  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.
