Double-beta decay investigation with highly pure enriched $^{82}$Se for the LUCIFER experiment

The LUCIFER project aims at deploying the first array of enriched scintillating bolometers for the investigation of neutrinoless double-beta decay of $^{82}$Se. The matrix which embeds the source is an array of ZnSe crystals, where enriched $^{82}$Se is used as decay isotope. The radiopurity of the initial components employed for manufacturing crystals, that can be operated as bolometers, is crucial for achieving a null background level in the region of interest for double-beta decay investigations. In this work, we evaluated the radioactive content in 2.5 kg of 96.3\% enriched $^{82}$Se metal, measured with a high-purity germanium detector at the Gran Sasso deep underground laboratory. The limits on internal contaminations of primordial decay chain elements of $^{232}$Th, $^{238}$U and $^{235}$U are respectively: $<$61 $\mu$Bq/kg, $<$110 $\mu$Bq/kg and $<$74 $\mu$Bq/kg at 90\% C.L.. The extremely low-background conditions in which the measurement was carried out and the high radiopurity of the $^{82}$Se allowed us to establish the most stringent lower limits on the half-lives of double-beta decay of $^{82}$Se to 0$^+_1$, 2$^+_2$ and 2$^+_1$ excited states of $^{82}$Kr of 3.4$\cdot$10$^{22}$ y, 1.3$\cdot$10$^{22}$ y and 1.0$\cdot$10$^{22}$ y, respectively, with a 90\% C.L..


Introduction
The observation of neutrinoless double-beta decay (0νββ) would demonstrate lepton number violation, and at the same time it would necessarily imply that the neutrinos have a Majorana character. Under the assumption that 0νββ decay is induced by the exchange of light Majorana neutrinos, the partial width of the decay is proportional to the square of the effective neutrino Majorana mass. A measurement of the half-life of this process would supply information to fundamental open questions in Particle Physics: which is the mass hierarchy of neutrinos? Which is their absolute mass scale?
The Standard Model counterpart of the 0νββ decay, is the 2νββ decay. It is the rarest nuclear weak process experimentally observed in dozen of nuclei with halflives in the range of 10 18 -10 22 y [1].
Double-beta (ββ) decay can occur through different channels other than the ground state to ground state transitions. In Fig.1 the scheme for ββ 82 Se decay is shown. The transition into different excited levels of the daughter nucleus can also take place, if energetically allowed. The study of ββ decay into excited states can arXiv:1508.01709v3 [physics.ins-det] 1 Dec 2015 supply futrher information about the nuclear matrix elements that describe 0νββ decay; specifically, a more detailed description of the nuclear model and structure could be gained [2].  In 1990, the first publication on the potential to observe 2νββ decay to excited levels of daughter nuclei was reported [3]. Therein an estimation of the expected half-lives for 2νββ decay to the first 0 + 1 level for some nuclei was provided. Given the large transition energy involved in such decays -few MeV -the detection seemed to be accessible to the former technology.
Two neutrino double-beta decay to the first 2 + excited level, according to the nuclear matrix elements computed by Haxton and Stephenson [4], seemed to be experimentally inaccessible to detection, due to the smaller phase-space factor compared to the 0 + level. However, later on in the early nineties, J. Suhonen and O. Civitarese demonstrated [5] that this suppression was not as large as calculated in [4] in 1984, and that the observation of these transitions was within reach. In fact, in [2] the half-life for the 2νββ decay of 82 Se to the 2 + 1 excited level of 82 Kr was computed to be 5.71·10 21 y.
In order to enhance the experimental sensitivity to the investigation of rare decays it is mandatory to reduce any possible background source. In the ββ decay context, a material selection is needed to single out the ββ decay source with the lowest content of radioactive impurities, which may mimic the signal under investigation. Among the various techniques for material screening a very common one is γ-spectroscopy using high-purity germanium (HP-Ge) detectors, since they ensure a rather low background level, gain stability and high energy resolution. Such detectors match exactly the needs for a high sensitivity investigation of ββ decay on excited levels of daughter nuclei, where single γ quanta or cascades are produced during the de-excitation. In literature, half-life measurements of nuclides which undergo ββ decay on excited levels are mostly performed by means of γ spectroscopy [6,7,8,9].
In this work, we report on the analysis of the radiopurity level of the ββ decay source for the LUCIFER experiment [10], namely 96.3% enriched 82 Se metal, performed at the Gran Sasso Underground Laboratory (LNGS) of INFN, sited in Italy. Thanks to the high purity of the sample, new results on the experimental investigation of ββ decay of 82 Se to the excited states 0 + 1 , 2 + 1 and 2 + 2 of 82 Kr are presented.

The LUCIFER project
In order to detect the elusive signal rate of 0νββ there are two main requirements that must be fulfilled: employing a large mass source and operating the detector in almost zero-background conditions. Present experiments are already designed to investigate the 0νββ decay in ton-scale sources, and a further increase in the source mass seems not to be within the reach of the present technology. Acceptable background rates in the region of interest are of the order of 1-10 counts/y/ton if the goal is just to approach or touch the inverted hierarchy region of neutrino masses, whereas at least one order of magnitude lower values are needed to fully explore it [11]. This is the goal of CUPID [12], a proposed future tonne-scale bolometric neutrinoless double-beta decay experiment to probe the Majorana nature of neutrinos in the inverted hierarchy region of the neutrino mass [13].
Among the available detection techniques, bolometry is one of the most promising ones. Bolometers ensure high detection efficiency [14] -the detector embeds the decay source (detector=source) -excellent energy resolution [15] and, for luminescent bolometers, also the identification of the nature of the interacting particle [16,17,18,19,20], an excellent tool for background suppression. Furthermore, this technique shows the unique feature that detectors can be grown out of a wide choice of materials, allowing to probe different isotopes with the same technique.
LUCIFER (Low Underground Cryogenic Installation For Elusive Rates), being one of the first CU-PID demonstrators, aims at deploying the first close to background-free small-scale bolometric experiment for the investigation of 82 Se 0νββ decay [10]. Enriched scintillating bolometer of Zn 82 Se will be used for a highly sensitive search for this decay.
The selection of high-purity Zn and 82 Se is one of the most critical point that will undoubtedly affect the sensitivity of the final experiment. In fact, the starting materials for the Zn 82 Se synthesis and the crystal growth must show extremely low concentration of impurities, both radioactive and chemical.

Background sources at Q ββ
Selenium is an attractive isotope for the investigation of 0νββ decay, especially for its Q ββ -value, which is 2997.9±0.3 keV [21]. Since it lies above the most intense natural γ-line at 2.6 MeV, the β/γ background in the region of interest (ROI) is strongly reduced. Most of the background at this energy in bolometers is expected to come from α induced surface contaminations [22]. Thanks to a highly efficient particle discrimination, taking advantage of the heat-light read-out, such kind of background can be rejected in scintillating bolometers [16,17,18,20].
Given our present knowledge [10], the main background sources for the LUCIFER experiment will be: i) high energy γ emission from 214 Bi -up to 3.2 MeV -and ii) pile-up events from 208 Tl γ cascade. Even if the background induced by these sources can be suppressed, as discussed in [23], still it can not be completely neglected. The two previously mentioned nuclides are produced in the decay chains, following the decay of primordial 238 U and 232 Th. A thorough material selection is mandatory in order to reduce as much as possible their concentration in the Zn 82 Se crystals. In order to allow an almost zero-background investigation [24,25], 238 U and 232 Th contaminations inside the final crystal must be at the level of tens of µBq/kg or better.

Chemical impurities
When selecting the starting material for crystal growth, it is crucial that the raw materials exhibit high purity grades. This issue becomes even more relevant when dealing with bolometers. Point defects caused by impurities in the starting materials may act as traps both for phonons, involved in the bolometric signal development, and for free charge carriers, involved in the scintillation process. The achievement of high purity raw materials becomes more difficult while handling enriched selenium, given the complexity of the enrichment production process requiring large quantities of chemical reagents.
Elements of the VI and VII groups of the periodic table (e.g. V, Cr, Mn, Fe, Co, Ni) are defined as critical impurities for the scintillation performance of Zn 82 Se crystals [26,27]. Moreover, ferromagnetic and paramagnetic impurities can spoil the bolometric properties of the detector, since they add a contribution to the overall heat capacity of the system [28]. In fact, at low temperatures, low heat capacities are desirable because they will result in large thermal signals and thus higher energy resolutions.

Selenium enrichment
The entire enrichment process for the production of 15 kg of 82 Se for the LUCIFER experiment was carried out at URENCO, Stable Isotope Group in Almelo, in the Netherlands. In order to be able to achieve the required experimental sensitivity, the use of enriched Se is mandatory, given the relatively low natural isotopic abundance of 8.73% [29]. The enrichment is performed through a well established procedure: centrifugal enrichment. A dedicated line of centrifuges was employed for the enrichment of gaseous SeF 6 , that was fully separated from the one used for the 235 U enrichment. The technical details, i.e. the number of centrifuges in the cascade, the throughput and other specifications are property of URENCO. In order to prevent U, Th and other nuclides contaminations in the final product, a flushing of the entire centrifuge cascade was performed using fluorine, and providing a satisfactory cleaning of the system.
The production of enriched Se consists of 3 main steps: 1-procurement of SeF 6 gas; 2-centrifugal enrichment of 82 SeF 6 ; 3-conversion of 82 SeF 6 gas to 82 Se metal.
The starting material is natural SeF 6 gas, purchased by URENCO from an external supplier, which is fed into a cascade of centrifuges. The outcome of the process is 82 SeF 6 enriched gas at a ≥ 95% level. The subsequent step is the conversion from gas to metal, which is performed through a series of chemical reactions [30]. The final product is enriched 82 Se metal.
In order to minimize the risk of losses and of exposure to cosmic rays, thus to reduce cosmogenic activa-tion, the enriched 82 Se was divided into 6 batches, separately delivered to the LNGS by ground transportation and stored underground. Furthermore, special care was devoted to prevent any re-contamination of the isotope [22], for this reason each batch was packed in double vacuum sealed polyethylene bags before shipping.
For the LUCIFER experiment, 15 kg of enriched selenium were provided in form of small beads. Each gas-to-metal conversion yields about 200 g, for the production of the final enriched metal, 70 different processes were carried out. Each conversion was supplied with a set of witness samples for monitoring the purity and the enrichment level of selenium.
The purity grade of the reagents and the yield of the transformation affect the quality of the final product, for this reason the process is recognized to be most critical for the experiment. Thanks to the constructive collaboration with the producer all reagents employed for the chemical conversion of selenium were subjected to assay both from a chemical and radioactive point of view, using an Inductively Coupled Plasma Mass Spectrometer (ICP-MS) and γ-spectroscopy with HP-Ge. The contaminations of radioactive elements -U/Th primordial decay chains -and chemical -V, Cr, Mn, Fe, Co and Ni -were measured to be at a level of 10 −7 g/g . These values are within the requirements for the production of enriched selenium with an overall chemical purity better than 99.8% on trace metal base. All material screenings were performed at LNGS.
In Table 1 the abundance of the different selenium isotopes after the enrichment process, measured with ICP-MS are reported. The values reported in the table are the average over the 70 conversion processes weighted for their relative mass, while the uncertainty refers to the spread in the enrichment. As it is shown in the table, an enrichment above 95% on 82 Se is ensured on all the samples, in some cases an enrichment level up to 97.7% was achieved. For the sake of comparison, we report also the recommended natural occurring values [29].

Chemical and radiopurity assay
The analysis of chemical impurities inside the 6 different deliveries of 82 Se was performed using ICP-MS. The results are shown in Table 2, where for each batch we show the impurities of the sample which exhibits the highest concentration. Together with the previously mentioned elements, we investigated other impurities whose concentration is induced by the use of chemical reagents for the gas-to-metal conversion. Sodium and sulphur are the elements mostly involved in this chemical conversion [26], where they are employed in the form of salt like: NaI or Na 2 SO 3 . The concentration of these is not relevant for the final crystal production.
The investigation of the internal radioactive contamination of enriched Se metal for the LUCIFER experiment was carried out with γ-spectroscopy using a HP-Ge detector located in the underground Laboratory of LNGS (depth of 3600 m w.e. [31]), which ensures muon flux suppression by a factor of 10 6 compared to sea level. The detector, GeMPI-4 [32], is a p-type germanium crystal provided by Canberra company, with a volume of about 400 cm 3 . The crystal size was optimized for high counting efficiency in Marinelli type geometry. Details on the experimental set-up and detector performance can be found in [32].
Through γ-spectroscopy, background information is inferred for the most intense lines of the primordial decay chains 238 U/ 235 U, 232 Th and 40 K, but also on elements with antropogenic (e.g. 137 Cs) and cosmogenic ( 60 Co, 75 Se) origins. The overall background counting rate of the detector is 5.6 c/keV/kg/y over a large energy range [200,2700] keV. The FWHM energy resolution of the detector ranges from 1.5 keV at 609 keV to 2.2 keV at 1460 keV, while at higher energies, like 2615 keV, is 3.2 keV. Selenium beads were poured inside a 1.46 l volume  polypropylene container. A cylindrical Marinelli type beaker was chosen: the detector look at the whole lateral and top surfaces of the sample, whose net mass was 2500.5 g. Table 1 Isotopic abundance of natural (recommended values [29]) and enriched selenium. The values for the enriched isotope are averaged over 70 different gas-to-metal conversion processes, weighted for their relative mass.

Results and limits on contaminations
Data were acquired over 1798.2 hours, the final energy spectrum is shown in Fig. 2. Few lines are visible in the energy spectrum, these are produced by radioactive impurities inside the sample and in the HP-Ge detector itself.
The activity of radioactive nuclides inside the sample is computed following the same standard procedure described in [33]. In the evaluation of the contaminant concentrations we take into account the detector background as well as the detection efficiencies for the different gamma lines, which are calculated with Monte Carlo simulations based on the Geant4 code [34].
The internal contaminations of the sample, as well as their concentrations, are listed in Table ??. No evidence of nuclides from the natural chains of 235 U/ 238 U and 232 Th are detected, in agreement with the ICP-MS measurements (see Table 2). We report the limits of detectability for long-lived β/γ-emitters of the decay chains. Limits are set at an extremely low level -hundreds of µBq/kg, and they are competitive with values reported on other raw materials used for the crystal growth of ββ decay detectors [35,36,37].
Limits on the concentration of other commonly observed nuclides are also shown, specifically for 40 K and 60 Co.
In the sample, 75 Se is the only nuclide having a concentration at a detectable level, 110±40 µBq/kg. This isotope is not naturally occurring and it is mainly produced in significant amount by cosmogenic neutron spallation on 76 Se. The reaction 76 Se(n, 2n) 75 Se has a rather large neutron interaction cross section: 979±90 mb for 16 MeV neutrons [38]. According to [38], among the fast neutron induced reactions on selenium isotopes, 75 Se, with an half-life of 119.8 days, is the only longlived nuclide produced. 75 Se decays through an electron capture and has a rather small Q-value of 863.6 keV. This makes the isotope not dangerous for 82 Se ββ decay investigations. Moreover the measurement was started in October 2014, thus a strong reduction in the 75 Se activity is expected before the crystal production, that will be finalized in March 2016.
6 82 Se double-beta decay to 82 Kr excited levels The purity of the enriched selenium and the high performance of the HP-Ge detector allowed us to carry out a highly sensitive investigation of 82 Se ββ decay to the excited levels of 82 Kr. Specifically, we look for the γ signatures produced by the de-excitation of the nuclei that undergo a ββ decay to an excited level.
The technique adopted for this investigation does not allow us to distinguish between 0νββ and 2νββ decay of 82 Se. In fact the experimental efficiency for the detection of the two emitted electrons is insignificant, but on the other hand the set-up is sensitive to the γ emission from the source. The study of the ββ transition is mainly focused on the first three excited levels of 82 Kr: 0 + 1 , 2 + 1 and 2 + 2 . The decay scheme for the 82 Se ββ decay is shown in Table 3, where the four γ emissions under investigation are listed. We can parametrize the decay scheme as follows: (4) where N x (x = a, b, c, d) represents the observed number of events for the 4 different γ's, x the total detection efficiency of the process, ξ the total exposure (180.40 kg·days of 82 Se) and Γ y (y = 0 + 1 , 2 + 1 , 2 + 2 ) the partial width of the decays. BR represents the branching ratio of the decay which is 37% for the transition 2 + 2 → 0 + and 67% for the 2 + 2 → 2 + 1 (see Fig.1). Special care is also addressed to the 776.5 keV line, because it is produced through three different channels, as described by Eq. 4.
The detection efficiencies for the four different γ emissions, derived via simulations, are listed in Table 3. In our final calculation we neglect the 2 + 2 → 0 + transi- tion, given the relatively small detection efficiency.
We simultaneously extract the decay rate for the three excited levels of 82 Kr from the entire data set (180.40 kg·days of 82 Se) performing a global Binned Extended Maximum Likelihood fit in the energy range between 650 and 850 keV (ROI). The probability density function (p.d.f.) has four components, a flat background modelling the multi-scatter events produced by high energy γ's (e.g. 40 K, 208 Tl and 214 Bi) and three gaussian functions, with fixed central value (µ) and width (σ), for the (a), (c) and (d) transitions: . The energy resolution of the detector, which is represented by σ, is assumed to be constant over the narrow ROI, its value is 0.61 keV. This is evaluated on the 609 keV peak, the closest visible peak to the ROI, and it is produced by natural 214 Bi contaminations in the experimental set-up. The flat background assumption is verified by comparing the counting rate in the ROI and in adjacent regions at higher and lower energies.
The fit result is shown in Fig. 3. Since no signal for any ββ decay of 82 Se on exited levels is observed, a Bayesian lower limit at 90% C.L. on the three decay rates, Γ s, is set. These limits are evaluated marginalizing the profile negative log likelihood function over nuisance parameters, assuming a flat prior on the Γ s when they assume physical values: π(Γ ) = 1 if Γ ≥ 0, π(Γ ) = 0 otherwise. The limits evaluated for the decay rates are: The counting rate in the ROI is (9.6±0.5) c/keV/y, which is 2 σ compatible with the one measured in background conditions, (11.3±1.0) c/keV/y, when no 82 Se sample was on the detector. Most likely, the background in the ROI is caused by detector internal contaminations [32].
The corresponding lower limits on the partial halflives, calculated as T limit = ln(2)/Γ limit are: tivity surpasses the one of other works reported in literature [39,40] by about one order of magnitude. Furthermore the limit set for the decay to 2 + 1 state contradicts the theoretical calculations reported in [2].

Conclusions
The goal of next-generation ββ decay experiments is to explore the inverted hierarchy region of neutrino mass. In order to further enhance their sensitivity, future experiments should strive for a highly efficient background reduction, possibly to a zero level, and large mass ββ sources, at the tonne-scale. These must exhibit low levels of radioactive contaminations in order to suppress the background in the region of interest. Furthermore, if the bolometric technique is adopted, low concentrations of chemical impurities in the source materials are also needed, given the fact that the detector performances depends on the quality of the materials used for the detector manufacturing.
In this work we have investigated the purity of 96.3% enriched 82 Se metal for the production of scintillating bolometers for the LUCIFER project, which amounts to 15 kg. Out of the total, 2.5 kg were analyzed by means of γ spectroscopy and ICP-MS analyses for the evaluation of the internal radioactive and chemical impurities.
The exceptional purity of the source, which shows extremely low internal radioactive contamination, at the level of tens of µBq/kg and high chemical purity with an intrinsic overall contamination of few hundreds of 10 −6 g/g, allowed us to investigate also ββ decay of 82 Se. We established the most stringent limits on the half-life of 82 Se ββ decay to the excited levels 0 + 1 , 2 + 1 and 2 + 2 of 82 Kr . Previous limits are improved by one order of magnitude for all the investigated transitions. The technique used in this work does not allow for a distinction between the 2ν and the 0ν modes, therefore our results are the overlap of the two processes.
Our results give the opportunity to improve the accuracy of Nuclear Matrix Elements calculations, so that experimental and theoretical evaluations may have a direct comparison. Moreover, as discussed in [41], fine tuning of parameters relevant for the quasiparticle random-phase approximation (QRPA) model, such as the particle-particle strength interaction, g pp can be performed on intermediate states of ββ decays.