We study the molecular mode-coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\mathbf{F}}_{{\mathrm{ll}}^{\prime }}^m\mathrm{}\left(q\right)\mathrm{}$ and the critical amplitudes of the $\beta$ relaxation ${\mathbf{H}}_{{\mathrm{ll}}^{\prime }}^m\mathrm{}\left(q\right)\mathrm{}$ are solved up to a cutoff $l_{\mathrm{co}}=2\mathrm{}$ 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 nonergodicity 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 cutoff on the nonergodicity parameter, we also calculate the nonergodicity parameters for an upper cutoff $l_{\mathrm{co}}=4.\mathrm{}$ In addition, we also propose a method for the calculation of the critical nonergodicity parameter from the liquid side of transition.

• Received 17 July 2000

DOI:https://doi.org/10.1103/PhysRevE.62.8004