Parametrization of the statistical rate function for select superallowed transitions

We present a parametrization of the statistical rate function, $f$, for 20 superallowed $0^{+}\to 0^{+}$ nuclear $\beta$ transitions between $T=1$ analog states, and for 18 superallowed “mirror” transitions between analog $T=1/2$ states. All these transitions are of interest in the determination of $V_{ud}$. Although most of the transition $Q_{EC}$ values have been measured, their precision will undoubtedly be improved in the future. Our parametrization allows a user to easily calculate the corresponding new $f$ value to high precision $(\pm 0.01$%) without complicated computing.