The Triaxial Projected Shell Model (TPSM) has been successful in providing a microscopic description of the energies of multi-phonon vibrational bands in deformed nuclei. We report here on an extension of the TPSM to allow, for the first time, calculations of B(E2) values connecting gamma- and gamma-gamma-vibrational bands and the ground state band. The method is applied to 166,168Er. It is shown that most of the existing B(E2) data can be reproduced rather well, thus strongly supporting the classification of these states as gamma-vibrational states. However, significant differences between the data and the calculation are seen in those B(E2) values which involve odd-spin states of the gamma-band. Understanding these discrepancies requires accurate experimental measurements and perhaps further improvements of the TPSM.
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