Rotational Brownian Motion. II. Fourier Transforms for a Spherical Body with Strong Interactions

Abstract

Laplace and Fourier transforms of the distribution function for orientation, and related correlation functions, for a spherical body undergoing rotational Brownian motion are calculated by solving partial differential equations governing their behavior. Also calculated is the Fourier transform of a correlation function involving both the orientation and angular velocity of a spherical body, which occurs in the theory of spin relaxation by spin-rotational interactions. The solutions obtained are the first few terms of infinite series, which appear to converge rapidly if the frictional retarding torque acting on the body is sufficiently large. The first term in each series is identical to results obtained by use of a rotational diffusion equation. From experimental values of the correlation times for reorientation of fairly small molecules in liquids, it is inferred that the solutions obtained here are probably applicable, and that the higher-order terms calculated here may be important.