Radiative Correction to the anti-nu_e (nu_e) Spectrum in beta-Decay

We derive an analytic expression for the O(alpha) radiative correction to the anti-nu_e (nu_e) spectrum in allowed beta-decay. The m -> 0 limit is convergent and leads to a very simple result (m is the electron mass). This is in sharp contrast to the correction to the e^- (e^+) spectrum, that diverges as m -> 0, an important difference that we explain on theoretical grounds. After discussing some of their general properties, we use the corrections to the anti-nu_e and e^- spectra to derive the corresponding correction to the e^- -> anti-nu_e conversion, a relation that is of considerable interest for reactor studies of neutrino oscillations.