On the determination of anti-neutrino spectra from nuclear reactors

TL;DR

The paper tackles the challenge of deriving reactor antineutrino spectra from the beta-decay data of fission fragments by performing an independent inversion of the ILL beta spectra using virtual beta branches. It implements a detailed, branch-by-branch treatment of higher-order corrections to the beta spectrum, and develops a robust error framework via synthetic data to quantify bias and statistical uncertainties, with the effective nuclear charge $\bar{Z}$ playing a key role. Applied to $^{235}$U, $^{239}$Pu and $^{241}$Pu, the method yields an energy-averaged antineutrino flux shift of about $2$–$3\%$ upward relative to earlier inversions, along with significant high-energy shape differences; the uncertainty is dominated by induced-current effects, notably weak magnetism, which could offer a Standard Model explanation for the reactor antineutrino anomaly. The work provides a transparent, error-aware comparison to prior flux models and suggests that high-statistics neutrino data could discriminate between models, with implications for sterile neutrino searches. Overall, the study reinforces the importance of detailed beta-decay corrections and error propagation in reactor neutrino predictions and demonstrates a path toward more reliable flux determinations.

Abstract

In this paper we study the effect of, well-known, higher order corrections to the allowed beta decay spectrum on the determination of anti-neutrino spectra resulting from the decays of fission fragments. In particular, we try to estimate the associated theory errors and find that induced currents like weak magnetism may ultimately limit our ability to improve the current accuracy and under certain circumstance could even largely increase the theoretical errors. We also perform a critical evaluation of the errors associated with our method to extract the anti-neutrino spectrum using synthetic beta spectra. It turns out, that a fit using only virtual beta branches with a judicious choice of the effective nuclear charge provides results with a minimal bias. We apply this method to actual data for U235, Pu239 and Pu241 and confirm, within errors, recent results, which indicate a net 3% upward shift in energy averaged anti-neutrino fluxes. However, we also find significant shape differences which can in principle be tested by high statistics anti-neutrino data samples.

Figures (5)

• Figure 1: (Color online) Shown is the relative size of the various corrections listed in equation \ref{['eq:completebeta']} for a hypothetical $\beta$-decay with $Z=46$, $A=117$ and $E_0=10\,\mathrm{MeV}$. The upper panel shows the effect on the neutrino spectrum, whereas the lower panels shows the effect on the $\beta$-spectrum.
• Figure 2: (Color online) The basic inversion procedure, shown for a synthetic data set for $^{235}$U. The green (thin, gray) line shows the neutrino residuals in $50\,$keV bins and the blue (thin, black) line shows the $\beta$-residuals in $50\,$keV bins. The thick red line depicts the neutrino residuals in $250\,$keV bins.
• Figure 3: (Color online) The neutrino flux from the inversion of 1000 random realizations of a synthetic $\beta$-spectrum for $^{235}$U relative to the mean outcome of these 1000 trials. The red (thin, gray) lines show a subset of 100 trials. The thick, ragged black line shows one particular example. The smooth thick, blue (black) lines show the standard deviation in each bin, which is the same as the square root of the diagonal elements of the covariance matrix. The dark green (thick, dark gray) lines are the statistical error of the $\beta$-spectrum scaled up by a factor of 7.
• Figure 4: (Color online) The effective nuclear charge $\bar{Z}$ of the fission fragments of $^{235}$U as a function of $E_0$. The area of the each box is proportional to the contribution of that particular $Z$ to the fission yield in that energy bin. The lines are fits of quadratic polynomials: black -- ENSDF database, blue (dark gray) -- adding those isotopes missing from ENSDF by assuming that there is only one $\beta$-branch, each with $E_0=Q_\beta$, red (light gray) -- maximum pandemonium as defined in the text. The blue (dark gray, rightmost), filled boxes show the resulting distribution of adding the missing isotopes with $E_0=Q_\beta$. The red (light gray, leftmost), empty boxes show the distribution in the maximum pandemonium approximation.
• Figure 5: (Color online) Comparison of our result for $^{235}$U with previous inversions, labeled ILL for the results from Ref. Schreckenbach:1985ep and labeled 1101.2663 for the results from Ref. Mueller:2011nm. The thin error bars show the theory errors from the effective nuclear charge $\bar{Z}$ and weak magnetism. The thick error bars are the statistical errors, whereas the light gray boxes show the error from the applied bias correction. The green line, referred to as simple, shows the result, if we use the same description of $\beta$-decay as in Ref. Mueller:2011nm. The black line, referred to as ILL inversion, shows our result if we completely follow the procedure outlined in Ref. Schreckenbach:1985ep, including their effective nuclear charge.