Weak Magnetism Correction to Allowed Beta-decay for Reactor Antineutrino Spectra

The weak magnetism correction and its uncertainty to nuclear β decay play a major role in determining the significance of the reactor neutrino anomaly. Here in this paper, we examine the common approximation used for one-body weak magnetism in the calculation of fission antineutrino spectra, wherein matrix elements of the orbital angular-momentum operator contribution to the magnetic-dipole current are assumed to be proportional to those of the spin operator. Although we find this approximation invalid for a large set of nuclear structure situations, we conclude that it is valid for the relevant allowed β decays between fission fragments. In particular, the uncertainty in the fission antineutrino due to the uncertainty in the one-body weak magnetism correction is found to be less than 1%. Thus, the dominant uncertainty from weak magnetism for reactor neutrino fluxes lies in the uncertainty in the two-body meson-exchange magnetic-dipole current.