emission of γ-ray quanta with energy 411.8 keV that can be detected by γ-spectrometry methods too.  [30]. The energies of the excited level and of the emitted γ quantum are in keV. Q 2β is the double-beta decay energy of 198 Pt.
In the next Section we describe the high-purity platinum sample, precise measurements of its isotopic composition, and the ultralow background HPGe detector system used in the experiment. The data analysis and obtained limits on the 2ε and εβ + processes in 190 Pt and the 2β − decay of 198 Pt to the first excited level of the daughter are presented in Section 3. A summary of the experiment is given in the Conclusions section.

Experiment
2.1 Platinum sample, isotopic composition of the material A disk-shaped sample of metallic platinum with a diameter of 25.04(1) mm, a thickness of 14.07(2) mm, and with a mass of 148.122(1) g was used in the experiment. The purity grade of the platinum is 99.95% 3 . The representative isotopic abundance of 190 Pt in normal terrestrial materials has a rather big uncertainty δ = 0.012(2)% [26]. Thus, special mass-spectrometry measurements of the sample were realized.
The Pt isotopic measurements were acquired using a sector field ICP-MS ELEMENT XR (ThermoScientific) at the John de Laeter Centre for Isotope Research, Curtin University. Measurements of masses 190 Pt,192 Pt,194 Pt,195 Pt,196 Pt,and 198 Pt were performed in low resolution mode using electrostatic scanning (e-scan, i.e., peak jumping) from a set magnet mass at 190 Pt. Due to the drastically different abundances of Pt isotopes, the ELEMENT XR's triple detection mode is advantageous for such analyses as isotopes such as 190 Pt and 192 Pt can be measured in a pulse-counting detection mode, while the remaining masses can be analysed in analogue mode all within the same analytical session. Prior to the analysis of each sample, a blank solution of 2% HNO 3 was measured to correct for background. A summary of the platinum isotopic composition, as well as numbers of nuclei of the isotopes in the sample are presented in Table  1. Table 1: Isotopic composition (δ) of the platinum sample measured in the present work and the numbers of nuclei of each isotope in the sample calculated by using the measured isotopic concentrations. The combined standard uncertainties of the isotopic abundances are given with a coverage factor k = 2 (approximately 95% level of confidence). The representative isotopic abundances from [26] are given too.
Isotope δ (%) Number of nuclei IUPAC [26] this work in the sample

Ultralow-level gamma-ray spectrometry measurements
The platinum sample was measured in an ultralow-background HPGe-detector system located 225 m underground in the laboratory HADES (Belgium) [31,32]. The detector system consists of two p-type Extended Range HPGe-detectors facing each other (see a schematic of the set-up in Fig. 3). Both the detectors were manufactured by Canberra semiconductor (Olen, Belgium). The detectors were shielded by 35 mm electrolytic copper (innermost) then 40 mm ultralowlevel lead and on the outside 145 mm lead. The main characteristics of the HPGe detectors are presented in Table 2, more details of the detector system can be found in [33].

Radionuclides detected in the platinum sample
The sum energy spectra measured by the Ge7 and Ge15 detectors with the Pt sample and without sample (background) are shown in Fig. 4. The majority of the peaks can be assigned to 40 K and nuclides of the 232 Th, 235 U and 238 U decay families. There are also peaks of 22 Na, 26 Al, 54 Mn, 60 Co, 137 Cs and 110m Ag. The traces of 22 Na, 26 Al and 110m Ag that were detected are presumingly reminiscence from neutron activation of minor impurities of the Pt-sample during the neutron experiment in Dresden and during air-transport. Radioactive 22 Na and 26 Al can be also cosmogenically generated in the aluminum details of the HPGe detectors [34]. 54 Mn and 60 Co are typical cosmogenic radionuclides that can be produced in Pt, copper and some other materials of the set-up. Presence of 137 Cs can be a result of the set-up (sample) pollution after the Chernobyl or (and) Fukushima Daiichi nuclear disasters. In the Pt data there is a clear γ peak with energy 137.2 keV due to the α decay of 190 Pt to the 137.2 keV excited level of 186 Os [35] 4 . Also peaks due to neutron-gamma reactions on the materials of the set-up were observed: in particular, a 139.7-keV peak of 75m Ge produced by neutron-gamma reaction on 74 Ge, a 198.4-keV peak from 70 Ge(n,γ) 71m Ge reaction, a 202.6-keV peak from 115 In(n,γ) 116 In reaction. There is also a peak of 41 Ar with energy 1293.6 keV due to operation of the BR-1 nuclear reactor of the Belgian nuclear research centre. The peak is present on few specific days (approximately 15 days in total) during the measurements when air blows from the reactor towards the inlet of the ventilation for the HADES laboratory. We have decided to do not exclude the data with the 41 Ar peak taking into account a rather mild effect of the radioactivity in the energy intervals of interest.
The energy dependence of the energy resolution in the sum energy spectrum measured with the Pt sample by the detectors Ge7 and Ge15 was determined for the low energy region (65−352 keV) by using intense X-ray and γ-ray peaks with energies 65.1 keV and 66.8 keV (K α2 and K α1 X-ray of Pt), 137.2 keV ( 190 Pt), 238.6 keV ( 212 Pb), 295.2 keV and 351.9 keV ( 214 Pb) as: where E γ is in keV. For the energies above 352 keV we use an approximation obtained by analysis of the γ peaks 238.6 keV ( 212 Pb), 295.2 keV and 351.9 keV ( 214 Pb), 583.2 keV ( 208 Tl), 609.3 keV ( 214 Bi), 1173.2 keV and 1332.5 keV ( 60 Co) and 1460.8 keV ( 40 K): The specific activity 5 of all detected radionuclides was calculated using the following formula: where S sample (S bg ) is the area of a peak in the sample (background) spectrum; t sample (t bg ) is the time of the sample (background) measurement; ǫ is the γ-ray emission intensity of the corresponding transition; η is the full energy peak efficiency; m is the sample mass. The detection efficiencies were calculated with the EGSnrc simulation package [36,37], the events Counts / 5 keV were generated homogeneously in the Pt sample. The Monte Carlo models of the two detectors have being validated through several participations in proficiency tests and an additional validation measurement was done using a 57 Co point γ source. The standard deviation of the relative difference between the simulations and the experimental data is 3.3% for γ-ray peaks with energies 122.1 keV and 136.5 keV for the detectors Ge7 and Ge15. The estimated specific activities of radioactive impurities in the platinum are presented in Table 3.

Limits on the double-beta decay processes in 190 Pt
No peculiarity was observed in the experimental energy spectra that could be ascribed to the 2β decay processes in 190 Pt or 198 Pt. Thus, we set limits on different modes and channels of the decays by using the following formula: where N is the number of nuclei of interest in the sample (see Table 1), η is the detection efficiency for the γ-ray (X-ray) quanta searched for, t is the measuring time, and lim S is the number of events of the effect which can be excluded at a given C.L. In the present work all the lim S values and the half-life limits are given with 90% C.L. The detection efficiencies of the detector system to the γ (X-ray) quanta expected in different modes and channels of the double-beta processes in 190 Pt and 198 Pt were simulated with the EGSnrc simulation package [36,37], the decay events were generated by the DECAY0 events generator [38]. A cascade of X-rays and Auger electrons due to deexcitation of the Os electron shell with individual energies in the energy interval ≈ (61.5 − 73.4) keV is expected in the 2ν2K and 2νKL capture in 190 Pt. However, the energies of the L X-rays are very low, (7.8 − 12.5) keV, and therefore heavily attenuated by the sample and also by the aluminium-windows of the HPGe-detectors. The Auger electrons avoid detection for the same reason. Thus, the response of the detector system to the 2ν2K and 2νKL decays of 190 Pt was built assuming the following energies and intensities of X-rays from the K shell of the Os atom (only the X-rays with the intensities higher than 0.5% were considered): 61.5 keV (K α2 , 27.5%), 63.0 keV (K α1 , 47.3%), 71.1 keV (K β3 , 5.45%), 71.4 keV (K β1 , 10.50%), 73.4 keV (K β2 , 3.69%) [39]. The detection efficiencies to the X-ray quanta were simulated by the EGSnrc code. To estimate lim S values for the 2ν2K and 2νKL decays, the energy spectrum taken with the Pt sample was fitted in the energy interval 49 − 86 keV by the 2ν2K (2νKL) distribution 6  The half-life limits, the energies of the X-ray quanta (E γ ), which were used to set the T 1/2 limits, the detection efficiencies (η) and values of lim S are presented in Table 4 7 , where also results of the previous experiment [28] are given for comparison. The limit for the 2ν2K decay half-life slightly exceeds the one reported in the previous work [28], while the limit for the 2νKL capture is obtained for the first time.    [28] was set for the 2ν2K transition to the 186.7 keV level of 190 Os.
The 2ν double-electron capture in 190 Pt can undergo to several excited levels of 190 Os (see Fig. 1). In this case, in addition to X-rays cascade, γ-peaks at the energy of the excited level (in the transition to the first 2 + 186.7 keV excited level) and also at the energies of the transitions between the initial and final levels of the daughter are expected. To estimate lim S value for a possible 186.7-keV peak area, the experimental spectrum was fitted in the energy interval 176 − 194 keV by a model consisting of a straight line, peaks of 235 U and 226 Ra with energies 185.7 keV and 186.2 keV, respectively, and a Gaussian peak at 186.7 keV with the width fixed according to the formula (2) to describe the effect searched for. The fit returns a 186.7-keV peak area S = −28 (39) counts, that corresponds to lim S = 39 counts following the recommendations [40]. A part of the energy spectrum gathered with the Pt sample in the vicinity of γ peak 186.7 keV expected in the 2ε decay of 190 Pt to the 2 + 186.7 keV excited level of 190 Os is presented in Fig. 6. The half-life limits for the transitions to higher excited levels of 190 Os were obtained in a similar way. The limits are presented in Table 4.  In the 0ν double-electron capture in 190 Pt the energy excess is assumed to be emitted by bremsstrahlung γ-ray quanta with an energy E γ = Q 2β − E b1 − E b2 − E exc . To estimate values of lim S for the 0ν double-electron captures from K and L shells, the experimental spectrum was fitted in the regions of the expected peaks with energies (for the g.s. to g.s. transition) 1253.6±0.4 keV, 1315.5±1.4 keV and 1377.5±2.5 keV for the 0ν2K, 0νKL, and 0ν2L captures, respectively. The variations of the expected peaks energy are due to the Q 2β value uncertainty and different binding energies of the L atomic shells. Thus, the energy of a peak searched for was free parameter of the fits within the variations. A straight line was taken to describe the continuous background. The background model included background γ peaks present in the energy intervals of the fits: 1238.1 keV of 214 Bi (to estimate a lim S for the 0ν2K decay), and 1377.7 keV of 214 Bi plus 1384.3 keV of 110m Ag (in the case of the 0ν2L capture). The results of the fits are shown in Fig. 7. The biggest peak areas were taken to derive the lim S values for the peaks searched for (see Table 4).  Limits on the neutrinoless 2ε transitions to the excited levels of the daughter were set by using the lim S values obtained to estimate the half-life limits for the two-neutrino processes. However, the detection efficiencies for the 0ν modes are slightly smaller due to the energy transfer to the bremsstrahlung γ-ray quanta (absent in the 2ν decay mode, where the energy is carried out by neutrinos).
The 0νKN transition in 190 Pt to the 1,2 1326.9 keV excited level of 190 Os is of special interest: the decay can be an exactly resonant, up to six orders of magnitude faster, if the degeneracy parameter ∆ = Q 2β − E exc − E b1 − E b2 ∼ 10 eV. However, with the uncertainties of the decay energy (±0.4 keV [25]) and of the 1326.9-keV level energy (±1.0 keV [27]) the degeneracy parameter lies in the interval from −0.13 keV to +0.26 keV with a combined uncertainty ±1.1 keV, that is too big to make a clear conclusion about resonance enhancement of the transition. Nevertheless, development of experimental techniques to study the decay at, as much as possible, high sensitivity level is an important task. The energy spectrum gathered with the Pt sample was fitted in the energy interval 1310 − 1357 keV to estimate a half-life limit on the decay. The background was described by a straight line and by a peak at 1332.5 keV (γ-peak of 60 Co). The position of the peak searched for was bounded within ±1 keV, while the peak width was fixed as FWHM = 2.33 keV according to the formula (3). The fit (with χ 2 /n.d.f.= 41.4/88 = 0.47) returned a peak area S = 29 ± 32 counts 8 . Considering the peculiarity as a statistical fluctuation we have obtained lim S = 81 counts. Taking into account the detection efficiency for γ-ray quanta with energy 1326.9 keV (η = 0.0488), the resonant 0νKN transition in 190 Pt to the 1,2 1326.9 keV excited level of 190 Os is limited as: The energy spectrum in the region of interest, the result of the fit and excluded peak for the possible resonant 0νKN transition in 190 Pt to the 1,2 1326.9-keV excited level of 190 Os is shown in Fig. 8 (a).
The bound on the transition to the 1326.9 keV level of 190 Os is limited by 60 Co background, that can be attributed entirely to the setup contamination (see Table 3) and not to the Pt sample. One can try to estimate a limit on the transition by analysis of the no-sample spectra subtracted from the data taken with the Pt sample, eliminating in such a way the 60 Co background. A fit of the background-subtracted spectrum by a straight line (to describe the continuous background) plus a Gaussian peak with the bounded position and fixed width (the effect searched for) is shown in panel (b) of Fig. 8 9 . However, statistical fluctuations in the background-subtracted spectrum are rather big due to a comparatively short time of the background measurement. As a result, the limit from the background-subtracted spectrum (lim S = 109 counts) is worse than the one from the sample-only spectrum. Nevertheless, the both approaches give comparable results providing a useful cross-check of the analysis. 8 If no bounds were set to the peak parameters, the energy of the peak was 1328.1(4) keV, the peak width FWHM = 2.28(40) keV, and the peak area S = 41(22) counts. 9 A fit of the data with no bounds on the peak position and width returned the peak area S = 34(17) counts and the peak position 1327.8(5) keV, however, with an abnormally small peak width FWHM = 0.4(3) keV.  The 0νLM transition of 190 Pt to the (0, 1, 2) + 1382.4(2) keV level of 190 Os can be characterized as "near" resonant one since the degeneracy parameter in this case is rather big ∆ = (2.9 − 6.1) ± 0.6 keV. The estimation of half-life limit for the decay was performed by analysis of the experimental data in the vicinity of γ peak with energy 1195.7(2) keV emitted in the de-excitation of the 1382.4 keV level. The result of the data fit in the energy interval 1177 − 1220 keV by a simple model constructed from a straight line and a Gaussian peak at 1195.7(2) keV with a fixed width is presented in Fig. 9.  The annihilation peaks at 511 keV were analyzed in the data with (without) the Pt sample to estimate half-life limits for the electron capture with positron emission in 190 Pt to the energetically allowed transitions to the ground state and to the excited 186.7 keV level of the daughter. A fit of the data with (without) the Pt sample gives the 511-keV peak area S = 3143 ± 71 counts for measurement time 8946 h (S = 266±18 counts for 674 h) that leads to the difference: −388 ± 249 counts that results in lim S = 134 counts. The energy spectrum taken with the Pt sample and the background spectrum in the vicinity of the 511 keV annihilation peak with the results of fits are shown in Fig. 10. The detection efficiencies are slightly different for the decays to the ground state and to the first 186.7 keV excited level of the daughter, as well as for the 2ν and 0ν modes of the decays. The obtained half-life limits are presented in Table 4.
The obtained limits on the possible double-beta processes in 190 Pt are higher up to an order of magnitude than the limits set in the previous study [28]. Moreover, the expected peaks positions for the 0ν2ε decays were far from the actual ones, taking into account a rather different Q 2β value and much bigger uncertainty at the time when the experiment [28] was carried out. For this reason, the half-life limits for the 0ν2K, 0νKL and 0ν2L captures can be considered as obtained for the first time.
However, the sensitivity of the present study is very far from theoretical estimations of the 190 Pt decay probability. For instance, the calculations of the 190 Pt half-life relative to the  Table  IV in [24]). Nevertheless, achievement of the sensitivity on the level of T 1/2 ∼ (10 26 − 10 27 ) yr looks realistic taking into account the great progress in the ultralow-background HPGe [14] and low-temperature bolometers [13,15,16,41] detection techniques, the experimental approaches that look the most promising for possible large-scale searches for the resonant 0ν2ε decays.  (3) returning an effect area S = −13±26 counts, that corresponds to lim S = 31 counts (the energy spectrum in the region of the fit is presented in Fig. 11). Taking into account the detection efficiency (η = 0.0414 both for the 2ν and 0ν modes of the decay), the following limit was obtained: The limit is one order of magnitude higher than that set in the previous experiment [28]. Theoretical calculations for the 2ν2β − decay of 198 Pt to the ground state of the daughter are in the interval T 1/2 ∼ 5×10 21 −5×10 23 yr [42,43]. Similar estimations give semiempirical formulae: T 1/2 = (3.0 ± 1.5) × 10 23 yr [44] and T 1/2 = 3.3 × 10 22 yr [45]. A probability of the 2ν2β − decay to the 2 + 411.8 keV excited level is expected to be several orders of magnitude lower due to a smaller value of the phase space factor and the spin change. The theoretical estimations of the 0ν2β − decay of 198 Pt to the ground state of 198 Hg are much higher: T 1/2 ∼ 3 × 10 26 − 2 × 10 28 yr [42,46,47,48] 10 , while the 0ν2β − transition to the 2 + 411.8 keV excited level of 198 Hg is expected to be further suppressed. Thus, the sensitivity of the present experiment is rather far from the theoretical predictions for the two-neutrino mode of the decay, not to say for the neutrinoless process. All the limits obtained in the present experiment are summarized in Table 4 where also results of the previous study [28] are given for comparison.

Summary and conclusions
A high-purity disk-shaped platinum sample with mass 148 g was measured in an ultralow background HPGe-detector γ-ray spectrometry system located 225 m underground at the HADES laboratory over 8946 hours aiming at searching for double-beta decay of 190 Pt and 198 Pt with emission of γ-ray quanta. The isotopic composition of the platinum sample has been measured with high precision using inductively coupled plasma mass spectrometry. No effect was observed but lower limits on the half-lives for the different channels and modes of the decays of 190 Pt were set on the level of lim T 1/2 ∼ 10 14 − 10 16 yr. A possible exact resonant 0νKN transition to the 1,2 1326.9 keV level of 190 Os is limited for the first time as T 1/2 ≥ 2.5 × 10 16 yr. A new improved limit is set for the 2β − transition of 198 Pt to the 2 + 411.8 keV excited level of 198 Hg as T 1/2 ≥ 3.2 × 10 19 yr. All the obtained limits exceed the previously obtained values up to one order of magnitude mainly thanks to a substantially bigger exposure (55.2 kg×day in the present work and 3.2 kg×day in [28]). However, the sample geometry was not optimised since it was an existing sample foreseen for another project. Thus, a further improvement of the present experiment sensitivity can be achieved by decrease of the sample thickness by production of thin disk with a diameter comparable to the detectors size.
The sensitivity of the experiment to the 190 Pt decays, particularly to the potentially resonant transition to the 1326.9 keV level of 190 Os, could be advanced by using platinum enriched in the isotope 190 Pt, increasing the exposure and detection efficiency by utilization of thin samples and multi-crystal system of HPGe γ-ray detectors or low-temperature bolometers. However, such an experiment could be considered after more accurate determination of the 1326.9-keV level energy (presently known with a rather big uncertainty ±1.0 keV). Nevertheless, we realize that implementation of such an experiment is practically a rather difficult task, first of all due to the inaccessibility of methods for enrichment of platinum isotopes in the hundreds kilograms scale requested for a competitive experiment (in terms of the Majorana neutrino mass) even in a case of an exact resonant transition.