Beta-decay studies for applied and basic nuclear physics
EEPJ manuscript No. (will be inserted by the editor)
Beta-decay studies for applied and basic nuclear physics
A. Algora , , J. L. Tain , B. Rubio , M. Fallot , and W. Gelletly IFIC (CSIC-Univ. Valencia), Paterna, Spain Institute of Nuclear Research (ATOMKI), Debrecen, Hungary Subatech (CNRS/in2p3 - Univ. Nantes - IMTA), Nantes, France University of Surrey, Surrey, UKReceived: date / Revised version: date
Abstract.
In this review we will present the results of recent beta-decay studies using the total absorptiontechnique that cover topics of interest for applications, nuclear structure and astrophysics. The decaysstudied were selected primarily because they have a large impact on the prediction of a) the decay heatin reactors, important for the safety of present and future reactors and b) the reactor electron anti-neutrino spectrum, of interest for particle/nuclear physics and reactor monitoring. For these studies thetotal absorption technique was chosen, since it is the only method that allows one to obtain beta decayprobabilities free from a systematic error called the Pandemonium effect. The total absorption techniqueis based on the detection of the gamma cascades that follow the initial beta decay. For this reason thetechnique requires the use of calorimeters with very high gamma detection efficiency. The measurementspresented and discussed here were performed mainly at the IGISOL facility of the University of Jyv¨askyl¨a(Finland) using isotopically pure beams provided by the JYFLTRAP Penning trap. Examples are presentedto show that the results of our measurements on selected nuclei have had a large impact on predictionsof both the decay heat and the anti-neutrino spectrum from reactors. Some of the cases involve beta-delayed neutron emission thus one can study the competition between gamma- and neutron-emission fromstates above the neutron separation energy. The gamma-to-neutron emission ratios can be used to constrainneutron capture (n, γ ) cross sections for unstable nuclei of interest in astrophysics. The information obtainedfrom the measurements can also be used to test nuclear model predictions of half-lives and Pn valuesfor decays of interest in astrophysical network calculations. These comparisons also provide insights intoaspects of nuclear structure in particular regions of the nuclear chart. PACS. β decay; double β decay; electronand muon capture – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environ-ments – 29.30.h Spectrometers and spectroscopic techniques – 29.90.+r Other topics in elementary-particleand nuclear physics experimental methods and instrumentation Our knowledge of the properties of atomic nuclei is derivedalmost entirely from studies of nuclear reactions and ra-dioactive decays. The ground and excited states of nucleiexhibit many forms of decay but the most common are al-pha, beta and gamma-ray emission. Our focus here is onbeta decay in its various manifestations. A glance at theSegre Chart reveals that it is the most common way forthe ground states of nuclei to decay and it is frequentlythe observation of such beta decays that brings us our firstknowledge of a particular nuclear species and its proper-ties.The study of beta decay is intrinsically much moredifficult than the study of either alpha or gamma decay.The reason for this is straightforward. Alpha particles andgamma rays are emitted with discrete energies determinedby the differences in energy between the initial and final states involved. Thus characteristic alpha and gamma rayspectra exhibit a series of discrete lines. It requires sophis-ticated detection and analysis techniques to determine theexcitation energies of the states involved, their lifetimesand the transition rates between states. Beta decay carriesthe same information, but the difficulties of measurementand interpretation are compounded because the spectrumis continuous, not discrete. In 1930 this was explained byPauli’s hypothesis [1] of the existence of a neutral, zeromass particle called in his letter the neutron that is emit-ted with the beta particle. The sharing of momentum andenergy then explains the continuous spectrum. Shortly af-terwards Fermi [2] was able to formulate a theory of betadecay based on this idea and coined the name neutrino (little neutral one) for the particle.A knowledge of beta decay transition probabilities isof particular importance for application to a) tests of nu-clear model calculations, b) the radioactive decay heat in a r X i v : . [ nu c l - e x ] J u l A. Algora et al.: Beta-decay studies for applied and basic nuclear physics
Fig. 1.
Schematic picture of how the beta feeding is deter-mined in a beta decay experiment employing Ge detectors.The beta feeding (I β ( i )) to level i is determined from the dif-ference of the total intensity feeding the level and those de-exciting it. The sum over (k) represents all transitions feedingor de-exciting the level. I γ k stands for the gamma intensity oftransition k and I CE k represents the conversion electron inten-sity. reactors, c) the reactor electron anti-neutrino spectrumand d) reaction network calculations for nucleosynthesisin explosive stellar events. In this article we will provideexamples of our recent studies of beta decays that involvethe use of total absorption gamma spectroscopy (TAGS)to tackle the topics listed above. The TAGS method wasadopted in our measurements because it overcomes thedifficulties inherent in the conventional use of Ge detectorarrays for this purpose. Such arrays are an important andessential tool for constructing nuclear decay schemes sincethey are very well suited to the study of gamma-gammacoincidences, the main basis for building such schemes.The normal practice is then to derive beta decay transi-tion probabilities for each level populated from the differ-ence in the total intensity of all the gamma rays feedingthe level and the sum of the intensities of all those de-exciting it, corrected by the effect of internal conversion(see Figure 1). In principle this allows us to obtain thebeta branching to every level, assuming that we are ableto determine by some other means the number of decaysthat go directly to the daughter ground state, which arenot accompanied by gamma emission.Unfortunately this ”simple” procedure does not neces-sarily give us the correct answers. States at high excita-tion energies in the daughter nucleus can be populated ifthe Q β value of the decay is large. In this case both thenumber of levels that can be directly populated by thebeta decay is large and the number of levels available towhich they can gamma decay is also large. As a result, ingeneral, individual gamma rays (emitted by levels at highexcitation energy) have low intensity. Ge detectors, indeedeven gamma-ray arrays, have limited detection efficienciesparticularly at higher energies and thus weak transitionsare often not detected in experiments. It is clear that this Fig. 2.
Simplified picture of a beta decay where only one ex-cited state is populated and it de-excites by the emission of agamma cascade. The left hand panel represents the case. Thecentral panel presents the Pandemonium effect, in this examplerepresented by missing, or not detecting the gamma transition γ . The right hand panel represents the displacement of thebeta decay intensity because of the non detection of the tran-sition γ . means that we have a problem that has become known asthe Pandemonium effect [3] (see Figure 2 for a simplifiedpicture).We can overcome this problem using the total absorp-tion gamma spectroscopy technique, where we take a dif-ferent approach. The method involves a large 4 π scintilla-tion detector and is based on the detection of the full de-excitation gamma cascade for each populated level, ratherthan the individual gamma rays. The power of TAGS tofind the missing beta intensity has been demonstrated ina number of papers [4,5,6,7,8,9,10,11,12,13]. The use ofthe TAGS method began at ISOLDE[14]. Its developmentand history are described in [15,16].Looking at a wider picture we see that many entriesin the international databases, that rely on measurementswith Ge detectors alone, will have systematic errors. Aswe shall see in the sections that follow this means thatthe results cannot be relied on for certain applications.The answer to the resulting difficulties lies in the use ofTAGS. In the remainder of this article we will describethe TAGS method in more detail and then use our resultsto illustrate how it can be applied.The structure of this article is the following: in Section2 details of the experimental method and the analysis ofthe spectra are described. Sections 3, 4, 5 and 6 deal withbeta decay studies related to a) radioactive decay heat(DH), b) reactor antineutrino spectra c) nuclear models,and d) astrophysical applications respectively. Finally, inSection 7, a summary will be presented. In Section 1 it was already explained why we need TAGSmeasurements. Figure 3 shows how the simple beta de-cay presented in Figure 2 is detected by typical detectors . Algora et al.: Beta-decay studies for applied and basic nuclear physics 3
Fig. 3.
Schematic picture of how the simple beta decay de-picted in Figure 2 is seen ideally by different detectors usedin beta decay studies. Left panel, representation of a total ab-sorption detector, rigth panel, ideally detected spectra with abeta dectector (a silicon detector), a Ge detector and a to-tal absorption detector after the simple decay represented inFigure 2. used in beta decay experiments. Because a TAGS detec-tor acts like a calorimeter, in an ideal TAGS experimentthe detected spectrum will be proportional to the betaintensity distribution. This spectrum is obtained in idealconditions, where there is no penetration of the beta parti-cles, or the radiation generated by them, into the detectorand the TAGS detector is 100% efficient up to the full en-ergy of the gamma rays that follow the beta decay. Thatmeans that only the full absorption peak corresponding tothe sum energy of the gamma cascade is detected in thecase of a β − decay.A real experiment does not quite match this ideal.In order to achieve very high detection efficiencies, large,close to 4 π , detector volumes are needed. Thus inorganicscintillation material has been the natural choice. Becauseof its good average properties NaI(Tl) has been used in allexcept one (see later) of the existing spectrometers. Nev-ertheless we need some opening to take the sources tothe centre of the spectrometer, either in the form of a ra-dioactive beam or deposited onto a tape transport system.The latter may also be needed to remove the sources aftersome measuring time. We may also need ancillary detec-tors for detecting coincidences and selecting the events inwhich we are interested. In addition TAGS detectors re-quire, in general, some form of encapsulation. All theserequirements mean that we have dead material and holesin our detector system. Accordingly the gamma detectionefficiency of our system will not be 100%. The consequenceis that to obtain the beta intensity distribution we needto solve the inverse problem represented by the followingequation: d i = j max (cid:88) j =0 R ij ( B ) f j + C i (1)where d i is the content of bin i in the measured TAGSspectrum, R ij is the response matrix of the TAGS setupand represents the probability that a decay that feeds level j in the level scheme of the daughter nucleus gives a count in bin i of the TAGS spectrum, f j is the beta feeding tothe level j (our goal) and C i is the contribution of the con-taminants to bin i of the TAGS spectrum. The index j inthe sum runs over the levels populated in the daugther nu-cleus in the beta decay. The response matrix R ij dependson the TAGS setup and on the assumed level scheme ofthe daughter nucleus. The dependence on the level schemeof the daughter nucleus is introduced through the branch-ing ratio matrix B . This matrix contains the informationof how the different levels in the assumed level schemedecay to the lower lying levels. To calculate the responsematrix R ij ( B ) the branching ratio matrix B has to bedetermined first. There are different ways to extract thefeeding distribution from equation 1 or, in other words, tosolve the TAGS inverse problem. One can assume the ex-istence of ”pseudo” levels that are added manually (withtheir decaying branches) to the known level scheme, cal-culate their response and see their effect in the calculatedspectrum (see for example [17,18]). In our analysis untilnow we have followed an alternative way for which thelevel scheme of the daughter nucleus is divided into tworegions, a low excitation part and a high excitation part.Conventionally the levels of the low excitation part andtheir gamma decay branchings are taken from high reso-lution measurements available in the literature, since it isassumed that the gamma branching ratios of these levelsare well determined. Above a certain energy, the cut-offenergy, a continuum of possible levels divided into 40 keVbins is assumed. From this energy up to the decay Q β value, the statistical model is used to generate a branch-ing ratio matrix for the high excitation part of the levelscheme. The statistical model is based on a level densityfunction and gamma strength functions of E1, M1, and E2character. Once the branching ratio matrix (B) is defined,the response of the setup R ij to that branching matrix B(or level scheme) is calculated using previously validatedMonte Carlo simulations of the relevant electromagneticinteractions in the experimental setup. The validation ofthe Monte Carlo simulations is performed by reproducingmeasurements of well known radioactive sources, that aremade under the same experimental conditions as the realexperiment. The Monte Carlo simulations require a care-ful implementation of all the details of the geometry ofthe setup, a proper knowledge of the materials employedin the construction of the setup and testing to find thebest Monte Carlo tracking options and physics modelsthat reproduce the measured sources. It should be notedthat from high resolution measurements we use only thebranching ratios of the levels, and not the information onthe feeding of these levels.Once the response function is determined we can solveEquation 1 using appropriate algorithms to determine thefeeding (or beta intensity) distribution. In our analyses wefollow the procedure developed by the Valencia group. In[19] several algorithms were explored. From those that arepossible, the expectation maximization (EM) algorithm isconventionally used, since it provides only positive solu-tions for the feeding distributions and no additional reg- A. Algora et al.: Beta-decay studies for applied and basic nuclear physics ularization parameters (or assumptions) are required tosolve the TAGS inverse problem.Clearly, the first level scheme (or defined branching ra-tio matrix) considered is not necessarily the one that willprovide a nice description of the measured TAGS spec-trum. For that reason, as part of the analysis the cut-offenergy and the parameters that define the branching ra-tio matrix can be varied until the best description of theexperimental data is obtained. Also assumptions on thespin and parity of the ground state of the parent nucleusand on the spins and parities of the populated levels canbe changed when they are not known unambigously, sinceto connect the levels in the continuum to levels in theknown part of the level scheme we need information abouttheir spin and parity. All these changes provide differentbranching ratio matrices (or daughter level schemes) thatare considered during the analysis and for all of them thecorresponding response matrixes are calculated and Equa-tion 1 is solved. The final analysis is then based on thelevel scheme (or branching ratio matrix) that is consis-tent with the available information from high resolutionmeasurements and at the same time provides the best de-scription of the experimental data. So in practical termsthe following steps are followed until the best descriptionof the data is obtained: a) define a branching ratio matrix B , b) calculate the corresponding response matrix R ij ( B ),and c) solve the corresponding Equation 1 using an appro-priate algorithm d) compare the generated spectrum afterthe analysis ( R ( B ) f + C ) with the experimental spectrum d . We have only mentioned briefly how the response func-tion R ij ( B ) is calculated. More specifically the responsefor each level can be determined recursively starting fromthe lowest level in the following way [20]: R j = j − (cid:88) k =0 b jk g jk ⊗ R k (2)where R j is the response to level j , g jk is the responseof the gamma transition from level j to level k which is cal-culated using Monte Carlo simulations, b jk is the branch-ing ratio for the gamma transition connecting level j tolevel k , and R k is the response to level k . Here the index k runs for all the levels below the level j . For simplicitywe have not included here in the formula the convolu-tion with the response of the beta particles and only thegamma part of the response is presented. Note that in thislast notation R j is a vector that contains as elements the R ij matrix elements mentioned above for all possible i -s(or channels) of the TAGS spectrum and the branchingratio matrix enters in the formula of the response matrixthrough the decay branches b jk -s. In the real calculation ofthe responses the internal conversion process is also takeninto account.Prior to the analysis, the contaminants in the TAGSspectrum ( C i ) have to be isolated and their individualcontributions evaluated. The nucleus to be studied is pro-duced by nuclear reactions together with a number of ad-ditional nuclei. Two alternative separation methods are normally used to isolate the nucleus of interest. On-linemass separators are used with low energy radioactive beamsto reduce the contamination represented by mass isobars.In-flight separation is used at high-energy fragmentationfacilities to reduce the number of nuclear species in the”cocktail beam” to suitable levels. Even if we can isolatethe nucleus of interest, daughter (and other descendants)activity can contaminate the measured spectrum depend-ing on the half-life of the studied decay. This contamina-tion can be determined through dedicated measurementson the decay of the contaminant nuclei under the sameconditions as the one of interest. Another source of con-tamination of the spectrum is the pile-up of signals. Thepile-up can distort the full TAGS spectrum and can gen-erate counts in regions of the spectra where there shouldnot be counts, as for example in the region beyond the Q β value of the decay. Also it can distort the spectrum inregions where we expect reduced statistics as for exampleclose to the Q β value of the decay. This is the reason whyestimating this contribution is of importance. Algorithmshave been developed to evaluate this contribution [21,22].Its determination is based on the random superpositionof true detector pulses, measured during the experiment,within the time interval defined by the acquisition gate ofthe data acquisition system.Another possible contamination appears when the de-cay is accompanied by beta delayed particle emission, sincethis process can lead promptly to the emission of gammarays from the final nucleus populated by the beta delayedparticle emission. The case of the emission of beta de-layed neutrons is even more complex. Neutrons interacteasily with the detector material and release their energythrough inelastic and capture processes. The proper eval-uation of this contamination is of great relevance in thestudy of beta decays far from stability on the neutron-richside of the Segre chart and requires careful Monte Carlosimulations of the neutron-detector interactions [22,23].The reproduction of this contamination is complicated be-cause it has two components: one, which is prompt withthe beta decay, is composed of gamma rays emitted in thefinal nucleus after the beta-delayed neutron emission whenan excited state is populated, the other component due toneutron interactions in the detector is delayed, since thespeed of neutrons is much lower than that of gamma-rays.To simulate these effects properly an event generator [24],that takes into account relative contribution of the twocomponents is required. It is also necessary to know theenergy spectrum of the emitted beta-delayed neutrons. Inaddition, the Monte Carlo simulation code should includean adequate physics model of the neutron interactions. Asan example, in Figure 4 [25] the contribution of the cal-culated beta delayed neutron contamination to the TAGSdecay spectrum of Rb is presented. Two available neu-tron energy spectra were used in the simulations [26,27],and clearly only one reproduces the experimental TAGSdata at high excitation energies. This figure shows the rel-evance of the neutron spectrum used in the simulations(for more details see [25]). Due to these complications wehave built
Rocinante [24,28] a spectrometer made of BaF . Algora et al.: Beta-decay studies for applied and basic nuclear physics 5 Energy [keV] 0 2000 4000 6000 8000 10000 C oun t s TAGS spectrum:Experiment from Kratz n MC with I from ENSDF n MC with I Sr → Rb
837 keV captureNeutron
Fig. 4.
Impact of the neutron energy spectrum ( I n ) in thesimulations of the contamination associated with the beta de-layed neutrons in the TAGS spectrum (for more details see[25]). Only the spectrum measured by Kratz et al. [26] re-produces the TAGS spectrum at high excitation energies. TheMonte Carlo (MC) spectra are normalized to the experimentalspectrum around the neutron capture peak indicated with anarrow. The prompt 836.9 keV γ -ray peak from the first excitedstate in the final nucleus after the beta-delayed neutron emis-sion Sr is highlighted. Reprinted figure with permission from[25], Copyright (2019) by the American Physical Society. material, aimed at the measurement of beta-delayed neu-tron emitters. BaF has a neutron capture cross-sectionone order-of-magnitude smaller than the NaI(Tl), that isconventionally used. This spectrometer was also the firstof a new generation of segmented devices designed to ex-ploit the cascade multiplicity information to improve theTAGS analysis, as will be mentioned later.It is important to first identify the different distor-tions or contaminations, but it is also important to deter-mine properly their corresponding weight in the measuredspectrum. Depending on the distortion, different strategieshave been followed. For example, the contribution fromcontaminant decays can be evaluated if there is a clearpeak identified in the spectrum that comes from this con-tamination that can be used for normalization. Anotheroption is the assessment of this contribution from the so-lution of the Bateman equations, using the informationon half-lives and measurement conditions (collection andmeasuring cycle times). In the case of high-energy frag-mentation experiments where the contamination is due tobeta-gamma events uncorrelated with the implanted ion itcan be evaluated from correlations backward in time. Thepileup distortion can be evaluated based on the number ofcounts in the TAGS spectra which lie beyond the highest Q β value in the decay chain and which are clearly abovethe contribution of the background, since we can assumethat those counts can only come from this contribution.When this option is not possible because of inadequatestatistics, a procedure is given in [21] for the normalisa-tion of this contribution based on the counting rate andthe length of the analogue to digital converter (ADC) gate.And finally if there is a contamination arising from beta- delayed neutrons, this contribution can be normalized tothe broad high-energy structure generated by neutron cap-tures in the detector material when possible, otherwise itshould be normalized to the Pn value of the decay.In Figure 5, we present as an example a total absorp-tion spectrum measured during our first experiment inJyv¨askyl¨a of the decay of Tc [7,8] which is relevant forthe decay heat application (see Section 3). In the upperpanel of this figure we show the spectrum of this decaycompared with the reproduction of the spectrum after theanalysis and the contribution of the contaminants (back-ground+daughter activity+pileup).In this measurement a TAGS detector that consistedof two NaI(Tl) cylindrical crystals with dimensions: (cid:31) =200 mm × l = 200 mm, and (cid:31) = 200 mm × l = 100 mmwas used (courtesy of Dr. L. Batist). The longer crystalhas a longitudinal hole of (cid:31) = 43 mm for the positioningof the sources in the approximate geometrical centre ofthe spectrometer using a tape system. In the experimentthe crystals were separated by 5 mm. This separation andthe ideal position of the sources inside the spectrometerwas studied previous to our experiment using Monte Carlosimulations in order to maximize the gamma efficiency ofthe setup [29]. This TAGS had a 57% peak and 92% to-tal efficiency for the 662 keV gamma transition emittedin Cs decay and 27% peak and 70% total efficiency fora 5 MeV gamma transition. This last value was obtainedfrom previously validated Monte Carlo simulations. Theefficiency of this setup is modest compared with recentlydeveloped total absorption spectrometers such as DTAS[30], or MTAS [31]. This detector was designed at the Nu-clear Institute of St. Petersburg (Russia) [32].This measurement was analyzed in singles, since theprecision and reproducibility of the tape positioning sys-tem was considered not sufficiently good to allow coinci-dence counting. The positioning of the sources is criticalin the determination of the efficiency of the Si detectorused as an ancilliary detector for coincidences with thebeta particles emitted in the decay. The efficiency of thebeta detector as a function of end-point energy has a di-rect impact on the normalization of the combined beta-gamma cascade response of the spectrometer ( R ij ). Usingsingles has the advantage of providing much higher statis-tics in the analysis compared with gated spectra. However,the use of gated spectra is preferred, eventually unavoid-able, in order to reduce contamination from ambient back-ground and the selection of events of particular interest.The lower panel of Figure 5 shows the feeding dis-tribution deduced for the Tc decay obtained from theTAGS measurement compared with the distribution ob-tained from high resolution measurements. From the fig-ure it is clear that the feeding distribution obtained withthe TAGS is shifted to higher energies in the daughternucleus, which is typical of a case suffering from the Pan-demonium effect [7,8,33]. Similar measurements will bediscussed in more detail in Section 3.As mentioned earlier, in this measurement a detectorwas used that was composed of two crystals. The new gen-eration of available detectors such as
Rocinante [24], SUN
A. Algora et al.: Beta-decay studies for applied and basic nuclear physics [34], MTAS [31] and DTAS [30] exploit segmentation to agreater degree to extract additional information from thedecay under study. Using the segmentation it is possibleto measure the detector fold (number of detectors fired inan event) which is related to gamma-cascade multiplicityas a function of excitation energy and ultimately to thede-excitation branching ratio matrix B . The lack of knowl-edge of the matrix B is the largest source of uncertainty inTAGS analysis and this can be greatly improved with seg-mented detectors. Our current approach to the iterativeprocedure for updating B described earlier in this Sec-tion, is to include in step d) the comparison to fold-gatedTAGS spectra and single module spectra. Reconstructedfold-gated spectra are obtained by MC simulation usingthe appropriate event generator since it is not possible todefine a fold-gated response in a manner similar to Equa-tion 2. This also prevents us from including them as partof the inverse problem (Equation 1). A different approachhas been taken by the ORNL group to analyze MTAS data[35,36]. They use the coincidence between one module andthe sum of all the modules to define total energy gated sin-gle detector spectra that are fitted by the sum of a numberof de-excitation cascades, usually taken from high resolu-tion spectroscopy and supplemented when necessary with”pseudo” levels with guess branching ratios and modifiediteratively until the best reproduction is achieved. Yet an-other approach is used by the NSCL group to extract B from SUN data [37]. They start from the same total en-ergy gated single detector spectra but apply the so calledOslo-method [38] to obtain the branching ratio matrix fora subset of levels. Because of this, the TAGS analysis isnot performed with this B but uses the ”pseudo” level ap-proach including in the fit the total absorption spectrumand the spectrum of detector multiplicities [39]. It shouldbe noticed that the traditional Oslo method is not strictlyapplicable to TAGS data because the assumed equivalenceof total deposited energy with excitation energy does nothold in general, due to the non-ideal detector response.Currently we are working in a method to solve the fullnon-linear inverse problem represented by Equation 1, toobtain feedings and branching ratios from the completedata set provided by a segmented spectrometer: sum en-ergy spectrum gated by detector fold, sum energy spec-trum versus single crystal spectrum and crystal-crystalcorrelations.In Figure 6 we show the spectrum of the beta decayof Tc measured in a recent campaign of measurementsat the IGISOL IV facility of the Univ. of Jyv¨askyl¨a [40,41] with the segmented DTAS detector. This single de-cay is part of the A=100 system of relevance for doublebeta decay studies (
Ru -
Tc -
Mo). Previous tothis study, only a high resolution measurement existedfor this single decay and there were doubts whether feed-ing at high excitation energy is not detected in the highresolution measurements. Single decays, like this one canbe of relevance for fixing model parameters used in the-oretical calculations for neutrino and neutrinoless doublebeta decay studies. Our TAGS results show only a modestimprovement with relation to the earlier high resolution
E [MeV] 0 1 2 3 4 5 6 C oun t s : analysis+contaminants: experimental data: contaminants (MeV) x E0 1 2 3 4 5 6 F ee d i ng : TAGS measurement: High resolution measurements Fig. 5.
Comparison of the measured TAGS spectrum of thedecay of
Tc with the spectrum generated after the analysis(reconstructed spectrum). This last spectrum is obtained bymultiplying the response function of the decay with the de-termined feeding distribution ( R ( B ) f final ). The lower panelshows the beta-decay feeding distribution obtained comparedwith that previously known from high resolution measurements[7,8,33]. Reprinted figure with permission from [7], Copyright(2010) by the American Physical Society. results, revealing that this decay did not suffer seriouslyfrom the Pandemonium systematic error (see Figure 7).This decay is not only important in the framework of dou-ble beta decay studies, it has also recently attracted atten-tion in another neutrino related topic [42]. The decay is arelevant contributor in a newly identified flux-dependentcorrection to the antineutrino spectrum produced in nu-clear reactors that takes into account the contribution ofthe decay of nuclides that are produced by neutron cap-ture of long lived fission products. In this particular case Tc is produced as a fission product, which after neutroncapture becomes
Tc that beta decays. The effect has anonlinear dependence on the neutron flux, because first afission is required and later a neutron capture. Effects likethis one are considered in order to explain features of thepredicted antineutrino spectrum for reactors not yet fullyunderstood (see Section 4).The study of this decay was the first time that theDTAS detector was used at a radioactive beam facility.Prior to the analysis of this case a full characterizationof the detector was performed [22,40]. This included acheck on the ability to reproduce with MC simulationsthe spectrum of decays obtained with different detectormultiplicity (fold) conditions. As an example we presentin Figure 8 the reproduction of the multiplicities for the Na source used in the characterization of the detector.The DTAS is constructed in a modular way that addsextra versatility to the setup [30]. Depending on the in-stallation, it can be used in an 18 detector configurationfor ISOL type facilities or in an 16 detector configurationfor fragmentation facilities, where the positioning of theimplantation detectors normally requires more space. . Algora et al.: Beta-decay studies for applied and basic nuclear physics 7
Fig. 6.
Comparison of the measured TAGS spectrum of thedecay of
Tc with the spectrum generated after the analy-sis (reconstructed spectrum). Reprinted figure with permissionfrom [41], Copyright (2017) by the American Physical Society.
Energy [keV]0 500 1000 1500 2000 2500 3000 [ % ] β I − − − − DTASENSDF
Fig. 7.
Comparison of the obtained TAGS feeding distributionin the decay of
Tc with the data available from high reso-lution measurement. This is an example of a case that did notsuffer from the Pandemonium effect. Reprinted figure with per-mission from [41], Copyright (2017) by the American PhysicalSociety.
Nuclear reactor applications require beta decay data. Therelevance of beta decay is shown by the fact that eachfission is followed by approximately six beta decays. Theenergy balance released in fission is presented in Table 1for
U and
Pu fissile isotopes [43]. In the case of
U,for example, 7.4 % of the energy released comes from thebeta decay of the fission products (FP) (gamma and betaenergy). Depending on the composition of the fuel in thereactor this percentage can change, but it is of the order of7% of the total released energy for a working reactor. Oncethe reactor is shut-down, the decay energy becomes dom-inant and the related heat has to be removed. If for somereason this is not possible, it can produce accidents likethe one caused originally by the tsunami that followed theGreat East Japan Earthquake (2011) in the FukushimaDaiichi power plant. Clearly one needs to estimate thissource of energy for the safety of any nuclear installation
Fig. 8.
Comparison of the measured spectrum of the decayof Na with different multiplicity conditions on the numberof detectors that fired (fold) with the results of Monte Carlosimulations for the DTAS detector [22,40]. How well the differ-ent multiplicity spectrum is reproduced, is a stringent test ofthe quality of the branching ratio matrix used in the analysis.Modified figure with permission from [22], Copyright (2018) byElsevier. (design of a reactor, storage of the nuclear waste, loss ofcoolant accident (LOCA), etc.).Decay heat is defined as the amount of energy releasedby the decay of fission products not taking into accountthe energy taken by the neutrinos. The first method to es-timate the decay heat was introduced by Way and Wigner[44], which was based on statistical considerations of thefission process. Their results provide a good estimate ofthe heat released, but the precision reached is not sufficientfor present-day safety standards. Nowadays the most ex-tended way to estimate the decay heat is to perform sum-mation calculations, which relies on the increased amountof available nuclear data. In this method, the power func-tion of the decay heat f ( t ) is obtained as the sum of theactivities of the fission products times the energy releasedper decay: f ( t ) = (cid:88) i ( E β,i + E γ,i ) λ i N i ( t ) (3)where E i is the mean decay energy of the ith nuclide( β or charged-particle and γ or electromagnetic compo-nents), λ i is the decay constant of the i th nuclide, and N i ( t ) is the number of nuclides of type i at the coolingtime t (for simplicity the α -decays of minor actinides arenot included here). These calculations require extensivelibraries of cross sections, fission yields and decay data,since the method first requires the solution of a system ofcoupled differential equations to determine the inventoryof nuclei N i ( t ) produced in the working reactor and aftershut-down.Several ingredients of this method depend on decaydata. The determination of the activities of the fissionproducts ( λ i N i ( t )) requires a knowledge of the half-livesof the decaying isotopes. The other important quantitiesare the mean energies released per decay ( E β,i , E γ,i ). Themean energies released per decay i can be obtained bydirect measurements as in the systematic studies by Rud- A. Algora et al.: Beta-decay studies for applied and basic nuclear physics
Table 1.
Division of the energy released by the most importantfissile isotopes
U and
Pu (values given in MeV/fission)[43].Contribution U PuFragments’ kinetic energy 166.2(13) 172.8(19)Prompt neutrons 4.8(1) 5.9(1)Prompt gamma rays 8.0(8) 7.7(14)Beta energy of fission fragments 7.0(4) 6.1(6)Gamma energy of fission fragments 7.2(13) 6.1(13)Subtotal 192.9(5) 198.5(8)Energy taken by the neutrinos 9.6(5) 8.6(7)Total 202.7(1) 207.2(3)
Table 2.
List of parent nuclides identified by the WPEC-25(Nuclear Energy Agency working group) that should be mea-sured using the total absorption technique to improve the pre-dictions of the decay heat in reactors [48,49]. These nuclidesare of relevance for conventional reactors based on
U and
Pu fission. The list contains 37 nuclides. Rel. (relevance)stands for the priority of the measurement. Isotopes markedwith asterisks show the measurements performed by our col-laboration. Nuclides marked with † are also relevant for the U/ Th fuel, see additional cases in Table 3. The isotopesare identified according to the Z-Symbol-A notation; m standsfor metastable or isomeric state.Isotope Rel. Isotope Rel. Isotope Rel.35-Br-86 †∗ † † †∗ †∗ † †∗ †∗ † † †∗ †∗ † †∗ † ∗ † †∗ †∗ † †∗ ∗ †∗ † ∗ † ∗ † ∗ †∗ † stam et al. [45] and Tengblad et al. [46]. These integralmeasurements (energy per decay) require specific setupsthat are only sensitive to the energy of interest and acareful treatment of all possible systematic errors. Alter-natively the mean energies can be deduced from availabledecay data in nuclear databases such as the Evaluated Nu-clear Structure Data File (ENSDF) [47] if the decay prop-erties are properly known. The term ”properly known”beta decay implies a knowledge of the Q β value of the de-cay, the half-life, the beta distribution probability to thelevels in the daughter nucleus and the decay branchingratios of the populated levels. If all this information is Table 3.
List of parent nuclides identified in [50] that should bemeasured using the total absorption technique to improve thepredictions of the decay heat in reactors based on U/ Thfuel. The list does not contain several relevant cases alreadymeasured by [17] and already included in Table 2 (marked with † ), for more details see [50]. Rel. (relevance) stands for thepriority of the measurement. Isotopes marked with asterisksshow the measurements performed by our collaboration. Formore details in the notation see Table 2.Isotope Rel. Isotope Rel. Isotope Rel.34-Se-85 1 38-Sr-92 2 51-Sb-128m 234-Se-86 2 39-Y-96m ∗ ∗ ∗ ∗ available, then it is possible to deduce the mean energiesreleased by the decay using the following relations: E γ = (cid:88) j I j ∗ E j , (4a) E β = (cid:88) j I j ∗ < E β > j , (4b)where E j is the energy of the level j in the daughternucleus, I j is the probability of a beta transition to level j , and < E β > j is the mean energy of the beta continuumpopulating level j . As can be seen from the formula themean gamma energy is approximated by the sum of theenergy levels populated in the decay weighted by the betatransition probability. This approximation assumes thateach populated level decays by gamma deexcitation andignores conversion electrons which are taken into accountin the complete treatment of the mean energy calculations.The mean beta energy, because of the continuum charac-ter of the beta distribution emitted in the population ofeach level, requires the determination of the released meanenergy < E β > j for each end-point energy of the betatransition ( Q β − E j ). Then the mean beta energy ( E β ) isobtained as the weighted sum of the mean beta energiespopulating each level by the beta transition probability.For the determination of < E β > j for each level one needsto make assumptions about the type of the beta transi-tion (allowed, first forbidden, etc.) and the knowledge ofthe Q β value of the decay is needed to determine the betatransition end-points.Pandemonium can have an impact in the determina-tion of the mean energies from data available in databases.If the beta decay data suffers from the Pandemonium ef-fect the beta decay probability distribution is distorted.This distortion, which implies increased beta probabilityto lower lying levels in the daugther nucleus, causes anunderestimation of the mean gamma energy and an over- . Algora et al.: Beta-decay studies for applied and basic nuclear physics 9 estimation of the mean beta energy. This is why TAGSmeasurements are relevant to this application.In fission more than 1000 fission products can be pro-duced. But not all of them are equally important. Whenaddressing a particular problem, like the decay heat, it isof interest to identify which are the most relevant con-tributors among the large number of fission products. Agroup of experts working for the International Atomic En-ergy Agency (IAEA) [48] identified high priority lists ofnuclei that are important contributors to the decay heatin reactors and that should be measured using the TAGStechnique. These lists included nuclides that are producedwith high yields in fission and for which the decay datawas suspected of suffering from the Pandemonium effect.One argument used for this last selection was if the decaydata shows no levels fed in the daughter nucleus in theupper 1/3 excitation energy window of the Q β value. It isworth noting that this can be considered only as an indi-cation of Pandemonium and not a rigorous rule. Anotherway of looking for questionable (or odd) data was to lookfor cases that show different mean energies in the differentinternational databases. The final lists were published intwo separate reports, first for U/Pu fuels [49] and thenlater for the possible future Th/U fuel [50].In 2004 we started a research programme aimed atstudying the beta decay of nuclei making important con-tributions to the decay heat in reactors. For the planningof any nuclear physics experiment the first step is to decidethe best facility to perform it in terms of the availability ofthe beams, their cleanness and their intensity. Since someof the most important contributors to the priority list for U and
Pu fission were refractory elements like Tc,Mo and Nb, the options were very limited. In a classicalISOL facility like ISOLDE, the development of a particu-lar beam can take some time if the beam of a particularelement is not available. It is a lengthy and complex taskto find the optimum chemical and physical conditions inthe ion source for the extraction of a particular element.We decided that the best option concerning the availabil-ity of the beams was to perform the measurements at theIGISOL facility in Jyv¨askyl¨a (Finland) [51]. The reasonfor that was the development of the ion-guide technique.The ion-guide technique, and more specifically the fissionion guide, allows the extraction of fission products inde-pendently of the element. In this technique, fission is pro-duced by bombarding a thin target of natural U with aproton beam. The fission products that fly out of the tar-get are stopped in a gas and transported through a differ-ential pumping system into the first accelerator stage ofthe mass separator. The dimensions of the ion guide andthe pressure conditions are optimized in such a way thatthe process is fast enough for the ions to survive as singlycharged ions. As a result the system is chemically insen-sitive and very fast (sub-ms) [52] allowing the extractionof any element including those that are refractory.Another important advantage of performing experi-ments at IGISOL is the availability of the JYFLTRAPPenning trap [53] developed for high precision mass mea-surements at this facility. JYFLTRAP can also be used as a high resolution mass separator for trap assisted spec-troscopy measurements, providing a mass resolving power(
M∆M ) of the order of 100 000 to be compared with theresolving power of approximately 500 of the IGISOL sep-arator magnet. The purity of the beams is particularlyimportant for calorimetric measurements like those withTAGS since it reduces systematic errors that can be as-sociated with contamination of the primary radioactivebeams. This advantage has also been used in other typesof calorimetric measurements at IGISOL such as the mea-surements of beta delayed-neutrons using He countersembedded in a polyethylene matrix [54].Three experimental campaigns have been performedat the IGISOL facility to study the beta decay of impor-tant contributors to the decay heat and to the antineu-trino spectrum in reactors using the TAGS technique [55,56,57,58]. One of the total absortion setups used in theexperiments is presented in Figure 9 (
Rocinante
TAGS).In a typical experiment, the radioactive beam extractedfrom IGISOL is first mass separated using the separatormagnet and then further separated using the JYFLTRAPPenning trap. Then the beam is transported to the mea-suring position, at the centre of the total absorption spec-trometer where it is implanted in a tape from a tape trans-port system. The tape is moved in cycles, which are opti-mized depending on the half-life of the decay of interest.As mentioned earlier, the reason for using a tape trans-port system is to reduce the effect of undesired daughter,grand-daughter, etc., decay contaminants in the measuredspectrum. If necessary, these contaminants have to be sub-stracted from the measured TAGS spectrum and requirededicated measurements. In this kind of measurement theTAGS detector is usually combined with a beta detectoras shown in the inset to the Figure 9. The beta detector isused to select coincidences of the beta particles with theTAGS spectrum, which essentially eliminates the effect ofthe ambient background.In Figure 10 we show an example of the recently mea-sured Br decay, which was considered priority one forthe decay heat problem. The spectrum shows the TAGSspectrum obtained with the beta-gate condition, and thecontribution of the different contaminants. The analysiswas performed as described earlier. Known levels up tothe excitation value of 3560 keV were taken from the com-piled high resolution data from [59]. From 3560 keV tothe Q β =7633(3) keV value, the statistical model is usedto generate a branching ratio matrix using a level den-sity function resulting from a fit to levels from [60] andcorrected to reproduce the level density at low excita-tion energy, and E1, M1, and E2 gamma strength func-tions taken from [61]. For more details see [62,63]. In Fig-ure 10 we also show the comparison of the beta gatedTAGS spectrum with the results from the analysis. Thereconstructed spectra are obtained by multiplying the re-sponse function of the detector with the final feeding dis-tribution obtained from the analysis. In this particularcase two results are presented. Response A corresponds tothe conventionally calculated branching ratio matrix thatfits better the experimental spectrum. Response B corre- Fig. 9.
Schematic picture of the
Rocinante total absorptionspectrometer used in one of the experiments performed at theIGISOL facility of the University of Jyv¨askyl¨a. The spectrom-eter is composed of 12 BaF crystals. In the lower part theendcap with the Si detector is also presented (not in scale).The thick black lines represent the tape used to move away theremaining activity and the blue line represents the direction ofthe pure radioactive beam that is implanted in the centre ofthe spectrometer. Reprinted figure with permission from [24],Copyright (2017) by the American Physical Society. C oun t s gated β Response AResponse BPile upBackground
Energy [keV] R e l . d e v . − Fig. 10.
Relevant histograms used in the analysis of the betadecay of Br: measured spectrum (squares with errors), recon-structed spectrum response A (red line), reconstructed spec-trum response B (blue line), summing-pileup contribution (or-ange line), background (green line). In the lower panel the rel-ative differences of the experimental spectrum vs the recon-structed spectrum are shown. Response A corresponds to theconventional analysis. Response B corresponds to a modifiedbranching ratio matrix to reproduce the measured gamma-rayintensities. For more details see Rice et al. [62]. Reprinted figurewith permission from [62], Copyright (2017) by the AmericanPhysical Society.
Energy [keV]0 2000 4000 6000 8000 [ % ] β I ∑ β Feeding B β feeding β ENSDF
Fig. 11.
Comparison of the accumulated feeding distributionsobtained in the work of Rice et al. [62] for the decay of Brwith available high resolution measurements. Feeding A and Bstands for the TAGS feedings determined. For more details seethe text. Reprinted figure with permission from [62], Copyright(2017) by the American Physical Society. sponds to a modified branching ratio matrix to reproducethe measured gamma-ray intensities de-exciting each levelas measured in high resolution experiments. In Figure 11the feeding distributions obtained are compared with theavailable high resolution measurements. This comparisonshows that Br decay was suffering from the Pandemo-nium effect.In Table 4 we show a summary of the mean energiesdeduced from TAS analyses obtained in our measurementsperformed at Jyv¨askyl¨a. It shows that most of the casesaddressed from the high priority list were suffering fromthe Pandemonium effect. Two cases, that originally weresuspected to be Pandemonium cases (
Tc,
Nb), werenot. Those cases also show the necessity of the TAGSmeasurements to confirm the suspicion of Pandemonium.Clearly the non existence of feeding in the last Q β / Tc,
Nb cases have strongground state feedings, which reduces the impact of theundetected gamma branches at high excitation. This isclearly reflected in the differences of the deduced mean en-ergies, when they are compared with the mean energies de-duced from high resolution data. The values for one-thirdof the Q β -value ( Q β /
3) are also given for comparison withthe mean energies. The Q β / et al. [17] and Rudstam et al. [45]. Greenwood and co-workers performed a systematicstudy of fission products at the Idaho National Engineer-ing Laboratory (INEL), Idaho Falls, USA, using a Cfsource and the He-jet technique. They employed a totalabsorption spectrometer built of NaI(Tl) with the follow-ing dimensions, 25 . (cid:31) × . . (cid:31) × . Algora et al.: Beta-decay studies for applied and basic nuclear physics 11 Table 4.
Mean gamma and beta energies deduced from ouranalyses of beta decays studied at Jyv¨askyl¨a in comparisonwith the values deduced from high resolution measurements(ENSDF database). The highest level identified in the decaystudies using high resolution and the decay Q β values are alsogiven for completeness (for more details see the text). Isotope High. Lev. Q β Q β / E HRγ E TAGSγ E HRβ E TAGSβ Br 6768 7633(3) 2544 3360(110) 3782(116) 1900(300) 1687(60) Br 5793 6818(3) 2273 3100(40) 3938( +40 − ) 1660(80) 1170( +32 − ) Br 6999 8975(4) 2992 2920(50) 4609( +78 − ) 2240(240) 1706( +32 − ) Rb 4793 5907(9) 1969 2270(40) 2669(95) 1580(190) 1389(44) Rb 7363 8095(6) 2698 170(9) 461(14) 3640(30) 3498(105) Rb 6064 10281(8) 3427 1750(50) 4063( +62 − ) 2020(90) 2450( +32 − ) Rb 4661 9284(21) 3095 2050(40) 3110( +17 − ) 2320(110) 2573( +18 − ) gs Nb 3130 6384(21) 2128 710(40) 959(318) 2540(210) 2414(154) m Nb 3647 6698(31) 2233 2210(60) 2763(27) 2000(200) 1706(13)
Nb 1099 4569(18) 1523 270(22) 445(279) 1800(300) 1797(133) gs Nb 2480 7210(40) 2403 2090(100) 2764(57) 2280(170) 1948(27) m Nb 1245 7304(40) 2435 1023(170) 2829(82)
Mo 2766 4953(35) 1651 551(24) 2407(93) 1900(120) 1049(44)
Tc 2909 4532(9) 1511 81(4) 106(23) 1945(16) 1935(11)
Tc 4268 5600(50) 1867 1890(30) 3229(24) 1590(70) 931(10)
Tc 2403 3644(35) 1215 671(19) 1825(174) 1310(210) 764(81)
Tc 3930 6547(11) 2182 2190(50) 3132(70) 1900(70) 1457(30)
Tc 2680 4820(90) 1607 511(11) 1822(450) 1890(240) 1263(212)
I 5170 5880(30) 1960 1071(2) 1220( +121 − ) 1897(15) 1934( +35 − ) . et al. providedTAGS data for 48 decays including the decay of three iso-meric states. Since a different analysis technique was used,it is interesting to compare the results of Greenwood withthe more recent results and look for possible systematicdeviations for cases where the comparison is possible.As mentioned earlier Rudstam et al. performed sys-tematic measurements of gamma and beta spectra anddeduced mean energies [45,46] of interest for the predic-tion of decay heat. Beta spectra of interest for the predic-tion of the antineutrino spectrum from reactors were alsomeasured [46]. The direct measurements were performedat ISOLDE and at the OSIRIS separator using setups op-timized for the detection of the gamma- and beta-raysemitted by the fission products. In the case of the meangamma energies, the setup required an absolute gammaefficiency calibration with the assumption that the decayused in the calibration did not suffer from the Pandemo-nium effect [45]. In their measurements the beta decayof Rb was used as a calibration. This decay with a Q β of 5907(9) keV shows a complex decay scheme from highresolution measurements that populates levels up to 4700keV in the daughter nucleus. So it was assumed naturallyby the authors of [45] that this decay was not a Pande-monium case (in the publication [45] it is mentioned thatthe gamma spectrum extends up to 4500 keV).In a contribution to the Working Party on Interna-tional Evaluation Co-operation of the NEA Nuclear Sci-ence Committee (WPEC 25) group activities [48], the lateO. Bersillon performed a comparison between the Green-wood and Rudstam mean gamma and beta energies for (MeV) β Q ( M e V ) γ E ∆ − Fig. 12.
Differences between the mean gamma energies ob-tained with TAGS measurements (see Table 5 and the textfor more details) and the direct measurements of Rudstam etal. [45] after renormalization by a factor of 1.14, which wasdeduced from the comparison of our newly determined meanenergy for the decay of Rb [62] with that employed by Rud-stam et al. [45]. Blue points represent Greenwood TAGS dataand red points represent results from our collaboration. A sys-tematic difference with a mean value of -180 keV remains.Reprinted figure with permission from [62], Copyright (2017)by the American Physical Society. those decays that were available in both data sets. Thiscomparison was revisited in [66]. A clear systematic differ-ence was shown, pointing to possible systematic errors inone or in both data sets [24,62,66]. For that reason it wasdecided to measure the Rb decay using the TAGS tech-nique, to see if the decay was suffering from the Pandemo-nium effect or not and accordingly check if this decay wasadequate as an absolute calibration point to obtain meangamma energies in [45]. The 2669(95) keV mean gammavalue obtained from our measurements [62] can be com-pared with the value used by Rudstam et al. (2335(33)keV) showing that this decay suffered from Pandemoniumand also showing the necessity of renormalizing the Rud-stam data by a factor of 1.14. With this renormalization,the mean value of the differences between the two datasets (TAGS vs Rudstam) reduces from -360 keV to -180keV, but still the discrepancy remains [62]. This is shownin Figure 12 and Table 5. It should be noted that our meangamma energy value for this decay agrees nicely with thevalue obtained by Greenwood et al. (2708(76) keV) [17].In Figs. 13(
Pu) and 14 (
U) the total impact of thetotal absorption measurements of the 13 decays ( , , Br, , , Rb,
Nb,
Mo, , , , , Tc) publishedin Refs. [7,8,24,62,67] is presented in comparison withthe decay heat measurements reported by Tobias [68] andDickens [69] for the electromagnetic component ( E γ ) ofthe decay heat. Similarly in Figs. 15-16 the impact of thesame decays is compared for the charged particle compo-nent ( E β ) of the decay heat. To show the impact of thetotal absorption measurements the data base JEFF3.1.1is used, in which no total absorption data is included. Cal-culations are performed using the bare JEFF 3.1.1 and amodified version of the JEFF3.1.1 database with the in-clusion of the total absorption data for the mean energies. Table 5.
Comparison of mean gamma energies obtained withthe TAGS measurements ( E Tγ ) with those obtained in the ded-icated measurements by Rudstam et al. ( E Rγ ) [45] (original val-ues, not renormalized). Marked with asterisks are our TAGSresults for the mean energies. The TAGS results not markedwith asterisks are taken from Greenwood et al. [17]. Isot. E Tγ E Rγ Isot. E Tγ E Rγ Br ∗ Y 1223(50) 1060(120) Br ∗ +40 − ) 3560(130) m Cs 426(27) 500(80) Br ∗ +78 − ) 4290(180) Cs 305(8) 299(21) Rb 2228(145) 1740(40)
Cs 1864(37) 1270(50) Rb 2272(79) 1710(50)
Cs 1708(29) 1140(90) m Rb 3866(115) 3690(110)
Ba 906(27) 620(40) Rb 2708(76) 2335(33)
Ba 1059(64) 760(80) Rb ∗ Ba 1343(49) 870(100) Rb ∗ Ba 785(33) 480(50) Rb 2523(53) 1920(100)
Ba 1831(44) 1460(130) Rb ∗ La 424(9) 130(40) Rb ∗ +62 − ) 4120(250) La 3158(68) 2240(230) Sr 2167(68) 1760(70)
La 2144(52) 1480(80) Sr 1419(135) 1450(10)
Ce 885(59) 770(70) Sr 1790(43) 1180(100)
Ce 1497(35) 620(10) Y 757(34) 900(50)
Pr 929(32) 840(190)
Time (s) −
10 1 10 D e c a t H ea t ( EE M ) i n M e V /f i ss i on Pu Tobias
Pu Dickens et al.
JEFF 3.1.1 + TAGSJEFF 3.1.1
Fig. 13.
Impact of the inclusion of the total absorptionmeasurements performed for 13 decays ( , , Br, , , Rb,
Nb,
Mo, , , , , Tc) published in Refs. [7,8,24,62,67] in the gamma component of the decay heat calculationsfor
Pu.
The results presented were provided by Dr. L. Giot [70]. Inthe figures, it can be noted the large impact of the men-tioned decays and the relevance of the total absorptionmeasurements for a proper assesment of the decay heatbased on summation calculations.From the Figure 14, it is clear that additional mea-surements are needed for improving the description of the
U fuel, and new measurements are certainly requiredfor future fuels like the U/ Th case.
Time (s) −
10 1 10 D e c a y H ea t ( EE M ) i n M e V /f i ss i on U Tobias
U Dickens
JEFF 3.1.1 + TAGSJEFF 3.1.1
Fig. 14.
Impact of the inclusion of the total absorption mea-surements performed for 13 decays in the gamma componentof the decay heat calculations for
U (see Figure 13 for moredetails).
Time (s) −
10 1 10 D e c a t H ea t ( E L P ) i n M e V /f i ss i on Pu Tobias
Pu Dickens et al.
JEFF 3.1.1 + TAGSJEFF 3.1.1
Fig. 15.
Impact of the inclusion of the total absorption mea-surements performed for 13 decays in the beta component ofthe decay heat calculations for
Pu (see Figure 13 for moredetails).
Nuclear reactors constitute an intense source of electronantineutrinos, with typically 10 antineutrinos per sec-ond emitted by a 1GWe reactor. The reactor at SavannahRiver was the site of the discovery of the neutrino in 1956by Reines and Cowan [71], thus confirming Pauli’s pre-dictions of twenty-six years earlier [1]. Just like the decayheat described above, antineutrinos arise from the betadecays of the fission products in-core. Their energy spec-trum and flux depend on the distribution of the fissionproducts which reflects the fuel content of a nuclear reac-tor. This property combined with the fact that neutrinosare sensitive only to the weak interaction could make an- . Algora et al.: Beta-decay studies for applied and basic nuclear physics 13 Time (s) −
10 1 10 D e c a y H ea t ( E L P ) i n M e V /f i ss i on U Tobias
U Dickens
JEFF 3.1.1 + TAGSJEFF 3.1.1
Fig. 16.
Impact of the inclusion of the total absorption mea-surements performed for 13 decays in the beta component ofthe decay heat calculations for
U (see Figure 13 for moredetails). tineutrino detection a new reactor monitoring tool [72].Both particle and applied physics are the motivations oftheir study at power or research reactors nowadays withdetectors of various sizes and designs placed at short orlong distances. In the last decade, three large neutrino ex-periments with near and far detectors, were installed atPressurized Water Reactors [73,74,75], to try to pin downthe value of the θ mixing angle parameter governingneutrino oscillations. These experiments have sought thedisappearance of antineutrinos by comparing the flux andspectra measured at the two sites, both distances beingcarefully chosen to maximise the oscillation probability atthe far site. The three experiments [73,74,75] have nowachieved a precise measurement of the θ mixing angle,paving the way for future experiments at reactors lookingat the neutrino mass hierarchy or for experiments at ac-celerators for the determination of the delta phase, thatgoverns the violation of the CP symmetry in the leptonicsector, thus shedding light on why there is an abundanceof matter rather than antimatter in the Universe.Though they have used one or several near detectorsin order to measure the initial flux and energy spectrumof the emitted antineutrinos, the prediction of the latterquantities still enters in the systematic uncertainties oftheir measurements, because their detectors are usuallynot placed on the isoflux lines of the several reactors ofthe plant at which they are installed [76]. In addition,the Double Chooz experiment started to take data withthe far detector alone, implying the need to compare thefirst data with a prediction of the antineutrino emissionby the two reactors of the Chooz plant. Two methodsemployed to calculate reactor antineutrino energy spectrawere revisited at that time, i.e. the conversion and thesummation methods.The conversion method consists in converting the inte-gral electron spectra measured at the research reactor at the Institute Laue-Langevin (ILL) in Grenoble (France)by Schreckenbach and co-workers [77,78,79,80] with U, Pu and
Pu thin targets under a thermal neutronflux. These spectra exhibit rather small uncertainties andremain a reference as no other comparable measurementhas been performed since. Being integral measures, no in-formation is available on the individual beta decay branchesof the fission products. This prevents the use of the conser-vation of energy to convert the beta into antineutrino spec-tra. Schreckenbach et al. developed a conversion model,in which they used 30 fictitious beta branches spread overthe beta energy spectrum to convert their measurementsinto antineutrinos. In 2011 Mueller et al. [81] revisited theconversion method and improved it through the use ofmore realistic end-points and Z distributions of the fis-sion products, available thanks to the wealth of nucleardata accumulated over 30 years, and through the applica-tion of the corrections to the Fermi theory at branch levelin the calculation of the beta and antineutrino spectra.After these revisions, the prediction of detected antineu-trino flux at reactors compared with the measurementsmade at existing short baseline neutrino experiments re-vealed a deficit of 3%. The result was confirmed immedi-ately by Huber [82] who carried out a similar calculationthough he did not explicitly use beta branches from nu-clear data. This antineutrino deficit was even increasedby the revision of the neutron lifetime and the influenceof the long-lived fission products recalculated at the time,to finally amount to 6% [83]. A new neutrino anomaly wasborn: the reactor anomaly. Several research leads were fol-lowed since to explain this deficit. An exciting possibilityis the oscillation of reactor antineutrinos into sterile neu-trinos [83], which has triggered several new experimentalprojects worldwide [84,85,86]. In 2015, the mystery deep-ened when Daya Bay in China, Double Chooz in Franceand RENO in Korea, reported the detection of a distortion(colloquially called bump) in the measured antineutrinoenergy spectrum with respect to the converted spectrum,which could not be explained by any neutrino oscillation.The three experiments rely on the same detection tech-nique and similar detector designs, which make it possiblethat they would all suffer from the same detection bias assuggested in [87]. But the three collaborations have thor-oughly investigated this hypothesis without success. In theface of the observed discrepancies between the convertedspectra and the measured reactor antineutrino spectra,it is worth considering more closely the existing methodsused to compute them and other possible explanations likethe case of nonlinear corrections discussed in Section 2 inrelation to the
Tc decay [42].Converted spectra rely on the unique measurementsperformed at the high flux ILL research reactor with thehigh resolution magnetic spectrometer BILL [88], usingthin actinide target foils exposed to a thermal neutronflux that was well under control. This device was excep-tional as it allowed the measurement of electron spectraranging from 2 to 8 MeV in 50 keV bins (smoothed over250 keV in the original publications) with an uncertaintydominated by the absolute normalization uncertainty of
3% at 90% C.L. except for the highest energy bins withpoor statistics [77,78,79,80]. The calibration of the spec-trometer was performed with conversion electron sourcesor (n,e − ) reactions on targets of Pb,
Au,
Cd andusing the beta decay of
In providing calibration pointsup to 7.37 MeV. The irradiation duration ranged from12 hours to 2 days. Two measurements of the
U elec-tron spectrum were performed, the first one lasting 1.5days and the second one 12 hours. The normalisation ofthe two spectra disagree because they were normalizedusing two different (n,e − ) reactions on Au and
Pbrespectively in chronological order. The measurement re-tained by the neutrino community is the second one. Theconversion procedure consists in successive fits of the elec-tron total spectrum with beta branches starting with thelargest end-points. The total electron spectrum is fitted it-eratively bin by bin starting with the highest energy bins,and the contributions to the fitted bin are subtracted fromthe total spectrum. The reformulation of the finite sizecorrections, as well as a more realistic charge distribu-tion of the fission products and a much larger set of betabranches have been the key for the newly obtained con-verted antineutrino spectra of [81] and [82]. But the possi-bility remains that the electron and/or converted spectrasuffer from unforeseen additional uncertainties. Indeed thenormalisation of the electron spectra relies on the (n,e − )reactions quoted above and on internal conversion coeffi-cient values that may have both been re-evaluated since[89]. In addition, the exact position of the irradiation ex-periment in the reactor is not well known and may havean impact on the results as well [89]. Another concernis associated with the conversion model itself, where un-certainties may not take into account missing underlyingnuclear physics. In Mueller’s conversion model, forbiddennon-unique transitions are replaced by forbidden uniquetransitions (when the spins and parities are known!). Theshapes of the associated beta and antineutrino spectra arenot well known and the forbidden transitions dominatethe flux and the spectrum above 4 MeV. Several theoret-ical works have attempted to estimate the uncertaintiesintroduced by this lack of knowledge [90,91,92]. The lat-est study [92] reports a potential effect compatible withthe observed shape and flux anomalies. Another sourceof uncertainties comes from the weak magnetism correc-tion entering in the spectral calculation [82,93] that is notwell constrained experimentally in the mass region of thefission products. These two extra uncertainties affect con-verted spectra and are not included in the published un-certainties. Eventually the conversion process itself couldbe discussed, as the iterative fitting procedure is not theonly possible conversion method and it is suspected of in-ducing additional uncertainties [94].In order to identify what could be at the origin of theseanomalies, the understanding of the underlying nuclearphysics ingredients is mandatory. Indeed, only the decom-position of the reactor antineutrino spectra into their in-dividual contributions and the study of the missing un-derlying nuclear physics will allow us to understand fullythe problem and provide reliable predictions. The best tool to address these questions is to use the summationmethod. This method is based on the use of nuclear datacombined in a sum of all the individual contributions ofthe beta branches of the fission products, weighted by theamounts of the fissioning nuclei. Two types of datasetsare thus involved in the calculation: fission product decaydata, and fission yields. This method was originally de-veloped by [95] followed by [96] and then by [46,97]. The β /¯ ν spectrum per fission of a fissile isotope S k ( E ) can bebroken down into the sum of all fission product β /¯ ν spec-tra weighted by their activity λ i N i ( t ) similarly to what isdone for decay heat calculations: S k ( E ) = (cid:88) i λ i N i ( t ) × S i ( E ) (5)Eventually, the β /¯ ν spectrum of one fission product( S i ) is the sum over the β branches (or beta transitionprobabilities) of all β decay spectra (or associated ¯ ν spec-tra), S bi (in equation 6), of the parent nucleus to thedaughter nucleus weighted by their respective beta branch-ing ratios according to: S i ( E ) = N b (cid:88) b =1 f bi × S bi ( Z i , A i , E b i , E ) (6)where f bi represents the beta transition probability of theb branch, Z i and A i the atomic number and the massnumber of the daughter nucleus respectively and E b i isthe endpoint of the beta transition b. In 1989 the mea-surement of 111 beta spectra from fission products byTengblad et al. [46] was used for a new calculation ofthe antineutrino energy spectra through the summationmethod. But the overall agreement with the integral betaspectra measured by Hahn et al. [80] was at the level of15-20% showing that a large amount of data were miss-ing at that time. Lately, the summation calculations werere-investigated using updated nuclear databases. Indeedthe summation method is the only one able to predictantineutrino spectra for which no integral beta measure-ment has been performed. The existing aggregate betaspectra needed to apply the conversion method are rela-tively few and were measured under irradiation conditionsthat are not exactly the same as those existing in powerreactors. Among the discrepancies, the energy distribu-tions of the neutrons generating the fissions in the ILLexperiments are different from those in actual power re-actors, and even more from the ones in innovative reactordesigns such as fast breeder reactors. The aggregate betaspectra were measured for finite irradiation times muchshorter than the typical times encountered in power reac-tors. These few spectra and the specific conditions are notusable for innovative reactor fuels or require correctionsfor longer irradiation times (called off-equilibrium correc-tions) or more complex neutron energy distributions in-core. Until the recent measurement of the U beta spec-trum at Garching by [98], the conversion method could notbe applied to obtain a prediction of the
U fast fissionantineutrino spectrum. This was one of the motivations forthe first re-evaluation of the summation spectra that was . Algora et al.: Beta-decay studies for applied and basic nuclear physics 15 performed in Mueller et al. , the second being to provideoff-equilibrium corrections [81] to the converted spectra.In this work, several important conclusions were alreadylisted regarding summation calculations for antineutrinos.The evaluated nuclear databases do not contain enoughdecay data to supply detailed beta decay properties for allthe fission products stored in the fission yields databases.The evaluated databases have thus to be supplemented byother data or by model calculations for the most exotic nu-clei. The relative ratio of the aggregate beta spectra withthe obtained summation spectra from databases exhibiteda shape typical of the Pandemonium effect, with an overes-timate of the high energy part of the spectra in the nucleardata. The maximum amount of data free of the Pande-monium effect should thus be included in the summationcalculations. The difficulty comes from the fact that thesePandemonium-free data are usually not included in theevaluated databases. One has thus to gather the exist-ing decay data and compute the associated antineutrinospectra. The Pandemonium-free data are mostly existingTAGS measurements [17] and the electron spectra directlymeasured by Tengblad et al. [46]. They were included inan updated summation calculation performed in [99], inwhich the seven isotopes measured with the TAGS tech-nique that had so much impact on the
Pu electromag-netic decay heat, i.e.
Mo, , − Tc, and
Nb [7],were taken into account. The calculation revealed thatthese TAGS results had a very large impact on the cal-culated antineutrino energy spectra, reaching 8% in thePu isotopes at 6 MeV. But it appeared that summationcalculations still overestimate the beta spectra at high en-ergy, indicating that there were large contributions fromnuclei where the data suffer from the Pandemonium ef-fect in the decay databases. The situation is thus similarto that already encountered in the decay heat summationcalculations. These conclusions reinforced the necessity fornew experimental TAGS campaigns and spread the mes-sage worldwide. New summation calculations were devel-oped and other experimental campaigns were launched us-ing the TAGS technique [100,101,102]. In [100] a carefulstudy of the existing evaluated fission yield databases wasperformed. It appeared that the choice of the fission yielddatabase had a large impact on the summation spectraobtained, because of mistakes identified in the ENDF/B-VII.1 fission yields for which corrections were proposed.Once corrected, the ENDF/B-VII.1 fission yields providespectral shapes in close agreement with the JEFF3.1 fis-sion yields. In 2012, the agreement obtained was at thelevel of 10% with respect to the integral beta spectrameasured at ILL and the number of nuclei requiring newTAGS measurements was considered as achievable. Listsof priority for new TAGS measurements were establishedfirst by the Nantes group [67] (which triggered our firstexperimental campaign devoted to reactor antineutrinosin 2009), then by the BNL team [100] and eventually a ta-ble based on the Nantes summation method was publishedin the frame of TAGS consultant meetings organized bythe Nuclear Data Section of the IAEA [103]. A portion ofthe table from [103] is shown in Table 6, with the mea-
Table 6.
List of nuclides identified by the IAEA TAGS Con-sultants that should be measured using the total absorptiontechnique to improve the predictions of the reactor antineu-trino spectra. These nuclides are of relevance for conventionalreactors based on
U and
Pu nuclear fuels. The list con-tains 34 nuclides [103]. Relevance (Rel.) stands for the priorityof the measurement. Isotopes marked with asterisks show themeasurements performed by our collaboration, m stands formetastable or isomeric state.Isotope Rel. Isotope Rel. Isotope Rel.36-Kr-91 2 39-Y-97m 1 53-I-138 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ surements performed by our collaboration marked withasterisks. More than half of the first priority nuclei havebeen measured by our collaboration with the TAGS tech-nique. The Oak Ridge group is involved in similar studies,see for example the results for several isotopes publishedin [101,102].In 2009, − Rb and − Br were measured with the
Rocinante
TAGS (for details see [24,62] and Figure 9)placed after the JYFLTRAP Penning trap of the IGISOLfacility [51]. Only , Rb were in the top ten of the nu-clei contributing significantly to the reactor antineutrinospectrum. Rb itself contributes 16% of the antineutrinospectrum emitted by a pressurized water reactor (PWR)between 5 and 8 MeV. Its contributions to the
U and
Pu antineutrino spectra are 32% and 25.7% in the 6 to7 MeV bin and 34 and 33% in the 7 to 8 MeV bin. In 2009,the ground state (GS) to GS beta intensity of this decaywas set to 56% in ENSDF. This value was revised in 2014to 95.2%. A maximum of 87% ± Rb case is worth noting be-cause it is not a case suffering from Pandemonium, but itsGS to GS beta branch was underestimated in former eval-uations. In the analysis of this nucleus, the sensitivity ofthe reconstructed spectrum (and thus of the χ obtained) to the value of the GS-GS branch was very high, becauseof the large penetration of the electrons in the TAGS. Thequoted uncertainties were obtained by varying the inputparameters entering into the analysis, such as the calibra-tion parameters, the thickness of the beta detector, thelevel density, the normalisation of the backgrounds, etc..The beta decay data for Rb that were used in the pre-vious summation calculations [99] were those from Teng- blad et al.
The impact of replacing these data with thenew TAGS results amounts to 4.5% for
U, 3.5% for
Pu, 2% for
Pu, and 1.5% for
U. A similar impactwas found on the summation model developed by Son-zogni et al. [100] but a much larger impact (more than25% in
U) was found on another model in which noPandemonium-free data were included [104].Though not motivated by neutrino physics, − Brand , Rb were measured in the same experiment. − Brand Rb were not in the priority list of [103]. The mainmotivation for those cases was the study of moderate betadelayed neutron emitters using complementary techniquesand the study of the decay used as normalization in themeasurements by Rudstam et al [45] already mentionedin Section 3. These TAGS measurements confirmed thePandemonium problem in the existing data. , Br and Rb did not show a large impact on the antineutrino spec-tra [12,24,62]. On the other hand, Rb, ranked as priority2 in the table from [103], and Br exhibited a quite largeimpact on the spectra. This was verified with two differentsummation calculations [24]. In one of the models, the newTAGS data replaced high resolution spectroscopy data,and thus the observed impact was typical of a correctionof the Pandemonium effect i.e. a decrease of the high en-ergy part of the aggregate antineutrino energy spectrum.The impact reached 4% in
U and
Pu in the case of Rb and was more modest as regards Br with a 2-3%decrease in the latter actinides between 8 and 9 MeV. Thelatter range explains the reason why Br did not belongto the priority list of [103] that was established for a con-tribution to the PWR antineutrino spectrum larger than1% between 3 and 8 MeV. In the second model the TAGSdata replaced data measured by Tengblad et al. that wereconsidered in the model because they were assumed tobe Pandemonium-free. The replacement of Br had littleimpact, that of Rb led to a 3% decrease at 8 MeV butthat of Br brought a 7% increase between 8 and 9 MeV,with a cancellation of the last two effects below 8 MeV.The cumulative impact of the TAGS beta intensitiesmeasured with the
Rocinante detector at Jyv¨askyl¨a on theantineutrino energy spectra generated after the thermalfissions of U, Pu and
Pu, and fast fission of
Uare presented in Figure 17 with respect to that built withthe most recent evaluation decay databases JEFF3.3 [105]and ENDF/B-VIII.0 [106] for the same nuclei and con-taining only the TAGS data from [7,17]. The decrease ofthe two plutonium spectra above 1.5 MeV is remarkable,reaching 8%. The impact on the two uranium isotopesamounts to about 2% and 3.8% in the 3 to 4 MeV rangein
U and
U respectively. These results were providedby Dr. M. Estienne [107].In our 2014 experimental campaign, we were almostexclusively focussed on nuclei of importance for the pre-diction of the reactor antineutrino spectrum and for decayheat calculations using the DTAS detector [30]. Twenty-three isotopes were measured, among them many isomerswhich require the separation power of the Jyv¨askyl¨a Pen-ning trap. An illustration of the experimental challenge isgiven by the case of the Niobium isomers , m, , m Nb.
Energy (MeV) R a t i o T A G S / G r een w ood U Energy (MeV) U R a t i o ( w / w o ne w da t a ) Pu Pu R a t i o T A G S / T A G S Energy (MeV)
Fig. 17.
Accumulated impact of the beta intensities of the , , Br and , , Rb [24,62,67] decays measured with thetotal absorption spectrometer
Rocinante on the antineutrinospectra with respect to that published in [99] (relative ratios)for the thermal fissions of U, Pu and
Pu, and the fastfission of
U [107].
Nb is a refractory element and the isomers in
Nb and
Nb are separated by only 313 keV and 94 keV respec-tively. The half-lives are very similar 1.5 s and 2.99 s in
Nb and 4.3 s and 1.3 s in
Nb for the ground andisomeric states respectively.
Nb and
Nb have beenassigned a top priority in the list of [103].
Nb is amongthe main contributors to the antineutrino flux in the re-gion of the shape distortion, along with Rb, Y and
Cs. The results showed that the high resolution mea-surements for , m Nb and gs Nb were affected by thePandemonium effect, while the beta-intensity distributionfor m Nb was determined for the first time [13]. Theimpact of these measurements on the summation calcu-lations was evaluated (see Figure 18) and resulted in alarge impact between 3 and 7 MeV, with a strong decreaseof the spectrum peaked at 4.5 MeV and a strong increasepeaked at 6.5 MeV, in the region of the shape distortion.In the calculation, the TAGS data replaced high resolu-tion spectroscopy data extracted from JEFF3.3 [105] andENDF/B-VIII.0 [106]. As a result, the discrepancy be-tween the summation antineutrino spectra including thesedata and the experimental reactor antineutrino spectra isdiminished in the region of the shape distortion, thoughthe distortion has not vanished completely [13]. The re-sults presented in this last figure were also provided byDr. M. Estienne [107].In parallel to the TAGS campaigns, the reactor an-tineutrino experiments have published their near detectormeasurement of the emitted antineutrino flux and spec-trum from PWRs. In 2017, the Daya Bay experiment . Algora et al.: Beta-decay studies for applied and basic nuclear physics 17
Energy (MeV) U Energy (MeV) U Pu Pu R a t i o T A G S / T A G S Energy (MeV)
Fig. 18.
Accumulated impact of the beta intensities measuredwith the DTAS detector on the antineutrino spectra with re-spect to that presented in Figure 17 (relative ratios) for thethermal fissions of U, Pu and
Pu, and the fast fissionof
U [107]. The figure represents the relative impact of the , m, , m Nb decays [13]. could measure the reactor antineutrino flux associatedwith various fuel compositions [108], and found a fluxcoming from
Pu fission in agreement with the predic-tion of the Huber-Mueller model, while the flux associatedwith
U fission exhibited a deficit of 7% thus nearly ex-plaining by itself the reactor anomaly. This new resultdoes not favour the idea of oscillation into sterile neutri-nos, as it would affect equally the antineutrinos arisingfrom both fuels. It would rather confirm the hypothesis ofan additional systematic uncertainty associated with the
U energy spectrum. These recent findings reinforcedthe necessity of an alternative approach to the convertedspectra which could be brought by the use of nucleardata. It was thus timely to perform a comparison of thesummation method spectra with the Daya Bay results.The first comparison was performed in [109] showing adiscrepancy with the measured antineutrino flux of only3.5%, nearly twice as small as that with the Huber-Muellermodel. We have performed an update of our summationmodel in [110] using the above-mentioned Pandemonium-free datasets improved by the TAGS campaigns of the lastdecade, the most recent evaluated databases (JEFF3.3,ENDF/B-VIII.0) and updated gross theory spectra [111]for the unknown beta decay properties.After folding with the Inverse Beta Decay (IBD) crosssection [112] the summation spectrum built with the ac-tinides spectra weighted with the fission fractions pub-lished by Daya Bay, the resulting detected spectrum wascompared with that of Daya Bay [113] and that built us-ing the Huber-Mueller model. In Figure 19, the top panel
Energy (MeV)
SM 2018/H.M.SM 2017/H.M.
DB/SM 2018DB/SM 2017DB/H.M. R a t i o D B / H . M . ( S M ) R a t i o S M / H . M . Energy (MeV)
Fig. 19.
Comparison of the summation antineutrino spec-trum obtained using the fission fractions published in [113]and all the TAGS data quoted in this section, with the exper-imental spectrum from reference [113]. Ratios to the Huber-Mueller (H.M.) model are also provided for comparison. SM-year stands for summation model using the TAGS data an-alyzed until the given year (see also Figure 20 for additionaldetails). Reprinted figure with permission from [110], Copy-right (2019) by the American Physical Society. F /f i ss i on ] [ c m f σ − × GWSM 2012SM 2015SM 2017SM 2018DB G r een w ood S M S M S M S M G r een w ood Fig. 20.
Comparison of the Inverse Beta Decay (IBD) yieldcomputed with the summation antineutrino spectrum obtainedusing the fission fractions published in [108] for
Pu and us-ing all the TAGS data quoted in this section (included succes-sively), with the experimental IBD yield from [108]. Greenwoodrepresents the result of the summation model [110] when onlythe TAGS results of Greenwood et al. [17] are included (formore details of the model see [110]). SM-2012 represents theadditional impact of the TAGS measurements published in [7]( , , , , Tc,
Nb and
Mo). SM-2015 contains inaddition the effect of Rb [67]. SM-2017 represents the impactof , , Br and , Rb decays [24,62], and SM-2018 containsthe impact of , m, , Nb decays [13] (always consideredin addition to the earlier version of the summation model).Reprinted figure with permission from [110], Copyright (2019)by the American Physical Society.8 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics shows the ratio of the Daya Bay antineutrino spectrumover that computed with the Huber-Mueller model (opendiamonds with error bars) superposed with the ratio ofDaya Bay over the summation method spectrum includ-ing the TAGS results from our first campaign (dashed line)and over the summation method spectrum including theTAGS results from both campaigns (plain line). The nor-malisation of the summation method spectrum is clearly inbetter agreement with the experimental data than that ofthe Huber-Mueller spectrum (closser to 1), which is con-sidered nowadays the model reference. The inclusion ofthe TAGS measurements of the Niobium isomers [13] hasfurther improved the shape agreement especially in theenergy region of the shape distortion. The bottom panelof Fig. 19 shows the ratio of the summation method spec-trum with that of Huber-Mueller. Here again the latestTAGS measurements have flattened the ratio which showsa rather good shape agreement, though located below oneat about 95-96%. Still the summation method spectrumdoes not reproduce the shape distortion seen by the reac-tor antineutrino experiments at PWRs. Figure 20 summa-rizes the detected antineutrino flux (called IBD yield) as afunction of the fission fraction of
Pu obtained with thesummation method spectra depending on the TAGS re-sults included in the calculation. The explicit labels of thelines describe the TAGS results introduced one after theother. It is noticable that the inclusion of more TAGS datasystematically decrease the detected antineutrino flux toend with an 1.9% discrepancy with the Daya Bay mea-sured IBD yield. This is a consequence of the correctionof the Pandemonium effect in nuclear databases and em-phasizes the importance of the TAGS method and mea-surements. More details are given in [110] in which theindividual IBD yields associated with U, Pu,
Pu,and
U obtained with the summation model are alsocompared with the Daya Bay results. The agreement isgood in general for all four isotopes. This is at variancewith the Huber-Mueller model for which a large discrep-ancy is observed in the case of
U while the three othercases are in very good agreement with the experiment.In our 2014 TAGS campaign at Jyv¨askyl¨a devoted toreactor antineutrinos and decay heat, , m Y, , Cs, I, I, Rb, Sr,
Mo and
Tc were measured aswell. These future TAGS results may complete the pic-ture that starts to be drawn of the reactor antineutrinoenergy spectra. In parallel to the nuclear physics effort,reactor antineutrino experiments at short baseline fromresearch reactors start to release their first results. Upto now, only the NEOS and Neutrino-4 collaborationshave released a combined result which signals the pres-ence of an oscillation [114]. Neither the STEREO [85]or the PROSPECT [86] experimental results confirm thisoscillation signal. Furthermore, the PROSPECT experi-ment has released their first spectral measurement of theantineutrino energy spectrum from Highly Enriched Fuel(HEU) which is equivalent to a pure spectrum from
U.It is remarkable that their shape-only result does not showsuch a pronounced shape distortion as the large experi-ments at PWRs. It thus excludes the idea that the shape anomaly arises solely from
U. It is worth mentioningalso that PROSPECT is the first detector using Li in-stead of Gd to capture the neutron formed in the IBDprocess since the Bugey experiment [115], which did notsee a shape anomaly either. Lately Double Chooz has alsoreleased their fourth measurement of the θ mixing angleobtained by cumulating neutron captures on Gd and the Hand C contained in the target and gamma catcher volumes[116]. They observe a shape distortion which could be fit-ted either with a single or a double Gaussian with a slope.One of their conclusions is that the one sigma envelopefor today’s prediction appears insufficient to accommo-date the mismatch between data and model for both rateand shape. A better understanding of the origin of modeldeviations remains critical and the role of nuclear data isdefinitely crucial at the time at which experiments are be-ing set up to measure the mass hierarchy of neutrinos. Ina recent publication [117], the global reactor antineutrinodata set was re-analyzed using three reactor antineutrinoflux predictions, the Huber-Mueller model, the summa-tion method of [110] and the model of [92] which includesa theoretical calculation of the form factors for the firstforbidden transitions. Relative to the traditional Huber-Mueller predictions, the two new calculations result in di-verging evidence for a sterile neutrino when total IBD ratemeasurements are considered. The summation calculationof [110] decreases the significance from 2.3 to 0.95 σ , whilethat of [92] increases the significance to 2.8 σ . However,the spectral anomaly is robust with any of the flux models.The accurate determination of the reactor antineutrinospectra is also mandatory to monitor future reactors withantineutrino detection. Predictions for innovative reactordesigns and fuels can only be obtained through the use ofnuclear data and the summation method. The fine struc-tures present in the antineutrino energy spectra inducedby the end-points of the individual beta branches from thefission products [104,118] could provide a benchmark fornuclear data and an insight of what is going on inside areactor. But they also degrade the sensitivity of detectorssuch as JUNO [119] by mimicking a periodic oscillationpattern. These fine structures may be directly observedby the JUNO-TAO one-ton detector that will be locateda few metres away from a PWR core [120]. In parallel,an experimental confirmation of the observed first hintof coherent elastic neutrino-nucleus scattering [121] woulddefinitely open new possibilities for neutrino applications. In an article about the application of TAGS, it would beremiss of us to neglect its application to the study of nu-clear structure. It is not our intention here to tell thereader all about beta decay. That can be found in textbooks (see for example [122,123,124,125]). Instead whatwe want to do is provide a few examples that show howuseful TAGS can be in testing nuclear models that con-tribute to our understanding of the underlying structureof the atomic nucleus, and in particular present some casesrecently studied in the framework of reactor applications. . Algora et al.: Beta-decay studies for applied and basic nuclear physics 19
In Section 2 we already mentioned the
Tc case,of relevance for double beta decay studies. Here we willfocus on two nuclear structure applications of TAGS thatare of significance, namely the study of of the quenching ofGamow-Teller transitions and the study of nuclear shapes.One essential concept in beta decay, important in theexamples that follow, is the beta strength function (see[14]), a quantity that can be deduced from experiment. Itis defined as: S β ( E ) = I β ( E ) f ( Q β − E ) T / (7)where I β ( E ) is the beta intensity to the level at exci-tation E in the daughter nucleus, f is the statistical rateFermi integral which depends on the energy available inthe decay ( Q β − E ) and T / is the half-life of the decay. S β ( E ) is in practical terms the reciprocal of the f t valuesgiven conventionally in the literature. We will concentrateon our contribution to the determination of the strengthby measuring the beta feeding in a reliable way, which isthe main subject of this article. The other two quantities,namely Q β − E or the T / are obtained from measure-ments dedicated to this purpose. In the following we willfocus on allowed Gamow Teller transitions, since allowedFermi transitions are normally concentrated in a singlestate, and not affected by P andemonium very much. Theexperimental beta strength is related to the experimentalB(GT) in the case of Gamow Teller transitions throughthe following equation: S β ( E ) = 16147 ( g A g V ) (cid:88) E B ( GT ) expi → f (8)where g A and g V are the axial-vector and vector cou-pling constants. The B ( GT ) as defined above can be re-lated to the transition probability calculated theoreticallybetween the parent state and the states populated in thedaughter defined as follows: B ( GT ) theoi → f = | (cid:104) Ψ f | (cid:88) µ (cid:88) k σ µk t ± k | Ψ i (cid:105) | (9)where σ and t represent the spin and isospin operatorsacting on the individual nucleons and Ψ i and Ψ f the initialand final nuclear states.In consequence, a comparison of the B ( GT ) theo shouldreproduce the B ( GT ) determined in the experiment. Ac-tually, the quality of the comparison reflects the good-ness of the nuclear model in describing the involved nu-clear states. In addition there is a model independent rule,called the Ikeda sum rule, that tells us how much strengthwe should observe. Curiously enough, the strength ob-tained experimentally seems to be systematically lowerthan theory. This is called the Gamow Teller quenchingproblem and it has been discussed for more than fourdecades and is not yet fully resolved (see for instance [126,127] and more recently [128] and references therein). Thediscussion of this mismatch between theory and exper-iment involves theoretical as well as experimental argu-ments. One main difficulty is that the full strength, in the case of GT transitions, is normally concentrated in aresonance at relatively high excitation energy, for exam-ple in the range of 8-15 MeV for A ∼ He,t) or(t, He), have been used to measure the full strength. Ex-tracting the GT strength from these probes is more com-plicated than extracting it from beta decay. Among otherreasons, this is because it relates to the penetrability ofthe hadronic probe in the nucleus and because of the dif-ficulty of selecting the GT process in a clean way. Betadecay, however, has its own difficulties. The principal one,as mentioned above, is to know how much of the strengthlies within the Q -value window, and the other difficulty isto be sure that we measure all the strength inside the Q β window, because of the Pandemonium effect. It is in over-coming this second difficulty that the TAGS technique hashad an impact in tackling this problem.In order to avoid the first problem, one can choosecases where most of the strength is expected to be locatedat relatively low energy, inside the Q β window, and thishappens, in principle, in the beta decay of nuclei south eastof Sn on the Nuclear Chart and in the rare-earth nucleiabove the spherical nucleus
Gd. These cases, even al-though they do not have a direct relation with the cases ofrelevance for reactor applications presented in this article,can provide information on the necessary corrections thatare required for a proper theoretical description of the betadecay process. The reason, in both the
Sn and above
Gd regions, is that there is only one main component inthe GT strength on the β + side, namely π g / → ν g / inthe Sn region and π h / → ν h / in the rare-earth case.All other proton occupied orbitals have no empty neutronorbital partner. Unfortunately, the expected B(GT) can-not be directly compared with the Ikeda sum rule in thesecases because this rule involves the B(GT) values for boththe β + and the β − decays and here only the former canbe measured. So, it has to be compared with theory. Arelatively simple but realistic calculation of the expectedbeta strength on the β + side was carried out by Towner[129] for decays in both of these regions of the Segre Chart.In this work [129] a hindrance factor h is defined as theratio between the summed GT strength from theory andexperiment. Initially he adopted the extreme single parti-cle approach ( s.p ), namely considering only the two pairsof orbitals, π g / - ν g / and π h / - ν h / . He then madea series of corrections to this approach taking into ac-count pairing, core polarization and higher-order effectsand then looked at how hindered the corrected theoreticalstrength would be in comparison with the extreme s.p pic-ture. This result defines a theoretical hindrance factor thatcan be compared later with the hindrance obtained fromthe ratio of the extreme single particle approximation andexperiment. The theoretical hindrance was calculated forthe range of cases from n=1 to n=10 active protons in theg / orbital in the Sn region and n=1 to n=12 in theh / orbital in the rare earths. A series of experiments were carried out at GSI (Ger-many) with heavy ion beams from the UNILAC at ener-gies slightly above the Coulomb barrier on the appropriatetargets to study relevant beta decays in these regions ofinterest. At these energies, the reaction was dominated bythe fusion evaporation channels which are fewer than inthe fission examples described in previous sections. Con-sequently, the separation achieved with the relatively sim-ple Mass SEParator (MSEP) [130], provides clean enoughsamples to perform the experiments. The GSI TAS [131]was built and briefly used at the Berkeley SuperHILACand after the accelerator was closed, it was installed atthe GSI MSEP. This spectrometer enjoyed two advan-tages over the INEL Idaho TAGS [65]. Firstly, the crys-tal was more than twice the size, secondly it included asmall cooled high purity Ge detector for X-Ray detection.The first improvement was important for a better responseof the spectrometer to the absorption of the gamma cas-cades, and the second to clean the EC (Electron Capture)component of the decays further and hence to obtain avery good Z separation. The results can be seen in refer-ences [132] (
In), [133] ( Ag), [134] (
Dy) [135,136] (
Ho) and [137] (
Tb(2 − and 9 + isomers), and Tm(2 − and 9 + isomers)). For the very special case of Sn, where the expectations are that all the strengthis concentrated in a a single 1 + state in the daughter, wewill consider the results of Hinke et al. [138] and the morerecent work by Lubos et al. [139] measured with Ge de-tectors. To study this case further, a TAGS experimenthas been proposed and partially carried out at RIKEN[140] and is currently under analysis [141]. In general, oneobserves that the calculations [129] reproduce the ob-served hindrance factor fairly well for the Sn region.One should mention here that this case is simple enoughthat it has been calculated from first principles reproduc-ing the experimental value also fairly well [128]. At thetime of this last work [128] only the [138] results wereavailable and included in the comparison, but the morerecent results of [139] show even better agreement withthese calculations, similar in quality to the agreement withthe systematic extrapolation of the strength from [142]. Incontrast, in the rare-earth region higher hindrance factorshave been observed experimentally compared to Towner’scalculations. One should note that, somewhat surprisingly,the GT resonance is clearly observed in this case. More-over, the tail below the resonance that has been observedexperimentally and discussed at length in the Charge Ex-change reaction experiments, is clearly seen in these betadecay experiments for the first time. As an example, weshow in Figure 21 the case of the decay of the
Ho 2 − isomer to Dy [135], with the TAGS measurement rep-resented by the spectrum under the black line. A similarresult was obtained in the
Tm case reported in [137].In this article, it was suggested that the missing strength,or in other words the explanation of the disagreement withTowner, is probably located in that part of the tail of theresonance which is cut off by the Q β window.The same Figure 21 can also be used to illustrate the importance of the TAGS experiments and the limitationsof the Ge detectors in terms of observing beta feeding athigh excitation energy that was discussed in the intro-duction. We see the B(GT) distribution measured withthe Cluster cube [135] and with the GSI TAS [136]. TheCluster cube was an array of six Euroball Ge cluster detec-tors in compact geometry. It was equivalent to forty twoindividual Ge detectors and had an efficiency of 10.2(5)% at a gamma-ray energy of 1332 keV. The figure showsclearly the importance of both types of measurement. Inthe Ge measurements 1064 gamma rays were identifiedand the coincidences between detectors allowed the con-struction of a decay scheme with 295 levels in Dy [135].Figure 21 shows in blue the B(GT) strength to each ofthese levels as deduced from the beta feedings in the de-cay scheme. Inspection of the total absorption spectrumreveals that the Ge array loses sensitivity as a function ofexcitation energy in the daughter nucleus when comparedwith the TAGS and our ability to determine the feed-ing or beta intensity distribution diminishes. Once con-verted into B(GT) strength we conclude that we lose 50%of the total strength compared with the TAGS measure-ment. Moreover, the tail of the resonance, one of the fociof interest in the experiments discussed above cannot beseen with the Ge detector array.In summary, returning to the discussion of the miss-ing B(GT) strength in beta decay, even though the ex-periments explained above are probably the best cases tostudy the Gamow Teller quenching, they rely very muchon comparison with theoretical calculations which, in gen-eral, cannot locate with sufficient precision whether thecalculated strength is inside the accessible beta windowor not. However, these measurements have demonstratedthat the tail below the Gamow Teller resonance exists, andthis observation is free of background ambiguities. More-over, in the future, when either the calculations are accu-rate enough to tell us how much of the strength shouldbe located within the accessible beta-window, or, alter-natively when we are able to perform charge exchangereactions using radioactive beams, we have here very reli-able measurements of that part of the spectrum that liesbelow the Q β energy. This can be used for normalisationpurposes as well as for control of the reaction mechanism.Another application of TAGS measurements, first pi-oneered at CERN-ISOLDE with the Lucrecia TAGS, re-lates to the shapes of nuclear ground states. The conceptof nuclear shape is deceptively simple. In practice it isdifficult to measure. The measurements with TAGS arebased on a theoretical idea put forward by Hamamoto andZhang [143], that was developed further by Sarriguren etal. [144] and Petrovici et al. [145]. They showed that thebeta strength distribution for transitions to excited statesin the daughter nucleus depends on the shape assumed forthe ground state of the decaying nucleus. Intuitively onecan see why this might be so if we look at the ordering ofdeformed single particle orbits on a Nilsson diagram. Thelevels on the prolate and oblate sides are in different order . Algora et al.: Beta-decay studies for applied and basic nuclear physics 21 channel (bin=20 keV) β - s t r eng t h ( - s - k e V - ) β -strength Ho(2 - ) Dy FWHM=240 keV Q E C Fig. 21.
Comparison of the beta strength deduced from thehigh resolution measurement of the beta decay of the
Ho 2 − isomer using the cluster cube setup [135] (shown in blue) withthe strength obtained from a total absorption measurement[136] (black) . The measurements were performed at the MassSeparator at GSI. Reprinted figure with permission from [135],Copyright (2003) by the American Physical Society. and thus filling them up to the Fermi level to determinethe ground state configuration of a particular nucleus in-volves different single particle contributions. Their betadecay strength distributions will also be different sincethey are dictated by angular momentum and parity selec-tion rules as well as the overlap of the wavefunctions ofthe states involved. The calculations by Hamamoto andZhang, Sarriguren et al. and Petrovici et al. , are of courserather more sophisticated than this simple picture whichis just used for understanding the underlying physics phe-nomena.In particular regions of the nuclide chart, nuclei canhave several minima in the potential energy surface withdifferent shapes for the ground state. The calculated B(GT)distributions for each of these states with a defined defor-mation are quite different in some but not all cases (seefor example [144]). Where they are different, the experi-mental B(GT) distribution measured with TAGS can thenbe compared with the theoretical distributions and theground state shape inferred. A number of studies of thiskind ([5], [6], [9], [10], [11]), have been carried out for nu-clei with A ∼
80 and A ∼ , Zr and
Mo [40,146]. In Figure 22 [40,147] we present a compar-ison of the deduced strength for the decay of
Mo withQuasiparticle Random Phase Approximation (QRPA) cal-culations performed by P. Sarriguren [148]. From this com-parison a preference for an oblate shape in the groundstate of
Mo can be inferred. In the calculations a quench-ing factor of ( g A g V ) eff = 0 . g A g V ) has been applied, whichis equivalent to a hindrance factor of 1.69 with respect tothe QRPA calculations used in the comparison.Another example of the importance of TAGS measure-ments in testing models is provided by Mo. The decayof
Mo was calculated using the FRDM-QRPA model[149,150]. The best theoretical description of this decay
Energy [keV]0 500 1000 1500 2000 2500 3000 ] π / A B ( G T ) [ g Σ Tc → Mo DTASOblateProlate
Fig. 22.
Comparison of the deduced beta strength for thedecay of
Mo [40,147] in comparison with QRPA calculationsassuming prolate or oblate deformations in the ground state of
Mo [148]. In the model a quenching factor of ( g A g V ) eff =0 . g A g V ) is applied. was obtained assuming a ground state deformation of (cid:15) =-0.31 for Mo. The experimental half-life of this decay is35.6 s, and this value can be better reproduced if first for-bidden transitions are included in the model calculation( T theo / =30.3 s), but in that case, the experimental betadistribution is not reproduced so well. This can be seenin Figure 23 where the experimental feeding distributionis compared with the theoretically deduced distributionswith and without first forbidden transitions. A better re-production of the beta distribution by theory is obtainedif no first forbidden component is included in the model.But in that case the experimental half-life is not so nicelyreproduced ( T theo / =150 s). This clearly shows a limitationof the performance of this model in a region which is dom-inated by shape effects and where triaxiality can play arole. QRPA calculations assume that both the parent andthe daughter have the same deformation, which might notalways be applicable in regions where shape transitionsare common. This example shows the relevance of havingin addition to the experimental half-life the possibility ofcomparing the theoretical strength (or the deduced theo-retical feeding) with reliable experimental data, like thatprovided by TAGS measurements. Based on the descrip-tion of the half-life only, we might conclude it is nece-sary to introduce the first forbidden component for thedescription of this decay, which does not reproduce wellthe experimental beta feeding. The relevance of this kindof model validation will be further discussed in the nextSection in relation to astrophysical applications. TAGS measurements are important also in the contextof nuclear astrophysics. We select here some examplesrelated to the astrophysical r process. As mentioned inthe previous Section, some of those examples will show astrong interrelation with nuclear structure studies.The r process is driven by a huge instantaneous fluxof neutrons that creates by successive neutron captures [MeV] x E0 1 2 3 4 5 [ % ] β I : TAGS feeding: theoretical feeding [MeV] x E0 1 2 3 4 5 [ % ] β I : TAGS feeding: theoretical feeding Fig. 23.
Comparison of the experimentally deduced beta feed-ing in the decay of
Mo with the results of theoretical cal-culations using the FRDM-QRPA model [149,150]. The upperpanel is obtained assuming only allowed GT transitions. Thelower panel shows the comparison with calculations that alsoinclude the first forbidden component. See more details in thetext. very neutron-rich nuclei, up to the heaviest ones, that thenbeta decay towards stability. About half of the observedabundance of elements heavier than Fe in the Universeis synthesized in this way. The identification of the astro-physical site where the process occurs is the subject of veryactive investigations. Core Collapse Supernovae were theclassical favoured site in spite of persistent difficulties metwhen trying to reproduce observations with calculations.On the other hand Neutron Star Mergers have recently be-come [151] a confirmed site for heavy element formationafter the first observation of the gravitational waves gen-erated and the analysis of the subsequent electromagneticradiation. Much remains still to be done in order to under-stand the role of both scenarios combining astrophysicalobservations and calculations that require nuclear physicsinput (see [152] for a recent review).Some of the key input parameters in r process cal-culations are the decay properties of neutron-rich nuclei,more specifically half lives ( T / ) and beta-delayed neu-tron emission probabilities ( P n ) that control the nucle-osynthesis flow. For such exotic nuclei the neutron sep- aration energy ( S n ) becomes smaller than the decay Q β value and neutron emission from populated neutron un-bound states occurs. In spite of current efforts at the mostadvanced radioactive beam facilities to determine this in-formation experimentally [153], most of the nuclei involvedcannot be accessed in the laboratory and need theoreti-cal estimates. The key point here is that both quantitiesare derived from the beta strength distribution S β ( E ) (seealso Equation 7)1 T / = (cid:90) Q β S β ( E ) f ( Q β − E ) dE (10) P n = T / (cid:90) Q β S n Γ n Γ n + Γ γ S β ( E ) f ( Q β − E ) dE (11)Equation 11 above includes the competition betweenneutron ( Γ n ) and gamma ( Γ γ ) emission. It should be notedthat models often assume that neutron emission prevailsalways and the competition is ignored.The quality of beta strength calculations is usually as-serted by global comparisons with measured half-lives andto a lesser extent with measured neutron emission proba-bilities. However it is found that different theoretical mod-els with comparable quality predict quite different T / and P n (see for example [154]). This clearly indicates thatthe quality assessment based on these integral quantities(Equations 10 and 11) is not good enough. This comesas no surprise since several (theoretical) strength distri-butions can lead to the same half-life for a particular nu-cleus. But the underlying nuclear structure can then pre-dict very different numbers for neighboring nuclei. Com-paring TAGS measurements of the beta strength with dif-ferent models then becomes the only reliable validationmethod (see the Mo case discussed in the previous Sec-tion). Moreover it can give us hints on how to improve thenuclear structure calculations.Another example is related to the determination ofneutron capture (n , γ ) cross-sections for very exotic neutron-rich nuclei, that also controls the nucleosynthesis flow inthe r process. These are even more difficult to determineexperimentally because of the need to prepare suitabletargets. Direct measurements will require very imagina-tive techniques thus current efforts concentrate on indi-rect methods [155]. Theoretical estimates are based onthe statistical Hauser-Feshbach model [156] that uses av-erage quantities: nuclear level densities, photon strengthfunctions and neutron transmission coefficients. These areparameterized using data measured mostly close to stabil-ity and consequently there is considerable uncertainty onthe values needed in r process calculations.We have proposed a way to obtain experimental con-straints on the quantities that intervene in the Hauser-Feshbach estimate for very exotic neutron rich nuclei [12,24]. It is based on the analogy between radiative neutroncapture reactions and the process of beta-delayed neutronemission. The former depends mostly on Γ γ and weaklyon Γ n and the latter can provide the ratio Γ γ /Γ n providedthat we are able to measure the (expected weak) gamma . Algora et al.: Beta-decay studies for applied and basic nuclear physics 23 emission from neutron unbound states. This is where thesensitivity of the TAGS technique comes into play. Themain advantage of the method is that the measurementscan be extended into regions quite far from stability.In [12,24] the gamma-neutron competition was studiedfor the , Br and Rb decays and more recently in [25]for Rb and
I . The results are summarized in Table7, which shows P γ , the gamma emission probability above S n defined by analogy with P n (also shown). Observationof Table 7 reveals that in most of the cases P γ is large,even larger than P n . The large P γ for I is confirmed bythe TAGS measurement of [35]. The reason for this sur-prising result is to be found in the nuclear structure of thenuclei in the decay chain. A large mismatch between spinand parity of unbound states in the daughter nucleus andthe available states in the final nucleus means that neu-tron emission is hindered by the centrifugal barrier. Othermeasurements have also found large P γ values in the decayof Co [157] and Ga [158] and different nuclear struc-ture effects were invoked to explain it. This notable resultwarns us about the neglect of gamma-neutron competitionin theoretical estimates of P n (see also [159]), but doesnot tell us about the statistical parameters of the Hauser-Feshbach model. The most interesting case from that pointof view is the decay of Rb where level densities in thedaughter nucleus are large and neutron emission is nothindered by angular momentum mismatch, making it agood test case for the statistical model. In this case gammaemission above S n represents only 5% of neutron emissionbut even so it is more than one order-of-magnitude largerthan Hauser-Feshbach calculations using standard statis-tical parameters. This is a challenging outcome. Howeverin order to translate a constraint in Γ γ /Γ n into a con-straint on (n , γ ) cross-section we need additional informa-tion. If we follow the assumption that extrapolating farfrom stability nucleon optical parameters (that determine Γ n ) is more reliable than extrapolating photon strengthfunctions (that determine Γ γ ) then this result would in-dicate one order-of-magnitude increase in the calculatedcapture cross-section. Clearly more investigations are re-quired and new TAGS measurements on suitable isotopesare planned.A different method to obtain constraints on (n , γ ) cross-sections for unstable nuclei using TAGS measurements hasbeen proposed by the NSCL group [37]. It was alreadymentioned in Section 2 in connection with the extractionof the branching ratio matrix, which is the first step of theOslo method [38]. The goal of the Oslo method is to obtainthe shape of the nuclear level density and photon strengthfunction from the branching ratio matrix (in their termi-nology: primary gamma ray intensities) and it was origi-nally applied to nuclear reaction experiments. Going froma relative quantity (branching ratios) to absolute quanti-ties (photon strength functions and nuclear level densities)requires the use of normalization parameters coming fromexternal sources. In the case of beta decay TAGS mea-surements away from the stability these are systematics,extrapolations or theory. Thus the impact of this method is mainly that of the shape of the photon strength func-tion.A closely related topic and also very interconnectedwith nuclear structure is the potential provided by betadecay in relation to the study of collective phenomena.Beta decay could constitute a new means to investigatethe presence and maybe some of the properties of low-lying collective modes, such as pygmy dipole modes pre-dicted to appear at lower energies as nuclei become moreneutron rich. Collective modes are of crucial importance innuclear structure as they reflect the ability of the nucleonsto move coherently and provide insights into the proper-ties of the nuclear force. The study of collective modesputs constraints on theoretical models as well. They arealso the only observables that we can study on earth pro-viding access to the intrinsic properties of nuclear mat-ter, entering into the modelling of astrophysics phenomenalike supernovae or neutron stars. Pygmy dipole resonances(PDR) could be the consequence of the appearance of neu-tron skins in medium to heavy neutron-rich nuclei. ThePDR might deliver information on neutron-star proper-ties [160]. Important information on the equation of state(EOS) of neutron-rich matter via strength-neutron-skinthickness correlation could be obtained [161].The presence of low-lying PDR could influence pro-cesses of nucleosynthesis, especially (n, γ ), ( γ ,n) reactionsplaying an important role in the r-process [162] as men-tioned earlier. Several questions remain unanswered aboutthe collective modes when nuclei become more exotic. Onelimitation up to now has been the low intensity of theaccessible exotic beams which limits the possible stud-ies using standard nuclear or electromagnetic probes. Inthis context beta decay constitutes a new probe for low-lying collective modes. Further away from stability, as theenergy window opened by beta decay increases, the en-ergy of the pygmy modes decreases, allowing their exci-tation through the Gamow-Teller operator when the spinand parity conservation conditions are fulfilled. Beta de-cay then offers new possibilities to study systematicallythe presence of low-lying collective modes with the ex-isting exotic beam intensities. Our collaboration was firstto propose an experiment on this topic [163]. Later on,the theoretical demonstration was provided by two mod-els [158,164]. The quasi-particle model of [164] predictsthat other components of the collective mode are excitedthrough beta decay than those excited by the usual nu-clear and electromagnetic probes. In particular, beta de-cay would feed preferentially two-particle two-hole compo-nents of the collective mode, being thus complementary tonuclear reactions. In the experimental results of [164] and[158], high resolution setups with a relatively small detec-tion efficiency were used and the data may suffer from thePandemonium effect. The TAGS technique, using modernsegmented spectrometers, seems to be very well adaptedto tackle this problem, especially to evidence high energygamma-rays feeding the daughter ground state or the firstexcited state. In parallel, ways to obtain experimental ev-idence of the collectivity of the states fed by beta decay, Table 7. P γ obtained from our measurements [24,25] in com-parison with the Pn values of the decays. P γ is defined as thegamma emission probability above the S n value (in analogy to P n ). The values are given in % (see the text for more details).Isotope P γ ( T AGS ) P n Br 3.50 +0 . − . Br 1.59 +0 . − . Rb 0.53 +0 . − . Rb 2.92 +0 . − . I 9.25 +1 . − . which would not rely on theoretical predictions, shouldalso be investigated. In this article we have presented a review of the impactof our total absorption studies of beta decays that arerelevant for reactor applications. The measurements pre-sented have been performed at the IGISOL facility of theUniversity of Jyv¨askyl¨a employing the high isotopic pu-rity beams provided by the JYFL Penning Trap. Thesemeasurements are not only relevant for the decay heatpredictions and for the predictions of the reactor neutrinofrom reactors, but also provide results of interest for nu-clear structure and astrophysics. In particular they offerthe possibility of testing nuclear models in a more strin-gent way and can provide additional information for theestimation of (n, γ ) cross sections of astrophysical interestfor cases not directly accessible using reactions.Considerable progress has been made, but the ulti-mate goal of the work presented in this article has notyet been reached. From the comparisons of the measureddecay heat with the predictions of summation calcula-tions, it is clear that there is still work to be done, inparticular for the U fuel. The situation is similar in re-lation to the prediction of the antineutrino spectrum inreactors, where the remaining discrepancies still requireto measurements of a number of decays. Our collabora-tion is still working on these subjects and has approvedproposals to continue our studies at the IGISOL IV facil-ity in order to measure new decays that are important inthe next relevant order. In this publication we have con-centrated mainly on the discussion of results obtained byour collaboration, but other groups are also involved insimilar research programmes at other facilities that pro-vide experimental results relevant to the topics discussedhere (see for example [35,101,102,157]). The upgrade andadvent of a new generation of radioactive beam facilitieslike FRIB (Michigan, USA), RIBF (RIKEN, Japan), FAIR(Germany), Spiral2 (France), etc. extends the possibili-ties of TAGS measurements to more exotic domains thanthose offered by the present and future ISOL facilities.These measurements represent new challenges concerningthe purity of the beams and require the development of detectors adapted to the experimental conditions of sucha facilities. From those facilities new and exciting resultswill appear in the near future.This work has been supported by the Spanish Min-isterio de Econom´ıa y Competitividad under Grants No.FPA2011-24553, No. AIC-A-2011-0696, No. FPA2014-52823-C2-1-P, No. FPA2015-65035-P, FPA2017-83946-C2-1-P, No.FPI/BES-2014-068222 and the program Severo Ochoa (SEV-2014-0398), by the Spanish Ministerio de Educaci´on un-der the FPU12/01527 Grant, by the European Commis-sion under the European Return Grant, MERG-CT-2004-506849, the FP7/EURATOM contract 605203 and theFP7/ENSAR contract 262010, and by the
Junta para la Ampliaci ´ on de Estudios Programme (CSIC JAE-Doc contract) co-financed by FSE.We acknowledge the support of STFC(UK) council grantST/P005314/1. This work was supported by the CNRSchallenge NEEDS and the associated NACRE project, aswell as the CHANDA FP7/EURATOM project (ContractNo. 605203), and SANDA project ref. 847552, the CNRS/-in2p3 PICS TAGS between Subatech and IFIC, and theCNRS/in2p3 Master projects Jyv¨askyl¨a and OPALE. Thanksare also due to all collaborators who participated in themeasurements, to the IGISOL and University of Jyv¨askyl¨acolleagues for their continous support and help and in par-ticular to the PhD students and colleagues who worked inthe analysis of the data and made this work possible (D.Jordan, E. Valencia, S. Rice, V. M. Bui, A. A. Zakari-Issoufou, V. Guadilla, L. Le Meur, J. Briz-Monago andA. Porta). We also thank A. L. Nichols and T. Yoshidafor their support in the earlier stages of the work and P.Sarriguren, A. Petrovici, K. L. Kratz, P. M¨oller and col-laborators for providing theoretical calculations for someof the cases studied. Thanks are also due to A. Sonzogniand L. Giot for providing decay heat calculations and toM. Estienne for providing antineutrino summation calcu-lations. The work of J. Agramunt in the development ofour data acquisition system used in all the experimentsis acknowledged. Support from the IAEA Nuclear DataSection is acknowledged.
All the authors were involved in the preparation of themanuscript. All the authors have read and approved thefinal manuscript.
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