On three-dimensional rotational averages of odd-rank tensors

The recent growing interest in nonlinear optical spectroscopy in optically active medium demands the three-dimensional rotational average of high-rank tensors. For example, calculations of the coherent anti-Stokes Raman scattering in optically active medium requires the averaging of the ninth rank tensor. Following the classic work of Andrews et al (1977 J. Chem. Phys. 67 5026) we present a method for finding the rotational average of odd-rank tensors in an overcomplete basis of isotropic tensors. The method is successfully applied to the rotational averages of tensors of rank n = 5, 7, 9, 11. Explicit new results for ninth- and eleventh-rank tensors are given. (paper)