BNL-113870-2017-JA

Total absorption gamma-ray spectroscopy of the beta-delayed neutron emitters Br-87, Br-88, and Rb-94

E. Valencia, J. L. Tain, A. Algora, J. Agramunt, E. Estevez, M.D. Jordan, B. Rubio, S. Rice, P. Regan, W. Gelletly, Z. Podolyak, M. Bowry, P. Mason,

G. F. Farrelly, A. Zakari-Issoufou, M. Fallot, A. Porta, V. M. Bui, J. Rissanen, T. Eronen, I. Moore, H. Penttila, J. Aysto, V.-V. Elomaa, J. Hakala, A. Jokinen, V. S. Kolhinen, M. Reponen, V. Sonnenschein,

D. Cano-Ott, A. R. Garcia, T. Mart´ınez, E. Mendoza, R. Caballero-Folch, B. Gomez-Hornillos, V. Gorlichev, F. G. Kondev, A. A. Sonzogni, and L. Batist

Submitted to the Physical Review C

May 10, 2017

National Nuclear Data Center

Brookhaven National Laboratory

U.S. Department of Energy USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

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Total absorption gamma-ray spectroscopy of the beta-delayed neutron emitters Br-87, Br-88, and Rb-94

E. Valencia, J. L. Tain,∗ A. Algora,† J. Agramunt, E. Estevez, M.D. Jordan, and B. RubioInstituto de Fisica Corpuscular (CSIC-Universitat de Valencia), Apdo. Correos 22085, E-46071 Valencia, Spain

S. Rice, P. Regan, W. Gelletly, Z. Podolyak, M. Bowry, P. Mason, and G. F. FarrellyUniversity of Surrey, Department of Physics, Guilford GU2 7XH, United Kingdom

A. Zakari-Issoufou, M. Fallot, A. Porta, and V. M. BuiSUBATECH, CNRS/IN2P3, Universit de Nantes, Ecole des Mines, F-44307 Nantes, France

J. Rissanen, T. Eronen, I. Moore, H. Penttila, J. Aysto, V.-V. Elomaa, J.

Hakala, A. Jokinen, V. S. Kolhinen, M. Reponen, and V. SonnenscheinUniversity of Jyvaskyla, Department of Physics, P.O. Box 35, FI-40014 University of Jyvaskyla, Finland

D. Cano-Ott, A. R. Garcia, T. Martınez, and E. MendozaCentro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

R. Caballero-Folch, B. Gomez-Hornillos, and V. GorlichevUniversitat Politecnica de Catalunya, E-08028 Barcelona, Spain

F. G. KondevNuclear Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

A. A. SonzogniNNDC, Brookhaven National Laboratory, Upton, New York 11973, USA

L. BatistPetersburg Nuclear Physics Institute, Gatchina, Russia

(Dated: September 21, 2016)

We investigate the decay of 87,88Br and 94Rb using total absorption γ-ray spectroscopy. Theseimportant fission products are β-delayed neutron emitters. Our data show considerable βγ-intensity,so far unobserved in high-resolution γ-ray spectroscopy, from states at high excitation energy. Wealso find significant differences with the β intensity that can be deduced from existing measure-ments of the β spectrum. We evaluate the impact of the present data on reactor decay heat usingsummation calculations. Although the effect is relatively small it helps to reduce the discrepancybetween calculations and integral measurements of the photon component for 235U fission at cool-ing times in the range 1 − 100 s. We also use summation calculations to evaluate the impact ofpresent data on reactor antineutrino spectra. We find a significant effect at antineutrino energies inthe range of 5 to 9 MeV. In addition, we observe an unexpected strong probability for γ emissionfrom neutron unbound states populated in the daughter nucleus. The γ branching is compared toHauser-Feshbach calculations which allow one to explain the large value for bromine isotopes as dueto nuclear structure. However the branching for 94Rb, although much smaller, hints of the needto increase the radiative width Γγ by one order-of-magnitude. This leads to a similar increase inthe calculated (n, γ) cross section for this very neutron-rich nucleus with a potential impact on r

process abundance calculations.

I. INTRODUCTION

Neutron-unbound states can be populated in the β-decay of very neutron-rich nuclei, when the neutron sep-aration energy Sn in the daughter nucleus is lower than

∗ Corresponding author:tain@ific.uv.es† Institute of Nuclear Research of the Hungarian Academy of Sci-

ences, H-4026 Debrecen, Hungary

the decay energy window Qβ. The relative strength ofstrong and electromagnetic interactions determines thepreponderance of neutron emission over γ-ray emissionfrom these states. These emission rates are quantifiedby the partial level widths Γn and Γγ respectively. Thefraction of β intensity followed by γ-ray emission is givenby Γγ/Γtot, with Γtot = Γγ +Γn. There is an analogy [1]between this decay process and neutron capture reac-tions populating unbound states. Such resonances in thecompound nucleus re-emit a neutron (elastic channel) or

2

de-excite by γ-rays (radiative capture). Indeed the reac-tion cross section is parametrized in terms of neutron andγ widths. In particular the (n, γ) cross section includesterms proportional to ΓγΓn/Γtot. Notice that the spinsand parities of states populated in β-decay and (n, γ) donot coincide in general because of the different selectionrules.

Neutron capture and transmission reactions have beenextensively used [2] to determine Γγ and Γn of resolvedresonances, or the related strength functions in the unre-solved resonance region. An inspection of Ref. [2] showsthat in general Γn is measured in eV or keV while Γγ ismeasured in meV or eV, in agreement with expectation.Current data is restricted, however, to nuclei close tostability since such experiments require the use of stableor long-lived targets. On the other hand, (n, γ) capturecross sections for very neutron-rich nuclei are a key in-gredient in reaction network calculations describing thesynthesis of elements heavier than iron during the rapid(r) neutron capture process occurring in explosive-likestellar events. In the classical picture of the r process [3]a large burst of neutrons synthesizes the elements along apath determined by the (n, γ)− (γ, n) equilibrium. Afterthe exhaustion of neutrons these isotopes decay back tothe β-stability valley. In this simplified model the cap-ture cross section magnitude plays no role. However itis known [4–6] that for realistic irradiation scenarios thefinal elemental abundance is sensitive to the actual (n, γ)cross-sections. This is the case for the hot (classical) rprocess, due to the role of late captures during the decayback to stability. It is also the case for a cold r-process,where the formation path is determined by competitionbetween neutron capture and beta decay.

Lacking experimental information, the cross sectionfor these exotic nuclei is typically obtained from Hauser-Feshbach statistical model calculations [7]. This model isbased on a few quantities describing average properties ofthe nucleus: the nuclear level density (NLD), the photonstrength function (PSF) and the neutron transmissioncoefficient (NTC). The PSF determines Γγ , NTC deter-mines Γn and NLD affects both (see Appendix). Theparameters describing the dependence of these quantitieson various magnitudes are adjusted to experiment closeto β stability. It is thus crucial to find means to verifythe predictions of the model far from stability. For exam-ple, the use of surrogate reactions with radioactive beamshas been suggested as a tool to provide experimental con-straints on (n, γ) cross sections [8] for unstable nuclei, butits application is very challenging and restricted to nucleiclose to stability. On the other hand the study of γ-rayemission from states above Sn observed in β decay cangive quantitative information on Γγ/Γtot for unstable nu-clei. This information can be used to improve neutroncapture cross-section estimates for nuclei far away fromβ stability.

The emission of γ rays from neutron unbound statespopulated in β decay has been observed in very fewcases studied with high-resolution germanium detectors.

It was first detected in 1972 in the decay of 87Br [9]which remains one of the best studied cases [10–12]. Theother cases are: 137I [13–15], 93Rb [16–18], 85As [14, 19],141Cs [20], 95Rb [21], 94Rb [17], 77Cu [22], and 75Cu [23].In the decay of 87Br up to a dozen states emitting singleγ-rays have been identified within 250 keV above Sn, witha total intensity of about 0.5% compared with a neutronemission intensity of 2.6%. The observation of relativelyintense γ-rays in this measurement was explained as be-ing due to nuclear structure since some of the levels pop-ulated could only decay through the hindered emissionof a high orbital angular momentum neutron. On theother hand, it was pointed out [24] that a sizable γ-rayemission from neutron unbound states could be a mani-festation of Porter-Thomas (PT) statistical fluctuationsin the strength of individual transitions. The extremelyasymmetric shape of the PT distribution can lead to verylarge enhancement of the Γγ/Γtot ratio with respect tothe average. However a general characterization of thephenomenon is still lacking, in particular the relative im-portance of the different mechanisms governing the com-petition.

It is difficult to pursue these studies using high-resolution γ-ray spectroscopy. Since the β intensity isdistributed over many highly excited states, germaniumdetectors are prone to miss the γ-ray de-excitation in-tensity, further fragmented over multiple cascades. Thishas come to be known as the Pandemonium effect [25].Therefore in order to measure the full γ intensity onemust resort to the Total Absorption Gamma-ray Spec-troscopy (TAGS) technique aimed at detecting cascadesrather than individual γ rays. The power of this methodto locate missing β intensity has been demonstrated be-fore [26–28]. However its application in the present caseis very challenging, since the expected γ branching isvery small. As a matter of fact previous attempts at theLeningrad Nuclear Physics Institute (LNPI) [17] did notlead to clear conclusions. In this work we propose anddemonstrate for the first time the use of the TAGS tech-nique to study β-delayed neutron emitters and extractaccurate information that can be used to constrain (n, γ)cross-section estimates for very unstable nuclei.

For this study we selected three known neutron emit-ters: 87Br, 88Br and 94Rb. The relevant decay param-eters are given in Table I. The quoted quantities: T1/2

(half life), Pn (neutron emission probability), Qβ and Sn

are taken from the ENSDF data base [29–31]. The caseof 87Br has been included in the study on purpose sinceit allows a comparison of our results with high resolutiondecay measurements [12] and with neutron capture andtransmission experiments [12, 32]. The case of 93Rb wasalso measured and will be presented separately [33].

The results of our TAGS analysis are also relevant forreactor decay heat and anti-neutrino spectrum calcula-tions.

The knowledge of the heating produced by radioac-tive products in a reactor and the time evolution afterreactor shutdown is important for reactor safety. In con-

3

TABLE I. Half-life T1/2, neutron emission probability Pn,decay energy window Qβ , and daughter neutron separationenergy Sn for each measured isotope. Values taken fromRef. [29–31].

T1/2 Pn Qβ Sn

Isotope (s) (%) (MeV) (MeV)87Br 55.65(13) 2.60(4) 6.852(18) 5.515(1)88Br 16.34(8) 6.58(18) 8.975(4) 7.054(3)94Rb 2.702(5) 10.18(24) 10.281(8) 6.828(10)

ventional reactors the decay heat (DH) is dominated byfission products (FP) for cooling times up to a few years.An issue in reactor DH studies has been the persistentfailure of summation calculations to reproduce the re-sults of integral experiments for individual fissioning sys-tems. Summation calculations are based on individualFP yields and average γ-ray and β energies retrieved fromevaluated nuclear data bases. In spite of this deficiencysummation calculations remain an important tool in re-actor safety studies. For example, after the FukushimaDai-ichi nuclear plant accident it was pointed out [34]that summation calculations are relevant to understandthe progression of core meltdown in this type of event.The Fukushima accident was the consequence of a fail-ure to dissipate effectively the DH in the reactor coreand in the adjacent spent fuel cooling pool. Summationcalculations are particularly important in design studiesof innovative reactor systems (Gen IV reactors, Accel-erator Driven Systems) with unusual fuel compositions(large fraction of minor actinides), high burn ups and/orharder neutron spectra, since integral data are missing.Yoshida and Nakasima [35] recognized that the

Pandemonium systematic error is responsible for a sub-stantial fraction of the discrepancy between DH integralexperiments and calculations. Pandemomium has the ef-fect of decreasing the average γ-ray energy and increasingthe average β energy when calculated from available levelscheme information obtained in high resolution measure-ments. The average γ and β energy for each isotope, Eγ

and Eβ respectively, can be computed from Iβ(Ex), theβ intensity distribution as a function of excitation energyEx as

Eγ =

∫ Qβ

0

Iβ(Ex)ExdEx (1)

Eβ =

∫ Qβ

0

Iβ(Ex)〈Eβ(Qβ − Ex)〉dEx (2)

Here 〈Eβ(Qβ − Ex)〉 represents the mean value of theβ energy continuum leading to a state at Ex.The TAGS technique, free from Pandemonium, was

applied in the 1990s by Greenwood and collaborators atINEL (Idaho) [18] to obtain accurate average decay en-ergies for up to 48 FP with impact in DH calculations.

Recognizing the importance of this approach to improvesummation calculations, the OECD/NEAWorking Partyon International Evaluation Cooperation (WPEC) estab-lished subgroup SG25 to review the situation [36]. Theymade recommendations, in the form of priority lists, forfuture TAGS measurements on specific isotopes for theU/Pu fuel cycle. The work was later extended to theTh/U fuel cycle by Nichols and collaborators [37]. Sub-sequently, the results of Algora et al. [38] demonstratedthe large impact of new TAGS measurements for a fewisotopes selected from the priority list.From the nuclei included in the present work 87Br was

assigned priority 1 in Ref. [36, 37] for a TAGS mea-surement, although it is an example of a well studiedlevel scheme [29] with up to 374 γ transitions de-exciting181 levels. The justification for the high priority comesfrom: 1) the large uncertainty (25%) on average ener-gies coming from the spread of intensity normalizationvalues between different measurements, 2) a potentialPandemonium error suggested by the number of ob-served levels at high excitation energies (less than halfof the expected number according to level density esti-mates), and 3) the large contribution to DH around 100 scooling time. 88Br also has priority 1 in Ref. [36, 37].It contributes significantly to the DH at cooling timesaround 10 s. The known decay scheme [30] is ratherincomplete above Ex = 3.5 MeV, from level density con-siderations, as shown in the RIPL-3 reference input pa-rameter library web page [39]. We estimate that morethan 300 levels should be populated in the decay aboveEx = 3.5 MeV and below Sn in comparison with the ob-served number of 33. 94Rb is not included in the prioritylist of Ref. [36] but is considered of relative importancein Refs. [37] and [40] for short cooling times. The de-cay scheme is very poorly known [31]. Only 37 levels areidentified above Ex = 3.4 MeV, regarded as the maxi-mum energy with a complete level scheme [39]. We esti-mate that more than 900 levels could be populated belowSn thus pointing to a potentially strong Pandemoniumeffect.Summation calculations are also a valuable tool to

study reactor anti-neutrino νe spectra. Accurate knowl-edge of this spectrum is of relevance for the analysis ofneutrino oscillation experiments [41, 42] and for exploringthe use of compact anti-neutrino detectors in nuclear pro-liferation control [43]. Summation calculations for the νespectrum suffer from the same problem as DH summationcalculations: inaccuracies in fission yields and individualprecursor decay data.For each fission product the electron antineutrino spec-

trum Sν(Eν), and the related β spectrum Sβ(Eβ), can becomputed from the β intensity distribution

Sν(Eν) =

∫ Qβ

0

Iβ(Ex)sν(Qβ − Ex, Eν)dEx (3)

Sβ(Eβ) =

∫ Qβ

0

Iβ(Ex)sβ(Qβ − Ex, Eβ)dEx (4)

4

where sν(Qβ − Ex, Eν) and sβ(Qβ − Ex, Eβ) repre-sent the shape of νe and β energy distributions for thetransition to a state at Ex, which depends on the nu-clear wave functions. For each Ex, sν and sβ are re-lated by energy-conservation Eν = Qβ − Ex − Eβ to agood approximation [44]. Thus distortions of the ob-served Iβ(Ex) distribution in high-resolution γ-ray spec-troscopy due to Pandemonium tend to produce calcu-lated νe spectra shifted to high energies.

Currently the most reliable reactor νe spectra are ob-tained from integral β-spectrum measurements of 235U,239Pu and 241Pu thermal fission performed by Schreck-enbach et al. at ILL-Grenoble [45, 46]. Data on 238Ufast fission also became available recently [47]. The con-version of integral β spectra to νe spectra requires anumber of approximations. These are needed because,as pointed out above, the transformation is isotope andlevel dependent. The global conversion procedure hasbeen revised and improved recently [48, 49]. As a con-sequence of this revision a change of normalization inthe spectrum is found that contributes to a consistentdeficit when comparing νe rates from short base line ex-periments with calculations [50], a surprising effect whichis termed the reactor neutrino anomaly. The effect hasbeen related to an abundance of transitions of the firstforbidden type with a β spectrum departing from the al-lowed shape [51]. The experimental investigation of thisor similar effects requires accurate measurements of in-dividual fission products and the use of the summationmethod as was argued in [52].

The statistics accumulated in the three running reactorνe experiments, Double Chooz [53], RENO [54] and DayaBay [55], has revealed differences between the shape ofthe calculated νe spectra and the measured one. Theobserved excess between 5 and 7 MeV Eνe could be due tothe contribution of a few specific FP [56, 57] which is notreproduced by the global conversion method. Thus thestudy of this new antineutrino shape distortion requiresthe use of the summation method and reinforces the needfor new accurate decay data with the TAGS technique.As a matter of fact one of the key isotopes in this list,92Rb, was part of the same experiment analyzed hereand its impact on the antineutrino spectrum was alreadyevaluated [58].

Another approach to the improvement of decay datafor νe summation calculations was followed in the past byTengblad et al. [59]. They measured the spectrum of elec-trons emitted in the decay of individual FP using chargedparticle telescopes. Measurements were performed for upto 111 fission products at ISOLDE (Geneva) and OSIRIS(Studsvik). The β spectra are converted into νe spec-tra and both are tabulated for 95 isotopes in Ref. [60].This large set of data is free of Pandemonium and can beused both in decay-heat and antineutrino spectrum sum-mation calculations. It was pointed out by O. Bersillonduring the work of WPEC-SG25 [36] that average β en-ergies from Tengblad et al. [59] can be compared withaverage β energies calculated from TAGS data obtained

by Greenwood et al. [18] for up to 18 fission products.The comparison shows that Eβ energies from Tengbladet al. are systematically larger than those from Green-wood et al.. The average difference is +177 keV witha spread of values from −33 keV to +640 keV. In viewof the relevance of both sets of data it is important toconfirm the discrepancy and investigate possible causes.The list of measured isotopes in [59, 60] includes 87,88Brand 94Rb thus they can be compared with our data.Partial results of the work presented here were already

published in Ref. [61]. There we concentrated on the β-intensity distribution above Sn and the possible impacton (n, γ) cross section estimates for unstable neutron-richnuclei. Here we present these results in greater detail andenhance them with the investigation of new sources ofsystematic error. In addition we present the complete βintensity distributions and discuss their relevance in re-lation to reactor decay-heat and anti-neutrino spectrumcalculations.

II. MEASUREMENTS

The measurements were performed at the CyclotronLaboratory of the University of Jyvaskyla. The isotopesof interest are produced by proton-induced fission of Ura-nium in the ion-guide source of the IGISOL Mass Sep-arator [62]. The mass separated beam is guided to theJYFLTRAP Penning Trap [63], for suppression of con-tamination. The JYFLTRAP mass resolving power offew tens of thousands is sufficient to select the isotopeof interest from the rest of isobars. The beam comingout of the trap is implanted at the centre of the spec-trometer onto a movable tape, in between two rollersholding the tape in place. A cross-sectional view of thedetection setup is shown in Fig. 1. During the measure-ments the beam gate is open for a time period equiva-lent to three half-lives. This optimizes the counting ofparent decays over descendant decays. After this periodof time the tape transports the remaining activity awayand a new measuring cycle starts. The tape moves in-side an evacuated aluminium tube of 1 mm thickness and47 mm diameter. Behind the tape implantation point isplaced a 0.5 mm thick Si detector with a diameter of25 mm, mounted on the aluminium end-cap. The β de-tection efficiency of the Si detector is about 30%. TheValencia-Surrey Total Absorption Spectrometer “Roci-nante” is a cylindrical 12-fold segmented BaF2 detectorwith a length and external diameter of 25 cm, and a lon-gitudinal hole of 5 cm diameter. Each BaF2 crystal isoptically isolated by means of a thin reflector wrapping,and viewed by a single 3” photo-multiplier tube (PMT).The crystals are mounted inside the aluminium housingwhich has a 0.8 mm thick wall around the central hole.The total efficiency of “Rocinante” for detecting a sin-gle γ ray with the setup described here is larger than80% in the energy range of interest. The spectrometeris surrounded by 5 cm thick lead shielding to reduce the

5

detection of the ambient background signals.The new spectrometer has a reduced neutron sensitiv-

ity compared to existing instruments based on NaI(Tl)crystals. This is a key feature in the present measure-ments as will be shown later. In addition, the segmen-tation of the detector allows one to obtain informationon γ-ray cascade multiplicities which helps in the dataanalysis. The signal amplitudes from the 12 independentPMTs are digitized in a peak sensing analog-to-digitalconverter (ADC) and stored on disk for each event. Theevent trigger is provided whenever the hardware sum ofthe PMT signals fires a constant fraction discriminator(CFD). The signal from the Si detector is processed in ananalogous manner providing another trigger for read-outand storage of events. In the off-line analysis the PMTsignals are gain matched and those surpassing a commonthreshold of 65 keV are added to obtain the total absorp-tion spectrum. The gain-matching procedure uses as areference the position of the α-peaks visible in the en-ergy spectra coming from the Ra contamination alwayspresent in BaF2 crystals. In order to eliminate this intrin-sic background as well as the ambient background we usein the present analysis β-gated total absorption spectra.The threshold in the Si β detector is set to 100 keV. Nev-ertheless other sources of background need to be takeninto account.

FIG. 1. (Color online) Cross-sectional view of the detectorgeometry. BaF2 crystals in red. Si detector in blue. Thebeam enters from the left and is deposited on the tape (notshown) in front of the Si detector.

Firstly there is the decay descendant contamination,which was computed using Monte Carlo (MC) simula-tions performed with the Geant4 simulation toolkit [64].In the case of daughter decay we use an event generatorbased on β intensity distributions and γ branching ra-tios obtained from the well known [29–31] decay scheme.The normalization of the daughter contamination is es-timated from the known half-lives and the measurementcycle time information and eventually adjusted to providethe best fit to the recorded spectrum. The measurementof 88Br was accidentally contaminated with 94Y, the long-

lived grand-daughter of 94Rb that was measured imme-diately beforehand. It was treated in the same manner.

The contamination due to the β-delayed neutronbranch is more challenging. The decay simulation mustexplicitly include the neutrons emitted. These neu-trons interact with detector materials producing γ-raysthrough inelastic and capture processes, which are readilydetected in the spectrometer. A specific event generatorwas implemented which reproduces the known neutronenergy distribution, taken from [65], and the known γ-ray intensity in the final nucleus, taken from [29–31]. Theevent generator requires the β intensity distribution fol-lowed by neutron emission Iβn(Ex) and the branching toeach level in the final nucleus. We have used the sim-plifying assumption that this branching is independentof the excitation energy in the daughter nucleus to ob-tain Iβn(Ex) from the neutron spectrum. The deconvo-lution of the neutron spectrum using calculated Γγ andΓn within the Hauser-Feshbach model (see below) leadsto similar Iβn(Ex) but does not reproduce the γ inten-sity in the final nucleus. Another issue is whether theinteraction of neutrons with the detector can be simu-lated accurately. We have shown recently [66] this to bethe case for a LaBr3:Ce detector, provided that Geant4 isupdated with the newest neutron data libraries and theoriginal capture cascade generator is substituted by animproved one based on the nuclear statistical model. Wehave followed the same approach for our BaF2 detector.The normalization factor of the β-delayed neutron decaycontamination is fixed by the Pn value.

Another important source of spectrum distortion isthe summing-pileup of events. If more than one eventarrives within the same ADC event gate, a signal withthe wrong energy will be stored in the spectrum. Apartfrom the electronic pulse pile-up effect for a single crys-tal, which can be calculated using the methodology de-scribed in [67], one must consider the summing of signalsfrom different crystals. A new Monte Carlo procedureto calculate their combined contribution has been devel-oped. The procedure is based on the superposition of tworecorded events, selected randomly. The time of arrivalof the second event is sampled randomly within the ADCgate length. The normalization of the resulting summing-pileup spectrum is fixed by the true rate and the ADCgate length [67]. To calculate the rate a dead time cor-rection is necessary and this is obtained by counting thesignals from a fixed frequency pulse generator feeding thepreamplifier. The use of real events to calculate the spec-trum distortion is valid if the actual summing-pileup rateis small enough. For this reason we kept the overall rateduring the measurements below 7 kcps. The method isvalidated with measurements of laboratory sources.

Several sources, 22Na, 24Na, 60Co and 137Cs, wereused to determine both the energy calibration and theresolution versus energy dependency of the spectrome-ter. The latter is needed to widen the MC simulatedresponse and is parametrized in the form of a Gaussianwith σE =

√aE + bE2. The highest calibration point

6

energy (MeV) 0 1 2 3 4 5 6 7

coun

ts

-110

1

10

210

310 Br87↓nS

↓β

Q

energy (MeV) 0 1 2 3 4 5 6 7 8 9

coun

ts

-110

1

10

210

310 Br88↓nS

↓β

Q

energy (MeV) 0 2 4 6 8 10

coun

ts

1

10

210

310Rb94

↓nS

↓β

Q

FIG. 2. (Color online) Relevant histograms for the analysis:parent decay (gray filled), daughter decay (pink), delayed neu-tron decay (dark blue), accidental contamination (light blue),summing-pileup contribution (green), reconstructed spectrum(red). See text for details. The neutron separation energy Sn

and decay energy window Qβ are also indicated.

is at 4.123 MeV. At this energy the energy resolution(FWHM) is 265 keV which becomes 455 keV at 10 MeV.The ungated spectra measured with the sources servealso to verify the accuracy of the Geant4 MC simula-tions of the spectrometer response to the decay. Thisrequires a detailed description in the simulation code ofall materials in the measurement setup (tape transportsystem and detectors) . The use of β-gated spectra inthe analysis requires additional verifications of the sim-ulation. Due to the existence of an electronic thresh-old in the Si detector (100 keV) and the continuum na-ture of the β spectrum the efficiency for β-detection hasa strong dependency with endpoint energy up to about2 MeV. It should be noted that this affects the spectralregion above Sn in which we are particularly interested.To investigate whether the MC simulation can reproducethis energy dependency accurately we used the informa-tion from a separate experiment [68] measuring Pn val-ues with the neutron counter BELEN and the same β

detector and implantation setup. Several β-delayed neu-tron emitters with known neutron energy spectra weremeasured, including 88Br, 94,95Rb and 137I. They havedifferent neutron emission windows Qβ − Sn, thereforethe neutron-gated β efficiency samples different portionsof the low energy part of the efficiency curve. Indeed themeasured average β detection efficiency for each isotopechanges by as much as 25%. Using the above mentionedβ-delayed neutron decay generator in Geant4 we are ableto reproduce the isotope dependent efficiency to withinbetter than 4%, determining the level of accuracy of thesimulation.Figure 2 shows the β-gated TAGS spectrum measured

for all three isotopes. Also shown is the contribution tothe measured spectra of the daughter decay, the neutrondecay branch, and the summing-pileup effect. In the caseof 88Br it also includes the contribution of the accidentalcontamination with 94Y decay. Note that there are netcounts above the background beyond the neutron sep-aration energy. The fraction of counts that are to beattributed to states above Sn populated in the decay de-exciting by γ-ray emission is obtained after deconvolutionwith the spectrometer response. In this region the ma-jor background contribution comes from summing-pileupwhich is well reproduced by the calculation as can be ob-served. The contribution of neutron capture γ-rays inthe detector materials is much smaller, thanks to the lowneutron sensitivity of BaF2, as can be seen. The contri-bution of γ-rays coming from neutron inelastic scatteringis important at energies below 1 MeV.

III. ANALYSIS

The analysis of the β-gated spectra follows the methoddeveloped by the Valencia group [69, 70]. The deconvo-lution of spectra with the spectrometer response to thedecay is performed using the Expectation-Maximization(EM) algorithm described there. The spectrometer re-sponse is constructed in two steps. First the responseto electromagnetic cascades is calculated from a set ofbranching ratios and the MC calculated response to in-dividual γ-rays. In the simulation we use a single crystallow energy threshold of 65 keV from experiment. Whennecessary, the electron conversion process is taken intoaccount while building the response [71]. Branching ra-tios are taken from [29–31] for the low energy part of thelevel scheme. In the present case this involves 4 levels upto 1.6 MeV for 87Kr, 8 levels up to 2.5 MeV for 88Kr and11 levels up to 2.8 MeV for 94Sr. The excitation energyrange above the last discrete level is treated as a contin-uum and is divided into 40 keV bins. Average branch-ing ratios for each bin are calculated from the NLD andPSF as prescribed by the nuclear statistical model. Weuse the NLD calculated using a Hartree-Fock-Bogoliubov(HFB) plus combinatorial approach adjusted to experi-mental information [39, 72], which includes parity depen-dence. The PSF is obtained from Generalized Lorentzian

7

(E1 transitions) or Lorentzian (M1 and E2 transitions)parametrization using the parameters recommended inthe RIPL-3 reference input parameter library [39]. Inthe second step of the response construction, the previ-ously obtained electromagnetic response for each level orenergy bin is convoluted with the simulated response toa β continuum of allowed shape. The β response is ob-tained under the condition that the energy deposited inthe Si detector is above the 100 keV threshold.

The spins and parities of some of the discrete states inthe daughter nucleus are ambiguous but they are neededin order to calculate the branching ratio from states inthe continuum. In the analysis different spin-parity val-ues are tested and those giving the best fit to the spec-trum are taken. The spin and parity of the parent nu-cleus ground state is also uncertain, however it deter-mines the spin and parity of the states populated in thecontinuum needed to construct the branching ratio ma-trix. We assume that the Gamow-Teller selection ruleapplies for decays into the continuum, i.e., the paritydoes not change and the spin change fulfill |∆J | ≤ 1. Inthe calculation of the branching ratios we further assumethat different spins J are populated according to the spinstatistical weight 2J + 1. Our choices of spin and parityfor the ground state are 3/2− for 87Br, 1− for 88Br and3− for 94Rb, based again on the quality of reproductionof the measured spectra. The spin-parity of 87Br is givenas 3/2− in Ref. [29], however Ref. [73] proposes 5/2−.We do not find significant differences in the analysis as-suming these two values and we choose the former. Thespin-parity of 88Br is uncertain and is given as (2−) inRef. [30]. However Ref. [74] suggests 1−. In our analysiswe use the latter value since it clearly provides a muchbetter reproduction of the measured TAGS spectrum. Inthe case of 94Rb 3(−) is proposed [31] and is adopted,since other alternatives did not lead to a better repro-duction of the spectrum.

In the analysis we permit decays to all discrete states,many of which are of the forbidden type. Forbidden tran-sitions to the ground state or low lying excited statesare known to occur in this region of the nuclear chart.Indeed sizable decay intensity for some forbidden tran-sitions is obtained in our analysis. In the case of 87Brwe find a ground state intensity Igsβ = 10.1% quite close

to 12%, the quoted value in Ref. [29]. However in con-trast to [29], the first four excited states included in thediscrete part receive negligible intensity. The summeddecay intensity to the discrete part becomes 51% of thatin Ref. [29]. In Ref. [30] an upper limit of 11% is givenfor the 88Br ground state decay intensity, and a sizableintensity is quoted for some of the eight excited statesincluded in the analysis. We obtain 4.7% and 5.6% forthe β intensity to the ground state and first excited staterespectively, and small or negligible intensity for the re-maining states. Overall the intensity to this part of thelevel scheme is reduced by 64%. No intensity is assignedin [31] to 94Rb decaying to the ground state (third for-bidden) and first excited state (first forbidden). In our

analysis we forbid the decay to those states after veri-fying that the decay intensity obtained when left free isonly 0.5% and 0.02% respectively. A large decay inten-sity of 23.7% is observed for the allowed transition to thestate at Ex = 2414 keV, even larger than the value of21.4% found in [31]. The intensity to the discrete levelscheme included in our analysis (11 states) is 78% of thatin ENSDF.

In the final analysis we applied a correction to branch-ing ratios deduced from the statistical model. The aim isto obtain a spectrometer response that is as realistic aspossible. We scale the calculated branching ratios goingfrom the unknown part of the level scheme to discretelevels in the known part of the level scheme, in order toreproduce the observed γ-ray intensities as tabulated inRef. [29–31]. Here we are making the assumption that theabsolute γ intensity is correctly determined in the highresolution measurements for the lowest excited levels. Wefound that this adjustment did not lead to significantchanges in the quality of reproduction of the measuredTAGS spectra and has a small impact on the results ofthe deconvolution.

Figure 3 shows the final β intensity distributionIβγ(Ex) resulting from the deconvolution of TAGS spec-tra for all three isotopes with the chosen branching ratiomatrices. The intensity is normalized to (100−Pn)%. Ineach case the spectrum reconstructed with this intensitydistribution gives a good reproduction of the measuredspectrum as can be seen in Fig. 2. The full β intensitydistribution including statistical uncertainties is given asSupplemental Material to this article [75]. The uncer-tainty due to the statistics in the data is computed ac-cording the prescription given in Ref. [70] and is verysmall.

We evaluate the impact of several sources of systematicuncertainty on the shape of the β intensity distribution.These include both uncertainties in the calculated decayresponse and uncertainties in the subtraction of back-ground components. To study their effect we follow asimilar procedure in all the cases. The chosen systematicparameter is varied and a new deconvolution is performeduntil we observe an appreciable deterioration in the re-production of the measured spectrum. This is quanti-fied by the increase of chi-square between the measuredand reconstructed spectra. In this way we obtain themaximum acceptable deviation of the Iβγ(Ex) from theadopted solution for each investigated systematic uncer-tainty. As a reference the maximum chi-square increaseis always below 5%.

Uncertainties in the calculated decay response are oftwo types. Uncertainties in the branching ratio matrix,which were discussed above, and uncertainties in the MCsimulation of the response to γ and β radiation. As al-ready explained we take great care to describe accuratelythe geometry used in the Geant4 simulation, which isvalidated from the comparison with measurements withlaboratory sources. However these sources emit β par-ticles with rather small energy and they are not useful

8

(MeV) xE0 1 2 3 4 5 6 7

(%

)

βI

-310

-210

-110

1

10

Br87↓

nS

↓β

Q

(MeV) xE0 1 2 3 4 5 6 7 8 9

(%

)

βI

-210

-110

1

10

Br88↓nS

↓β

Q

(MeV) xE0 2 4 6 8 10

(%

)

βI

-510

-410

-310

-210

-110

1

10Rb94↓

nS

↓β

Q

FIG. 3. (Color online) Beta intensity distributions: TAGSresult (red line), high-resolution measurements (blue filled),from delayed neutron spectrum (gray filled). See text fordetails.

to verify the β response. The simulated β efficiency ofthe Si detector and in particular its variation with end-point energy was studied in a separate measurement [68]as already discussed. The response of the spectrometerto β particles depositing energy in the Si is not easy toverify. The response is a mixture of β penetration andsecondary radiation produced in dead materials. Theaccurate simulation of the interaction of low energy elec-trons is a challenging task for any MC code. They relyon models to describe the slowing down of electrons andchanges in their trajectory. Typically a number of track-ing parameters are tuned to obtain reliable results. Weuse in the present simulations the Livermore Electromag-

netic Physics List of Geant4 (version 9.2.p2) with originaltracking parameters. This physics list has been devel-oped for high accuracy tracking of low energy particles.We verified that limiting the tracking step length (pa-rameter StepMax) to values much smaller than defaultvalues, increased computing time considerably but didnot significantly affect the simulated response. To studythe effect of a possible systematic error on the β response

we take a pragmatic approach. We scale arbitrarily thesimulated spectrometer response while keeping the sameβ efficiency. In this way we find that solutions corre-sponding to changes of ±10% in the β response normal-ization represent the maximum deviation with respect tothe adopted solution that can be accepted.

(MeV) xE0 1 2 3 4 5 6 7

(%

)

γβI

-410

-310

-210

-110

1

10

Br87

↓nS

↓β

Q

(MeV) xE0 1 2 3 4 5 6 7 8 9

(%

)

γβI-310

-210

-110

1

10

Br88

↓nS

↓β

Q

(MeV) xE0 2 4 6 8 10

(%

)

γβI

-510

-410

-310

-210

-110

1

10Rb94

↓nS

↓β

Q

FIG. 4. (Color online) Beta intensity distributions fromTAGS. The thin black line is the adopted solution, the lightblue filled region indicates the spread of solutions due to thesystematic effects investigated. See text for details.

The individual γ response is well tested up to Eγ =2.754 MeV, the maximum energy for the 24Na source.To investigate the effect of a possible systematic errorin the total γ efficiency εγ or in the peak-to-total ratio(P/T) we introduce a model that varies linearly one ofthe two parameters, εγ or P/T, above Eγ = 3 MeV.We found that variations of εγ amounting to ±15% atEγ = 10 MeV or variations of P/T amounting to ±30%at the same energy are the maximum allowed by goodreproduction of the spectrum. When considering thesenumbers one should bear in mind that the de-excitationof highly excited states populated in the decay of thethree isotopes proceeds with an average γ multiplicity of2 to 4 in such a way that the energy of most γ rays inthe decay does not exceed 3 MeV.

9

Uncertainties in the normalization of background com-ponents also have an impact on the β intensity distribu-tion. We consider the two main components, summing-pileup which affects the high energy part of the spectrum,and the β-delayed neutron decay branch, which affectsthe low energy part of the spectrum (see Fig. 2). Thecomponent due to summing-pileup is normalized usingthe same ADC gate length (5 µs) for all three isotopes.We estimate however that the reproduction of the end-part of the spectra allows for a variation of up to ±15%in the normalization factor. The normalization of theβ-delayed neutron decay component is fixed by the Pn

value. Likewise we find that the reproduction of the lowenergy part of the spectrum allows for a variation of upto ±15% in the normalization factor.Finally we also check the impact on the result associ-

ated with the use of a different deconvolution algorithm,by using the Maximum Entropy Method as described inRef. [70]. This leads to changes in the Iβ(Ex) noticeableboth at the high-energy end and at low Ex.There is no straightforward way to quantify and com-

bine the systematic uncertainties associated with the ef-fects investigated. One of the reasons is that they arenot independent since we are requiring reproduction ofthe data. It would have been a formidable task to ex-plore in a correlated way the full parameter space. Weuse a different point of view here. The solutions we ob-tain through the systematic variation of each parameterrepresent maximum deviations from the adopted solu-tion, thus altogether define an estimate of the space ofsolutions compatible with the data. This is representedin a graphical way in Fig. 4 showing the envelope of thedifferent solutions described above corresponding to themaximum accepted deviation from the adopted solution.In total there are 14 solutions for 87Br, 13 for 88Br, and15 for 94Rb. As can be seen the different solutions differlittle except for specific Ex regions, where the β inten-sity is low, in particular at the high energy end of thedistribution or at low excitation energy.

IV. AVERAGE BETA AND GAMMA DECAY

ENERGIES AND DECAY HEAT

Figure 3 shows in addition to Iβγ(Ex) obtainedfrom our TAGS data the intensity obtained from high-resolution measurements retrieved from the ENSDF database [29–31]. The effect of Pandemonium is visible here.Our results show a redistribution of Iβγ(Ex) towards highEx, which is significant for 87Br, and very large for 88Brand 94Rb. This is even clearer in the accumulated βintensity distribution as a function of excitation energy

IΣβγ(Ex) =∫ Ex

0Iβγ(E)dE, depicted in Fig. 5. The in-

tensity is normalized to 100%−Pn except in the case ofthe 94Rb ENSDF intensity that only reaches 59.8% sincethe evaluators of Ref. [31] recognize the incompletenessof the decay scheme.Table II shows Eγ and Eβ obtained from Iβγ(Ex) us-

(MeV) xE0 1 2 3 4 5 6 7

(%

)

γβΣ I

20

40

60

80

100

Br87

↓nS

↓β

Q

(MeV) xE0 1 2 3 4 5 6 7 8 9

(%

)

γβΣ I

20

40

60

80

100

Br88

↓nS

↓β

Q

(MeV) xE0 2 4 6 8 10

(%

)

γβΣ I

20

40

60

80

100

Rb94

↓nS

↓β

Q

FIG. 5. (Color online) Accumulated β intensity distributionIΣβγ : TAGS result (red line), high-resolution measurements(blue line).

ing Eq. 1 and Eq. 2 respectively. The β continuum andits average energy 〈Eβ(Qβ − Ex)〉 for each Ex is calcu-lated using subroutines extracted from the LOGFT pro-gram package maintained by NNDC (Brookhaven) [76].In the calculations we assume an allowed β shape. Ascan be seen in Table II the redistribution of β intensityleads to large differences in the average emission energieswhen comparing high resolution data (ENSDF) and thepresent TAGS data. The difference has opposite direc-tions for γ and β energies, as expected, except in thecase of 94Rb due to the use of a different normalization.For Eγ the difference is 0.9 MeV for 87Br, 1.7 MeV for88Br, and 2.3 MeV for 94Rb. The uncertainty quotedon the TAGS average energies in Table II is systematicsince the contribution of statistical uncertainties in thecase of Iβγ(Ex) is negligible. The values of Eγ and Eβ

were computed for each intensity distribution that wasused to define the space of accepted solutions in Fig. 4,and the maximum positive and negative difference withrespect to the adopted solution is the value quoted in theTable.

10

TABLE II. Average γ and β energies calculated using Iβγ(Ex)intensity distributions from ENSDF [29–31] and presentTAGS data. The contribution of the β-delayed neutronbranch is not included.

Eγ(keV) Eβ(keV)

Isotope ENSDF TAGS ENSDF TAGS87Br 3009 3938+40

−67 1599 1159+32

−19

88Br 2892 4609+78

−67 2491 1665+32

−38

94Rb 1729 4063+62−66 2019 2329+32

−30

Table III shows the Eβ given in Ref. [60] obtained fromthe β spectrum measurements of Tengblad et al. [59].For comparison the average β energy obtained from thepresent TAGS data, given in Table II, is incremented withthe average β energy corresponding to the β delayed neu-tron branch. The contribution of the βn branch is calcu-lated from the Iβn(Ex) distribution obtained as explainedin Section II. We find that the values of [60] agree withour result for 88Br but differ by 240 keV for 87Br and by380 keV for 94Rb. This situation is comparable to thatobserved for Greenwood et al. [18] TAGS data. Figure 6presents in a graphical way the difference of average βenergies ∆Eβ between the results of Tengblad et al. andthe results of both Greenwood et al. and ourselves. Inthe figure the differences are represented as a function ofQβ to illustrate what seems a systematic trend. Althoughthe scattering of values is relatively large, on average thedifferences are smaller below∼ 5 MeV. The isotopes fromRef. [18] shown in Fig. 6 are: 146Ce, 145Ce, 144Ba, 141Ba,143La, 94Sr, 93Sr, 145La, 143Ba, 89Rb, 141Cs, 145Ba, 91Rb,95Sr, 140Cs, 90Rb, 90mRb, and 93Rb, in order of increas-ing Qβ .

TABLE III. Comparison of average β energies obtained fromdirect β spectrum measurement (Tengblad et al. [60]) withthose obtained combining Iβγ(Ex) from present TAGS dataand Iβn(Ex) derived from neutron spectrum data. See textfor details.

Eβ(keV)

Isotope This work Ref. [60]87Br 1170+32

−19 1410 ± 1088Br 1706+32

−38 1680 ± 1094Rb 2450+32

−30 2830 ± 70

More illustrative than the comparison of average val-ues is the comparison of β energy distributions Sβ(Eβ)as is done in Fig. 7. Large differences in shape betweenthe results of Tengblad et al. and the present TAGSresults are clearly seen, even for 88Br where the aver-age values agree. The contribution of the β-delayed neu-tron branch, added to the TAGS result for the compar-ison, is shown. For reference we also include in the fig-

(MeV) βQ0 2 4 6 8 10

(M

eV)

βE ∆

-0.2

0

0.2

0.4

0.6

0.8

FIG. 6. Difference between average β energies obtained bydirect β spectrum measurements (Tengblad et al. [60]) andfrom TAGS β intensity distributions. TAGS results are from[18] (open circles) and from the present work (filled circles).

ure the distribution calculated from the high-resolutionlevel scheme in ENSDF. The Sβ(Eβ) distribution calcu-lated from the TAGS data is shifted to lower energies forthe three isotopes, in comparison to the direct β spec-trum measurement. We should point out that a similartrend is found for the remaining isotopes included in thesame experimental campaign, 86Br and 91Rb [77], and92,93Rb [33, 58], where we find deviations in ∆Eβ in therange 200 to 400 keV. Moreover, our results for 91Rb and93Rb agree rather well with those obtained by Greenwoodet al. [18].

The assumption of an allowed shape used here to cal-culate Sβ(Eβ) from Iβ(Ex) introduces some uncertaintyin the comparison. However it is likely to be a goodapproximation. Thus to explain the difference betweenTAGS results and the direct β spectrum measurementone is forced to consider systematic errors in the use ofeither one of the two techniques or both. As explainedabove we investigated carefully sources of systematic un-certainty which can lead to distortions of the β energydistribution and found that none of them can explain theobserved differences (see Table III). Moreover as shownin Fig. 4 the measured TAGS spectrum imposes a strongconstraint on the bulk of the β intensity distribution. Itis difficult to imagine additional sources of systematicuncertainty which can have a significant impact on theshape of this distribution. To clarify the discrepancy newmeasurements of the spectrum of β particles emitted inthe decay of a number of selected isotopes would be ofgreat value.

To finalize this part of the discussion we should pointout that Eγ can be obtained from the β spectra mea-sured in [59]. This can be achieved by deconvolution ofthe β spectra with appropriate β shapes sβ(Qβ −Ex, E)to obtain the Iβ(Ex) (see Eq. 4). As a matter of factthis procedure is needed (and applied in [59]) to obtainthe antineutrino spectrum using Eq. 3. The average γenergies obtained in this way would show systematic dif-

11

(MeV) βE0 1 2 3 4 5 6 7

/100

keV

βN

0

0.02

0.04

0.06

Br87

(MeV) βE0 1 2 3 4 5 6 7 8 9

/100

keV

βN

0

0.01

0.02

0.03

0.04Br88

(MeV) βE0 2 4 6 8 10

/100

keV

βN

0

0.01

0.02

0.03

Rb94

FIG. 7. (Color online) Comparison of β spectra Sβ. Tengbladet al. [60]: black circles; present TAGS result: dashed redline; present TAGS plus β delayed neutron contribution: con-tinuous red line; high-resolution measurements [29–31]: blueline.

ferences with respect to TAGS results of opposite signto those found for Eβ . Rather than using this approachthe authors of [60] determine average γ energies Eγ froman independent set of measurements using a NaI(Tl) de-tector to obtain the spectrum of γ-rays for the decay ofeach isotope. There are also large discrepancies betweenthese results and those obtained from TAGS measure-ments. We postpone the discussion of these differencesto a forthcoming publication [77].

The impact of the present TAGS results for Eγ andEβ on decay-heat summation calculations was evaluated.Figure 8 shows the ratio of calculations using TAGS datato calculations using high-resolution data. The figureshows the evolution of the ratio as a function of coolingtime following the prompt thermal fission of 235U and239Pu. Both together account for most of the power re-leased in most reactors. The calculation is similar tothat described in Ref. [57]. It uses fission yields fromJEFF-3.1 [78] and the ENDF/B-VII updated decay datasublibrary. The update introduces β-intensity distribu-

tions from previous TAGS measurements and, for a fewisotopes, from β-spectrum measurements and from theo-retical calculations. As is customary the DH is evaluatedseparately for the electromagnetic energy (EEM), or pho-ton component (γ rays, X rays, . . . ), and for the light par-ticle energy (ELP), or electron component (β particles,conversion electrons, Auger electrons, . . . ). The ratio iscomputed for each individual isotope and for the threeisotopes together. As expected the effect of the inclu-sion of TAGS data is largest for 94Rb and smallest for87Br. The largest variation in the EEM component oc-curs at short cooling times between 1 and 10 s. Due tothe particular normalization of the high-resolution 94Rbβ-intensity distribution mentioned above the effect is notobserved in the ELP component (see also Table II). Theeffect is larger for 235U fission, due to the larger fissionyields for the three isotopes, reaching an increment of3.3% for the combined contribution to the EEM compo-nent at t = 3.5 s. For 239Pu the increment reaches 1.8% .Although the impact is somewhat small the present datacontribute to reduce the discrepancy between DH inte-gral measurements and summation calculations for 235Uin the range of 1 to 100 s (see for example Fig. 12 ofRef. [79]).

t (s) -110 1 10 210 310

DH

rat

io

0.98

1

1.02

1.04

U235

t (s) -110 1 10 210 310

DH

rat

io

0.98

1

1.02

1.04

Pu239

FIG. 8. (Color online) Ratio of decay heat as a function ofcooling time calculated for 235U and 239Pu when our TAGSdata replaces high-resolution data. Continuous line: photoncomponent; dashed line: electron component. Red: 87Br;green: 88Br; blue: 94Rb; black: all three isotopes.

12

V. ANTINEUTRINO SPECTRA

The impact of our data on calculated antineutrinospectrum is shown in Fig. 9 and Fig. 10. The νe sum-mation calculation of Fig. 9 is analogous to the DH cal-culation of Fig. 8. It shows for 235U and 239Pu fissionthe ratio of calculated νe spectrum when our TAGS datareplaces the high resolution data. The effect of each in-dividual isotope and of the three together is shown. Forboth fissioning systems the impact of 87Br is negligible,while the effect of 88Br peaks around 8.5 MeV (3%) andthat of 94Rb peaks around 7 MeV (4%). The combinedeffect is a reduction of the calculated νe spectrum whichreaches a value of 6% around 7.2 MeV. Similar figures areobtained for 238U and 241Pu. It is remarkable that theeffect of our TAGS data for 88Br and 94Rb is of equal im-portance to that of the combined effect of recently mea-sured [80] TAGS data for 92Rb, 96Y and 142Cs. CompareFig. 9 in the present work with Fig. 6 of Ref. [80], whichshows an effect of similar shape and magnitude. Thesethree isotopes contribute most to the νe spectrum around7 MeV, with 92Rb being the largest contributor [58]. Dueto current uncertainties in the summation method it isnot easy to draw conclusions on the impact of both exper-iments on the origin of the antineutrino spectrum shapedistortion. Note that they lead to a reduction of the cal-culated spectrum which is maximum about 1 MeV abovethe center of the observed excess. Better quality datafor a larger set of isotopes, including decay data and fis-sion yields, is required. Our result shows the importanceof performing TAGS measurements for fission productswith very large Qβ-value, which are likely to be affectedby large Pandemonium systematic error, even if theyhave moderate fission yields.

Figure 10 shows a different set of νe summation calcu-lations. The calculation is analogous to that describedin Ref. [52]. It uses a different selection of decay datafrom the calculation shown in Fig. 9. More specificallyit uses antineutrino spectra derived from the β spectraof Tengblad et al. [59] for 87,88Br and 94Rb instead of νespectra derived from high-resolution data. Thus Fig. 10shows the effect of replacing Tengblad et al. data withour TAGS data. As can be seen the replacement of87Br has little impact, while there is a cancellation be-low Eνe = 8 MeV between the 88Br and 94Rb deviations.However the difference between our TAGS data and thedata of Tengblad et al. for 88Br produces an increasein the calculated antineutrino spectra of about 7% be-tween 8 and 9 MeV. Note that although 94Rb has a Qβ

of 10.28 MeV we do not observe appreciable β intensitybelow 2.41 MeV excitation energy, thus the maximumeffective endpoint energy is below 8 MeV. The relativelylarge impact of 88Br is due to the fact that only a few de-cay branches contribute to the spectrum here. Note thatin this energy interval the uncertainty of the integral β-spectrum measurements [45, 46] is relatively large, thussummation calculations are particularly relevant. Thispoints again to the need to perform TAGS measurements

(MeV) eνE

1 2 3 4 5 6 7 8 9 10

spec

trum

rat

io

0.94

0.96

0.98

1

1.02

U235

(MeV) eνE

1 2 3 4 5 6 7 8 9 10sp

ectr

um r

atio

0.94

0.96

0.98

1

1.02

Pu239

FIG. 9. (Color online) Ratio of antineutrino spectra as afunction of energy calculated for 235U and 239Pu when ourTAGS data replaces high-resolution data. Red: 87Br; green:88Br; blue: 94Rb; black: all three isotopes.

for fission products with very large Qβ.

VI. GAMMA INTENSITY FROM NEUTRON

UNBOUND STATES

Figure 3 shows for all three isotopes a sizable TAGSintensity Iβγ(Ex) above Sn. This intensity extends wellbeyond the first few hundred keV where the low neu-tron penetrability makes γ-ray emission competitive. Forcomparison the figure includes the β-intensity distribu-tion followed by neutron emission Iβn(Ex) deduced fromthe neutron spectrum as explained above. The inte-grated decay intensity above Sn followed by γ-ray emis-

sion Pγ =∫ Qβ

SnIβγ(Ex)dEx obtained from the TAGS

measurement is compared to the integrated Iβn(Ex) orPn value in Table IV. Surprisingly large values of Pγ areobtained, which in the case of 87Br is even larger than Pn.The γ branching represents 57% of the total for 87Br, 20%for 87Br and 4.5% for 94Rb. In the case of 87Br we find8 times more intensity than the high-resolution experi-ment [12], which can be explained by the Pandemonium

effect. The quoted uncertainty on the TAGS integratedintensity Pγ is completely dominated by systematic un-certainties since the uncertainty due to data statistics is

13

(MeV) eνE

0 2 4 6 8 10

spec

trum

rat

io

0.95

1

1.05

1.1

U235

(MeV) eνE

0 2 4 6 8 10

spec

trum

rat

io

0.95

1

1.05

1.1

Pu239

FIG. 10. (Color online) Ratio of antineutrino spectra as afunction of energy calculated for 235U and 239Pu when ourTAGS data replaces the data Tengblad et al. Red: 87Br;green: 88Br; blue: 94Rb; black: all three isotopes.

below 0.6% (relative value) in all cases.

TABLE IV. Integrated β-intensity Pγ from TAGS data aboveSn compared to Pn values from [29–31].

Isotope Pγ Pn

(%) (%)87Br 3.50+49

−40 2.60(4)88Br 1.59+27

−22 6.4(6)94Rb 0.53+33

−22 10.18(24)

We have evaluated several sources of systematic uncer-tainty. In the first place we consider uncertainties thataffect the overall β intensity distributions, which werealready detailed in Section III. To quantify the uncer-tainties in Pγ coming from the spread of possible solu-tions compatible with the data (see Fig 4) we follow theapproach used in Section IV and take the maximum pos-itive and negative difference with respect to the adoptedsolution as a measure of this uncertainty.In addition to this we consider other sources of uncer-

tainty which mostly affect the integral value.A possible source of uncertainty is related to the corre-

lations introduced by the finite energy resolution in the

deconvolution process. This can cause a relocation ofcounts in a region of rapidly changing intensity [70], suchas the region around Sn. However we estimate from amodel deconvolution that this effect is not relevant in thepresent case. Likewise the uncertainty on width calibra-tion also has an impact on the redistribution of countsaround Sn. The highest width calibration point is at4.123 MeV. From the comparison of different fits, vary-ing the number and distribution of calibration points, wedetermine that the extrapolation of the calibration curvecan vary by up to ±15% at 10 MeV. This introduces anuncertainty in Pγ of 2% for 87Br and 6% for 88Br and94Rb.The uncertainty in the energy calibration of TAGS

spectra might have an impact on the result because ofthe dependence of the response on energy. However weverified that this effect is negligible. The main effect ofthe uncertainty on the energy calibration is on the inte-gration range. Since the intensity is rapidly changing inthe region around Sn the effect can be large. The factthat the structure observed in the distribution of Fig. 11around 7−8 MeV for 94Rb coincides with the levels pop-ulated in the final nucleus (see next Section) allows usto conclude that the energy calibration at Sn is correctto about one energy bin (40 keV). We evaluate the un-certainty in the integral, equivalent to changes of halfa bin, to be 11% for the bromine isotopes and 15% forrubidium.The uncertainty values entered in Table IV correspond

to the sum in quadrature of the three types of uncertaintymentioned above: uncertainties in the deconvolution, anduncertainties in the resolution and energy calibration.

VII. COMPARISON WITH

HAUSER-FESHBACH CALCULATIONS

We show in Fig. 11 the ratio Iβγ(Ex)/(Iβγ(Ex) +Iβn(Ex)) as a function of excitation energy. The shadedarea represents the uncertainty in the ratio coming fromthe spread of solutions Iβγ(Ex) to the TAGS inverseproblem shown in Fig. 4. It should be noted that theratio is affected also by systematic uncertainties in theIβn(Ex) distribution coming from the deconvolution ofneutron experimental spectra as well as by uncertaintiesin the neutron spectra themselves, but they are not con-sidered here.The experimental intensity ratio in Fig. 11 is identical

to the average ratio 〈Γγ(Ex)/Γtot(Ex)〉. The average istaken over all levels in each bin populated in the decay.Thus the experimental distribution can be directly com-pared with the results of Hauser-Feshbach calculationsof this ratio. The NLD and PSF used in the calcula-tions are the same as used to construct the spectrometerresponse to the decay (see Section III). The new ingredi-ent needed is the NTC which is obtained from the Opti-cal Model (OM). It is calculated with Raynal’s ECIS06OM code integrated in the TALYS-1.4 software pack-

14

age [81]. OM parameters are taken from the so-calledlocal parametrization of Ref. [82]. Neutron transmissionis calculated for final levels known to be populated in thedecay: g.s. of 86Kr, g.s and first excited state of 87Kr,and g.s. plus 8 excited states of 93Sr. With these ingre-dients one obtains the average widths 〈Γγ〉 and 〈Γn〉 (seeAppendix).

In the case of 87Kr we can compare the calculated av-erage values with experimental data obtained from neu-tron capture and transmission reactions [12, 32]. In par-ticular for 1/2− and 3/2− resonances which are popu-lated in the decay of a 3/2− 87Br ground state. Upto fifty 1/2− and sixty-six 3/2− resonances were iden-tified in an interval of 960 keV above Sn. The NLD ofRef. [72] predicts 46 and 90 respectively, in fair agreementwith these values. The distribution of neutron widths for1/2− resonances in the interval En = 250 − 960 keV iscompatible with a PT distribution with average width〈Γn〉 = 1.95 keV. The same is true for 3/2− resonanceswith 〈Γn〉 = 2.79 keV. In the same interval the Hauser-Feshbach calculated widths vary between 0.3 keV and0.7 keV for 1/2− states and between 0.5 keV and 0.9 keVfor 3/2− states. In both cases the calculation is about4 times too low. The information on 〈Γγ〉 is less abun-dant. The γ width has been determined for six 1/2−

and ten 3/2− resonances, with values in the range 0.075-0.48 eV, and is fixed to 0.255 eV, from systematics, forthe remaining resonances. The Hauser-Feshbach calcula-tion gives values in the range 0.08-0.12 eV. On averagethe calculation is about a factor three too low. Sincethe NLD reproduces the number of resonances, to reachsuch values for the partial widths requires a renormal-ization by a factor of 3-4 for the PSF and the NTC in87Kr, which seems large. The reader should note thatvariations of similar magnitude and direction for boththe PSF and NTC have little impact on the calculatedratio 〈Γγ/Γtot〉. It should also be noted that this ratio isinsensitive to changes in NLD.

We show in Fig. 11 the ratio 〈Γγ/Γtot〉, calculated withnuclear statistical parameters as described above, for thethree spin-parity groups populated under the Gamow-Teller selection rule. Due to statistical fluctuations af-fecting individual widths [24], this cannot be obtainedas 〈Γγ〉/(〈Γγ〉 + 〈Γn〉). Rather than trying to obtain aformula for the average correction factor to be appliedto this ratio, which is the common practice for cross sec-tion calculations [81], we use the Monte Carlo method toobtain directly the average of width ratios. The proce-dure to obtain a statistical realization (or sample) fromthe model is similar to that described in Ref. [69]. Levelenergies for each spin-parity are generated according toa Wigner distribution from the NLD. For each state thecorresponding Γγ and Γn to individual final states aresampled from PT distributions with the calculated av-erage values (see Appendix). The total γ and neutronwidths are obtained by summation over all possible fi-nal states and the ratio is computed. The ratio is aver-aged for all levels lying within each energy bin (40 keV).

(MeV) xE5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4

⟩) nΓ+ γΓ/( γΓ⟨

-210

-110

1

Br87

: 1/2-

: 3/2-

: 5/2-

: exp

(MeV) xE7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

⟩) nΓ+ γΓ/( γΓ⟨

-310

-210

-110

1Br88

: 0-

: 1-

: 2-: exp

(MeV) xE7 7.2 7.4 7.6 7.8 8 8.2 8.4

⟩) nΓ+ γΓ/( γΓ⟨

-410

-310

-210

-110 Rb94: 2-

: 3-

: 4-

: exp

FIG. 11. (Color online) Average gamma to total width fromexperiment (black line) and calculated for the three spin-parity groups populated in allowed decay (red, green, blue).The gray-shaded area around the experiment indicates thesensitivity to systematic effects. See text for details.

In order to eliminate fluctuations in the calculated av-erages, the procedure is repeated between 5 and 1000times depending on level density. Very large average en-hancement factors are obtained, reaching two orders-of-magnitude, when the neutron emission is dominated bythe transition to a single final state.In the case of the decay of the 3/2− ground state in

87Br one can see in Fig. 11 that the strong γ-ray emissionabove Sn can be explained as a consequence of the largehindrance of l = 3 neutron emission from 5/2− statesin 87Kr to the 0+ g.s. of 86Kr. This is the explana-tion already proposed in [12]. The situation is even morefavorable to this explanation if the spin-parity of 87Brwere 5/2− as suggested in [73]. In this case the neu-tron emission is hindered for both 5/2− and 7/2− statespopulated in the allowed decay. In the case of 88Br 1−

decay a similar situation occurs for 0− states in 88Krbelow the first excited state in 87Kr at 532 keV, whichrequires l = 3 neutron emission to populate the 5/2+ g.s.in 87Kr. It should be noted that if the spin-parity of 88Br

15

were 2− as suggested in [30] the three allowed spin-paritygroups (1−, 2−, 3−) will have similar gamma-to-total ra-tios, a factor of 3 to 5 too low compared to experiment,which reinforces our choice of 1− for the 88Br g.s. A morequantitative comparison of the experimental and calcu-lated ratios requires a knowledge of the distribution ofβ intensity between the three spin groups. This can beobtained from β strength theoretical calculations, suchas those in [83] for example. It is clear however thatfor both bromine isotopes the large γ branching aboveSn can be explained as a nuclear structure effect: theabsence of states in the final nucleus which can be pop-ulated through the emission of neutrons of low orbitalangular momentum.The case of 94Rb 3− decay is the most interesting. The

final nucleus 93Sr is five neutrons away from β stability.Although the γ intensity is strongly reduced, only 5 %of the neutron intensity, is detectable up to more than1 MeV above Sn. The structure observed in the distri-bution of the average ratio 〈Γγ/Γtot〉, can be associatedwith the opening of βn channels to different excited statesin 93Sr. As can be seen the structure is reproduced bythe calculation, which confirms the energy calibration athigh excitation energies. In any case the calculated av-erage gamma-to-total ratio is well below the experimen-tal value. In order to bring the calculation in line withthe experimental value one would need to enhance theγ width, or suppress the neutron width, or any suitablecombination of the two, by a very large factor of aboutone order-of-magnitude. A large enhancement of the γwidth, and thus of the calculated (n, γ) cross sections,would have an impact on r process abundance calcula-tions [4–6]. It would be necessary to confirm the largeenhancement of the 〈Γγ/Γtot〉 ratio observed in 94Rb withsimilar studies on other neutron-rich nuclei in this massregion as well as in other mass regions. It will also beimportant to quantify the contribution of a possible sup-pression of the neutron width to the observed ratio.

VIII. SUMMARY AND CONCLUSION

We apply the TAGS technique to study the decay ofthree β-delayed neutron emitters. For this we use a newsegmented BaF2 spectrometer with reduced neutron sen-sitivity, which proved to be well suited to this purpose.The three isotopes, 87Br, 88Br and 94Rb, are fission prod-ucts with impact in reactor decay heat and antineutrinospectrum summation calculations. We obtain β intensitydistributions which are free from the Pandemonium sys-tematic error, affecting the data available in the ENSDFdata base for the three isotopes. The average γ-ray ener-gies that we obtain are 31%, 59% and 235% larger thanthose calculated with this data base for 87Br, 88Br and94Rb respectively, while the average β energies are 28%,33% and 13% smaller.We compare the energy distribution of β particles emit-

ted in the decay derived from our β intensity distribu-

tions with the direct β spectrum measurement performedby Tengblad et al., and find significant discrepancies.Our distributions are shifted to somewhat lower energies.This is reflected in the average β energies, which we findto be 17% and 13% smaller for 87Br and 94Rb respec-tively. Similar systematic differences are found when theTAGS data of Greenwood et al. for 18 isotopes is com-pared with the data of Tengblad et al.. We performeda thorough investigation of possible systematic errors inthe TAGS technique and find that none of them can ex-plain the observed differences. It will be important toperform new direct measurements of the β spectrum fora few selected isotopes in order to investigate this issuefurther.

We estimate the effect of the present data on DH sum-mation calculations. We find a relatively modest impactwhen the high resolution decay data are replaced by ourTAGS data. The impact in the photon component islargest at short cooling times. For 235U thermal fissionit reaches an increment of 3.3% around 3.5 s after fissiontermination. This is mainly due to the decay of 94Rb.The influence of 88Br is smaller and peaks at around25 s. In spite of being small it contributes to reduce thediscrepancy between DH integral measurements of theEEM component and summation calculations for 235U inthe range of 1 to 100 s. Many FP contribute in this timerange, thus additional TAGS measurements of short livedFP are required to remove the discrepancy. In the caseof 239Pu the maximum increment is about 1.8%.

We also evaluate the impact of the new TAGS data onantineutrino spectrum summation calculations. Whenour data replace the data from high-resolution measure-ments we observe a reduction of the calculated νe spec-trum which reaches a maximum value of 6% at 7 MeV forthe thermal fission 235U. A similar value is obtained for239Pu. The reduction is mainly due to the decay of 94Rb.The effect of 88Br, somewhat smaller, peaks at 8.5 MeV.It is remarkable that we find an impact similar to thatobserved for 92Rb, 96Y and 142Cs which make the largestcontribution to the antineutrino spectrum at these en-ergies. The reason is that the large value of the Pan-

demonium systematic error prevails over the relativelysmall fission yield for the isotopes studied in this work.We also verified the effect of replacing our TAGS datawith Tengblad et al. β-spectrum data. We found a rel-atively small impact below Eνe = 8 MeV in part dueto a compensation effect of the deviations for 94Rb and88Br. However between 8 and 9 MeV the use of TAGSdata for 88Br leads to an increase of about 7% in thecalculated antineutrino spectrum. This relatively largeimpact is due to the small number of decay branches inthis energy range. All this underlines the need for TAGSmeasurements for fission products with a very large Qβ

decay energy window.

We confirm the suitability of the TAGS technique forobtaining accurate information on γ-ray emission fromneutron-unbound states. In order to assess the relia-bility of the result we examined the systematic errors

16

carefully since they dominate the total uncertainty bud-get. Surprisingly large γ-ray branchings of 57% and 20%were observed for 87Br and 88Br respectively. In the caseof 94Rb the measured branching of 4.5% is smaller butstill significant. For 87Br we observe 8 times more inten-sity than previously detected with high resolution γ-rayspectroscopy, which confirms the need to use the TAGStechnique for such studies.

Combining the information obtained from TAGS mea-surements about the γ intensity from states above Sn

with the β-delayed neutron intensity we can determinethe branching ratio 〈Γγ/(Γγ + Γn)〉 as a function of Ex.The information thus acquired, can be used to constrainthe neutron capture cross-section for unstable neutron-rich nuclei. This opens a new field for applications ofβ-decay TAGS studies. It also provides additional ar-guments for the need for accurate measurements of β-delayed neutron emission in exotic nuclei. The measure-ments should cover neutron spectra and yields as well asneutron-γ coincidences.

From the comparison of our experimental results withHauser-Feshbach calculations we conclude that the largeγ branching observed in 87Br and 88Br is a consequenceof the nuclear structure. Some of the resonances popu-lated in the decay can only disintegrate via the emissionof a kinematically hindered neutron to the levels avail-able in the final nucleus. A similar situation can occurfor other β-delayed neutron emitters, when the numberof levels in the final nucleus within the emission windowQβ − Sn is small. It should be noted that such strong γto neutron competition introduces a large correction tothe estimation of β-delayed neutron emission probabili-ties from β-strength calculations and should be taken intoaccount when comparing experiment with calculation.

The case of 94Rb, is more representative of the situ-ation expected for nuclei far from stability, where manylevels are available thus the decay by low l neutron emis-sion is always possible. For 94Rb we find that the γ-ray emission from neutron-unbound states is largely sup-pressed, but still much larger (an order-of-magnitude)than the result of Hauser-Feshbach calculations usingstandard parameters for level density, photon strengthand neutron transmission. If such enhancement with re-spect to the Hauser-Feshbach model is due mainly to anincrement in the radiative width, then a similar increaseis obtained for the neutron capture cross-section. Thiscan have a significant impact on calculated elementalabundances in the astrophysical r process. It is neces-sary to confirm and generalize the result obtained for theneutron-rich nucleus 94Rb extending this type of studyto other β-delayed neutron emitters in the same and dif-ferent mass regions, in particular farther away from thevalley of β-stability. Such measurements using the TAGStechnique are already underway and additional studiesare planned.

ACKNOWLEDGMENTS

This work was supported by Spanish Ministerio deEconomıa y Competitividad under grants FPA2008-06419, FPA2010-17142, FPA2011- 24553, FPA2014-52823-C2-1-P,CPAN CSD-2007-00042 (Ingenio2010) andthe program Severo Ochoa (SEV-2014-0398). WG wouldlike to thank the University of Valencia for support. Thiswork was supported by the Academy of Finland underthe Finnish Centre of Excellence Programme 2012-2017(Project No. 213503, Nuclear and Accelerator-BasedPhysics Research at JYFL). Work supported by EP-SRC(UK) and STFC(UK). Work partially supported bythe European Commission under the FP7/EURATOMcontract 605203. We thank D. Lhuillier for making avail-able in digital form data tabulated in Ref. [60].

APPENDIX

The average γ width for initial levels (resonances) ofspin-parity Jπ

i at excitation energy Ex can be obtainedby summation over all final states of spin-parity Jπ

f andexcitation energy Ex − Eγ :

〈Γγ(Jπi , Ex)〉 =

1

ρ(Jπi , Ex)

∑f

∑XL

E2L+1γ fXL(Eγ) (5)

where ρ(Jπi , Ex) represents the density of initial levels

and fXL(Eγ) is the photon strength for transition energyEγ . The appropriate electric or magnetic character Xand multipolarity L of the transition is selected by spinand parity conservation. We have used the common prac-tice of restricting the transition types to E1, M1 and E2with no mixing, which leads to a single XL choice foreach final state.For transitions into a bin of width ∆E in the contin-

uum part of the level scheme the density weighted aver-age over final levels should be used:

〈Γγ(Jπi , Ex)〉 =

1

ρ(Jπi , Ex)

∑f

∑XL

∫ E+∆E

E

E2L+1γ

× fXL(Eγ)ρ(Jπf , Ex − Eγ) dEγ (6)

Likewise the average neutron width can be obtainedby summation over all final states of spin-parity Jπ

f andexcitation energy Ex − Sn − En in the final nucleus:

〈Γn(Jπi , Ex)〉 =

1

2πρ(Jπi , Ex)

∑f

∑ls

T ls(En) (7)

where T ls(En) is the neutron transmission coefficient,a function of neutron energy En. The orbital angularmomentum l and channel spin s are selected by spin andparity conservation for each final level.

17

[1] K.L. Kratz et al., Astron. Astrophys. 125, 381 (1983).[2] S. Mughabghab, Atlas of Neutron Resonances (Elsevier

Science, 2006).[3] E.M. Burbidge et al., Rev. Mod. Phys. 29, 547 (1957).[4] S. Goriely, Phys. Lett. B 436, 10 (1998).[5] R. Surman et al., Phys. Rev. C 64, 035801 (2001).[6] A. Arcones et al., Phys. Rev. C 83, 045809 (2011).[7] T. Rauscher et al., Atom. Data and Nucl. Data Tables

75, 1 (2000).[8] J. E. Escher et al., Rev. Mod. Phys. 84, 353 (2012).[9] D.R. Slaughter et al., Phys. Lett. B 38, 22 (1972).

[10] H. Tovedal et al., Nucl. Phys. A 252, 253 (1975).[11] F.M. Nuh et al., Nucl. Phys. A 293, 410 (1977).[12] S. Raman et al., Phys. Rev. C 28, 602 (1983).[13] F.M. Nuh et al., Phys. Lett. B 53, 435 (1975).[14] K.L. Kratz et al., Nucl. Phys. A 317, 335 (1979).[15] H. Ohm et al., Z. Phys. A 296, 23 (1980).[16] C.J. Bischof et al., Phys. Rev. C 15, 1047 (1977).[17] G. D. Alkhazov et al., Leningrad Nuclear Physics Insti-

tute, Preprint 1497 (1989).[18] R.C. Greenwood et al., Nucl. Instrum. Methods Phys.

Res., Sect. A 390, 95 (1997).[19] J.P. Omtvedt et al., Z.Phys. A 339, 349 (1991).[20] H. Yamamoto et al., Phys. Rev. C 26, 125 (1982).[21] K.L. Kratz et al., Z. Phys. A 312, 43 (1983).[22] S.V. Ilyushkin et al., Phys. Rev. C 80, 054304 (2009).[23] S.V. Ilyushkin et al., Phys. Rev. C 83, 014322 (2011).[24] B. Jonson et al., Proc. 3rd Int. Conf. on Nuclei far from

stability, CERN Report 76-13 (1976) 277[25] J. Hardy et al., Phys. Lett. B 71, 307 (1977).[26] A. Algora et al., Nucl. Phys. A 654, 727c (1999).[27] A. Algora et al., Phys. Rev. C 68, 034301 (2003).[28] Z. Hu et al., Phys. Rev. C 60, 024315 (1999).[29] R. G. Helmer, Nucl. Data Sheets 95, 543 (2002).[30] E.A. McCutchan and A.A. Sonzogni, Nucl. Data Sheets

115, 135 (2014).[31] D. Abriola and A.A. Sonzogni, Nucl. Data Sheets 107,

2423 (2006).[32] R. F. Carlton et al., Phys. Rev. C 38, 1605 (1988).[33] A.-A. Zakari-Issoufou, PhD. Thesis, University of

Nantes, to be published.[34] K. Okumura et al., Proceedings of the 2012 Sympo-

sium on Nuclear Data, Kyoto, JAEA-Conf 2013-002,INDC(JPN)-198, p. 15, 2013.

[35] T. Yoshida and R. Nakasima, J. Nucl. Sci. Technol., 18,393 (1981).

[36] T. Yoshida et al., Assessment of Fission Product DecayData for Decay Heat Calculations, OECD/NEA WorkingParty for International Evaluation Co-operation, Volume25, 2007.

[37] M. Gupta et al., Decay Heat Calculations: Assessmentof Fission Product Decay Data Requirements for Th/UFuel, IAEA report INDC(NDS)-0577, 2010.

[38] A. Algora et al., Phys. Rev. Lett. 105, 202501 (2010).[39] RIPL-3, R. Capote et al., Nucl. Data Sheets 110, 3107

(2009).[40] M. Fleming and J. C. Sublet, Decay Data Comparisons

for Decay Heat and Inventory Simulations of FissionEvents, UK Atomic Energy Authority, Culham ScienceCentre, CCFE-R(15)28/S1, 2015.

[41] C. Bemporad et al., Rev. Mod. Phys. 74, 297 (2002).

[42] S.-B. Kim et al., Adv. High Energy Phys. 2013, 453816(2013).

[43] M. Cribier, Nucl. Phys. B (Proc. Suppl.) 221, 57 (2011).[44] X. Mougeot, Phys. Rev. C 91, 055504 (2015).[45] K. Schreckenbach et al., Phys. Lett. B 160, 325 (1985).[46] A. A. Hahn et al., Phys. Lett. B 218, 365 (1989).[47] N. Haag et al., Phys. Rev. Lett. 112, 122501 (2014).[48] Th. A. Mueller et al., Phys. Rev. C 83, 054615 (2011).[49] P. Huber, Phys. Rev. C 84, 024617 (2011).[50] G. Mention et al., Phys. Rev. D 83, 073006 (2011).[51] D. L. Fang and B.A. Brown, Phys. Rev. C 91, 025503

(2015)[52] M. Fallot et al., Phys. Rev. Lett. 109, 202504 (2012).[53] Y. Abe et al., J. High Ener. Phys. 10, 086 (2014).[54] J. H. Choi et al., Phys. Rev. Lett. 116, 211801 (2016).[55] F. P. An et al., Phys. Rev. Lett. 116, 061801 (2016).[56] D. A. Dwyer and T. J. Langford, Phys. Rev. Lett. 114,

012502 (2015).[57] A. A. Sonzogni et al., Phys. Rev. C 91, 011301 (2015).[58] A. A. Zakari-Issoufou et al., Phys. Rev. Lett. 115, 102503

(2015).[59] O. Tengblad et al., Nucl. Phys. A 503, 136 (1989).[60] G. Rudstam et al., Atomic Data and Nuclear Data Tables

45, 239 (1989).[61] J. L. Tain et al., Phys. Rev. Lett. 115, 062502 (2015).[62] I. Moore et al., Nucl. Instrum. Methods Phys. Res., Sect.

B 317, 208 (2013).[63] T. Eronen et al., Eur. Phys. J. A 48, 46 (2012).[64] S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 506, 250 (2003).[65] ENDF/B-VII.1, M.B. Chadwick et al., Nucl. Data Sheets

112, 2887 (2011).[66] J. L. Tain et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 774, 17 (2015).[67] D. Cano-Ott et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 430, 488 (1999).[68] J. Agramunt et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 807, 69 (2016).[69] J. L. Tain et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 571, 719 (2007).[70] J. L. Tain et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 571, 728 (2007).[71] D. Cano-Ott et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 430, 333 (1999).[72] S. Goriely et al., Phys. Rev. C 78, 064307 (2008).[73] M.-G. Porquet et al., Eur. Phys. J. A 28, 153 (2006).[74] J. Genevey et al., Phys. Rev. C 59, 82 (1999).[75] See Supplemental Material at link for tables of the β in-

tensity distribution from this work.[76] ENSDF Analysis Programs - LOGFT, National Nu-

clear Data Center, Brookhaven National Laboratory,http://www.nndc.bnl.gov/nndcscr/ensdf pgm/analysis/logft/

[77] S. J. Rice, Decay Heat Measurements of Fission Frag-ments 86Br, 91Rb and 94Sr Using Total AbsorptionGamma-ray Spectroscopy, PhD Thesis, University ofSurrey, 2014 (to be published).

[78] A. J. Koning et al., Journal of the Korean Physical Soci-ety 59, 1057 (2011).

[79] D. Jordan et al., Phys. Rev. C 87, 044318 (2013).[80] B. C. Rasco et al., Phys. Rev. Lett. 117, 092501 (2016).[81] A. J. Koning et al., Proceedings International Conference

18

on Nuclear Data for Science and Technology, April 22-27,2007, Nice, France, EDP Sciences (2008) 211.

[82] A. J. Koning et al., Nucl. Phys. A713 (2003) 231[83] P. Moller et al., Phys. Rev. C 67, 055802 (2003).