Determination of antineutrino spectra from nuclear reactors

In this paper we study the effect of well-known higher-order corrections to the allowed $\beta$-decay spectrum on the determination of antineutrino 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 greatly increase the theoretical errors. We also perform a critical evaluation of the errors associated with our method to extract the antineutrino 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 ${}^{235}$U, ${}^{239}$Pu, and ${}^{241}$Pu and confirm, within errors, recent results, which indicate a net $3\%$ upward shift in energy-averaged antineutrino fluxes. However, we also find significant shape differences which can, in principle, be tested by high-statistics antineutrino data samples.

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Figure 1

Relative size of the various corrections listed in Eq. (4) for a hypothetical $\beta$ decay with $Z=46$, $A=117$, and $E_0=10\mathrm{MeV}$. The top panel shows the effect on the neutrino spectrum, whereas the bottom panel shows the effect on the $\beta$ spectrum.

Figure 2

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

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

The effective nuclear charge $\overline{Z}$ of the fission fragments of ${}^{235}$U as a function of $E_0$. The area of 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), with addition of 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 obtained by addition of 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

Comparison of our result for ${}^{235}$U with previous inversions, labeled ILL for the results from Ref. [7] and 1101.2663 for the results from Ref. [6]. The thin error bars show the theory errors from the effective nuclear charge $\overline{Z}$ 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. [6]. The black line, referred to as ILL inversion, shows our result if we completely follow the procedure outlined in Ref. [7], including the effective nuclear charge given there.