Measurement of the double-β decay of 150Nd to the 0+1 excited state of 150Sm in NEMO-3

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Measurement of the double-β decay of 150Nd to the 0+1 excited state of 150Sm in NEMO-3 © The Author(s) 2023 Published version Aguerre, X.; Arnold, R.; Augier, C.; Barabash, A. S.; Basharina-Freshville, A.; Blondel, S.; Blot, S.; Bongrand, M.; Breier, R.; Brudanin, V.; Busto, J.; Bystryakov, A.; Caffrey, A. J.; Cerna, C.; Cesar, J. P.; Ceschia, M.; Chauveau, E.; Chopra, A.; Dawson, L.; Duchesneau, D.; Durand, D.; Evans, J. J.; Flack, R.; Franchini, P.; Garrido, X.; Girard-Carillo, C.; Guillon, B.; Guzowski, P.; Hoballah, M.; Hodák, R.; Hubert, P.; Hussain, M. H.; Jullian, S.; Klimenko, A.; Kochetov, O.; Konovalov, S. I.; Koňařík, F.; Křižák, T.; Lalanne, D.; Lang, K.; Lemière, Y.; Li, P.; Loaiza, P.; Lutter, G.; Macko, M.; Mamedov, F.; Marquet, C.; Mauger, F.; Minotti, A.; Morgan, B.; Nemchenok, I.; Nomachi, M.; Nowacki, F.; Ohsumi, H.; Oliviéro, G.; Palušová, V.; Patrick, C.; Perrot, F.; Petro, M.; Pin, A.; Piquemal, F.; Povinec, P.; Pratt, S.; Přidal, P.; Quinn, W. S.; Ramachers, Y. A.; Remoto, A.; Reyss, J. L.; Riddle, C. L.; Rukhadze, E.; Saakyan, R.; Salamatin, A.; Salazar, R.; Sarazin, X.; Sedgbeer, J.; Shitov, Yu.; Simard, L.; Šimkovic, F.; Smetana, A.; Smolnikov, A.; SöldnerRembold, S.; Štekl, I.; Suhonen, J.; Szklarz, G.; Tedjditi, H.; Thomas, J.; Timkin, V.; Tretyak, V. I.; Tretyak, V. I.; Umatov, V. I.; Vanushin, I.; Vereshchaka, Y.; Vorobel, V.; Waters, D.; Xie, F. Aguerre, X., Arnold, R., Augier, C., Barabash, A. S., Basharina-Freshville, A., Blondel, S., Blot, S., Bongrand, M., Breier, R., Brudanin, V., Busto, J., Bystryakov, A., Caffrey, A. J., Cerna, C., Cesar, J. P., Ceschia, M., Chauveau, E., Chopra, A., Dawson, L., . . . Xie, F. (2023). Measurement of the double-β decay of 150Nd to the 0+1 excited state of 150Sm in NEMO-3. European Physical Journal C, 83(12), Article 1117. https://doi.org/10.1140/epjc/s10052-023-12227-x 2023 Eur. Phys. J. C (2023) 83:1117 https://doi.org/10.1140/epjc/s10052-023-12227-x Regular Article - Experimental Physics Measurement of the double-βdecay of 150Nd to the 0+ 1excited state of 150Sm in NEMO-3 X. Aguerre1, R. Arnold2, C. Augier3, A. S. Barabash4, A. Basharina-Freshville5, S. Blondel3,S.Blot 6, M. Bongrand3,R.Breier 7, V. Brudanin4, J. Busto8, A. Bystryakov4,A.J.Caffrey 9, C. Cerna1, J. P. Cesar10, M. Ceschia5, E. Chauveau1, A. Chopra5,L.Dawson 5, D. Duchesneau12, D. Durand11,J.J.Evans 6, R. Flack5, P. Franchini13, X. Garrido3, C. Girard-Carillo3, B. Guillon11, P. Guzowski6, M. Hoballah3, R. Hodák14, P. Hubert1, M. H. Hussain5, S. Jullian3, A. Klimenko4, O. Kochetov4, S. I. Konovalov4,F.Koˇnaˇrík14,15,T.Kˇrižák14,15, D. Lalanne3, K. Lang10 ,Y.Lemière 11,P.Li 16, P. Loaiza3,G.Lutter 1, M. Macko14, F. Mamedov14, C. Marquet1, F. Mauger11, A. Minotti12, B. Morgan17, I. Nemchenok4, M. Nomachi18, F. Nowacki2, H. Ohsumi19, G. Oliviéro11, V. Palušová14, C. Patrick16 , F. Perrot1,M.Petro 7,14,A.Pin 1, F. Piquemal1, P. Povinec7, S. Pratt16,P.Pˇridal14, W. S. Quinn5, Y. A. Ramachers17, A. Remoto12, J. L. Reyss20, C. L. Riddle9, E. Rukhadze14, R. Saakyan5, A. Salamatin4, R. Salazar10, X. Sarazin3, J. Sedgbeer13, Yu. Shitov14, L. Simard3,21,a,F.Šimkovic 7,14, A. Smetana14, A. Smolnikov4, S. Söldner-Rembold6, I. Štekl14, J. Suhonen22 , G. Szklarz3, H. Tedjditi8, J. Thomas5,V.Timkin 4, V. I. Tretyak23,24 , V. I. Tretyak4,V.I.Umatov 4, I. Vanushin4, Y. Vereshchaka3, V. Vorobel25, D. Waters5,F.Xie 5 1Université de Bordeaux, CNRS/IN2P3, LP2i Bordeaux, UMR 5797, 33170 Gradignan, France 2Université Louis Pasteur, CNRS/IN2P3, IPHC, 67037 Strasbourg, France 3Université Paris-Saclay, CNRS, IJCLab, 91405 Orsay, France 4Affiliated with a member institute of the NEMO-3 collaboration, Modane, France 5University College London, London WC1E 6BT, UK 6University of Manchester, Manchester M13 9PL, UK 7Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovakia 8Aix-Marseille Université, CNRS, CPPM, 13288 Marseille, France 9Idaho National Laboratory, Idaho Falls, ID 83415, USA 10 University of Texas at Austin, Austin, TX 78712, USA 11 Normandie Université, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, 14000 Caen, France 12 Université de Savoie, CNRS/IN2P3, LAPP, UMR 5814, 74941 Annecy-le-Vieux, France 13 Imperial College London, London SW7 2AZ, UK 14 Institute of Experimental and Applied Physics, Czech Technical University in Prague, 11000 Prague, Czech Republic 15 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7, 115 19 Prague, Czech Republic 16 University of Edinburgh, Edinburgh EH9 3FD, UK 17 University of Warwick, Coventry CV4 7AL, UK 18 Osaka University, 1-1 Machikaneyama Toyonaka, Osaka 560-0043, Japan 19 Saga University, Saga 840-8502, Japan 20 LSCE, CNRS, 91190 Gif-sur-Yvette, France 21 Institut Universitaire de France, 75005 Paris, France 22 Jyväskylä University, 40351 Jyvaskyla, Finland 23 Institute for Nuclear Research of NASU, Kyiv 03028, Ukraine 24 INFN-Laboratori Nazionali del Gran Sasso, 67100 Assergi, AQ, Italy 25 Faculty of Mathematics and Physics, Charles University in Prague, 12116 Prague, Czech Republic Received: 30 August 2023 / Accepted: 6 November 2023 © The Author(s) 2023 Abstract The NEMO-3 results for the double-βdecay of 150Nd to the 0+ 1and 2+ 1excited states of 150Sm are reported. Deceased: R. Arnold, V. Brudanin, D. Lalanne, I. Vanushin. ae-mail: [email protected] (corresponding author) The data recorded during 5.25 year with 36.6 g of the isotope 150Nd are used in the analysis. The signal of the 2νββ transition to the 0+ 1excited state is detected with a statistical significance exceeding 5σ. The half-life is measured to be T2νββ 1/2(0+ 1)=1.11+0.19 −0.14 (stat)+0.17 −0.15 (syst)×1020 year, 0123456789().: V,-vol 123 1117 Page 2 of 12 Eur. Phys. J. C (2023) 83:1117 which is the most precise value that has been measured to date. 90% confidence-level limits are set for the other decay modes. For the 2νββ decay to the 2+ 1level the limit is T2νββ 1/2(2+ 1)>2.42 ×1020 year. The limits on the 0νββ decay to the 0+ 1and 2+ 1levels of 150Sm are significantly improved to T0νββ 1/2(0+ 1)>1.36×1022 year and T0νββ 1/2(2+ 1)> 1.26 ×1022 year. 1 Introduction The double-βdecay is a nuclear process that changes the charge of a nucleus by two units through the simultaneous β-decay of two constituent neutrons to protons. The twoneutrino double-βdecay (2νββ) is a rare second-order weak interaction process occurring with emission of two electrons and two antineutrinos. It was observed for several nuclear isotopes [1,2]. The community’s interest in the double-βdecay is particularly motivated by the search for its hypothetical neutrinoless mode (0νββ)[3]. This process violates the lepton number conservation and is only possible if the neutrino has mass and is a Majorana particle [4], i.e. ν≡¯ν. The discovery of 0νββ would indicate the physics beyond the Standard Model (BSM). The rates of two-neutrino and neutrinoless double-βdecay maybeexpressedas 1/T2ν 1/2=G2νg4 A|M2ν|2,(1) 1/T0ν 1/2=G0νg4 A|M0ν|2η2,(2) where G2ν,0νare the phase space factors, gAis the axial vector coupling constant, M2ν,0νare the nuclear matrix elements (NMEs) for the corresponding decay modes, and η is a parameter of the underlying BSM physics model (in the case of the commonly considered mass mechanism of the 0νββ decay, the exchange of a light Majorana neutrino, η is the effective neutrino mass). The phase space factors can be accurately calculated while the model-dependent NME calculations have a substantial theoretical uncertainty. The measurement of the 2νββ decay half-life provides valuable information for nuclear structure models used in NME calculations. The double-βdecay can proceed through transitions either to the ground state or to excited states of the daughter nucleus. The latter occurs at a lower rate because of its smaller transition energy Qββ leading to the correspondingly suppressed phase space factor. Nevertheless, the measurement of the 2νββ decay to excited states provides supplementary information for nuclear models. Additionally, in the case of the 0νββ decay discovery, the ratio of half-lives for transitions to the 0+first excited state and the ground state may allow the Fig. 1 Scheme of the 150Nd ββ-decay to the lowest excited states of 150Sm dominant decay mechanism to be determined [5]. Information on the results of experiments on the ββ-decay to excited states of daughter nuclei can be found in [6]. The isotope 150Nd is one of the best candidates for neutrinoless ββ-decay searches because of its high transition energy Qββ = 3371 keV and highest phase space factor [7]. However, a modest isotopic abundance of 5.638(28)% and difficulties in isotopic enrichment limit its use in large-scale experiments. The decay scheme of 150Nd to the 2+ 1and 0+ 1excited states is shown in Fig. 1. The half-life for the transition to the first 0+excited state was first measured in 2004 [8]. These data were subsequently re-analysed, with the final result published in [9]. The measurements of this decay were obtained with γ-ray spectrometry using high-purity germanium detectors [9–11]; none of the previous measurements detected a signal with a 5σstatistical significance. For other excited states, only lower limits on the half-life were established; the best available limit for the transition to the 2+ 1state set at 90% confidence level (C.L.) is Tββ 1/2(2+ 1)>2.2×1020 year [9]. The most precise measurement for the ββ-decay of 150Nd to the ground state was performed by NEMO-3 [12]: T2νββ 1/2(0+ g.s.)=[9.34 ±0.22 (stat)+0.62 −0.60(syst)]×1018 year. (3) It is based on the data recorded for 5.25 years with 36.6 g of 150Nd. The same data set is used in this analysis. 2 NEMO-3 detector The NEMO-3 experiment in the Modane Underground Laboratory (LSM) took data from February 2003 to January 123 Eur. Phys. J. C (2023) 83:1117 Page 3 of 12 1117 Fig. 2 Schematic view of the NEMO-3 detector with the source foils (1), scintillators (2), photomultipliers (3), and wire chamber (4) 2011. The NEMO-3 detector, designed to search for the 0νββ decay, uses both a tracking device and a calorimeter, which enables the direct detection of electrons, positrons, photons, and α-particles. A schematic view of the NEMO-3 detector is shown in Fig. 2. The detector was a hollow cylinder with a diameter of 5m and a height of 3m and was composed of 20 equal sectors. These hosted thin source foils of 7 different enriched ββdecaying isotopes (100Mo, 82Se, 116Cd, 130Te, 150Nd, 96Zr, and 48Ca) with a total mass of about 10 kg. The source foils were suspended vertically between two concentric cylindrical tracker volumes, parallel to the wires of the tracking detector. The tracking detector was composed of 6180 open octagonal drift cells arranged in 18 concentric layers, with 9 layers in each of the two volumes. The tracker was filled with a gas mixture of helium (94.9%), ethyl alcohol (4%), argon (1%), and water vapour (0.1%) at 7 mbar above atmospheric pressure. The drift cells operating in the Geiger mode enabled three-dimensional measurements of trajectories and decay vertices of charged particles. The average Geiger cell resolution was 0.5 mm in the horizontal plane and 8mm in the vertical direction (parallel to the wires). The tracking chamber was surrounded by a calorimeter composed of 1940 plastic scintillator blocks coupled to low-radioactivity 3-inch and 5-inch photomultiplier tubes (PMTs). The calorimeter provided both time and energy measurements. The energy resolution of the calorimeter was σ = (5.8 – 7.2)%, and the time resolution was σ= 250 ps for 1-MeV electrons. A vertical magnetic field of 25 Gauss inside the wire chamber was provided by a solenoidal coil. The detector was surrounded by the passive shielding consisting of 19-cm-thick iron plates to suppress the external γ-ray flux and also of borated water, paraffin, and wood to thermalize and absorb environmental neutrons. The experimental hall is located at a depth of 4800m.w.e., to reduce the cosmic-ray flux. The 150Nd foil was manufactured using Nd2O3powder provided by the Institute for Nuclear Research of RAS in Moscow. Neodymium was enriched by electromagnetic separation to (91.0±0.5)% of the isotope 150Nd and chemically purified. A total of 46.64 g of Nd2O3powder mixed with a concentration of 8% PVA glue was uniformly distributed between two layers of mylar to produce a composite foil with a total mass of 56.68 g. The foil was 2484mm long and 65mm wide. The total mass of the isotope 150Nd in the foil was 36.6±0.2 g [13]. The 150Nd composite foil was located in Sector 5 of the NEMO-3 detector between a foil of 100Mo and a foil containing 96Zr and 48Ca. A more detailed description of the NEMO-3 detector, its calibration and performance can be found in [13,14]. 3 Analysis and results The ββ-decay of 150Nd to the lowest (2+ 1and 0+ 1) excited states of 150Sm has been investigated. The contribution from the higher excited states was neglected. According to the decay scheme in Fig. 1, two electrons from the ββ-decay are accompanied by one γin the case of the transition to the 2+ 1excited state and by two photons in the transition to the 0+ 1excited state. We therefore select for this analysis twoelectron one-γ(eeγ) and two-electron two-γ(eeγγ) event topologies. After the event selection, the ββ-decay signal is identified by an excess in the data over the expected background. Both a measurement of the two-neutrino ββ-decay and a search for the neutrinoless ββ-decay to the 0+ 1excited state are carried out in the eeγγ and eeγchannels. The ββ-decays to the 2+ 1excited state are explored in the eeγchannel. A multivariate analysis improves the separation of the signal from the background. To this end the Boosted Decision Tree (BDT) method is used. The analysis employs a BDT algorithm with adaptive boosting, part of the ROOT [15] TMVA package [16]. Where no evidence of a signal in the data is found, a limit on the corresponding decay half-life is set. The 90% C.L. limit is calculated using the CLsmethod employing the modified frequentist approach [17–19]. 3.1 Event selection In this analysis, the eeγγ and eeγevent topologies are used. Events are selected by requiring two reconstructed electron tracks coming from the source foil, with each depositing in a separate scintillator block an energy greater than 150keV. Extrapolating each track to the source foil gives the posi123 1117 Page 4 of 12 Eur. Phys. J. C (2023) 83:1117 tion of its decay vertex, and extrapolating to the calorimeter associates the track with the scintillator block of an optical module for energy and time measurement. A scintillator hit associated with a track must be isolated, i.e. no hits should be found in neighboring scintillator blocks. Each of the two electron tracks must have a length greater than 50cm and originate from a common vertex in the 150Nd source foil: the separation between the two individually reconstructed track vertices is required to be less than 4cm in the horizontal plane and less than 8cm in the vertical direction. An event is excluded if its vertex is found in one of the regions of the enhanced activity in the foil corresponding to the localized contamination from 234mPa and 207Bi (hot spots). The locations of the hot spots, which amount to 7% of the 150Nd foil area, were determined in [12]. To ensure that an event corresponded to the simultaneous emission of two electrons from a common vertex, the corresponding time-of-flight (TOF) probability is required to be higher than 5%. The TOF probability is calculated using energy and time measurements from the calorimeter and the distances travelled by particles in the event; see [13,14]for details. Aγ-ray is identified as either a single calorimeter hit or a cluster of neighbouring hits that are not associated with any track. A minimum threshold of 100keV for the energy deposited in each of these calorimeter blocks is required. It is also required that no prompt Geiger hits are detected within 20cm of any scintillator block attributed to a γ-ray. Events are rejected if the TOF probability exceeds 1% for the hypothesis that the event originates from an external γray. The probability for the hypothesis that the photon(s) originated from the event vertex simultaneously with two electrons is required to be higher than 5%. An event is rejected if it contains a recognized delayed alpha-particle track, as described in [14], to reduce the background from 214Bi decays. AsshowninTable1, a total of 142 eeγγ and 571 eeγ events are selected from the full data set. 3.2 Background model The main source of background events is trace amounts of naturally occurring radioactive isotopes that come from the 238U and 232Th radioactive series. The most important of them are (β,γ)-emitting isotopes with high Qβvalues, such as 208Tl (Qβ= 4.99 MeV) and 214Bi (Qβ=3.27MeV). According to their origin with respect to the source foil, the background events are classified as internal or external ones. The largest background contribution comes from the internal contamination of the source foil. The decay of a βemitting isotope inside the foil can mimic the ββ-decay signal through several different mechanisms, such as a single βdecay combined with Møller scattering or a single β-decay Table 1 Expected number of events from different sources of the background with statistical and systematic uncertainties and the number of the observed events in the eeγγ and eeγchannels after the event selection Contribution eeγγ eeγ 228Ac+212Bi+208Tl 65.81±0.39±4.61 279.0±0.9±19.5 214Bi 7.33±0.08±1.69 48.5±0.2±11.2 152Eu+154Eu 3.57±0.08±0.42 36.5±0.3±5.1 207Bi 1.78±0.06±0.10 41.2±0.3±2.3 234mPa 0.02±0.02±0.002 4.9±0.3±0.5 Radon 3.26±0.11±0.33 23.3±0.3±2.3 External background 2.74±0.54+0.85 −0.63 47.0±2.4+14.6 −10.8 Neighbouring foils 0.59±0.03±0.14 4.6±0.5±1.0 150Nd ββ →g.s. 0.25±0.02±0.02 27.4±0.2±1.9 Total bkg 85.35±0.69+5.01 −4.98 512.5±2.7+27.6 −25.8 Data 142 571 to an excited state of the daughter nucleus followed by the emission of a conversion electron or a γ-ray that undergoes Compton scattering in the foil. From these mechanisms, additional γ-rays could be produced by bremsstrahlung or from a decay to an excited state. In addition to the radioactive impurities, a decay in a neighbouring NEMO-3 source foil can be misinterpreted to have its vertex in the 150Nd foil. The 150Nd ββ-decay to the ground state also contributes to the background for the excited-state measurement; two electrons are produced in the decay, and one or two γ-rays could be emitted via bremsstrahlung. The external background is there due to the radioactivity outside of the source foil. Radioactive decays within the detector components (mainly PMT glass), the shielding and rock, surrounding the laboratory, generate the external γray flux. γ-ray interactions with the source foil can cause electron-positron pair production, a Compton interaction followed by Møller scattering, or double Compton scattering. In the case of electron-positron pair production, two photons can be produced through annihilation of the positron. A subset of the external background is induced by radon. Radon is a highly diffusive gas and is outgassed into the air from the rock walls of the LSM laboratory. It is present in the tracker volume due to diffusion from laboratory air through detector seals and emanation from detector materials. The decay of radon progenies (mainly 214Bi) near the source foil can produce signal-like events similar to internal background decays. Details of the background model and measured values of activities that are used in this analysis are provided in [12]. The DECAY0 event generator [20] is used to simulate the signal and backgrounds, and particles are tracked through a detailed GEANT3-based detector simulation [21]. Both the data and Monte Carlo (MC) events are processed by the same 123 Eur. Phys. J. C (2023) 83:1117 Page 5 of 12 1117 Fig. 3 Distributions of the measured quantities for the eeγγ events from the 150Nd foil after the preliminary event selection: energy sum of two electrons E2e, minimal electron energy Emin e,minimalγenergy Emin γ, maximal electron energy Emax e, maximal γenergy Emax γ,total measured energy ETOT, cosine of the angle between two electrons cos(ee), between two photons cos(γγ), and between electron and γ cos(eγ)for all eγcombinations. Data are compared to the MC prediction with the resulting number of 0+ 1signal events obtained by background subtraction reconstruction and selection algorithm. The number of the expected background events with the eeγγ and eeγtopologies is given in Table 1. 3.3 Measurement of 2νββ decay to 0+ 1excited state An excess in the data over the total expected background is observed both in the eeγγ and eeγchannels (see Table 1) and can be attributed to the signal of the ββ-decay to the excited states of the daughter nucleus 150Sm. 3.3.1 Use of eeγγ events The eeγγ event topology is the best one for measuring the transition to the 0+ 1excited state when both electrons, produced in the ββ-decay, and both photons from deexcitation of 150Sm are detected. Distributions of measured quantities for the selected eeγγ events are demonstrated in Fig. 3. The number of the 0+ 1 signal events S=N−B=56.6±11.9 is obtained by subtracting the expected background from the number of events observed. This corresponds to the signal-tobackground ratio S/B=0.66 and to the statistical signal significance Nσ=S/√S+B=4.8. The 0+ 1signal efficiency is =0.87%. This corresponds to the following half-life estimation: T2νββ 1/2(0+ 1)=8.18+2.18 −1.42(stat)×1019 year.(4) 123 1117 Page 6 of 12 Eur. Phys. J. C (2023) 83:1117 Fig. 4 BDT score distribution for the eeγγ events used for the signal of the 150Nd 2νββ decay to the 0+ 1excited state. The vertical dashed line denotes the optimal cut position maximizing the signal significance In order to suppress the background and maximize the signal significance, the event classification employed the BDT method. Using MC of the 0+ 1signal and the background, the BDT training is performed on the set of observables shown in Fig. 3, with the total measured energy ETOT and the maximal γenergy Emax γbeing the most important variables. After training, both the data and MC were processed by the BDT algorithm which assigned a BDT score to each event to aid discrimination of the signal from the background. The BDT score is a continuous variable with lower values for more background-like events and higher values for more signallike events. The resulting BDT score distribution for the signal of the 150Nd 2νββ decay to the 0+ 1excited state in the eeγγ channel is presented in Fig. 4. The vertical dashed line in this figure denotes the optimal cut on the BDT score to maximize the signal significance. After rejecting the events with lower BDT score values, we are left with 53 data events and a total expected background of 13.9 events, see Table 2. This requirement suppresses the background by a factor of 6.1 and reduces the signal efficiency by a factor of 0.88 to = 0.76%. After background subtraction, 39.1 events attributed to the signal remain. This provides the signal-to-background ratio S/B=2.8 and the signal statistical significance Nσ=S/√S+B=5.4. The corresponding half-life is estimated to be T2νββ 1/2(0+ 1)=1.04+0.24 −0.16 (stat)+0.12 −0.11 (syst)×1020 year.(5) This half-life value statistically agrees within 1σwith the result in Eq. (4) obtained after preliminary event selection, but is more precise. The distributions of the measured kinematic variables after the cut on the BDT score are shown in Fig. 5.The data show good agreement with MC for the measured quanTable 2 Number of the expected events from different sources of the background with statistical and systematic uncertainties and the number of the observed events in the eeγγ and eeγchannels after the BDT cut Contribution eeγγ eeγ 228Ac+212Bi+208Tl 7.54±0.13±0.52 22.83±0.26±1.60 214Bi 1.65±0.04±0.38 6.88±0.07±1.58 152Eu+154Eu 1.53±0.05±0.21 2.18±0.07±0.31 207Bi 0.57±0.03±0.03 2.80±0.07±0.16 234mPa – 0.47±0.08±0.05 Radon 0.65±0.05±0.06 3.13±0.12±0.31 External bkg 1.70±0.43+0.53 −0.39 3.50±0.65+1.08 −0.80 Neighbour foils 0.12±0.01±0.03 0.64±0.17±0.15 150Nd ββ →g.s. 0.12±0.01±0.01 3.48±0.06±0.24 Total bkg 13.88±0.46+0.86 −0.79 45.91±0.75+2.56 −2.45 Data 53 85 tities. The Kolmogorov-Smirnov probability values obtained for them are in the range from 10% to 98%. In particular, this probability is equal to 29% for the cos(γγ) distribution representing the γγ angular correlation. This correlation is measured for this decay for the first time and is found to agree well with 1 −3cos2θ+4cos4θbehaviour characterizing the 0+→2+→0+cascade [22]. 3.3.2 Use of eeγevents The two-electron one-γevents are also used to measure the decay to the 0+ 1excited state since one of two emitted photons can remain undetected. The 0+ 1signal efficiency in this channel = 2.2% is higher than in the eeγγ channel. With N=571 data events and the total expected background of B=512.5 events (see Table 1), for the 0+ 1signal contribution defined by background subtraction S=N−B=58.5±23.9 events, we obtain the half-life estimation T2νββ 1/2(0+ 1)=1.98+1.37 −0.58(stat)×1020 year.(6) This is less precise than the estimate for the eeγγ channel due to the worse signal-to-background ratio S/B=0.11 and the low signal statistical significance Nσ=S/√N=2.5in this channel. The effect of systematic uncertainty on background rates also becomes more significant with larger backgrounds. Nevertheless, this estimation is statistically compatible with the measurement obtained using the eeγγ events. The background decomposition for the selected events is presented in Table 1and the measured energy and angular distributions are shown in Fig. 6. A possible contribution from the ββ-decay of 150Nd to the 2+ 1level is neglected. If the 0+ 1contribution is normalized to the half-life value 123 Eur. Phys. J. C (2023) 83:1117 Page 7 of 12 1117 Fig. 5 Distributions of the two-electron two-γevents from the 150Nd foil after the cut on BDT score: energy sum of two electrons E2e,minimal electron energy Emin e, minimal γenergy Emin γ, maximal electron energy Emax e, maximal γenergy Emax γ, total measured energy ETOT, cosine of the angle between two electrons cos(ee), between two photons cos(γγ), and between electron and γcos(eγ)for all eγcombinations. The 0+ 1signal contribution is defined by performing background subtraction obtained in the eeγγ channel, the resulting data deficit does not leave space for the 2+ 1contribution. The photon energy Eγand the total measured energy ETOT are the most important variables in the set of observables used for BDT training in this channel. The BDT score distribution obtained after the event classification is shown in Fig. 7.The position of the optimal BDT cut to maximize the 0+ 1signal significance is marked by a vertical dashed line. After the BDT cut, 85 data events remain, with B=45.9 expected background events (see Table 2). Subtracting the background leaves S=39.1 events attributed to the 0+ 1signal. The resulting signal-to-background ratio is S/B=0.85, with a statistical signal significance of Nσ=S/√S+B=4.2. The distributions of the measured kinematic variables for these events are shown in Fig. 8. The signal efficiency after the BDT cut is =0.88% and the half-life estimate is T2νββ 1/2(0+ 1)=1.21+0.37 −0.23 (stat)+0.26 −0.20 (syst)×1020 year.(7) 3.3.3 Systematic uncertainties Several sources of systematic uncertainty were investigated, with the most significant effect on the precision of the measured decay rate being the uncertainty on the event selection efficiency. It is estimated by measuring the calibrated 232U source activities. These activities, measured by the NEMO-3 detector for eeγγ and eeγevents, are found to be in agreement with true values within 7.8%. This value, taken into 123 1117 Page 8 of 12 Eur. Phys. J. C (2023) 83:1117 Fig. 6 Distributions for the two-electron one-γevents from the 150Nd foil after the preliminary selection: energy sum of two electrons E2e, γenergy Eγ, minimal and maximal electron energy Emin e,Emax e,total measured energy ETOT, cosine of the angle between electron, and γ cos(eγ)for both eγcombinations. Data are compared to the MC prediction with the number of 0+ 1signal events obtained by background subtraction Fig. 7 BDT score distribution for the 2νββ decay to the 0+ 1excited state in the eeγchannel. The vertical dashed line denotes the optimal cut position maximizing the signal significance account both for signal and background events, leads to the decay rate uncertainty of (+11.5, −9.8)% in the eeγγ and (+18.4, −15.7)% in the eeγchannel. The systematic uncertainty on the number of background events (see Tables 1,2) was calculated from those of the individual background components’ activities estimated in [12]. It contributes to the decay rate uncertainty of (+2.3, −2.5)% in the eeγγ and (+6.6, −6.8)% in the eeγchannel. The effect of the limited accuracy in simulation of ionization energy loss and of bremsstrahlung in the foil on the measured decay rate was studied. This was done by generating additional MC data samples varying the relevant parameters within their expected uncertainty. The decay rate uncertainty due to ionization energy loss was evaluated to be ±1.6% in the eeγγ and ±2.8% in the eeγchannel. The uncertainty due to bremsstrahlung is ±1.2% in the eeγγ and ±4.4% in the eeγchannel. The effect of energy calibration accuracy was studied by altering measured energies according to the energy scale uncertainty; it yields a systematic uncertainty of ±1% on the decay rate measurement in the eeγγ and ±1.6% in the eeγchannel. Finally, a ±0.5% uncertainty on the mass of 150Nd translates into the same uncertainty on the measured decay rate. All these contributions are summarized in Table 3, with the total uncertainty calculated by summing the individual contributions in quadrature. 3.3.4 Mean half-life from eeγγ and eeγchannels The individual half-life estimates from the eeγγ and eeγ channels in Eqs. (5) and (7) are in good agreement. The mean value of the two measurements was calculated using their statistical weights: 123