Angular Relaxation of the Symmetrical Top

Abstract

The calculation of ${\mathrm{〈P}}_n[\cos \mathrm{\theta (t)]〉}$ is formulated for the symmetric top, and evaluated for several special models; $P_n$ is the Legendre polynomial and $\mathrm{\theta (t)}$ the angle made by the symmetry axis with its initial direction. The collision operator is presumed to arise from a time independent transition probability, and includes the Boltzmann integral operator or Langevin differential operator as special cases. Diffusional relaxation is recovered only if the collision frequency is large, and is not the general behavior for large $t$ .