γ-ray emission from symmetric ordered nuclear spin structures at low temperatures

The temperature dependence of $\gamma$-ray emission patterns from symmetric ordered nuclear-spin systems is discussed with particular reference to planar spin configurations. In particular, explicit expressions for "average statistical tensors" ${\overline{\rho }}_q^{\lambda }\mathrm{}\left(I\right)\mathrm{}$ are derived, for nuclear-spin structures with two-, three-, four-, and six-fold axes of symmetry. Several interesting identities are derived, which are useful aids in the analysis of a given nuclear orientation experiment. For example, if the nuclear structure possesses either a twofold or an effective twofold axis of symmetry, then the temperature isotherms for ${\rho }_2^2$ vs ${\rho }_0^2$ statistical-tensor diagrams are simply parallel straight lines.