Multi-Phonon $\gamma$-Vibrational Bands and the Triaxial Projected Shell Model

We present a fully quantum-mechanical, microscopic, unified treatment of ground-state band and multi-phonon $\gamma$-vibrational bands using shell model diagonalization with the triaxial projected shell model. The results agree very well with data on the g- and $\gamma$-band spectra in $^{156-170}$Er, as well as with recently measured $4^+$ 2-phonon $\gamma$-bandhead energies in $^{166}$Er and $^{168}$Er. Multi-phonon $\gamma$-excitation energies are predicted.