Precision Measurements of $\beta $-Energy Spectra in Nuclear Decays: Study of the Sensitivity to the Detector Calibration

A study of the detector calibration sensitivity for measurements of the shape of beta-energy spectra is reported using Monte Carlo simulated spectra. An auto-calibration method is proposed which can be carried out simultaneously to the actual measurements. The statistical impact of such a procedure results in a 30% larger uncertainty on the Fierz term compared to a situation in which the detector calibration was exactly known.