Linear polarization-direction correlations in $\gamma$-ray scattering experiments

TL;DR

This paper develops a formalism for analyzing angular correlations in linearly polarized gamma-ray scattering experiments, aiding in the extraction of nuclear structure information and optimizing experimental setups.

Contribution

It introduces a comprehensive formalism for gamma-ray angular correlation analysis, including phase conventions and a proposed experimental geometry with measured anisotropies.

Findings

Derived expressions for three-dimensional radiation patterns.

Clarified relationships between different phase conventions.

Provided measured anisotropies for a four-detector geometry.

Abstract

Scattering measurements with incident linearly polarized $\gamma$ rays provide information on spins, parities, and $\gamma$-ray multipolarity mixing coefficients, and, therefore, on the nuclear matrix elements involved in the transitions. We present the general formalism for analyzing the observed angular correlations. The expressions are used to compute three-dimensional radiation patterns, which are important tools for optimizing experimental setups. Frequently, $\gamma$-ray transitions can proceed via two multipolarities that mix coherently. In such cases, the relative phases of the nuclear matrix elements are important when comparing results from different measurements. We discuss different phase conventions that have been used in the literature and present their relationships. Finally, we propose a basic experimental geometry consisting of detectors located at four different spatial locations. For this geometry, we present the measured anisotropies of the emitted $\gamma$ rays in graphical format as an aid in the data analysis.