Rotational Correlation Function of Spherical Rotors and Neutron Scattering

The rotational correlation function for non-interacting spherical molecules is treated exactly in an analytical form. The result is then applied to the inelastic scattering of neutrons by gas of spherical molecules. The intermediate scattering function for hydrogenic molecules is studied on the basis of its integral representation with a known transcendental function. It is shown that the above function is, in the limiting case of short time, identified with the basic equation in the effective mass theory of Sachs and Teller. The intensity to be attributed to the quasi-elastic peak is given also analytically. Both the quasi-classical approximation and the effective mass theory are examined in comparison of their results with the exact one for the inelastic neutron spectra for some scattering angles, with a specific reference to methane.