Rotational motion of molecules and neutron scattering

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Abstract
The differential neutron scattering cross section for scattering from a rigid rotating molecule in a general isotropic medium (condensed or gas state of matter) is presented. It is based on a model, which assumes the complete rotational motion to consist of a damped form of free rotations and of damped librations, respectively. The two phases of rotation are assumed to be coupled to microscopic density fluctuations in the medium in such a way that densities larger than the average allow only damped librations, whereas densities lower than the average allow only damped rotations. The cross section is derived with the aid of a step function formalism first used by Singwi and Sjölander. Further, use is made of Sears' earlier work on rotational scattering cross sections. The resulting cross section describes the molecular motions in a range of conditions from free rotations to undamped libration including all possible intermediate damped motions. The model differs from those created earlier insofar as the rotational diffusion is not necessarily described as a motion consisting of free rotations over smaller or larger angles interrupted by brief collisions. The collisions may in the present model be replaced by shorter or longer periods of libration. Numerical calculations of the Fourier transform, S1(ω), of the first rotational relaxation function, F1(t), is performed using explicit models for the librational and rotational relaxation functions and for such a choice of numerical constants, that the results should describe various hypothetical rotational motions of the methane molecule.