One-centre matrix elements of the spin-other orbit operator in linear molecules: diagonal terms

The quasi-elastic scattering of cold neutrons from liquid and solid C₆H₆ and C₆D₆ has been measured at temperatures between 260 K and 325 K for incident wavelengths between 4·07 Å and 7·05 Å and for angles of scatter between 20° and 90° by means of a chopper time-of-flight apparatus. From the results, the total quasi-elastic intensity and the width of the corresponding broadening, presumed Lorentzian, were extracted. The broadening of the incoherent component in the scattering is discussed in terms of various models designed to combine the effects of centre of mass and jump rotational diffusion. All the models could be fitted to the results, using a root-mean-square jump length approximately equal to the nearest H-H distance. Using the ‘effective mass approximation’ the model can be extended to cover the coherent contributions to the scattering. When this is done, it is found that the fit is rather better if the rotational jumps are assumed not to contribute to the coherent broadening. The mean interval between jumps at 293 K was found to be 2·2 ± 0·5 × 10^-12 s with an activation energy of 2·1 ± 0·6 kcal/mole, in good agreement with 1·4 × 10^-12 s and 1·8 kcal/mole obtained by N.M.R. techniques.