A Fermi transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin , leading to an angular momentum change  between the initial and final states of the nucleus (assuming an allowed transition). In the non-relativistic limit, the nuclear part of the operator for a Fermi transition is given by
with  the weak vector coupling constant,  the isospin raising and lowering operators, and  running over all protons and neutrons in the nucleus.