THEORY OF COLD NEUTRON SCATTERING BY HOMONUCLEAR DIATOMIC LIQUIDS: II. HINDERED ROTATION

Abstract

The partial wave expansion of the cold neutron scattering cross section for a homonuclear diatomic liquid in terms of the angular momentum transfer, which was introduced in a previous article for the case of free rotation, is generalized to include hindered rotation. The cross section is expressed in terms of an orientational distribution function that is the rotational analogue of the Van Hove self-correlation function. The rotational scattering function for the lth partial wave is shown to be the Fourier transform of a rotational relaxation function, Fl(t), which is also the lth coefficient of the expansion of the orientational distribution function in terms of spherical harmonics. The functions Fl(t) are calculated for the limiting cases of free rotation and rotational diffusion. The problem of neutron diffraction by homonuclear diatomic liquids is also investigated, and it is shown that the small angle scattering is determined by the isothermal compressibility. This is a generalization of the well-known result for monatomic liquids.