Nuclear Hexadecapole Interactions

The nuclear hexadecapole matrix elements for the static and the one-phonon nuclear interactions are developed and are evaluated for $\Delta m=\pm 3$ and $\Delta m=\pm 4$ nuclear transitions involving a spin-$\frac{9}{2}$ nucleus in a crystal with $\overline{4}3m$ symmetry. An expression for the saturation factor for a general interaction which gives rise to nuclear-spin transitions involving the change in the $z$ component of the spin by any amount $\Delta m=\pm n$ is developed and is used to derive the angular variation of the one-phonon, $\Delta m=\pm 3$ and $\Delta m=\pm 4$ nuclear hexadecapole interactions. Finally a way to end the speculation about the observation of the hexadecapole interaction is presented.