Knowledge Bank

The problem of nuclear hyperfine interactions in spherical rotors has been solved by the methods of group theory. From this solution, the energy levels for the complete spin-rotation and dipoledipole interactions for a simple tetrahedral molecule have been determined. The frequencies for transitions corresponding to the reorientation of the total spin with respect to a large external magnetic field have been calculated, and the resulting theoretical spectrum has been generated on a high-speed computer. Experimental $data1$ on $CH4,SiH4$ and $GeH4$ have been fitted in terms of this theory, and the corresponding spin rotation constants have been evaluated. The results for $CH4$ agree with the earlier measurements of Anderson and $Ramsey2$, obtained by a different method. The solution of this problem should simplify the analysis of many experiments that involve spherical tops, both in resonance work and in nuclear spin relaxation. This theory also predicts the existence of certain symmetry-breaking transitions between states of different total nuclear spin. These transitions have been observed in methane by means of a level-crossing technique. From the data, it has been possible to measure accurately, for the first time, the centrifugal distortion constant $Dt$ in a spherical rotor. $Dt=+(140.3\pm 1.0)kHz.$ This value agrees with Hecht's earlier $estimate3$ of the magnitude of this constant from infrared data. It should be possible with existing experimental techniques, to apply this beam method to many other spherical rotors.