Phased and Boltzmann-weighted rotational averages

This paper deals with two types of rotational average which arise in a number of physical processes in fluids. The first are termed "phased averages," and occur in the theory of bimolecular interactions with radiation; the second are "Boltzmann-weighted" averages, which occur in the theory of anisotropic media. A general method for obtaining these results is presented, and analytic results are given for tensorial interactions up to and including the fourth rank. Several applications are discussed including laser-induced forces, cooperative two-photon absorption, and electric-field-induced harmonic generation. The proof of a relation involving conventional rotational averages is also given.