Radiative corrections to the end point of the tritium $\beta$ decay spectrum

We compute the effect of radiative corrections on the shape of the end point in tritium beta decay. In order to obtain a correction which is finite relative to the uncorrected spectrum, it is necessary to sum the contribution of soft real photons to all orders. A technique for performing this sum taking into account the constraints of energy conservation is presented. While radiative effects make a relatively small change in the electron spectrum, they could prove important in precise end point measurements designed to determine the neutrino mass.

RADIOACTIVITY Calculation of radiative corrections to the ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ $\beta$ spectrum.