Improved limits on β + EC and ECEC processes in 74 Se
A.S. Barabash, V.B. Brudanin, A.A. Klimenko, S.I. Konovalov, A.V. Rakhimov, E.N. Rukhadze, N.I. Rukhadze, Yu.A. Shitov, I. Stekl, G. Warot, V.I. Umatov
aa r X i v : . [ nu c l - e x ] J a n Improved limits on β + EC and ECEC processes in Se A.S. Barabash a, ∗ , V.B. Brudanin b , A.A. Klimenko b , S.I. Konovalov a ,A.V. Rakhimov b , E.N. Rukhadze c , N.I. Rukhadze b , Yu.A. Shitov b ,I. Stekl c , G. Warot d , V.I. Umatov a a NRC ”Kurchatov Institute”, Institute of Theoretical and Experimental Physics, B.Cheremushkinskaya 25, 117218, Moscow, Russian Federation b Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia c Institute of Experimental and Applied Physics, Czech Technical University in Prague,12800, Prague, Czech Republic d Laboratoire Souterrain de Modane, F-73500, Modane, France
Abstract
New limits on β + EC and ECEC processes in Se have been obtained usinga 600 cm HPGe detector and an external source consisting of 1600 g of anatural selenium powder. For different β + EC and ECEC transitions (to theground and excited states) obtained limits are on the level ∼ (0 . − . × yr at 90% C.L. In particular, for the potentially resonant transition into the1204.2 keV excited state of Ge a lower half-life limit of 1 . × yr at90% C.L. has been obtained. Possibility to increase the sensitivity of suchmeasurements is discussed. Keywords: double-beta decay, double electron capture, low-backgroundHPGe detector. ∗ Corresponding author
Email address: [email protected] (A.S. Barabash)
Preprint submitted to Nuclear Physics A January 22, 2020 . Introduction
Search for neutrinoless double beta decay is one of the most interestingtasks in nuclear physics, particle physics and astrophysics. The discovery ofthis process will automatically lead to two fundamental conclusions - 1) thelepton number is violated, and 2) the neutrino is a Majorana particle. Inaddition, it will provide information on such fundamental problems as theabsolute neutrino mass scale, the type of hierarchy and the CP violation inthe lepton sector (see discussions in [1, 2, 3]).The current most stringent half-life limits on 0 νββ decay are of the orderof 10 − yr (see recent reviews [4, 5, 6]). The standard process (2 νββ ),which implies also the emission of two electron antineutrinos, is the rarestnuclear decay ever observed and has been registered in ten nuclei with half-lives in the range of 10 − yr (see [7] and references therein).Much less attention is paid to the study of 2 β + , β + EC and ECEC pro-cesses although such studies are constantly being conducted and interest inthem is only increasing (see reviews [8, 9, 10, 11]). Let us consider neutrino-less decay: (
A, Z ) → ( A, Z −
2) + 2 e + (1) e − + ( A, Z ) → ( A, Z −
2) + e + + X (2) e − + e − + ( A, Z ) → ( A, Z − ∗ → ( A, Z −
2) + γ + 2 X (3)The existence of these processes means that similarly to the 0 νββ decay,the lepton number is violated and the neutrino is a Majorana particle, whichwould require particle physics beyond the Standard Model.Process (1) has a very nice signature. This is due to the fact that inaddition to two positrons there are also four annihilation 511 keV gammaquanta, which could be detected. But the probability for such a search ismuch lower compared to 0 νββ decay because of significantly lower kineticenergy realized in such a transition and because of the Coulomb barrier forpositrons. There are only 6 candidates for such a decay: Kr, Ru,
Cd,
Xe,
Ba and
Ce (with energy of 2 β + transition ∼ ∼ − yr(for < m ν > = 1 eV) [12, 13] and this is approximately 10 − times longerthan for the 0 νββ decay for nuclei such as Ge,
Xe,
Mo, Se and
Te(see reviews [4, 5, 6]). The best present limits for 2 β + (0 ν ) transition are onthe level ∼ yr (see reviews [8, 9, 10].2he process (2) has a good signature too and is not as strongly suppressedas 2 β + decay. The most optimistic estimates for the half-life give values ∼ − yr (for < m ν > = 1 eV) [12, 13]. The best present experimentallimits for β + EC(0 ν ) transition are on the level ∼ − yr (see reviews[8, 9, 10] and recent paper [14]).In process (3) the atom de-excites emitting two X-rays and the nucleusde-excites emitting one bremsstrahlung photon . In the case of a transitionto an excited state of a daughter nuclei, besides a bremsstrahlung photon, aone or a few γ -rays are emitted from the excited state. The probability ofthe process does not depend on decay energy and increases with decreasingbremsstrahlung photon energy and increasing Z [16, 17]. The probability ofsuch a process, even for heavy nuclei, is low, leading to T / ∼ − yrfor < m ν > = 1 eV [16]. The best present limits for ECEC(0 ν ) transitionsare on the order ∼ − yr (see reviews [8, 9, 10] and recent papers[14, 18, 19]).In [20], it was first noted that in the case of ECEC(0 ν ) a resonant condi-tion can be realized for transition to an excited level in the daughter nucleuswith a ”correct energy” (when decay energy to this level is close to zero).The same idea was proposed for transition to the ground state in 1982 [21].One year later the Sn -
Cd (0 + ; 1871 keV) transition was discussed [22].Then the idea was reanalyzed in 2004 [16]. The enhancement of the transitionrate was estimated as ∼ − [22, 16, 23, 24]. It means that this processstarts to be competitive with 0 νββ decay (in the sense of the sensitivity toneutrino mass). There are many candidates for such resonant transitions, tothe ground ( Gd,
Eu and
W) as well as to the excited states of thedaughter nuclei ( Se, Kr, Ru,
Cd,
Sn,
Xe,
Ba,
Ce,
Sm,
Gd,
Dy,
Er,
Yb, W, Os and
Pt) (see [23], for example).The accuracy of matching to the resonance ought to be better than 1 keV.Thus, to choose the best candidate from the above list it is necessary to knowthe atomic mass difference with an accuracy much better than 1 keV. Themeasurements have been done for all above mentioned isotopes, and in a fewcases resonance conditions were found. But in all these cases (
Gd [25],
Cd [26],
Dy [27] and
Pt [28]) there is an additional suppression of the In [15] (see also discussion in [16]), it was mentioned that processes with emission ofinner conversion electron, e + e − pair or two γ are also possible. And this is especiallyimportant in the case of ECEC(0 ν ) transition with capture of two electrons from K shell(in this case the transition with emission of one γ is forbidden [15]). + , 2 − , 1 − ,...) and ”not optimum” orbits ofatomic electrons involved in the process (for example, LL , NM , KN , ...). Andthe most optimistic predictions for T / are in the order of ∼ − yr only (for < m ν > = 1 eV) [29, 30]. Thus, such experiments cannot becompetitive with experiments for search for 0 νββ decay. The best presentexperimental limits for possible resonant transitions are on the level ∼ yr ( Sn [31],
Cd [32] and Kr [33]). At the same time, it should be notedthat there is an unsatisfactory knowledge about the excited states, and thereis still a chance that ”promising” candidates can be found.A search for Se- Ge (1204.2 keV) resonant transition was first timeproposed in [34]. The decay scheme of this transition is presented in Fig. 1.The atomic mass difference ∆ M ( Se and Ge) was known at that time withaccuracy ± L shell for the transitionto the 1204.2 keV level in Ge. This process would be accompanied by acascade of two γ -quanta with energies 608.4 and 595.8 keV (68.5%) or one γ -quantum with energy 1204.2 keV (31.5%). For the first time the searchfor this transition was done in [35]. But later atomic mass difference ∆ M was measured with high accuracy (Q = 1209.169(49) keV [36] and Q =1209.240(7) [37]) and it was demonstrated that the resonance condition isnot met in this case. Nevertheless, such measurements were done againin [38, 39] and [40]. In [40] it was shown that limits in [38] and [39] wereoverestimate in ∼ β + , β + EC and ECECprocesses: (
A, Z ) → ( A, Z −
2) + 2 e + + 2 ν (4) e − + ( A, Z ) → ( A, Z −
2) + e + + 2 ν + X (5) e − + e − + ( A, Z ) → ( A, Z −
2) + 2 ν + 2 X (6)These processes are not forbidden by any conservation laws. Processes(4) and (5) are strongly suppressed because of low phase-space volume. Fromthe experimental point of view it is very difficult to investigate the process4 + Ge +1 ↓ +2 ↓ ↓ − As + Se ←←←→ KK ∼ . → KL ∼ . → LL ∼ . Q = 1209 . nuclear level ⇐ = 1204 . +1 ) ✬✫ ✩✪ Figure 1: Energetics of the Se ECEC0 ν decay indicating the near degeneracy of the Seground state and the second excited state in Ge. The circle marks the part, which ismagnified in the lower part of the figure. Energy is indicated in keV. (6), because one has to detect only low energy X-rays (or Auger electrons).Nevertheless, exactly the process (6) was detected in a few nuclei. In geo-chemical experiment with
Ba ECEC(2 ν ) this process was detected withhalf-life value (2 . ± . × yr [41]. Recently, positive results from directcounting-rate experiments were reported for 2 K (2 ν ) process in Kr [42] and
Xe [43] with half-life (1 . +1 . − . ) × yr and (1 . ± . × yr, respectively(see discussion about these results in [44]).This work is devoted to search for β + EC and ECEC processes in Se.
2. Experimental
The experimental work has been performed in the Modane UndergroundLaboratory (LSM, France, 4800 m w.e.), which provides the suppression of a5 igure 2: HPGe detector in a passive shielding. muon flux by ∼ × times and fast neutrons by ∼ times. The naturalselenium powder sample was measured using the detector OBELIX [45].The low background HPGe detector, OBELIX, was produced by the com-pany Canberra. The detector is a P-type crystal with a sensitive volume of600 cm . The mass of the detector is approximately 3.2 kg and the detectorrelative efficiency is 160%. The crystal was mounted in an ultra low back-ground U-type cryostat. The energy resolution of the detector is ∼ Co) and ∼ Co).The detector part of the cryostat is encircled by passive shielding of sev-eral layers of lead. The Roman lead (PbI) with a total thickness of ∼ <
60 mBq/kg) and low-activity (PbII) lead (activity of ∼ ∼
20 cm, and placed inside atightly closed stainless steel cover (see Fig. 2). The electronic part of thespectrometer is based on NIM electronic modules produced by Canberra. A3106D High Voltage module of Canberra supplies a voltage of +6000 V tothe detector. Signals from the preamplifier PSC761 coupled to the detectorpart are passed through the Spectroscopy Amplifier 2022 and then digitizedby 16384 channels ADC Multiport II. The energy threshold of the HPGedetector is about 10 keV. The software used for data taking and analysis ofspectra is Genie 2000 version 3.2.1.A detailed description of the detector and its characteristics can be found6n [45].The sample of natural selenium powder was packed in a plastic box andput on the endcap of the HPGe detector. The mass of the powder was 1600 gand mass of Se - 14.24 g (natural abundance is 0.89%). The measurementtime was 3283.45 hours.A search for different β + EC and ECEC processes in Se has been per-formed using the HPGe detector to look for γ -ray lines corresponding to theseprocesses. Q ′ is the effective Q -value defined as Q ′ = ∆ M − ǫ − ǫ where∆ M is the difference of parent and daughter atomic masses, ǫ i are electronbinding energy in the daughter nuclide.The ECEC(0 ν ) transitions were considered for three cases of electron cap-tures as it is shown in Fig. 1.1) Two electrons are captured from the L -shell. Q ′ is ∼ .
41 keV andthree transitions are investigated, i.e.a) to the second 2 + level of Ge (1204.20 keV), accompanied by de-excitation γ -quanta, 595.85 and 608.35 keV (68.5%) or 1204.20 keV (31.5%);b) to the first 2 + level of Ge (595.85 keV), accompanied by the bremsstrahlung γ -quantum (610.56 keV) and one de-excitation γ -quantum (595.85 keV);c) to the ground state of Ge, accompanied by the bremsstrahlung γ -quantum(1206.41 keV).2) One electron is captured from the K -shell, another from the L -shell. Q ′ is ∼ .
73 keV and two transitions are investigated, i.e.a) to the first 2 + level of Ge, accompanied by the bremsstrahlung γ -quantum (600.88 keV) and one de-excitation γ -quantum (595.85 keV);b) to the ground state of Ge, accompanied by the bremsstrahlung γ -quantum (1196.73 keV).3) Two electrons are captured from the K -shell. In this case Q ′ is ∼ . + level of Ge, accompanied by the bremsstrahlung γ -quantum (591.19 keV) and one de-excitation γ -quantum (595.85 keV);b) to the ground state of Ge, accompanied by the bremsstrahlung γ -quantum (1187.04 keV).The β + EC(0 ν +2 ν ) transition is possible only to the ground state of Ge,accompanied by one positron which gives two annihilation γ -quanta.The ECEC(2 ν ) transitions, accompanied by detectable γ -rays, area) the transition to the second 2 + level of Ge with the γ -rays, 595.85 and608.35 keV (68.5%) or 1204.20 keV (31.5%),b) the transition to the first 2 + level of Ge with one de-excitation γ -quantum7 Tl591.19595.85600.88
Bi0510152025301170 1180 1190 1200 1210 12201187.04 1196.73 1204.201206.41
Energy (keV) C oun t s / . k e V Figure 3: Energy spectra with 1600 g of natural Se in the ranges of investigated γ -rays.The measurement time is 3283.45 hours. (595.85 keV).The γ -ray spectra in the energy ranges corresponding to the differentdecay modes of Se are shown in Fig. 3. No extra events (statisticallysignificant, i.e. more than 3 σ over background) are observed for investigatedenergies.The limits on transitions of Se to the ground and excited states of Gewere estimated according to the procedure of the Particle Data Group [47]using the Bayesian approach (section 39.4.1). The every bin of the spectrumis supposed to have a Poisson distribution with its mean µ i and the numberof events equal to the content of this i th bin. The mean µ i can be written ingeneral form as µ i = N X m ε m a mi + X k P k a ki + b i (7)8he first term describes the contribution of the investigated process thatmay have a few γ -lines contributing appreciably to the i th bin. In (7) theparameter N is the number of decays, ε m is the detection efficiency of the m th γ -line of the transition under study and a mi is the part of m th line coveringthe i th bin. For low-background measurements a γ -line may be taken in agaussian shape. The second term gives contributions of background γ -lines.Here P k is the area of the k th γ -line and a ki is its part covering the i th bin.The third term represents so named ”continuous background” b i obtainedby a spectrum smoothing after rejecting all peaks. The likelihood functionis the product of probabilities for bins selected for the investigated process.Normalizing it to 1 on parameter N it becomes probability density functionfor N which is used to calculate limits for N .Limits have been calculated for different combinations of γ -lines corre-sponding to the transitions under study. The best results are given in Table 1.For transitions to the 2 +2 level, the limits are given for the joint analysis of twogamma quanta (595.85 and 1204.20 keV). Taking into account the gammaline of 608.35 keV led to a worse value for the limit, since this line coincideswith the intense line from Bi (609.32 keV) and this limit is not presented.For ECEC (0 ν ) transitions to the 2 +1 level, the limits for individual γ -quantaare given, since the combined consideration of both gamma quanta does notlead to a more stringent limit. The limit for the β + EC(0 ν + 2 ν ) transitionwas determined from the 511 keV line. It was conservatively assumed thatall recorded events belong to this transition.
3. Discussion
The obtained limits on ECEC(0 ν + 2 ν ) transitions of Se to excitedstates of Ge are 1.2-11.2 times higher than the limits obtained in previousexperiments [35, 40]. In particular, for the potentially resonant transition intothe 1204.2 keV excited state of Ge a lower half-life limit of 1 . × hasbeen obtained, which is 1.6 times better than in [40]. In fact, the ”sensitivity”of the experiment for this transition is ∼ . × years. The lower valueof the obtained limit is associated with the presence of extra events ( ∼ σ effect) for the 595.85 keV line. The limit on β + EC(0 ν + 2 ν ) transition to theground state of Ge is improved by 20% compared to the limit in [35].For ECEC(0 ν ) process, the main hopes in the past were connected withrealization of resonant condition for the transition to the 1204.2 keV excitedstate of Ge. Unfortunately, recently it was demonstrated (in two indepen-9 able 1: The limits on double beta decays of Se. The second column presents gamma-rays in keV and their efficiencies used to estimate half-lives. Limits on half-lives T / aregiven at 90% C.L. Transitions γ -ray (efficiency) T / , yrto Ge This work [35] [40]ECEC(0 ν ); LL +2 (1204.20-keV) 1204.20 keV (0.57%)ECEC(0 ν ); LL +1 (595.85 keV)ECEC(0 ν ); LL ν ); KL +1 (595.85 keV) 595.85 keV (1.81%) 1.57ECEC(0 ν ); KL ν ); KK +1 (595.85 keV) 595.85 keV (1.81%) 1.57ECEC(0 ν ); KK ν ) 595.85 keV (1.23%)+ 1.10 0.55 0.70to (2 +2 )(1204.20 keV) 1204.20 keV (0.57%)ECEC(2 ν ) 595.85 keV (2.11%) 1.83 0.77 0.92to the 2 +1 (595.85 keV) β + EC(0 ν + 2 ν ) 511.00 keV (4.32%) 0.23 0.19 -to g.s.dent measurements [36, 37]) that resonant condition is not met in this case. Q ′ value for Se (0 + ) − Ge (2 +2 ) transition is ∼ L -shell). This is why there is no enhancement forthe transition in this case. And recently the half-life value for this transition10as theoretically estimated to 2 × − × yr [48]. Such a large pre-dicted half-life value is associated not only with the absence of resonance, butalso with a very small value of the Nuclear Matrix Element for this transitionand with the need to capture electrons from the L shell.One can conclude that Se is not a good candidate to search for β + EC(2 ν )and ECEC(2 ν ) processes too and chance to detect these decays is small (eventaking into account the possible increase in the sensitivity of such experimentsin the future). Nevertheless, the obtained results are interesting because thepresent experimental limits largely exclude the existence of some unexpected(exotic) processes.Future experimental possibilities are: if 3 kg of enriched Se are usedthen after one year of measurement with the same HPGe detector sensitivityof such experiment would be ∼ yr. If one investigated 200 kg of en-riched Se using such installation as LEGEND [49] (where 200-1000 kg lowbackground HPGe detectors are planned for experimental use) then for 10years of measurement the sensitivity would increase up to ∼ yr.
4. Conclusion
A search for β + EC and ECEC transitions of Se has been performed intothe 595.9 keV and 1204.2 keV excited states as well as into the ground stateof Ge. No significant signal was detected for any of the decay modes. Lowerhalf-life limits have been obtained which are up to a factor 10 larger than pre-vious limits. The limit for the possible resonant decay to the 1204.2 keV statewas found as 1 . × yr (90% C.L.), which is ∼ (1.6-2) times stronger thanprevious results [35, 40]. Apparently no resonance enhancement is visible.The realization of a resonance enhancement is anyhow strongly disfavoredby precision Q-value measurements [36, 37]. It is demonstrated that in thefuture larger-scale experiments sensitivity to ECEC(0 ν ) processes for suchisotopes can be on the level ∼ yr. Acknowledgment
We thank the staff of the Modane Underground Laboratory for their tech-nical assistance in running the experiment. This work was performed withinLEA-JOULE agreement and IN2P3-JINR collaboration agreement No.15-93and partly supported by the Ministry of Education, Youth and Sports of theCzech Republic under the Contract Number CZ.02.1.01/0.0/0.0/ 16 019/0000766.11ortions of this work were supported by a grant from Russian Scientific Foun-dation (No. 18-12-00003).————————————————————–