New realization of the conversion calculation for reactor antineutrino fluxes

Validation of the effective conversion method in the reactor antineutrino flux calculation is examined using the ab initio calculation of the electron and antineutrino spectra from the state-of-the-art nuclear database. It turns out that neglecting the shape variation of beta decay branches between the allowed and forbidden transitions would induce significant bias in the total inverse-beta-decay yields and energy spectral distributions. We propose a new realization of the conversion method with both the allowed and forbidden virtual branches, and apply it to both the simulated data from the nuclear database and real data from the fission measurements at Institut Laue-Langevin by virtue of statistical properties of the allowed and forbidden decays in the database. Two kinds of dominant uncertainty sources are identified and it turns out that the new realization of the conversion calculation can largely reduce the rate and spectral bias and thus present a reliable prediction of the antineutrino fluxes if accurate beta decay information is available in the high end point energy range.

Figure 1

The antineutrino spectra with different decay transition types with $Z=47$, $A=117$ for the daughter nucleus and $E_0-m_e=10\mathrm{MeV}$. The left, middle and right panels are for the cases of forbidden GT transitions of $0^{-}$, $1^{-}$ and $2^{-}$ respectively. The black lines are the shape of allowed GT transitions. The red dotted and blue dashed lines stand for the spectra obtained in the plane wave approximation (PWA) and the exact relativistic calculation (ERC) of the Dirac wave function respectively. The ratios between the allowed and forbidden spectra are also shown in the corresponding lower panels.

Figure 2

The relative ratios of different beta decay transitions as the function of the end point energy for the ${}^{235}\mathrm{U}$ fission isotope.

Figure 3

The relation between the effective nuclear charge number $\overline{Z}$ and end point energy $E_0-m_e$ for the ${}^{235}\mathrm{U}$ fission isotope. All the decay branches are assumed to be the allowed GT transition in the left panel, and the results for the allowed and forbidden transitions are illustrated separately in the right panel. The second-order polynomial curves are fitted as the dashed or dashed and dash-dotted lines in the left and right panels.

Figure 4

The ratios of the true electron or antineutrino spectra of the ab initio calculations to the corresponding converted spectra for ${}^{235}\mathrm{U}$, where case A assumes all the branches are the allowed GT transition (first panel), and cases B, C, and D assume that the nonunique forbidden decays are subject to the GT $0^{-}$ transition (second panel), the GT $1^{-}$ transition (third panel) or a mixture of GT $0^{-}$ and $1^{-}$ transitions (fourth panel). The unique forbidden decays are taken as the GT $2^{-}$ transition for the last three cases.

Figure 5

The ratios of the true antineutrino spectra of the ab initio calculations to the corresponding converted spectra for ${}^{235}\mathrm{U}$, where all the forbidden transitions are treated as the GT $0^{-}$ (upper panel), $1^{-}$ (middle panel), and $2^{-}$ (lower panel) transitions respectively. The cases of conversions with all allowed virtual branches are shown in black lines and the cases of conversions with both allowed and forbidden virtual branches are shown in red lines. The red shadowed bands are shown as the standard deviations of 100 converted antineutrino spectra.

Figure 6

The ratios of the converted ${}^{235}\mathrm{U}$ antineutrino spectra after and before changing the relative ratios in the selected end point energy windows, where a benchmark requirement of the spectral deviation better than 3% is assumed. The contributions of the allowed and GT $2^{-}$ transitions are fixed to their true values of Fig. 2.

Figure 7

Conversion results of the ILL ${}^{235}\mathrm{U}$ beta spectrum using allowed GT transitions. The ratio is defined as the fitted spectrum to the ILL data for electrons, whereas it is the ratio of the fitted spectrum to the model prediction of Ref. [16] for antineutrinos.

Figure 8

Conversion results of the ILL ${}^{235}\mathrm{U}$ beta spectrum using both allowed and forbidden transitions. The first, second, and third panels are the results for the GT $0^{-}$, $1^{-}$, $2^{-}$ respectively, and the ratio is defined as the fitted spectrum to the ILL data for electrons, and as the converted spectrum using both allowed and forbidden virtual transitions to the spectrum using only the allowed transition for antineutrinos. The red shadowed bands are shown as the standard deviations of 100 converted antineutrino spectra.

Figure 9

Conversion results of the ILL ${}^{235}\mathrm{U}$ beta spectrum using both allowed and all types of GT $0^{-}$, $1^{-}$, $2^{-}$ forbidden transitions. the ratio is defined as the fitted spectrum to the ILL data for electrons, and as the converted spectrum using both allowed and forbidden virtual transitions to the spectrum using only the allowed transition for antineutrinos. The red shadowed bands are shown as the standard deviations of 100 converted antineutrino spectra.