Exact relativistic tritium β-decay endpoint spectrum in a hadron model

Abstract

We present the relativistic calculation of the \ensuremath{\beta}-decay of tritium in a hadron model. The elementary particle treatment (EPT) of the transition $^{3}\mathrm{H}$ $\ensuremath{\rightarrow}$$^{3}\mathrm{He}$ $+{e}^{\ensuremath{-}}+{\overline{\ensuremath{\nu}}}_{e}$ is performed in analogy with the description of the \ensuremath{\beta}-decay of neutron. The effects of higher order terms of hadron current and nuclear recoil are taken into account in this formalism. The relativistic Kurie function is derived and presented in a simple form suitable for the determination of neutrino masses from the shape of the endpoint spectrum. A connection with the commonly used Kurie function is established.