Double-$\gamma$ vibrations in deformed nuclei are analyzed in the context of the interacting boson model. A simple extension of the original version of the model towards higher-order interactions is required to explain the observed anharmonicities of nuclear vibrations. The influence of three- and four-body interactions on the moments of inertia of ground- and $\gamma$-bands, and on the relative position of single-$\gamma$ and double-$\gamma$ bands is studied in detail. As an example of a realistic calculation, spectra and transitions of the highly $\gamma$-anharmonic nuclei $^{ 164}$Dy, $^{ 166}$Er, and $^{ 168}$Er are interpreted in this approach.
Categories: nucl-th