Random motion of a uniaxial rotator in anN-fold cosine potential: Correlation functions and neutron incoherent scattering law

The properties of a particle undergoing circular rotational motion in an N-fold cosine potential is investigated in detail. The rate equation for the probability function is given and order parameters are defined. The self-correlation functions of cos nϕ and sin nϕ (ϕ is the azimuthal angle) are calculated. The neutron incoherent scattering law is derived. The elastic incoherent structure factor is calculated directly. The jump model among N equidistant sites and the continuous rotational diffusion model are found as limiting cases. The problem of a more general potential is also discussed.