First limits on double beta decays in 232 Th
EEur. Phys. J. C manuscript No. (will be inserted by the editor)
First limits on double beta decays in Th M. Laubenstein a,1 , B. Lehnert b,2 , S. S. Nagorny c,3 INFN - Laboratori Nazionali del Gran Sasso, 67100 Assergi (AQ), Italy Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A. Queen’s University, Physics Department, Kingston, ON, K7L 3N6, CanadaReceived: date / Accepted: date
Abstract
As one of the primordial radioactive iso-topes,
Th mainly undergoes α -decay with a half-lifeof 1 . · yr. However, it is also one of 35 doublebeta decay candidates in which the single β -decay isforbidden or strongly suppressed. 181 mg of thoriumcontained in a gas mantle were measured in a HPGewell-detector at the Gran Sasso Underground Labora-tory (LNGS) with a total exposure of 3.25 g × d.We obtain half-life limits on all double beta de-cay modes of Th to excited states of
U on theorder of 10 − yr. For the most likely transitioninto the 0 +1 state we find a lower half-life limit of6 . · yr (90% C.I.). These are the first constraintson double beta decay excited state transition in Th.
Keywords double beta decay · excited states · gammaspectroscopy Double beta decay (DBD) is a second order weak nu-clear decay and subject to intense study. While theStandard Model process of two neutrino double beta(2 νββ ) decay is experimentally observed in 11 out of35 possible DBD nuclides, the lepton number violatingprocess of zero neutrino double beta (0 νββ ) decay re-mains elusive to date. The latter would have profoundimplications for particle physics and cosmology, imply-ing the Majorana nature of the neutrino and allowingto understand the matter-antimatter asymmetry in theUniverse via Leptogenesis [1].Even though the 2 νββ and 0 νββ modes requirefundamentally different physics, they are connected a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] through the same experimental techniques and sharecommon challenges for nuclear theory. In order to in-terpret experimentally measured decay rates as a newlepton number violating process, nuclear matrix ele-ments (NME) are required which are notoriously dif-ficult to calculate. These calculations can be improvedand tested by any additional experimental informationof observable 2 νββ decays.The most likely transition for DBD is into theground state of the daughter nucleus which is typicallya 0 + − + transition. However, if the Q-value of the iso-tope is large enough, also transitions into excited statecan occur. Especially useful for testing nuclear mod-els are observed decay rates for the ground and excitedstates of the same nucleus. Comparing both rates, can-cels many poorly constraint model parameters and al-lows for a more direct test of nuclear theory [2].The end of 20 th century and the first quarter ofthe 21 st century could be considered as a “goldenage” for direct counting experiments looking for DBD.Many experiments exploiting various detector tech-niques were proposed and realized within this time pe-riod. The highest sensitivities were achieved with the“source=detector” approach, where the isotope of in-terest is embedded into the material of the detector.In most cases, the experimental signature is the sim-ple sum energy of the two electrons even though sometechniques aim at more advanced topology identifica-tion [3]. Leading experiments reach half-life limits andsensitivities of over 10 yr [4,5]. However, this way onlycertain DBD isotopes can be investigated which occurin elements suitable for a working detector technology.On the other hand, the “source (cid:54) =detector” ap-proach, where e.g. a sample containing the isotope ofinterest is placed on a High Purity Germanium (HPGe)detector, can be applied to searches for DBD in vir- a r X i v : . [ nu c l - e x ] A p r tually any isotope. The ground state transitions arenot accessible with this technique and the experimen-tal signature are the de-excitation γ -rays from excitedstate transitions. Consequently, the 2 νββ and 0 νββ modes cannot be distinguished since the electrons re-main in the external sample . Such experiments havetypically a smaller detection efficiency, not exceedinga few %, and about two orders of magnitudes lowersensitivity but benefit from very unique experimentalsignatures of multiple γ -rays. The best limit with thistechnique was achieved for the DBD of Se to thefirst excited 0 +1 state with T / > · yr [7]. Alsoa combination of these two concepts is used in largescale segmented “source=detector” experiments suchas GERDA, CUORE and CUPID where the decay oc-curs in one detector and the γ -rays are detected in an-other. These searches have half-life sensitivities of about10 − yr [8,9,10], but are again limited to certain iso-topes within the detection technique.Measuring samples on a HPGe detector in the“source (cid:54) =detector” approach resulted in the first andonly 2 νββ decay transitions into excited states in Ndand
Mo with measured world average half-lives of1 . +0 . − . · yr and 5 . +0 . − . · , respectively [11].Lower limits for excited state transitions in otherDBD isotopes which were established in Pd isotopes[12], Ce isotopes [13], Zr [14],
Er [16],
Yb [16],Sm isotopes [17], Se [18], and
Hf [19] within thelast 5 years with half-life values in the range from 10 to 10 yr.Most of the investigated isotopes are “classical”DBD emitters, where a nucleus A ( Z, N ) cannot un-dergo single beta-decay to A ( Z ± , N ±
1) becauseit is energetically forbidden or heavily suppressed byan unfavorable isospin configuration. However, someof these classical DBD emitters can decay via othermodes. Recent measurements with a platinum sampledemonstrated a search for DBD in the unstable
Ptnuclide, which has a more favorable decay through con-ventional α -decay with significantly shorter half-life.Systems with ββ -processes in unstable nuclides werediscussed in [20], where lower limits on DBD of pri-mordial U, U, Th nuclides and their daugh-ters were established. The authors have been utilizinglong term low-background measurements with CaWO , CdWO and Gd SiO scintillating crystals for theseanalyses. The isotopes of interest were determined asinternal contamination of these scintillating crystals.Despite a very low concentration of the isotopes of in-terest, half-life limits in the range 10 − yr were set An exception are the NEMO and SuperNEMO experimentsin which a thin target foil is sandwiched between ionizationchambers [6]. for the first time for the 0 νββ and 2 νββ decay modesto the ground state.In this work we investigate DBD of
Thwith the “source (cid:54) =detector” approach using HPGe γ -spectroscopy. Thorium is a mono-isotopic element andthus, the isotopic abundance of Th is 100% in naturalthorium. The single β -decay of Th to
Pa is ener-getically forbidden but the α -decay to Ra is possiblewith 1 . · yr half-life. DBD of Th is possibleinto the ground state as well as into a variety of excitedstates of
U. The possible decay modes are illustratedin Fig. 1. The most likely excited state transition is the0 +1 state at 691.4 keV. To our knowledge there wereno previous attempts to search for DBD excited statetransitions in Th.
The measurement of a gas mantle sample containing0.1811(5) g thorium was carried out in the STELLA(SubTerranean Low Level Assay) facility in the under-ground laboratories of LNGS (Laboratori Nazionali delGran Sasso) of INFN in Assergi, Italy, which providedan average shielding of ≈ × <
100 Bq/kg of
Pb), followed by another 5 cm ofeven lower activity lead ( < Pb) and then5 cm of oxygen-free high conductivity (OFHC) copper,exposed only for a very short time to cosmic rays aboveground. Finally, the shield and detector are enclosedin an air tight housing kept at slight overpressure andcontinuously flushed with boil-off from liquid nitrogento prevent and remove radon gas from the setup. Anillustration of the setup is shown in Fig. 2.The energy spectrum of the thorium sample wasaccumulated over 378.1 h, and is presented in Fig. 3.The energy resolution of the spectrometer is nominallycalibrated at 2.0 keV FWHM at 1332 keV from Co;however, the high trigger rate of the detector of about800 Hz can deteriorate the nominal resolution perfor-mance. Thus, the abundance of γ -lines in the Thspectrum was used for an in-situ calibration. The cali-brated resolution used in the analysis is 3.7 keV FWHMat 1332 keV. The efficiencies for the full-energy absorp-tion peaks used for the quantitative analysis were ob-
Fig. 1
Decay scheme of all possible
Th double beta decay transitions. The 0 + transitions are highlighted. Data taken from[21]. Fig. 2
Setup and sample configuration of the measurement.Figure adopted from [22]. tained by Monte-Carlo simulation with the MaGe codebased on the GEANT4 software package [26,27].
The analysis is based on peak searches for de-excitation γ -rays from the various excited state decay modes. Thefull spectrum is shown in Fig. 3 (left). The high triggerrate of the detector results in 10 − counts per 0.68 keVbin which requires the search for rare events on top of alarge background. The background expectation in suchsearches is typically taken from a background modelbuilt by Monte Carlo simulations or empirically by as-suming a linear behavior around the peak. However,given the large number of events per bin, the back-ground expectation requires per cent or even per milleprecision which is not realistically achievable. Fig. 3(right) shows a zoom into the spectrum around the643.5 keV γ -line of the 0 +1 transition clearly indicat-ing that a linear behavior cannot be assumed with therequired precision. Thus, we obtain count limits of thesignal peaks by excluding Gaussian peak shapes on topof the observed number of events without assuming ana-priori background. This method does not allow to dis-cover a signal since all observed events are interpretedas background.The peak fits are performed in a Bayesian regime,exemplarily described for the 0 +1 decay mode and thenapplied to all possible double beta decay modes of Th. The likelihood L is defined as the product ofthe Poisson probabilities over each bin i for observing Fig. 3
Measured HPGe spectrum of the 0.181 g thorium sample obtained in 15.8 days. Left: full spectrum with prominent γ -lines highlighted. Right: zoom in to the region of interest for the 643.5 keV γ -line of Th double beta decay transitionto the 0 +1 state. Significant spectral substructures are clearly visible in-between the main peaks due to the large number ofrecorded events. n i events while expecting λ i , in which λ i is the sum ofthe signal S i and background B i expectation: L ( p | n ) = (cid:89) i λ i ( p ) n i n i ! e − λ i ( p ) , λ i ( p ) = S i + B i . (1)Here n denotes the data and p the set of floatingparameters. S i is taken as the integral of the Gaussian peakshape in this bin given the total signal peak counts sS i = (cid:90) ∆E i s √ πσ E · exp (cid:18) − ( E − E ) σ E (cid:19) dE , (2)where ∆E i is the bin width, σ E the energy resolu-tion and E the γ -line energy as the mean of the Gaus-sian. B i , the background expectation, is implemented asa free parameter for each bin with a Gaussian prior withmean n i and width √ n i B i = n i · √ πn i · exp (cid:18) − ( b i − n i ) n i (cid:19) . (3)This method adds an additional fit parameter foreach bin but correctly distinguishes between the back-ground expectation b i in the fit and the observed num-bers of events n i on which the expectation is based.The best fit for b i will be identical to n i , but the addi-tional degrees of freedom widens the posterior distribu-tion and results in half-life limits which are about 30%more conservative compared to simply fixing b i ≡ n i inthe analysis.The signal counts are connected with the half-life T / of the decay mode as s = ln 2 · T / · (cid:15) · N A · T · m · f · M , (4)where (cid:15) is the full energy peak detection effi-ciency, N A is the Avogadro constant, T is the live-time (15.75 d), m is the mass of the sample (0.181 g), and f is the isotopic fraction of Th (100%) and M itsmolar mass (232).Each free parameter in the fit has a prior associated.The prior for the inverse half-life ( T / ) − is flat. Priorsfor energy resolution, peak position and detection effi-ciencies are Gaussian, centred around the mean valuesof these parameters. The width of these Gaussians arethe uncertainty of the parameter values. This naturallyincludes the systematic uncertainty into the fit result.The uncertainty of the peak positions are set to0.1 keV. The energy scale and resolution is obtainedwith the Th decay chain γ -lines in the spectrum. Aresolution of σ = 1 .
48 keV was determined at 643.5 keVwith an estimated uncertainty of 10% which also ac-counts for slightly non-Gaussian peak shapes due topile-up from the high rate operation. The full energypeak detection efficiencies are determined with Geant4Monte-Carlo simulations and are 14.4% at 643.5 keVwith an assumed uncertainty of 10%. Systematic uncer-tainties on the measured sample mass and the isotopicfraction in the sample are negligible with respect to theuncertainty of the detection efficiency.The posterior probability distribution is calculatedfrom the likelihood and prior probabilities with theBayesian Analysis Toolkit (BAT) [28] and marginalizedfor ( T / ) − . The best fit is always zero signal countsin this method since all observed events are consistentwith the background by design. The 90% quantile of themarginalized posterior distribution of ( T / ) − is usedto set the 90% credibility limits including systematicuncertainties. For the 0 +1 transition, 3145 counts areexcluded in the 643.5 keV peak on top of a backgroundof 3 . · cts/keV. The lower half-life limit is T / > . × yr (90% CI) . (5) Fig. 4
Region of interest and fit for the 0 +1 transition. Thedata is shown in black. The mean background expectationin each bin identical to the data by construction is shown inblue. The signal peak excluded by 90% probability is shownin red on of the data as well as independently at the bottom. The fit is shown in Fig. 4 illustrating the fit functionin red with the signal peak set to the strength excludedwith 90% credibility. The fit function for the best fit,i.e. without signal strength and background equivalentto the observed number of events, is shown in blue.The other decay modes are treated similarly and re-sults are shown in Tab. 1. In case multiple γ -lines areconsidered, a combined fit is performed by extendingthe likelihood in Eq. 1 over multiple regions of inter-est with common ( T / ) − parameter. The 47.6 keV γ -line is part of all decay modes but due to its low en-ergy it has only a small detection efficiency and higherbackground level in the setup. It is only considered forthe first excited state (2 +1 ) where it is the only γ -lineand where the obtained half-life limit is about 3 or-ders of magnitude smaller than for the other modes.The 578.0 keV γ -line of the 5 − state is omitted due toits low branching ratio. The complete list of considered γ -lines is also presented in Tab. 1 for each decay mode. decay level T / (90% CL) γ -lines energies[keV] ( J π ) [yr] [keV]47.6 (2 +1 ) > . · +1 ) > . · +1 ) > . · +1 ) > . · +1 ) > . · +1 ) > . · +1 ) > . · +2 ) > . · − ) > . · +1 ) > . · +2 ) > . · Table 1
Lower half-life limits on
Th double beta decaymodes set in this work. The last column shows the γ -linesused in the combine fit. We performed a first search for double beta decays of
Th into all possible excited states of
U using athorium containing gas mantle sample and a HPGe welldetector. The established limits are valid for both the2 νββ and 0 νββ mode. The large intrinsic background ofthe experiment did not allow to model the backgroundprediction with sufficient precision. Thus the analysiswas performed without background model and limitson
Th DBDs were set under the assumption that allobserved events are background, i.e. a discovery withthis method is not possible.Future improvements of this measurement shouldaim at reducing the intrinsic background in the search.The vast majority of background originates from thedecay daughters of the sample nuclide itself which buildup over time. This could be reduced by using a Thsample right after the separation/purification process,for example by anion-exchange resin, so that existingdaughter isotopes are chemically removed.The Th-daughter nuclides will then again accumu-late with time. Thus the mass of the sample mustbe well chosen based on the acceptable count ratefor the used detector setup. Moreover, one could con-sider a campaign of several subsequent runs of thesame measurement, interrupted by intermittent re-purification/separation of
Th from its daughter nu-clides accumulated within the previous measurementperiods.For investigating the DBD ground state transition,only the “source=detector” approach can be used. Inthis situation it is difficult to realize campaigns with in-termittent purification since the extraction of Th fromany detector material is a more complicate and time-consuming process. However, using a detector technol-ogy with high characteristic time-response, such as fastscintillators, would allow to deploy a larger amountof thorium. For characteristic scintillating times in therange 1-50 µ s, one could load a scintillator with a fewhundred kBq activity of Th. Taking into accountthat activities of its daughter will rise with time andtheir beta components create a large continuous back-ground, the initial
Th amount should be reduced toa few kBq. A potential type of detector are scintillatingcrystals grown by the Bridgman technique in a closedquartz ampule. This allows the whole growing setup tobe safely contained and avoid contaminations from theradioactive Th-chain isotopes during production. Ad-ditional precaution must be taken during the machin-ing and handling of such Th-loaded crystals. In orderto avoid a possible interference between an activatorin the scintillator and the
Th load, the scintillator should be self-activated. Potential candidates are halidecrystals, such as NaI (undoped), CsI, or a new type ofCs HfCl crystals.Here, we investigated only DBDs of Th but inprinciple also other radioactive DBD isotopes in the
Th decay chain can be search for, as suggested in[20]. However, given their low abundance as
Thdaughters and much shorter half-lives than
Th, theresulting half-life limits would be significantly lower.There are no existing theoretical estimations of half-lives for excited state transitions of
Th. Such calcula-tions require significant effort and are limited to certainnuclear models e.g. QRPA, since the daughter nuclide
U is heavily deformed and has strong rotation bands.From the Q ββ dependence of 2 νββ half-lives, one cancrudely extrapolate from observed 2 νββ decays in otherisotopes that the here established sensitivities are about10 orders of magnitude lower than needed. The half-lifeof the first excited 0 +1 state is expected to be about6000 times longer for the 0 + ground state.Nevertheless, steady progress in improving half-lifelimits for DBD isotopes, other than the ones used inlarge scale experiments (i.e. Ge,
Mo, Se,
Te,
Xe), will eventually help to tune theoretical modelsto better describe the nuclear physics behind doublebeta decay.
Acknowledgements
We would like to thank Dr. FedorˇSimkovic for interesting and useful discussion about theoret-ical half-life estimates.