\subsection{Matching of reconances and continuum}
Weak decays of densely spaced high radial excitationens of $\eta_t$ lead to
a form of the cross section below the threshold that is difficult to
distinguish from continuum production in its shape and in the structure of the
final state.
Since QCD corrections are available for unpolarized photon beams only,
the initial electron and laser beams are correspondingly considered
to be unpolarized. The cross section with and without QCD
corrections is shown in Fig. \ref{effmuo}.
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild9.eps,width=12cm}}
\end{center}
\caption{Matching between perturbative and bound state region with various
renormalization scales and $m_t=150$ GeV. The best matching in the
intermediate region is obtained for $\mu=2p$.}
\label{matching}
\end{figure}
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild11.eps,width=12cm}}
\end{center}
\caption{The cross section with and without QCD corrections,
for $m_t$ = 150 GeV and $\mu=2p$.}
\label{mitundohne}
\end{figure}
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild10.eps,width=12cm}}
\end{center}
\caption{Effective cross section with (solid) and without (dashed) QCD corrections, ($\omega_0$ = 1.26 eV, $m_t$ = 150 GeV and $\mu=2p$).}
\label{effmuo}
\end{figure}
QCD corrections
enhance the effective cross sections by a large factor of about 40\% in the
region of interest. The resonance structures however, are completely
smeared and do not show up in the total cross section.
A fairly smooth transition between resonance and continuum region was obtained
by adopting for the QCD corrections the two loop formula for
$\alpha_{\overline{MS}}$, and a renormalization scale
$\muq=4p^2$, similar to the matching condition for $t\bar{t}$
production in $\eplus\eminus$ annihilation.
We assumed $\lms=200$ MeV.
%We set $\lms$ to the fixed value of 200 MeV and vary the coupling
%constant by choosing different $\muq$. Our choises for $\mu$ are $E_{CM}$,
%$m_t$,
%$p$ and $2p$, where $p$ denotes the total value of the three momentum of the
%quarks.
%The third and fourth choise leads to an infinite coupling strength at
%$s=4 m_t^2$. This behaviour of ${\alpha}_s$ near the threshold does not
%disturb
%our discussion because the coupling constant only effects the pertubativ
%expansion which is anyway not valid for $s$ close above $4 m_t^2$. For the
%calculation of the cross section in the bound state region we've used a
%program written by T. Teubner \cite{thomas} in compliance with the second
%method referted to in section \ref{resonanz}. We converted the program from
%the $\eplus\eminus$ case to the $\gamma\gamma$ case multiplying with a
%factor $\frac{8}{9}$ established by the considerations of section
%\ref{born_niveau} and \ref{resonanz}
%and a factor $1-\frac{4}{3}\frac{{\alpha}_s}{\pi}\left(5-\frac{{\pi}^2}{4}
%\right)$ with ${\alpha}_s={\alpha}_s \left(2 \mt\right)$ due to the exchange
%of transverse gluons as mentioned in section \ref{qcd}.
%The plots in fig.
%\ref{matching} are for $m_t$ = 150 GeV and a $V_j$-potential \cite{scenario}:
%\input{v_j}
%where
%\input{v_f}
%We have adopted the following set of parameters:
%\input{v_j_parameter}
In Fig. \ref{diff} the effective differential mass distribution
$$ \frac{d\sigma}{dz}=\frac{dL}{dz}\sigma\left(z^2 s\right)$$
is displayed for a $ee$ center of mass energy of 500 GeV.
Given high counting rates and a detector with sufficiently good
mass resolution the resonant structures could be recovered.\\
\begin{figure}
\begin{center}
\mbox{\epsfig{file=bild18.eps,width=12cm}}
\end{center}
\caption{The effective differential mass distribution for a $ee$ center
of mass energy of 500 GeV}
\label{diff}
\end{figure}
\noindent
{\bf To summarize:}\\
Top quark production at a Compton collider has been studied.
The importance of providing polarized laser and electron beams
has been stressed and the impact of this polarization on the
production rate has been demonstrated. QCD corrections to the
reaction without polarization have been calculated
and found to be large.\\[8mm]
\noindent
{\bf Acknowledegement:}\\[1mm]\nopagebreak
We thank M. Kr\"amer, P. Zerwas and J. Zunft for discussions and for
communicating us their results prior to publication and M. Jezabek and
T. Teubner
for providing the program for calculating the Greensfunction.\\[1cm]
{\bf Appendix:}\\[1mm]\nopagebreak
The functions $\Phi_i$ characterizing the differntial luminosities are
given as follows.
\input{phi}
\input{la}
\input{lb}
\input{lc}