\subsection{QCD corrections}
\label{qcd}
The born cross section ${\sigma}_{\gamma\gamma\rightarrow t\bar{t}}^0$
for open production does not contribute
at the threshold. This behavior is caused by a factor $\beta=\sqrt{
1-4 m_t^2/s}$ from
the phase space suppressing the finite matrix element.
The order ${\alpha}_s$ corrections are
nececarry for a smoth matching between the resonance and open flavor region.
We used the formulas and the distinction between the virtuell + soft and hard
contributions given in reference \cite{bkns,guku}.
The integrations have been carried out numerically by using VEGAS
\cite{vegas} and the table of integrals in reference \cite{bkns}.
The series expansion in powers of $\beta$ off the
matrix element for these corrections contains a coefficient to the power
${\beta}^{-1}$. The ${\beta}^{-1}$ term compensates the $\beta$ from the
phase space and avoid the descent off the cross section at the threshold.
The series expansion up to linear terms is
\input{entwicklung}
It is well known that the QCD corrections in the bound state region are
given by the coefficient of the linear term of the above expansion
whereas the constant term is allready included in the potential.
The cross section can be written as
\input{skalen_funktionen}
leading to a funktion $\fgge$ which is independent of any choise of the
running coupling constants $\alpha$ and ${\alpha}_s$. This allows a precise
comparison between different results. We added the virtuell + soft part to
the hard part before the integration \cite{schuler}. We checked that $\fgge$
is cutoff independent if the cutoff is small enough. A plot of $\fgge$ is
shown in figure \ref{s_funktionen}. The agreement between our values in
table \ref{f_tabelle} and the values we received from M. Kr\"amer and
\\
\input{tabelle_f}
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild8.eps,width=12cm}}
\end{center}
\caption{Plot of $\fgge$ over ${\rho}^{-1}=\frac{s}{4 m^2_t}$}
\label{s_funktionen}
\end{figure}