Reliability of usual assumptions in the calculation of $β$ and $ν$ spectra

International audienceTo test the relevance of the most common assumptions in the calculation of beta ($β$) and neutrino ($ν$) spectra, a database of measured shape factors was created, containing 130 distinct transitions. Some analysis parameters were defined to characterize the quality of the calculated spectra. Results from this systematic comparison between theory and experiment are presented in detail. The $\lambda_{k}=1$ approximation for forbidden unique transitions is shown to be systematically worse than the correct calculation of the theoretical shape factors, where the energy dependence of the $\lambda_{k}$ parameters is included. Regarding forbidden nonunique transitions, the $\xi$ approximation is found to be valid for only about half of the first forbidden nonunique transitions and incorrect in all other cases. The criterion $2\xi/E_0≫1$ is proved to be insufficient in itself if $2\xi/E_0