Detector calibrations and systematic uncertainties of the precision measurement of $\beta-\bar\nu_e$ angular correlation coefficient in $^6$He decay

Precision measurement of the $\beta-\bar\nu_e$ angular correlation coefficient a can be used for searching for tensor-type weak currents. We constructed a system which detects $\beta$-particles and recoil ions from the $\beta$-decay of magneto-optical-trapped $^6$He atoms in coincidence. The time-of-flight of the $^{6}{\rm Li}$ ions guided by an electric field onto a Micro Channel Plate detector will be measured and the coefficient a can be extracted. Calibrations of the $\beta$ and recoil-ion detectors as well as estimations of systematic uncertainties via Monte Carlo simulations will be presented.