The beta asymmetry in neutron beta decay is used to determine the ratio of axial-vector coupling to vector coupling most precisely. In electron spectroscopy, backscattering of electrons from detectors can be a major source of systematic error. We present the determination of the correction for undetected backscattering for electron detection with the instrument PERKEO III. For the electron asymmetry, undetected backscattering leads to a fractional correction of $5times 10^{-4}$, i.e. a change by 40% of the total systematic uncertainty.
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