Nonfuel Antineutrino Contributions in the High Flux Isotope Reactor
A.B. Balantekin, H.R. Band, C.D. Bass, D.E. Bergeron, D. Berish, N.S. Bowden, J.P. Brodsky, C.D. Bryan, T. Classen, A.J. Conant, G. Deichert, M.V. Diwan, M.J. Dolinski, A. Erickson, B.T. Foust, J.K. Gaison, A. Galindo-Uribarri, C.E. Gilbert, B.T. Hackett S. Hans, A.B. Hansell, K.M. Heeger, B. Heffron D.E. Jaffe, X. Ji, D.C. Jones, O. Kyzylova, C.E. Lane, T.J. Langford, J. LaRosa, B.R. Littlejohn, X. Lu, J. Maricic, M.P. Mendenhall, R. Milincic, I. Mitchell, P.E. Mueller, H.P. Mumm, J. Napolitano, R. Neilson, J.A. Nikkel, D. Norcini, S. Nour, J.L. Palomino-Gallo, D.A. Pushin, X. Qian, E. Romero-Romero, R. Rosero, P.T. Surukuchi, M.A. Tyra, R.L. Varner, C. White, J. Wilhelmi, A. Woolverton, M. Yeh, A. Zhang, C. Zhang, X. Zhang
NNonfuel Antineutrino Contributions in the High Flux Isotope Reactor
A.B. Balantekin n , H.R. Band o , C.D. Bass g , D.E. Bergeron h , D. Berish k , N.S. Bowden f , J.P. Brodsky f , C.D. Bryan i ,T. Classen f , A.J. Conant * ,c,i , G. Deichert i , M.V. Diwan a , M.J. Dolinski b , A. Erickson c , B.T. Foust o , J.K. Gaison o ,A. Galindo-Uribarri j,l , C.E. Gilbert j,l , B.T. Hackett j,l , S. Hans a , A.B. Hansell k , K.M. Heeger o , B. Heffron j,l , D.E. Jaffe a ,X. Ji a , D.C. Jones k , O. Kyzylova b , C.E. Lane b , T.J. Langford o , J. LaRosa h , B.R. Littlejohn e , X. Lu j,l , J. Maricic d M.P. Mendenhall f , R. Milincic d , I. Mitchell d , P.E. Mueller j , H.P. Mumm h , J. Napolitano k , R. Neilson b , J.A. Nikkel o ,D. Norcini o , S. Nour h , J.L. Palomino-Gallo e , D.A. Pushin m , X. Qian a , E. Romero-Romero i,k , R. Rosero a , P.T. Surukuchi o ,M.A. Tyra h , R.L. Varner j , C. White e , J. Wilhelmi k , A. Woolverton m , M. Yeh a , A. Zhang a , C. Zhang a , X. Zhang f a Brookhaven National Laboratory, Upton, NY 11973, USA b Department of Physics, Drexel University, Philadelphia, PA 19104, USA c George W. Woodruff School of Mechanical Engineering,Georgia Institute of Technology, Atlanta, GA 30332, USA d Department of Physics & Astronomy, University of Hawaii, Honolulu, HA 96822, USA e Department of Physics, Illinois Institute of Technology, Chicago, IL 60616, USA f Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA g Department of Physics, Le Moyne College, Syracuse, NY 13214, USA h National Institute of Standards and Technology, Gaithersburg, MD 20899, USA i High Flux Isotope Reactor, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA j Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA k Department of Physics, Temple University, Philadelphia, PA 19122, USA l Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA m Institute for Quantum Computing and Department of Physics and Astronomy,University of Waterloo, Waterloo, ON N2L 3G1, Canada n Department of Physics, University of Wisconsin, Madison, Madison, WI 53706, USA and o Wright Laboratory, Department of Physics, Yale University, New Haven, CT 06520, USA (PROSPECT Collaboration) ∗ (Dated: April 1, 2020)Reactor neutrino experiments have seen major improvements in precision in recent years. With the experi-mental uncertainties becoming lower than those from theory, carefully considering all sources of ν e is importantwhen making theoretical predictions. One source of ν e that is often neglected arises from the irradiation of thenonfuel materials in reactors. The ν e rates and energies from these sources vary widely based on the reactortype, configuration, and sampling stage during the reactor cycle and have to be carefully considered for eachexperiment independently. In this article, we present a formalism for selecting the possible ν e sources arisingfrom the neutron captures on reactor and target materials. We apply this formalism to the High Flux IsotopeReactor (HFIR) at Oak Ridge National Laboratory, the ν e source for the the Precision Reactor Oscillation andSpectrum Measurement (PROSPECT) experiment. Overall, we observe that the nonfuel ν e contributions fromHFIR to PROSPECT amount to 1% above the inverse beta decay threshold with a maximum contribution of 9%in the 1.8–2.0 MeV range. Nonfuel contributions can be particularly high for research reactors like HFIR be-cause of the choice of structural and reflector material in addition to the intentional irradiation of target materialfor isotope production. We show that typical commercial pressurized water reactors fueled with low-enricheduranium will have significantly smaller nonfuel ν e contribution. CONTENTS
I. Introduction 2II. Nonfuel Production of Antineutrinos 3III. Case Study: HFIR 4IV. Reactor Modeling and Simulation 5V. Calculation of Nonfuel Excess in ν e Spectrum 7A. Structural 8 ∗ [email protected]
1. Aluminum 82. Chromium, Copper, and Manganese 9B. Beryllium Reflector 9C. Target Materials 101. Vanadium 102. Curium 103. Neptunium 11D. Cycle Average Nonfuel Contribution to ν e Spectrum 11VI. Note on Commercial Reactor Comparisons 11VII. Conclusions 12VIII. Acronyms 13IX. Acknowledgments 13References 13
I. INTRODUCTION
Many experiments have been performed to measure theelectron antineutrino ( ν e ) flux and spectrum from nuclear re-actors over the past several decades to advance our knowledgeof the standard model. Nuclear reactors are intense sources of ν e ; approximately six ν e per fission are produced, resulting inthe emission of ∼ ν e s − by a 1 gigawatt electric (GWe)commercial light water reactor. Typically, detectors are placednear nuclear reactors to detect ν e via the inverse beta decay(IBD) reaction. Many experiments have been conducted atcommercial nuclear reactors with baselines ranging from tensof meters to hundreds of kilometers. Recent interest in thesearch for sterile neutrino oscillations has motivated a newseries of short-baseline experiments. The need for close prox-imity to a compact ν e source and the desire to measure the ν e production from individual fissile isotopes make researchreactors an excellent choice for these experiments [1]. An out-line of major neutrino experiments can be found in Ref. [2].The detection of ν e at a nuclear reactor is dependent onmany parameters of the reactor and detector systems [3]: d N ν e ( E, t ) dEdt = N prot σ IBD ( E ) η P ( E, L )4 πL d φ ( E, t ) dEdt , (1)where N ν e is the number of neutrinos detected in the activevolume, N prot is the number of target protons in the detector, σ IBD is the energy-dependent IBD cross section, η is a detectorefficiency parameter, P is the oscillation survival probability,and L is the distance from fission site to IBD interaction posi-tion. The last differential term accounts for the magnitude andrelative change in the emitted spectrum from the source: d φ ( E ν e , t ) dE ν e dt = (cid:88) i f i ( t ) dN i dE ν e , (2)where f is the fission rate of isotope i and the dN i /dE ν e is the ν e spectrum of that isotope.If the focus turns to the reactor as the ν e source with thefission rate of Equation 2 analogous to power, Equation 1 re-duces to a simple calculation of the detected ν e [4]: dN ¯ ν e dt = γ [1 + k ( t )] P th , (3)where γ takes into account all detector properties, P th is thethermal power of the reactor, and k ( t ) takes into account thechange in ν e flux due to isotopic evolution. The Daya Bay[3, 5] and RENO [6] collaborations have investigated andquantified this k ( t ) term for commercial reactors. The de-tected ν e rate is proportional to reactor power. There exists variation in the signal due to the evolution of isotope fissionfractions with fuel burnup, depending on the reactor.The proportionality of detected ν e rate to reactor power hasbeen observed in many reactor experiments, most recentlyDaya Bay [3, 5], Double Chooz [7], and RENO [6], all ofwhich focused on measuring ν e disappearance. However, re-evaluation of theoretical predictions [8–10] in preparation forthese experiments lead to a 6% deficit of the observed flux,the “reactor antineutrino anomaly.” Additionally, the shape ofthe overall ν e spectrum does not agree with predictions withan excess in the 5–7 MeV range, known as the “bump,” as themost prominent feature. Causes of these phenomena could benew physics in the form of sterile neutrinos [8] or incompletetreatment of the complex nature of nuclear reactions and de-cays in the predictions or both [11–14].Previous work has addressed some aspects of reactor de-sign and operation as they affect the reactor ν e spectrum. Theeffect of “nonequilibrium” isotopes, i.e., fission products thathave not reached equilibrium contributions, factored in irradi-ation time as a variable in reactor operation, impacting com-parisons with the aggregate beta spectra measured at the In-stitut Laue-Langevin (ILL) reactor [15–17]. Another observa-tion is the contribution from neutron capture on fission prod-ucts [17, 18]. Similarly, the contributions from stored spentfuel have been studied [19, 20]. However, the exact contri-bution of ν e from nonfission products, primarily via thermalneutron capture on reactor materials, has yet to be addressed.Huber and Jaffke discussed the ν e contributions on nonequi-librium isotopes, but this effect was examined for neutron cap-ture on fission products only [18]. These contributions can beadditional terms in Equation 2: d φ ( E ν e , t ) dE ν e dt = (cid:88) i f i ( t ) dN i dE ν e c i ne ( E ν e , t )+ s SNF ( E ν e , t ) + a NF ( E ν e , t ) , (4)where the contribution from nonequilibrium isotopes, c i ne , is acorrection factor to the isotope spectra. The contribution fromspent nuclear fuel, s SNF , and the nonfuel activations, a NF , areadditional terms. Note that all these additional contributionsare highly reactor-specific and time dependent. Most modernreactor ν e experiments account for the time dependent c i ne and s SNF but do not account for a NF because it has been un-derexplored or considered to be a trivial contribution [12].The goal of this paper is to develop a formalism for de-termining the nonfuel candidates that produce ν e above theIBD threshold. The Precision Reactor Oscillation and Spec-trum Measurement (PROSPECT) experiment at the High FluxIsotope Reactor (HFIR) at Oak Ridge National Laboratory(ORNL) is used as a case study to apply this formalism. Theunique configuration of this research reactor provides an op-portunity to highlight materials and processes that can makenon-negligible contributions to the total emitted ν e spectrum.Research reactors typically have very different design andmissions compared to commercial nuclear reactors, which re-sults in significantly different nonfuel contributions. The for-malism defined here can be used by all the reactor ν e experi-ments, but it is particularly important for the experiments us-ing research reactors like PROSPECT [21], STEREO [22],and SoLid [23] to account for the nonfuel contributions intheir predictions.There has been increased interest in measuring the coher-ent elastic neutrino-nucleus scattering (CE ν NS) reaction us-ing reactors as a source after a first measurement of this re-action by the COHERENT experiment [24]. Using reactorsas the source measuring the CE ν NS requires an update in thepredicted ν e spectrum below the IBD threshold, which hasnot been given much attention so far [25]. Because nonfuelsources of ν e primarily contribute at low energies, includ-ing these contributions in the ν e predictions is critical. Themethodology provided here can be individually used by eachexperiment to predict the ν e spectrum provided by the reactor.Section II outlines the methodology for selection of can-didates for nonfuel ν e emissions in a nuclear reactor, andthis methodology can be applied to any reactor. Section IIIpresents HFIR as a case study for the selection process. A listof candidate isotopes are considered for HFIR, and the detailsof those isotopes in the reactor are discussed with the materi-als grouped into three general categories: structural, reflector,and target. Section IV discusses the reactor modeling method-ology and its uncertainty considerations. In Section V, reactormodeling to obtain reaction rates and conversion to ν e spec-trum are performed. Section VI discusses the extension of thiswork to commercial nuclear power plants, and Section VIIcontains the conclusions. Finally, Section VIII contains a listof relevant acronyms. II. NONFUEL PRODUCTION OF ANTINEUTRINOS
This section discusses a procedure for selection of nonfuel ν e sources in a reactor. One feature of reactor ν e sources thathas sometimes been neglected is the emission from nonfuelmaterials. The design and operation of certain reactors requirespecific considerations for nonfuel materials. Nonfission re-actions, such as neutron capture, can generate beta-decayingproducts that are accompanied by ν e . These ν e from fissionsources are an additional contribution that must be consideredfor precision measurements at certain classes of reactors. Thecontribution of these nonfuel sources needs to be taken intoaccount in ν e predictions.The isotopes of most concern for predicting an accurate fis-sion ν e spectrum would be those that contribute to the ν e fluxcoming from the core materials, which alters the ν e fissionspectrum. Neutron capture reactions—such as (n, γ ), (n,2n),or (n,p)—release significantly less energy than fission reac-tions; therefore they contribute negligibly to the core power. ν e production that is not tracked via the power level dis-rupts the predicted linear relationship between detected ν e andpower level [26]. The isotope content of all nonfuel materialsin or near the reactor core must be evaluated for their abil-ity to produce ν e . The isotopes with significant contributionswill be referred to as “antineutrino candidates.” Here, reac-tion rates greater than 0.1% of the fission rate are consideredsignificant. To contribute significantly to the spectrum, the combinationof parent and daughter isotopes of the neutron capture reactionmust fulfill certain criteria. These criteria serve to identifypotential contributors to the antineutrino flux. Each isotopeneeds to fulfill all criteria, but in some cases unmet criterionare balanced by enhancements in other criteria.First, an antineutrino candidate must have a relatively highconcentration in the core. It cannot be contained in traceamounts or be infrequently irradiated in the core. This cri-terion ensures a sufficient number of target atoms for neutroncapture. In addition, a high abundance in the core relativeto other isotopes is ideal to maximize the number of targetatoms. No quantitative criteria is given here. Although com-mercial reactors have a smaller number of isotopes present inthe core, many isotopes can be considered for research reac-tors.Second, the neutron-induced reaction of interest must havea non-negligible neutron cross section to produce the daugh-ter. The reaction of interest is almost always neutron capture(i.e., AZ X + n → A +1 Z X followed by γ emission), but reactionsthat result in the ejection of other particles (e.g, α , H, etc.)also can result in daughter isotopes prone to β − decay. Be-cause the neutron-induced reaction rate of an isotope i ( R i ) isa product of the parent isotope concentration ( N p ) and energy-dependent neutron cross section ( σ i ) and neutron flux ( φ ), thesecond criteria seeks to have a maximum of this product: R i = N p ( t ) (cid:90) (cid:90) φ ( (cid:126)r, E, t ) σ i ( (cid:126)r, E ) dEd(cid:126)r (5)For example, a structural material has a relatively high atomicconcentration in the core but a relatively low cross section,whereas neutron poisons for reactivity control have the in-verse characteristic. Both of these can still be considered as ν e candidates due to the product of concentration and crosssections. In this work, a non-negligible cross section is de-fined to be greater than 0.1 barns, although some exceptionsare made because of the combination of criteria one and two.Because most ν e experiments have occurred at thermal reac-tors, thermal neutron-induced reaction are primarily consid-ered here. The mean energy of thermal neutrons in a nuclearreactor is 0.0253 eV, for which ENDF/V-VII.1 cross sectionscan be readily obtained [27]. Fast neutron-induced reactionscan be important in certain areas of the core or for fast neutronspectrum reactors, which is beyond the scope of this work.Third, the daughter product ( A +1 Z X ) must β − decay with ashort half-life relative to the cycle of the reactor so that it isgenerated with a sufficient activity. If the half-life is too longrelative to the reactor cycle length, it will not decay with ahigh enough frequency. The relative magnitude of half-life tocycle length will determine how quickly, if at all, the activitywill reach secular equilibrium with its production rate. Half-lives of up to a certain length relative to the cycle length maybe considered depending on the application. For example, iso-topes with a half-life two orders of magnitude lower than thecycle length will have their activity saturated for 95% of thecycle. This value will be used for this criterion, although mostactivated products have half-lives much shorter than this. Ashort time until an isotope reaches its saturated activity in-creases the value and decreases the time variation of the ν e contribution.Fourth, the β − transition of the daughter must releaseenough energy to be above the IBD threshold of 1.8 MeV( E ν e ,max = Q − E γ > ν e reac-tions should take into account a lower energy threshold, as inRef. [29].An isotope that fulfills all of these criteria is considered asan antineutrino candidate. In a reactor, the concentration ofthe candidate, N i , from its parent, N p , assumed to be stableand not appreciably burnt out, is equivalent to: N i ( t ) = N p ( t ) λ i (cid:2) − e − λ i t (cid:3) (cid:90) φ ( E, t ) σ i ( E ) dE, (6)where λ i is the decay constant of the daughter isotope ( λ = ln /t / ). If the decay constant of the product is large (mean-ing a short half-life) relative to the irradiation period, the de-cay term quickly declines and the candidate concentration be-comes proportional to the time-dependent neutron flux andparent isotope concentration.For any reactor ν e experiment, the above criteria can beapplied to its reactor materials to select non-fissionable iso-topes that may contribute significantly to the reactor ν e spec-trum. The selection process will result in isotopes that shouldbe considered for reactor analysis and modeling to quantifynonfuel ν e rates. Each reactor can be analyzed based on thematerials under consideration. III. CASE STUDY: HFIR
For this paper, HFIR is used as a case study. As a researchreactor, HFIR is smaller than traditional commercial reactorsand is not used to generate electricity. It also is fueled withhighly enriched uranium, whereas typical commercial reac-tors are fueled with low-enriched uranium. HFIR currentlyhosts the PROSPECT detector, which is measuring the ν e flux from HFIR. HFIR is similar in design to other researchreactors, such as the National Bureau of Standards Reactor[30, 31], the ILL reactor [32] which hosts the STEREO exper-iment [22], and the BR2 reactor in Belgium [33] which hoststhe SoLid experiment [23]. The study of the nonfuel ν e couldbe applicable to these other highly enriched uranium reactors.HFIR is a major U.S. research reactor with missions of neu-tron scattering, isotope production, materials irradiation, andneutron activation analysis [34]. It is one of the few highly en-riched uranium–fueled research reactors in the United Statesand has been operating since 1965. HFIR is a compact reac-tor that can attain high thermal neutron fluxes—greater than × cm − s − —in its central region. It nominally op-erates at a power of 85 megawatts thermal (MWt) for a cy-cle length of 23–26 days, i.e., 1,955–2,210 megawatt days(MWd) of operation with seven cycles annually. Figure 1shows the side view of HFIR.The central region of the core is the flux trap target (FTT)region. The FTT region contains a total of 37 target positions,which includes 30 interior positions, 6 peripheral target posi-tions, and one hydraulic tube. The contents of the FTT varyfrom cycle to cycle depending on experimental demand forisotope production and materials irradiation. A model with arepresentative loading, for example, contains target materialscomposed of V, Ni ( Ni), Mo, W, Se, Ni, Fe, and Cm [35].The curium targets are used to produce
Cf [36], which re-sults in its spontaneous fissions and other neutron-inducedfission of higher actinides. In more recent cycles since thatreport, experiments have included previously mentioned iso-topes as well as silicon carbide, steels, and other ferritic al-loys. These isotopes are important for PROSPECT, which wasdeployed in early 2018.Radially outward of the FTT are the two fuel element re-gions, the inner and outer fuel elements (IFE/OFE). The fuelis a U O -Al dispersion fuel (uranium dispersed in an alu-minum matrix) enriched to 93% by mass U (5–6%
Uand 1%
U) and manufactured in the form of involute plates[37]. The fuel region is contoured along the arc of the involuteto allow for sufficient thermal safety margin. The IFE con-tains a burnable poison, B, to flatten the power distributionand ensure a longer cycle. The IFE and OFE contain 171 and369 fuel plates, respectively, and have separate fissile load-ings. Fresh IFE and OFE fuel assemblies are loaded into thecore for each cycle, unlike most commercial reactors that op-erate with some previously irradiated fuel elements containingplutonium.The fuel regions are surrounded by two concentric controlelements (CEs). Both control elements are partially insertedat the beginning of cycle (BOC) and are gradually withdrawnin opposite directions throughout the cycle. The inner controlelement (ICE) is the control cylinder that descends through-out the cycle; the outer control element (OCE) is a set of foursafety plates, each of which can individually scram the reac-tor, move upward throughout the cycle. The CE positions atvarious points in the cycle are shown in Figure 1. Both con-trol elements contain Eu, Ta, and Al in their absorbing regions[35]. The end of cycle (EOC) occurs when both elements arefully withdrawn and the reactor can no longer maintain crit-icality. Both the ICE and OCE are replaced approximatelyevery 50 cycles.The beryllium reflector occupies the outermost radial re-gion and serves to moderate neutrons for reflection back intothe active core or transport them down the beam tubes. Thereflector region is split up into three regions: the removable(RB), semi-permanent (SPB), and permanent (PB) berylliumregions. The RB is replaced every several years, and the SPBand PB are replaced every few decades. The PB contains 22vertical experimental facilities (VXFs), including inner small,outer small, and large VXFs. The four horizontal beam tubes(HBs) penetrate the outer radial areas in order to support coldFIG. 1: Side view of HFIR with core regions (top) andmovement of inner and outer CEs throughout the cycle(bottom).and thermal scattering experiments. Recent cycles have in-cluded neptunium oxide (NpO ) targets to produce Pu forthe National Aeronautics and Space Administration (NASA)[38–40]. All materials in the various components of the re-flector regions are included in the analysis. Because reflectorregions are exposed to neutron flux, they build up substantialneutron poisons, primarily Li and He, over multiple irra-diation cycles. Several reactions that produce these poisons and ν e candidates rely on fast neutrons, whereas captures inthe structural and target materials occur mostly from thermalneutrons.The ν e candidate selection process of Section II is appliedto the nonfuel materials in HFIR. The reactor is first dividedinto different regions according to primary function. Then, amix of publicly available and internal data at HFIR is used todetermine average quantities of materials in the core duringa typical cycle. The composition of the fuel elements is welldocumented and outlined in Ref. [35]. The control element(CE) and reflector materials change in composition with in-creasing irradiation time in the reactor. The target materialshave the potential to change each cycle according to user de-mand; a representative loading of targets in recent cycles isoutlined in Ref. [35]. Isotopic constituents of these materi-als are analyzed according to the four step selection processto generate ν e candidates to be analyzed with reactor model-ing. Candidates with contributions of greater than 0.1% areconsidered because this is the typical statistical uncertainty inreaction rate calculations.Antineutrino candidate selection process results can be seenin Table I. The β − decays of antineutrino candidates that areto be considered include three main groups. The first is struc-tural materials, which includes Al, Cr, Cu, and Mn.The second is the beryllium reflector, which includes He and Li. The last is the target materials, which include V in theFTT and two actinide targets, curium in the FTT, and neptu-nium in the VXFs. The next step for the antineutrino candi-dates is to quantify their activities in the reactor, discussed inSection IV, and convert the activities to ν e spectra to comparewith the nominal reactor spectrum in Sections V–VII. IV. REACTOR MODELING AND SIMULATION
After identifying antineutrino candidates for HFIR, the nextstep is to quantify the neutron-induced reaction rates in a typi-cal cycle of the reactor. The modeling methodology is to buildon a HFIR computer model developed by ORNL staff [35] us-ing the Monte Carlo particle transport code MCNP [41, 42].This model includes information and advancements from aHFIR Cycle 400 model [43, 44], including explicit modelingof the fuel plates and a representative target loading, and isthe basis for neutronic safety and performance calculations atHFIR. Models exist for BOC and EOC as well as in single daytime steps for each day of the cycle; the isotopics for each dayare calculated from the VESTA depletion code [45].Reaction rate calculations are added in MCNP to obtainthe energy-dependent neutron flux and reaction rates in user-defined, discrete cells containing the isotope of interest, andphantom materials (described in Ref [42]) are added to obtainisotope-dependent reaction rates. The lack of phantom ma-terials in a tally results in total reaction rates in a cell (e.g.for fission rates in a fuel cell summed over those for U, U, Pu,
Pu). MCNP cells are user-defined accordingto regions bound by surface descriptions (e.g., planes, spheres,cylinders). Volumes of these cells range from less than 1 cm for fuel and some flux trap cells to hundreds of cubic centime-TABLE I: A summary list of the antineutrino candidates in HFIR. The isotopes are grouped in coarse categories according tofunction or region in the reactor. The requirements for ν e candidate selection previously described are in bold in the second rowof the table. The failed criteria for each isotope, if any, is listed in the right-most column. El. A Abundance ENDF/B-VII.1 Daughter t / Q E final E β,max (MeV) Criteria(%) σ (barns) (s) (MeV) (MeV) [Mutliple] Failed Requirement 1 2 3 4High High β − decay Low High > Structural Al 27 100.0 0.23 Al 1.34E+02 4.64 1.78 2.86 NoneFe 54 2.8 2.25 Fe 356 91.8 2.59 Fe 357 2.1 2.43 Fe 358 0.3 1.00 Fe 3.84E+06 1.57 4Cr 50 4.3 15.40 Cr 352 83.8 0.86 Cr 353 9.5 18.09 Cr 354 2.4 0.41 Cr 2.10E+02 2.60 0.00 2.60 NoneCu 63 69.2 4.47 Cu 365 30.8 2.15 Cu 3.07E+02 2.64 0.00 2.64 NoneMg 24 79.0 0.05 Mg 325 10.0 0.19 Mg 326 11.0 0.19 Mg 5.73E+02 2.61 0.84 1.77 4Mn 55 100.0 13.27 Mn 9.28E+03 3.70 Various [0.250,2.849] NoneReflector Be 9 100.0 0.04 a He 8.07E-01 3.50 0.00 3.50 None10 trace B 4.75E+13 0.55 1,2Li 7 92.41 b Li 8.40E-01 16.00 3.03 12.97 NonePoisons B 10 80.1 3842.56 Li 3and CEs 11 19.9 0.01 3Eu 151 47.8 9200.73
Eu 4.22E+08 3153 52.2 358.00
Eu 2.71E+08 3Nb 93 7.59 1.16 Nb 6.41E+11 2.04 3Ta 181 99.99 8250.44
Ta 9.89E+06 1.81 Various 4Targets V 51 99.75 4.92 V 2.25E+02 3.97 1.434 2.54 None(FTT + Mo 98 24.4 0.13 Mo 2.38E+05 1.36 4VXFs) Se 78 23.8 0.43 Se 380 49.6 0.61 Se 1.11E+03 1.59 4Ni 58 68.1 4.22 Ni 3Np Various Various c None Various c Cm Various Various c None Various ca The cross-section listed is in the fast region due to the high energy threshold Be(n, α ) reaction b With a fresh beryllium reflector, no Li is present but it is produced gradually in its lifetime c Np, Cm, and products to which they transmute are fissile and produce fission ν e spectra that have been relatively unexplored ters for reflector regions. Tally results in MCNP are reportedper unit source particle (e.g., neutron). To normalize to abso-lute rates for comparison with fission rates, the power normal-ization factor (PNF), expressed in terms of a neutron rate inunits seconds − , sometimes called the source term S , [46, 47]is used: P N F = S = P th νk eff Q fiss , (7)where P is the thermal power of the reactor, ν is the number of neutrons generated per fission, k eff is the criticality eigenvaluereported in MCNP, and Q fiss is the energy released per fission.Typical values for ν are 2.4 for U and 2.9 for
Pu. k eff is unity for a critical reactor. The Q fiss is close to 200 MeVfor uranium and plutonium isotopes [48, 49]. The PNF inHFIR MCNP simulations is assumed to be accurate becausethe models result in eigenvalues close to unity (with small sta-tistical error) and the energy dependence of ν and Q fiss arenegligible for each fissile isotope [50]. Owing to the con-stant power and little fuel evolution, the PNF changes by 0.1%throughout a cycle and is therefore considered to be constant.The goal is to calculate the core reaction rate R core for eachcandidate for each isotope i for each cell j in the model, com-bining Equation 5 in discretized form and Equation 7: R i ,core ( t ) = P th νk eff Q fiss M cells (cid:88) j =1 N p, j ( t ) λ i (cid:90) E φ j ( E, t ) σ i ( E ) dE (8)so the atomic concentration of the isotope N i in the cell M i is multiplied by the integral, i.e., the output of the MCNP re-action rate tally. Given a low half-life of the product and lowtime variation of the reaction, the core production rate is ap-proximately equal to its activity early into the cycle, i.e., A i ≈ R i ,core (9)If not replaced every cycle, some of the ν e candidatesevolve in concentration throughout several cycles. Whennecessary, the COUPLE and ORIGEN (Oak Ridge IsotopeGeneration) modules in the SCALE modeling and simulationsuite [51] are used for production, depletion, and decay ofthese isotopes. The COUPLE and ORIGEN sequences arealso used for other isotopes as a cross-check to verify con-stant concentration ( dN i /dt ≈ ) within the duration of thecycle. For COUPLE/ORIGEN, an energy group-dependentneutron flux, total flux, and BOC cell isotope concentrationsare required inputs. These inputs are obtained from the MCNPoutputs, which are generated for each day in the cycle. TheMCNP cases provide the group-spectra using a 44-group en-ergy structure, a collapsed version of the commonly used238-group structure used in neutron activation problems [51].Therefore, the MCNP stand-alone and MCNP combined withORIGEN inputs are not expected to differ substantially un-less the parent isotope has undergone significant transmuta-tion. Note that MCNP uses continuous energy cross sectionsbased on ENDF whereas the multi-group COUPLE/ORIGENapproach was based on using the MCNP binned flux spectrumand JEFF for generating one-group cross sections.The missions, design, and operation of HFIR allow for alarge number of materials to be present and irradiated dur-ing a given cycle. In searching for candidate isotopes thatcould contribute to the ν e spectrum, all areas of the reactordiscussed previously were considered. This includes isotopesin the materials that make up the structural, control element,and reflector regions in addition to the large variety of targetmaterials that can be in the FTT positions or VXFs in the re-flector region.The modeling and simulation provide high-precision calcu-lations of the isotope-dependent fission rates in the core. Thefission rate changes negligibly from . × to . × s − from BOC to EOC due to the evolution of the power dis-tribution and gamma radiation. The fission fraction of Uremains above 99.5% throughout the cycle. The fission rate isimportant in determining the ν e production from fission ver-sus ν e candidates.The uncertainty in such reactor model predictions arisesfrom a variety of components. These include, but are not lim- ited to, the uncertainty in (1) model creation such as the preci-sion to which geometry and material compositions are known,(2) nuclear data, and (3) the modeling methodology itself. Inthe first case, HFIR has a consistent loading except for targetand reflector compositions, which change from cycle to cycle.The variation is expected to be small becasue of consistentfuel loading and power distribution within the core. Previousanalysis specific to HFIR have found that geometries and iso-tope concentrations of reactor components agree well with en-gineering drawings and material specifications, but note thatthe impurity levels among fabrications may vary which canresult in changes in isotope concentrations in components inreality compared to those modeled [34, 52]. Note, the modeldetail level is higher in the fuel and near experiments of in-terest as these calculations served to provide precise neutronflux values. Therefore the uncertainty associated with modelisotope concentrations is assumed to be ≤ V. CALCULATION OF NONFUEL EXCESS IN ν e SPECTRUM
The goal of this section is to take the reaction rates calcu-lated from the previous section and convert to ν e spectra forcandidates of interest. The Oklo nuclide tool kit [58] is usedto generate ν e for U and the candidates. Oklo uses tran-sition and energy level data from ENSDF-6 [28] and cumu-lative fission yield data from the and Evaluated Nuclear DataFile (ENDF) [27]. Both of these are combined to calculate ν e spectra from fissile isotopes. The Oklo calculation for ν e spectra includes terms and corrections from several sources[9, 59, 60]. The ENSDF data alone can be used to generate ν e spectra for individual β − decays. Summation predictions of e M e V r e a c t i o n Al-28He-6Li-8Cr-55Cu-66V-52
FIG. 2: Probability density function of ν e for nonfissioncandidates. Note that Cu has an additional 9% β − branchnot mentioned in Table I, and the Li endpoint isapproximately 13 MeV. ν e spectra, such as those produced by Oklo, can have uncer-tainties as high as 10% [61].The most commonly used reference reactor ν e spectrumis that generated by Huber via conversion of experimentallymeasured a reactor electron spectrum [9]. The U spectragenerated by Oklo from Huber have small differences. Themost notable differences are in the lower energies (below theIBD threshold) and therefore not of primary interest for thiswork. The theoretical predictions from Oklo return the fission ν e spectra in 10 keV bins.The end product is a prediction of the excess ν e that areproduced from candidates with respect to those from fuel fis-sions. The excess ν e from candidates is calculated by takingthe ratio of reaction rate of candidate X to the U fission rateand multiplying by the ratio of ν e produced per reaction abovethe IBD threshold ( N ν e ): ¯ ν cand ( E )¯ ν fuel ( E ) = AZ X (n,capture) U(n,fission) N ¯ ν,X ( E ) N ¯ ν, ( E ) . (10)In this equation, N ν is the number of ν e produced above theIBD threshold per reaction. Because the fission rate is themost frequent neutron-induced transmutation in a reactor andthe fact that fission always produces more ν e than a single β − decay, both ratios will always be less than unity. The resultwill be a fraction, or excess, of ν e above threshold producedby the candidate versus those from the fission process.Figure 2 shows the ν e spectra for the nonfissile candidates(i.e., not including NpO and curium oxide [CmO] targets)from a single β − decay, i.e., the spectra N ¯ ν,X ( E ) in Equa-tion 10. Lithium-8 is the only candidate with a ν e endpointabove 3.5 MeV. The Cu distribution experiences a dip be-cause there is a 9% branch that ends at 1.6 MeV. Most distri-butions have an average ν e energy lower than the IBD thresh-old. The two exceptions are He and Li, the two productsproduced in the beryllium reflector. The next several sections discuss each of the relevant can-didates in detail, quantify their decay rates in the reactor asa function of time, and calculate the antineutrino spectrum.Some candidates will then be eliminated from consideration.The elements are grouped into three sections according to pur-pose listed in Table I: structural (Section V A), reflector (Sec-tion V B), and targets (Section V C). Reaction rates and ac-tivites are calculated in these sections. The conversion to ν e spectrum and contributions of these isotopes relative to thefission spectrum is discussed in Section V D. A. Structural
The most prominent structural materials in HFIR includeAl, Cu, Cr, and Mn. Aluminum is included in the form of Al-6061, Al-1100, and several others. When HFIR was designed,aluminum was selected because of its low fabrication and re-processing costs [34]. It also has a lower reactivity penaltythan other structural materials; the only exception is zirco-nium, which is typically more expensive but more often usedin commercial reactors as cladding. Copper, chromium, andmanganese are present in much lower quantities in the corethan aluminum.
1. Aluminum
Aluminum is the most prominent structural material inHFIR. The natural abundance of aluminum is 100% Al. Inthe FTT region, aluminum makes up dummy targets, targetrod rabbit holders in the target positions, and capsule bodies.In the IFE and OFE, it is the largest atomic contributor in theU O -Al fuel and constitutes most of the filler material, whichis the nonfuelled region located within the aluminum cladding[44]. The unfueled regions of the fuel plates and side walls ofthe IFE/OFE are also predominately composed of aluminum.It exists in all regions of the control elements, although ab-sorption is dominated by neutron poisons. Some of the reflec-tor support and HB tube cells are also of relevance.The reaction of interest for aluminum is Al(n, γ ) Alwith a β − transition to Si [62]. The transition re-leases 4.642 MeV and results in an excited state of Si at1.779 MeV; therefore the β − endpoint energy is 2.864 MeV.The half-life of Al is 2.245 minutes; therefore, it is assumedthe Al activity reaches equilibrium quickly into the cycle.In the explicit representative HFIR MCNP model, alu-minum is contained in 1,967 cells and the mass is approxi-mately 250 kg. The Al(n, γ ) core activity is calculated ac-cording to Equation 8 and ranges from 4.0 to 5.4 × s − from BOC to EOC. These values equate to approximately 15–20% of the fuel fission rate, as shown in Figure 3. The increasethroughout the cycle is mostly due to the flux increase in manyregions of the core and withdrawal of the CEs; the shape mir-rors the CE withdrawal curves in Ref. [35]. The regions thatcontribute the most to the Al activity include the IFE/OFEsidewalls, structures in the FTT, reflector container, and the A l A c t i v i t y / F i ss i o n R a t e H e A c t i v i t y / F i ss i o n R a t e FIG. 3: Al and He activities to fuel fission rate ratio foreach day in the cyclewhite (minimally absorbing) regions of the control elements[63].A COUPLE-ORIGEN model of each of the aluminum cellsis created to compare to MCNP and to evaluate the deple-tion of aluminum throughout a cycle. The 44-group neutronflux from MCNP for each cell for each day in the cycle is in-put into COUPLE-ORIGEN to generate time-dependent ac-tivities. There were some differences between the MCNPand COUPLE-ORIGEN models, but the cycle average differ-ence was 2% between the two models. The choice of neutronenergy-group structure had little impact on the Al activitiesbecause nearly all captures occur in the thermal range. Mostcells deplete less than 0.01% from BOC to EOC. The mainexception is fuel structural materials, which deplete in alu-minum by more than 1% per cycle, yet the fuel assemblies arereplaced every cycle.
2. Chromium, Copper, and Manganese
Chromium, copper, and manganese are also structural ma-terial candidates. Most of these include the steel of the targetrod rabbit holder–bearing capsules, the stainless steel ends,and trace amounts in Al-6061 materials in HB tubes andIFE/OFE sidewalls. For these particular elements, only theEOC reaction rates are calculated in MCNP. Because flux inmost core regions is higher at EOC than BOC and becausemost nonfuel materials are not depleted significantly fromBOC to EOC, these calculations are considered to be a con-servative overestimate of their average ν e emissions.Chromium-55 is produced from the (n, γ ) reaction on Cr,which has the lowest abundance and cross section of thefour naturally occurring isotopes. The half-life of Cr is3.497 minutes. The β − transition releases 2.603 MeV. Al-though Cr decays to several excited states of Mn, the mostprobable ( > . ) is the ground state [64]. The β − endpointenergy is thus assumed to be 2.603 MeV. Chromium is con-tained in 221 cells of the model, totalling 16 g. The EOC Cr activity is found to be . × s − , which is lower than thefission rate by a factor of 10 and therefore rules out Cr as acandidate.Copper-66 is produced from the (n, γ ) reaction on Cu,which has the lower abundance and cross section of thetwo naturally occurring isotopes. The half-life of Cu is5.120 minutes. The β − transition releases 2.640 MeV. Theonly transition to the ground state of Zn that has a β − end-point energy above the IBD threshold occurs approximately90.77% of the time [65]. Copper is contained in 869 cellsof the model, totalling 161 g. The EOC Cu activity is . × s − . This is approximately 0.04% of the fissionrate. This results in an excess of no more than 0.02% in 10keV ν e bins; this value is small enough to rule out Cu as acandidate.Manganese-56 is produced from the (n, γ ) reaction on Mn, which is the sole naturally occurring isotope. The half-life of Mn is 2.578 hours. The β − transition releases 3.695MeV. The main transition of interest from Mn to Fe is tothe 0.846 MeV excited state, which occurs 56.6% of the time[66]. The β − endpoint energy for this transition is therefore2.849 MeV. Manganese is present in 226 cells of the model,totalling 109 g. The EOC Mn activity is . × s − .Because the endpoint energy is low compared to other candi-dates and the reaction rate ratio is comparable to that of Cu, Mn is also ruled out as a candidate.
B. Beryllium Reflector
The beryllium reflector region is the outermost radial re-gion of the core. A fresh RB, SPB, or PB contains almost ex-clusively beryllium ( >
99% atomically). The beryllium buildsup reaction products, including neutron poisons He and Li,throughout the many irradiation cycles. The transmutationchain also involves the production of the antineutrino candi-dates He and Li. Owing to the multicycle nature of the poi-son buildup and the beryllium replacement scheme, MCNPand ORIGEN are both used to generate cycle-dependent iso-topics and decay rates from a fresh reflector.Helium-6 is produced directly from the (n, α ) reaction onberyllium-9 with a neutron threshold of 0.67 MeV. It is theprecursor reaction to the production of both neutron poisons.The half-life of He is 0.806 seconds. The released and β − endpoint energy are both 3.507 MeV because all He decaysto the ground state of Li [67]. The Be(n, α ) rate during thecycle in the entire reflector ranges from 3.80 to . × s − , which is shown in Figure 3. The He increase is sharperthan that for Al because of the higher dependence of neu-tron flux on the CE position, and this behavior follows the CEwithdrawal curves [35]. The increase is largely caused by theCE withdrawal because there is a harder neutron spectrum atthe axial ends of the reflector which increases the (n, α ) reac-tion rate. Helium-6 activity decreases by no more than 1%between cycles due to the buildup and neutron absorption on Li; therefore, it is relatively independent of cycle and age ofreflector regions.Unlike the cycle-independent activity of He, the lithium0isotopes rely heavily on the number of cycles irradiated. The Li increases in concentration until it reaches equilibrium af-ter five cycles. Because of the overwhelming (n, α ) cross sec-tion of Li, the higher isotopes Li and Li increase slowlyand linearly with irradiation time from the lower-probabilityneutron capture. The Li activity linearly increases to approx-imately 10 Bq after 50 cycles which is six orders of mag-nitude less than the fission rate. The RB, which is the mostfrequently replaced and has the largest proportion of He ac-tivity, is replaced around this cycle limit.In summary, He does produce significant activity relativeto the fission rate. Although the Li has a large β − endpointenergy, it pales in comparison to the fission reaction rate bya factor of . Thus, the Li is not considered as a candi-date. Further studies can be performed to quantify intentionalproduction of Li from lithium-filled target regions for high-energy ν e spectrum [56]. C. Target Materials
The three main target material candidates are vanadiumand the two actinide-containing targets recently irradiated inHFIR, CmO and NpO . Vanadium is a common material ir-radiated in the flux trap. The two actinide targets are used forisotope production. Table II shows the loadings of the twotypes of actinide targets for the four most recent HFIR cycles.The actinide targets are usually irradiated for multiple cyclesto produce the isotopes desired.TABLE II: Loading of materials in cycles of HFIR for CmOand NpO (number of target positions filled) with previousnumber of cycles irradiated in parentheses and vanadium(total grams in FTT). Cycle Dates (MM/DD/2018) CmO ( (
1. Vanadium
Vanadium is a target material that is primarily irradiatedin the FTT region. The representative model [35] containsmany vanadium-bearing targets. Many of these targets are notsolely composed of vanadium as a target material; the repre-sentative model contains many generic homogeneous targetsto obtain representative loading of elements. The FTT regionalso has some vanadium capsules in the PTPs and target rodrabbit holders that make up part of its composition. SincePROSPECT has begun taking data, the loading of vanadiumin the FTT region has not changed drastically.Vanadium-52 is produced from the (n, γ ) reaction on V,which is the main naturally occurring isotope. The only other naturally occurring isotope is V, which constitutes 0.25%of vanadium in nature and is not a candidate. The cross sec-tion for neutron capture on V is approximately an order ofmagnitude higher than that of V. Capture tallies in vana-dium materials showed that the ratio of captures in V to Vroughly follows this product of abundance and cross section,i.e., V(n, γ )/ V(n, γ ) is approximately 2.5%. Therefore, as-suming natural abundance, most of the neutron captures stilloccur in V despite the higher cross section of V.The half-life of V is 3.743 minutes. The β − transitionreleases 3.974 MeV. The main transition is to a 1.434 MeVexcited state of Cr, the only transition that has a β − endpointenergy above the IBD threshold, occurs approximately 99.2%of the time [68]. The endpoint energy is 2.540 MeV.To calculate approximate ν e rates from V, several simu-lated loadings of vanadium-bearing generic targets are mod-eled in several positions in the flux trap; these targets containvanadium in a similar concentration to that in the V+Ni tar-gets in the representative model [35]. Several cases are cre-ated at BOC and EOC with full-axial vanadium targets loadedinto up to 10 FTT positions. Table II shows the approximateloading in grams of vanadium (total) in the FTT region forthe past four cycles, which has typically been in the range of200–300 g. The loading in the simulation cases created herehave vanadium masses between 150 and 370 g, which coversthe entire spread of vanadium loading over the previous fivecycles.The capture rates of V (and V) are calculated on a per-gram basis for the various cases at both BOC and EOC. Linearregression is performed for the capture rate of V as a func-tion of mass in the FTT region for both BOC and EOC witha correlation coefficient > . . The number of grams fromthe four cycles can be used to calculate approximate V ac-tivities at BOC and EOC from the linear regression. The ratesrange from 1.58 to . × s − for the minimum loadingand from 1.70 to . × s − for the maximum loading ofthe previous four cycles.
2. Curium
Targets made of CmO have been irradiated in the FTT re-gion to produce
Cf in many recent cycles. The CmO targetstake up the full length of the active fuel region. Although theprimary actinide composition in the targets is Cm, they alsocontain smaller concentrations of Pu and Am [35].Calculations of CmO fission and heat generation rates havebeen performed at HFIR for safety analysis. The cycle-dependent fission rates of the CmO targets are obtained andanalyzed. The fission rates in the targets are dominated bythe fission of
Cm and
Cm, which account for morethan two-thirds of the CmO fission rates. Plutonium-241 andcalifornium-251 each contribute at the 5–12% level. The fis-sion yield data are not available for
Cm in ENDF or otherdatabases.The representative model contains five CmO targets, allnear the center of the flux trap [35]. The average fission ratesamong the five targets is between . × (BOC) and1 . × (EOC) s − . This is roughly 0.01–0.02% of thetotal core fission rate. Even with five such targets in the fluxtrap, which is considered typical for a production campaign,the fraction relative to the U fission rate would be approxi-mately 0.1%. The isotopes that contribute most to this fissionrate are
Cm and
Cm. It is assumed that the change tothe
U spectrum would be relatively unaffected by curiumfissions. The fission yield differences for the rest of the knownisotopes is not significant enough to consider the curium targetisotopes as candidates. Note, these targets were analyzed forone cycle but are typically irradiated for many. The total tar-get fission rates decrease with each subsequent cycle so thisis deemed to be a conservative estimate of multicycle CmOtarget irradiations.
3. Neptunium
Neptunium oxide (NpO ) targets have been irradiated inseveral past cycles to produce Pu for NASA. The targetsare irradiated in the VXFs for nominally three cycles. Thefission rates in the NpO targets are dominated by two iso-topes: Pu and
Np. The
Np dominates for the firsttwo cycles, and
Pu becomes the dominant contributor atthe beginning of the third cycle.The PROSPECT experiment collected data during threeNpO irradiation cycles. Nine VXFs were filled with NpO targets starting in Cycle 479 and continued into Cycle 480.Cycle 481 contained zero targets with Np and Pu. Cycle 482continued with the targets’ third and final irradiation cycle todate, which is shown in Table II.The Np and Pu fission rates are converted to ν e spectra us-ing the ENSDF and fission yield data and compared with the U nominal spectrum of HFIR. The Np ν e spectrum wascalculated using Oklo, and its resulting spectrum is compara-ble to that of U but higher by 4–8% in the 2–6 MeV energyrange. The reaction rate ratio of target to fuel fission rate isconverted to relative ν e production rate in a way that is sim-ilar to that used in Equation 10. Heat power in the reactor ismaintained at 85 MW by decreasing the fission rate of Uto offset the target (Np and Pu) fission rate; this is assumed tobe valid because the fission energy release is comparable forthe actinides. Note, the core power at HFIR has uncertaintiesof 2% due to instrument uncertainty [56]. Figure 4 shows therelative change to the nominal U ν e spectrum for the threecycles of irradiation at BOC/EOC.To only examine the impact of widely used Pu spectra,only the
Pu fission rates in the targets are compared to thatfor
U in the fuel using the Huber–Mueller data. The ratio of
Pu fissions is highest in the their third cycle of irradiation,so this case is considered for the maximum difference fromthe nominal
U spectrum. With the inclusion of the nineNpO VXFs, each containing seven targets in their third cycleof irradiation, when the
Pu contribution is the highest, the ν e spectrum decreases by no more than 0.35% in any energybin according to the Huber data. This difference is shownin Figure 4. The decrease in the spectrum below the bumpregion is largely a result of the fission rate and lower ν e yield R a t i o t o U Sp e c t r u m BOC1EOC1BOC2EOC2 BOC3EOC3BOC3 Huber-PuEOC3 Huber-Pu
FIG. 4: ν e spectrum changes from U based on Oklo forbeginning and end of a typical three-cycle irradiation of theNpO targets using the summation method. BOC/EOC3Huber-Pu includes differences in the third irradiation cyclebetween the inclusion of Pu only (no
Np) using Huberpredictions.of
Pu.
D. Cycle Average Nonfuel Contribution to ν e Spectrum
The results presented so far show that Al, He, and Vare the most significant candidates of nonfissile ν e in HFIR.The ratio of ν e spectrum, according to Equation 10, is usedto calculate cycle-average excess from the selected ν e candi-dates. For aluminum and helium, the cycle-average reactionrate is used. For vanadium, an activity corresponding to anaverage loading in the flux trap is used.Figure 5 shows the excess contributions in 200 keV binsfor the three largest contributions. Aluminum-28 contributesover 8% in the low-energy range and all three isotopes com-bine to more than 9%. The Al had by far the largest contri-bution between 1.8 and 2.86 MeV, its β − endpoint. The Hehas a peak contribution of 0.5–0.75% effect around 2.5 MeVbut drops toward its endpoint 3.5 MeV. The V contributionpeaks at about 0.5%, and its endpoint is comparable to Al.In total, these three isotopes increase the expected magnitudeof detected reactor spectra by 1%.
VI. NOTE ON COMMERCIAL REACTOR COMPARISONS
Most reactor ν e measurements have been collected at com-mercial nuclear power plants, mainly light water reactors(LWRs). The natural question arises of how nonfuel ν e mayaffect the spectrum for a commercial LWR compared to HFIR.A full analysis was not performed, but some insight can beprovided based on this analysis. The larger core size and lackof significant experimental facilities at commercial reactorsresults in less neutron activation of nonfuel materials on a per-2 R a t i o o f A n t i n e u t r i n o s t o U F i ss i o n Al-28He-6V-52Total
FIG. 5: Average excess of Al, He, and V contributionsto the ν e spectrum.fission basis. Commercial LWRs also have a small variety ofmaterials that are contained in the core. The primary nonfuelmaterials that exist in commercial LWRs include Zircaloy as acladding material and variations of stainless steels in supportstructures such as the reactor pressure vessel.Almost all of the main LWR isotopes of iron and zirconiumwould be ruled out by the ν e candidate selection process (Sec-tion II); the only exception is Zr, the isotope of zirconiumwith the lowest natural abundance. The Zr(n, γ ) Zr transi-tion has only one, albeit dominant, transition that results in a β − endpoint (1.915 MeV) slightly higher than the IBD thresh-old [69]. This transition has a half-life of 16.749 hours, whichis not negligible but longer that that of most isotopes consid-ered in this work.Chromium has one neutron capture reaction that results ina ν e above the IBD threshold, Cr. Its precursor, Cr, isthe isotope with the lowest abundance and cross section ofchromium isotopes, shown in Table I. Chromium can be con-tained in 300 series stainless steels, most commonly 304, 308,and 309 in the core structural and pressure vessel [70]. Theseforms of steel can have between 15% and 20% chromiumby mass [71]. Case studies for individual reactors and theirchromium content can be performed should precise ν e pre-dictions be needed.In summary, ν e contributions from the minor isotopes ofzirconium and chromium in LWRs are estimated to be at leastthree orders of magnitude lower than that of aluminum inHFIR. Further studies can be done to examine the activation ofzirconium or other isotopes (e.g., the chromium compositionin steels for specific commercial reactors). This effect is esti-mated to be small due to the lower ratio of absorption rate tofission rate and the lack of large quantities of chromium in thehigher flux regions of the core (i.e., near the center). The non-fuel contributions to the ν e spectrum should not be a cause forconcern for experiments at commercial reactors, such as DayaBay, Double Chooz, and RENO. VII. CONCLUSIONS
HFIR’s missions allow for a wide variety of different mate-rials to be deliberately or indirectly transmuted to β − decay-ing products during operation. Potential candidates are exam-ined to find the largest emitters of ν e that need to be accountedfor in the U spectrum from HFIR.A methodology was created to select ν e candidates fromnonfuel materials in HFIR that would contribute nominallyto the ν e spectrum. Several candidates are identified as po-tentially problematic for the ν e measurement based on theirabundance in the core, cross section, and β − endpoint en-ergy. Reactor simulations were performed to calculate reac-tion rates and ν e spectra from the nonfuel materials.The most dominant nonfuel contributors to the ν e spectrumare the Al from structural materials and He from interac-tions in the beryllium reflector. Both of these ν e contributionswere found to be relatively cycle independent and to increasewith cycle time because of the flux increase in many regionsof the reactor. The contribution to the ν e energy spectrum wascalculated. Averaged over a cycle, the Al dominates with amaximum 7% contribution near threshold to about 1% at its β − endpoint. The He has a nearly uniform 0.5–0.75% con-tribution up until its endpoint. Based on typical loadings inthe flux trap, the V has a 0.25–0.5% contribution. For allenergy ranges, these contributions combine for 1% effect inthe total detected ν e . Such contributions should be calculatedfor reactors with comparable amounts of aluminum or similarreflector design to support future neutrino experiments.The contributions of target materials have a high depen-dence on the amount and location of loading in the core. Vana-dium is identified as the target material that was calculatedto have as high as a 0.26–0.51% in the low-energy ν e range.The irradiation of NpO targets has a small but non-negligibleimpact on the ν e spectrum. The effect of the recent loadingof nine VXF positions with multicycle irradiations of NpO yield a maximum of 0.35% relative change to the nominal U spectrum at high energy. Should HFIR irradiate moretargets or irradiate them more than three cycles, it would benecessary to analyze further the contribution of
Np and
Pu because the
U fuel fission rate will decrease as a re-sult of heat power conservation. The multicycle NpO targetscontribution to the spectrum would be exacerbated with subse-quent cycles irradiated because of the increase in Pu fissionrate and its low ν e yield compared to U. The CmO targetsgenerally would not contribute significantly unless large dis-crepancies between Cm or Cf and U ν e spectra were dis-covered.In summary, this analysis shows that nonfuel reactionsmake significant contributions to the ν e spectrum at HFIR.In particular, Al, He, and V contributions should be in-cluded in the analysis for a PROSPECT-like experiment atHFIR. We suggest that reactor modeling for research reactorsmay be necessary in the development and analysis of short-baseline antineutrino experiments to account for variations inresearch reactor design. Although we only examined HFIRin detail, other nonfuel emission candidates may need to beconsidered depending on reactor composition and missions.3The findings for these isotopes in HFIR are factored intothe PROSPECT detector response matrix. Integrated overthe whole ν e spectrum, the contributions of Al and Hecombined are found to have 1% effect on the total ν e flux[72]. For HFIR specifically, nonfuel contributions are not inthe energy range high enough to contribute to the bump in themeasured spectra. VIII. ACRONYMS
BOC beginning of cycleCE control elementENDF Evaluated Nuclear Data FileENSDF Evaluated Nuclear Structure Data FileEOC end of cycleFTT flux trap target regionHFIR High Flux Isotope ReactorIBD inverse beta decayIFE/OFE inner/outer fuel elementILL Institut Laue-LangevinMCNP Monte Carlo N-ParticleORNL Oak Ridge National LaboratoryORIGEN Oak Ridge Isotope GenerationPB permanent berylliumPNF power normalization factorPROSPECT Precision Reactor Oscillation and SpectrumRB removable berylliumSPB semi-permanent berylliumVXF vertical experiment facility
IX. ACKNOWLEDGMENTS
David Chandler at HFIR was instrumental in helping withreactor modeling efforts. Dan Dwyer is acknowledged for his help using the Oklo code. Additionally, discussions with GregHirtz at HFIR were useful in identifying candidates. The fis-sion rates in the CmO targets were provided by Susan Hoglefrom ORNL.This material is based upon work supported by the follow-ing sources: US Department of Energy (DOE) Office of Sci-ence, Office of High Energy Physics under Award No. de-sc0016357 and de-sc0017660 to Yale University, under AwardNo. de-sc0017815 to Drexel University, under Award No. de-sc0008347 to Illinois Institute of Technology, under AwardNo. de-sc0016060 to Temple University, under Contract No.de-sc0012704 to Brookhaven National Laboratory, and un-der Work Proposal Number SCW1504 to Lawrence Liver-more National Laboratory. This work was performed underthe auspices of the U.S. Department of Energy by LawrenceLivermore National Laboratory under Contract DE-AC52-07NA27344 and by Oak Ridge National Laboratory underContract DE-AC05-00OR22725. Additional funding for theexperiment was provided by the Heising-Simons Foundationunder Award No. [1] K. M. Heeger, B. R. Littlejohn, H. P. Mumm, and M. N. Tobin,Phys. Rev.
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