First-forbidden transitions in the reactor anomaly

We study the dominant forbidden transitions in the antineutrino spectra of the fission actinides from 4 MeV onward using the nuclear shell model. Through explicit calculation of the shape factor, taking into account Coulomb corrections, we show the expected changes on cumulative electron and antineutrino spectra. Compared to the usual allowed approximation this results in a minor decrease of electron spectra from 4 MeV and onward, whereas an increase of several percent is observed in antineutrino spectra. We show that, despite their limited number, forbidden transitions dominate the spectral flux for most of the experimentally accessible range. Based on the shell model calculations we attempt a parametrization of forbidden transitions and propose a spectral correction for all forbidden transitions. We enforce correspondence with the ILL dataset using a summation+conversion approach. When compared against modern reactor neutrino experiments, the resultant spectral change is observed to be of comparable magnitude and shape as the reported spectral shoulder, drastically decreasing the statistical significance of the latter.