# On three-dimensional rotational averages of odd-rank tensors

## TL;DR

This paper introduces a new method for calculating three-dimensional rotational averages of odd-rank tensors, which is essential for nonlinear optical spectroscopy in optically active media, and demonstrates its application to tensors of ranks 5, 7, 9, and 11.

## Contribution

A novel approach using an overcomplete basis of isotropic tensors for rotational averaging of odd-rank tensors in three dimensions.

## Key findings

- Successfully applied to tensors of ranks 5, 7, 9, 11
- Provides a systematic method for high-rank tensor averaging
- Enhances computational tools for nonlinear optical spectroscopy

## Abstract

The recent growing interest in nonlinear optical spectroscopy in optically active medium demands the three-dimensional rotational average of high-rank tensors. In the present paper, we present a new 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 5,7,9,11.