  We calculate the process $\gamma \gamma \rightarrow e^- \bar{\nu}_e u
\bar{d}$ with the full set of Feynman diagrams. We consider different
implementations of the $W$ width and different combinations of the photon
polarisations. The results of an improved narrow width approximation based on
$\gamma \gamma \rightarrow W^+ W^-$ with full spin-correlations that takes into
account different angular cuts as well as cuts on the invariant masses are
compared to those of the complete calculation.
