Development of a 4$\pi$ detection system for the measurement of the shape of $\beta$ spectra
Résumé
The need of precise measurements of the energy distribution of emitted β particles has been addressed developing a specific detection system. An ultra-thin radioactive source, prepared on purpose, is enclosed between two silicon detectors in a compact geometry with a quasi-4π sr solid angle. The remaining distortions have been corrected with a dedicated deconvolution process based on mono-energetic Monte Carlo simulations that are used to build the response matrix. The β spectra from $^{14}$C and $^{204}$Tl decays have been measured and analysed. Extracted maximum energies are fully consistent with the AME2020 recommended Q-values. A linear slope of a = -0.430 (23) MeV$^{-1}$ that comes from the weak magnetism term in $^{14}$C spectrum has been determined, in excellent agreement with the theoretical predictions. Knowledge of the $^{204}$Tl spectrum has been extended down to 60 keV and a
shape factor ($dq^2$ + $\lambda_2p^2$) has been extracted with $d$ = 1.075 (7)