Hexadecapole-Phonon versus Double-γ-Phonon Interpretation forKπ=4+Bands in Deformed Even-Even Nuclei

Recent interpretations of $K^{\pi }=4^{+}$ bands as double-$\gamma$ phonons in even-even nuclei of the deformed rare earth region are shown to be in serious conflict with single-nucleon-transfer results and other data. The main argument for the double-$\gamma$-phonon interpretation, the existence of large $B\left(E2\mathrm{}\right)\mathrm{}$ values connecting the $K^{\pi }=4^{+}$ bands with gamma bands, and all other available data, including $E4\mathrm{}$ strengths, single-nucleon-transfer results, allowed $\beta$ decays, etc., are explained if the $4^{+}$ bands are predominantly hexadecapole vibrations, or $g$-boson structures.