Statistical tensors for the analysis ofγ-ray emission from a non-axially-symmetric nuclear ensemble

A tabulation of statistical tensors ${\rho }_q^{\lambda }\mathrm{}\left(I\right)\mathrm{}$ for the analysis of $\gamma$-ray emission from a non-axially-symmetric nuclear ensemble $H=A{I}_z+P\{-\frac{1}{2}[I_z^2-\frac{1}{3}I(I+1\mathrm{})]+\frac{1}{2}(I_{+}^2+I_{-}^2\left)\right\}$ has been prepared. The tables cover all values of the magnetic and quadrupole hyperfine parameters $A$ and $P$, for $1<~I<~8$. Explicit rotation matrices are also given which enable the tabulated statistical tensors to be transformed into those appropriate to other frames of reference. Special attention is given to off-diagonal tensors ${\rho }_q^{\lambda }\mathrm{}\left(I\right)\mathrm{}$, $q\ne 0$, and it is suggested that statistical-tensor diagrams ${\rho }_2^2\mathrm{}\left(I\right)\mathrm{}$ vs ${\rho }_0^2\mathrm{}\left(I\right)\mathrm{}$, etc., are a useful way of presenting nuclear-orientation data.