The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over the random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.
@article{arxiv.1902.02396,
title = {A general method for rotational averages},
author = {Reed Nessler and Tuguldur Begzjav},
journal= {arXiv preprint arXiv:1902.02396},
year = {2019}
}