Measurement of Individual Antineutrino Spectra from $\mathbf{^{235}U}$ and $\mathbf{^{239}Pu}$ at Daya Bay

This letter reports a new measurement of the prompt energy spectrum of reactor antineutrinos and the first measurement of individual spectra from $^{235}$U and $^{239}$Pu at Daya Bay. The analysis uses 3.5 million inverse beta decay (IBD) candidates in four near antineutrino detectors in 1958 days. The shape of the measured IBD prompt energy spectrum disagrees with the prediction of the Huber-Mueller model at $5.3\sigma$. In the energy range of 4--6~MeV, a maximal local discrepancy of $6.3\sigma$ is observed. The individual spectra of the two dominant isotopes, $^{235}$U and $^{239}$Pu, are extracted using the evolution of the prompt spectrum as a function of the isotope fission fractions. In the energy window of 4--6~MeV, a 7\% (9\%) excess of events is observed for the $^{235}$U ($^{239}$Pu) spectrum compared with the normalized Huber-Mueller model prediction.

This letter reports a new measurement of the prompt energy spectrum of reactor antineutrinos and the first measurement of individual spectra from 235 U and 239 Pu at Daya Bay. The analysis uses 3.5 million inverse beta decay (IBD) candidates in four near antineutrino detectors in 1958 days. The shape of the measured IBD prompt energy spectrum disagrees with the prediction of the Huber-Mueller model at 5.3σ. In the energy range of 4-6 MeV, a maximal local discrepancy of 6.3σ is observed. The individual spectra of the two dominant isotopes, 235 U and 239 Pu, are extracted using the evolution of the prompt spectrum as a function of the isotope fission fractions. In the energy window of 4-6 MeV, a 7% (9%) excess of events is observed for the 235 U ( 239 Pu) spectrum compared with the normalized Huber-Mueller model prediction.
Nuclear reactors are powerful sources of electron antineutrinos (ν e ) and have played an important role in neutrino physics. Most recently, Daya Bay [1][2][3][4][5][6], RENO [7,8], and Double Chooz [9,10] reported observations of neutrino oscillation induced by a non-zero mixing angle θ 13 . In addition, these experiments also provided measurements of reactorν e flux and spectrum [11][12][13][14] at distances of 300-500 m from the reactors. The flux measurements confirmed the ∼6% deficit found in the 2011 re-evaluation [15,16] of the reactorν e flux ("Reactor Antineutrino Anomaly" [17]). The measurement of an evolution of reactorν e flux with the fission fractions at Daya Bay suggested that 235 U, among the four major isotopes ( 235 U, 239 Pu, 238 U and 241 Pu), may be the primary contributor to the flux anomaly [18]. The spectral measurements indicated a new anomaly ("5-MeV bump") when compared with theoretical calculations, an observation further confirmed by NEOS [19], and by re-examination of earlier reactor antineutrino data [20]. Observation of evolution of the reactorν e spectrum from commercial reactors [18,[21][22][23] and measurement of the 235 Uν e spectrum from highly enriched uranium research reactors [24,25] have also been performed, providing first glimpses at the dependence of spectral features on reactor fuel content. Additional precision measurements are essential to fully investigate the origins of the reactorν e flux and spectrum anomalies, and provide crucial inputs to future reactor neutrino experiments [26].
This letter reports a new measurement of the prompt energy spectrum of reactorν e at Daya Bay with three times moreν e events and reduced systematic uncertainties compared with previous results [12]. Furthermore, the individual prompt energy spectra of two dominant isotopes ( 235 U and 239 Pu) are obtained for the first time by fitting the evolution of the prompt energy spectrum as a function of fission fractions from commercial reactors. A combined measurement of the 239 Pu and 241 Pu spectra is also reported with uncertainties reduced from that obtained for 239 Pu alone.
The Daya Bay Reactor Neutrino Experiment is located near the Daya Bay nuclear power complex, which hosts six commercial pressurized-water reactors (2.9 GW maximum thermal power). Identically designedν e detectors (ADs) are deployed in two near halls (EH1 and EH2) containing two ADs each and in the far hall (EH3) with four ADs. Each AD contains 20 tons of gadolinium-doped liquid scintillator (GdLS) serving as the primaryν e target. The analysis uses 1958 days of data from four near ADs which involves four to six refueling cycles for each reactor core. Details about the experiment and the data set are given in Ref. [6,27]. In a typical commercial reactor, antineutrinos are produced from thousands of beta decay branches of the fission products. Theν e spectrum is measured with inverse beta decay (IBD) reactions:ν e +p → e + +n. The predictedν e energy spectrum in a detector at a given time t is calculated as where E ν is theν e energy, d is the detector index, r is the reactor index, N d is the target proton number, d is the detection efficiency, L rd is the distance from detector d to reactor r, P ee (E ν , L rd ) is theν e survival probability in the standard three-neutrino model, and σ(E ν ) is the IBD cross section. The energy spectrum of antineutrinos from one reactor is where W r (t) is the thermal power of reactor r, e i is the energy released per fission for isotope i, f ir (t) is the fission fraction, s i (E ν ) is theν e energy spectrum per fission for each isotope, c ne i (E ν , t) is a function of the order of unity absorbing the correction to the energy spectrum due to nonequilibrium effects of long-lived fission fragments, s SNF (E ν , t) and s NL (E ν , t) are contributions from spent nuclear fuel (SNF) and from nuclides withν e flux with a nonlinear dependence on reactor neutron flux [28], respectively.
For s i (E ν ) in Eq. 2, the 235 U, 239 Pu, and 241 Puν e spectra from Huber [16] and 238 U spectrum from Mueller [15] are used in the prediction (Huber-Mueller model). Thermal power and fission fraction data are provided by the Daya Bay nuclear power plant with uncertainties of 0.5% and 5% [12], respectively. The correlations of fission fractions among the four isotope are taken from Ref. [12]. The energies released per fission (e i ) are taken from Ref. [29].
In contrast to previous Daya Bay analyses, the nonequilibrium correction and contributions from SNF and nonlinear nuclides are estimated and added to the flux prediction with time evolution. Long-lived fission fragments are accumulated during the fuel burning and are not in equilibrium for fresh fuel at the start of each refueling cycle. The nonequilibrium effect exists for ILL measurements [30][31][32], which are the basis of the Huber-Mueller model, due to a limited irradiation time. The correction of the nonequilibrium effect (0.7%) for each batch of fuel elements is calculated daily based on the irradiation time [15]. The SNF (0.2%), including contribution from the storage water pool and the shutdown reactor core, is calculated daily using the refueling history provided by the power plant. Theν e flux from some nuclides has a nonlinear dependence on the neutron flux in a reactor core [28]. The correction for these nonlinear nuclides is obtained as a function of time based on information provided by the power plant and contributes < 0.1% of the totalν e flux.
The ∼3.5 million IBD candidates in the four near ADs and the expected backgrounds from Ref. [6] are used in this analysis. The accidental and Am-C correlated backgrounds are estimated daily in each AD. The cosmogenic 9 Li/ 8 He, fast neutron, and 13 C(α, n) 16 O backgrounds are treated as constants in time. The IBD detection efficiency is 80.25% with a correlated uncertainty of 1.19% [33] and an uncorrelated uncertainty of 0.13% among ADs. The oscillation parameters sin 2 2θ 13 = 0.0856 ± 0.0029 and ∆m 2 ee = (2.522 +0.068 −0.070 ) × 10 −3 eV 2 from Ref. [6] are used to correct for the oscillation effect, namely P ee (E ν , L rd ) in Eq. 1.
The time-averaged IBD yield, defined as the number of antineutrinos per fission times IBD cross section, is measured to be (5.94 ± 0.09) × 10 −43 cm 2 /fission, where the statistical uncertainty is 0.05% and the systematic uncertainty is 1.5% taken from Table 1 in Ref. [33]. The corresponding average fission fractions for the four major isotopes 235 U, 239 Pu, 238 U and 241 Pu are 0.564, 0.304, 0.076, 0.056, respectively. The ratio of the measured IBD yield to the Huber-Mueller model prediction is 0.953 ± 0.014 (exp.) ±0.023 (model).
The predicted prompt energy spectrum is determined from theν e spectrum taking into account the effects of IBD kinematics, energy leakage and energy resolution. A model of the nonlinear energy response is used to correct the measured prompt energy spectrum of the IBD candidates [34] to facilitate comparison of spectra between different experiments [35]. The magnitude of the nonlinear correction is ∼10% at maximum with a 0.5% uncertainty at 3 MeV [34], improved from 1% previously [12]. Figure 1 shows the spectrum comparison of the measurement with the Huber-Mueller model prediction normalized to the measured number of events. The measurement and prediction show large discrepancy particularly near 5 MeV. With a sliding 2-MeV window scanning following Ref. [12], the largest local discrepancy is found in 4-6 MeV, with a significance of 6.3σ. The global discrepancy of the entire spectrum in 0.7-8 MeV has a significance of 5.3σ.  The evolution of fission fractions of the four major isotopes in multiple refueling cycles is shown in Fig. 2 for the six reactors during operation. The dominant isotopes contributing to the prompt spectrum are 235 U and 239 Pu, as their fission fractions add up to ∼87%. During a typical refueling cycle, 239 Pu is accumulated with fission fractions increasing from 15% to 38% while 235 U is consumed with fission fractions decreasing from 75% to 45%.
Each isotope produces a uniqueν e spectrum depending on its fission products and corresponding beta-decay spectra [36,37]. Since the observed prompt energy spectrum in one AD is a combination of the individual spectra of four isotopes, it evolves as a function of fission fractions [18,22,38]. In order to describe the relative contribution of each isotope in one AD from the six reactors, we define an effective fission fraction for isotope i observed by detector d as The variation of detector-wise effective fission fraction of 235 U ( 239 Pu) is 50%-65% (24%-35%), smaller than the variation of reactor-wise fission fraction.
To explore the evolution of the IBD prompt energy spectrum, the data are divided into 20 groups ordered by the 239 Pu effective fission fraction in each week for each AD. The evolution of the prompt energy spectrum is dominated by 235 U and 239 Pu, while it is less sensitive to 238 U and 241 Pu due to smaller fission fractions. To extract the individual spectra of the 235 U and 239 Pu isotopes, s 5 (η 5 ) and s 9 (η 9 ) respectively, from the prompt energy spectrum, a χ 2 function in the Poisson-distributed form is constructed as where d is the detector index, j is the index of the data groups, k is the prompt energy bin, M djk is the measured prompt energy spectrum of each data group, is a set of nuisance parameters, f ( , Σ) is the term to constrain the nuisance parameters incorporating systematic uncertainties and their correlations (Σ) among the reactors, detectors, and data groups, and is the corresponding expected prompt energy spectrum without normalization, s 5 k (η 5 k ) (s 9 k (η 9 k )) is the element of extracted 235 U ( 239 Pu) spectrum at energy bin k, α k ( ) (β k ( )) is the corresponding coefficient for the 235 U ( 239 Pu) taking into account the detector target mass, detection efficiency, baseline and number of fissions, s 238+241 k ( ) is the expected prompt energy spectra contributed from 238 U and 241 Pu, and c k ( ) includes contributions from the SNF, nonlinear nuclides, and backgrounds. The Huber-Mueller flux model is used to calculate the initial prompt energy spectrum for the four isotopes. Two sets of free parameters, η 5 and η 9 , are applied to the 26 energy bins correcting the initial 235 U and 239 Pu spectra, respectively. As a result, the individual 235 U and 239 Pu spectra corrected with the best fit values of η 5 and η 9 do not depend on the input of the initial spectra. For the 238 U and 241 Pu spectra, nuisance parameters are incorporated to vary the initial spectra within their uncertainties. We conservatively enlarge the uncertainties of the 238 U and 241 Pu spectra quoted in the Huber-Mueller model based on the investigations of the antineutrino spectrum evaluations from nuclear databases [15,17]. For the 238 U spectrum, the uncertainty is 15% in 0.7-4.5 MeV, 20% in 4.5-6 MeV, 30% in 6-7 MeV and 60% in 7-8 MeV, and for 241 Pu it is 10% in 0.7-7 MeV and 50% in 7-8 MeV. Additional normalization uncertainties of 15% and 10% [18] are assigned to the 238 U and 241 Pu spectra, respectively.
The time-dependence of reactor antineutrino production and detector response, and their impact on the 235 U and 239 Pu spectra, are examined. The drift of the energy scale is controlled to less than 0.1% using the calibration data and has negligible effect. The relative variation of energy resolution in the 20 data groups is 3% and has negligible effect on the extracted spectra. Therefore, the detector energy response [12] is treated as stable in the data-taking period, with its uncertainty treated as time-independent. The uncertainties of reactor power and fission fractions are treated as correlated between the data groups, and treating them as uncorrelated has a negligible effect in this analysis.
Removing the timedependence of the nonequilibrium effect, SNF and nonlinear nuclides produces a shift of less than 0.7% in the IBD yields of 235 U and 239 Pu.
The top panel of Fig. 3 shows the extracted 235 U and 239 Pu spectra together with their Huber-Mueller predictions normalized to the best-fit numbers of events for 235 U (0.920) and 239 Pu (0.990), respectively. In the middle panel, the ratios of the extracted spectra to the corresponding predicted spectra for 235 U and 239 Pu are shown. An edge around 4 MeV is found in the 239 Pu spectrum compared to the prediction.
Analysis with different data grouping, or analysis with only EH1 or EH2 data shows a similar edge. In the energy window of 4-6 MeV, a 7% (9%) excess of events is observed for 235 U ( 239 Pu) spectrum compared with the normalized Huber-Mueller model prediction. A χ 2 test is performed to quantify the local discrepancy between the extracted 235 U and 239 Pu spectra and their corresponding predicted spectra following the method in Ref. [12]. As shown in the bottom panel of Fig. 3, the maximum local discrepancy is 4.0σ for the 235 U spectrum, and only 1.2σ for the 239 Pu spectrum because of larger uncertainties. If the 239 Pu spectrum is fixed to have the same spectral shape discrepancy as the 235 U spectrum in 4-6 MeV, we obtain a change in the χ 2 value, ∆χ 2 /ndf = 4.0/8, corresponding to a 0.2σ inconsistency. Thus, the Daya Bay data indicates an incorrect prediction of the 235 U spectrum, but such a conclusion cannot be drawn for the other primary fission isotopes. Combining the results of IBD yield and spectral shape, we deduce that the 8% deficit of 235 U IBD yield is dominated by the deficit in the energy range below 4 MeV with a significance of 4σ with respect to the Huber-Mueller model prediction without normalization.  The fractional size of the diagonal elements of the covariance matrix is shown in the bottom panel of Fig. 4, which is 4% for 235 U and 9% for 239 Pu around 3 MeV. The statistical uncertainty contributes to about 55% (60%) of the total uncertainty of 235 U ( 239 Pu). The uncertainties from the input 238 U and 241 Pu spectra and rate contribute about 35% for both 235 U and 239 Pu. The other uncertainties contribute to about 10% (5%) for 235 U ( 239 Pu). The spectral uncertainties of 235 U and 239 Pu are anti-correlated with correlation coefficients between −0.8 and −0.3. Any comparison of the 235 U or 239 Pu spectra with reactor flux models should take into account the correlations. The 235 U and 239 Pu spectra as well as their associated covariance matrix are provided in the Supplemental Material [39]. An independent analysis based on Bayesian inference using Markov Chain Monte Carlo with different data grouping obtains consistent results.
The extracted spectra of 235 U and 239 Pu have a certain dependence on the inputs of the 238 U and 241 Pu spectra. The 239 Pu spectrum has a larger uncertainty than 235 U because it has a smaller fission fraction and a strong correlation with 241 Pu. The fission fraction of 241 Pu is approximately proportional to 239 Pu as shown in Fig. 2, thus they can be treated as one component in the contribution to the prompt energy spectrum. A combination of 239 Pu and 241 Pu spectra (s 239 and s 241 ), as an invariant spectrum independent of the fission fractions, is defined as s combo = s 239 + 0.183 × s 241 . The coefficient of 0.183 is the average fission fraction ratio of 241 Pu to 239 Pu in 1958 days, shown as a line in Fig. 2. For 20 data groups, the fission fraction ratios of 241 Pu to 239 Pu evolve from 0.164 to 0.202 for the AD1 and AD2 in EH1, and from 0.171 to 0.191 for the AD3 and AD4 in EH2. The residual contribution of 241 Pu spectrum is corrected using Huber-Mueller model for some data groups when the fission fraction ratios of 241 Pu to 239 Pu deviate from 0.183. With this combination of 239 Pu and 241 Pu, the dependence on the input 241 Pu spectrum is largely removed. The top panel of Fig. 4 shows the extracted 235 U spectrum and s combo compared with the normalized Huber-Mueller model predictions. The obtained 235 U spectrum and its uncertainty have negligible differences from the results shown in Fig. 3, since the systematic uncertainty of 235 U spectrum is dominated by the input 238 U spectrum instead of 241 Pu. The bottom panel shows the uncertainties of extracted spectra. The uncertainty of s combo is 6% around 3 MeV, improved from 9% in the case of no combination. The maximal local significance of the spectral shape deviation is 1.4σ in the energy range of 4-6 MeV between the combined spectrum of 239 Pu and 241 Pu and the model prediction. The combined spectrum of 239 Pu and 241 Pu can be used to predict theν e spectrum with higher precision in experiments with a similar fission fraction ratio of 241 Pu to 239 Pu.
In summary, an improved measurement of the prompt energy spectrum of reactorν e is reported with a more precise energy response model and 1958 days of data from Daya Bay. The discrepancy between the measured spectrum shape and the prediction is found to be 5.3σ and 6.3σ in the entire energy range of 0.7-8 MeV and in a local energy range of 4-6 MeV, respectively. The IBD yields and prompt energy spectra of 235 U and 239 Pu as the two dominant components in commercial reactors are obtained using the evolution of the prompt spectrum as a function of fission fractions. A comparison of the measured and predicted 235 U and 239 Pu IBD yields prefers an incorrect prediction of the 235 U flux as the primary source of the reactor antineutrino rate anomaly. The spectral shape comparison shows similar excesses of events in 4-6 MeV for both 235 U (7%) and 239 Pu (9%). The discrepancy of 4.0σ in the comparison of spectrum shape for 235 U suggests incorrect spectral shape prediction for the 235 U spectrum. However, no such conclusion can be drawn for the 239 Pu spectrum due to a larger uncertainty.