  We study the molecular mode coupling theory for a liquid of diatomic
molecules. The equations for the critical tensorial nonergodicity parameters
${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation
${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any
further approximations.
  Here $l,m$ are indices of spherical harmonics. Contrary to previous studies,
where additional approximations were applied, we find in agreement with
simulations, that all molecular degrees of freedom vitrify at a single
temperature $T_c$. The theoretical results for the non ergodicity parameters
and the critical amplitudes are compared with those from simulations. The
qualitative agreement is good for all molecular degrees of freedom. To study
the influence of the cut off on the non ergodicity parameter, we also calculate
the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we
also propose a new method for the calculation of the critical nonergodicity
parameter
