  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 $5\times 10^{-4}$, i.e. a change by 40% of the total
systematic uncertainty.
