The ͑n, n 0 g͒ reaction has been used to search for two-phonon g-vibrational states in 166 Er. Levels at 1943 and 2028 keV have been observed with collective transitions to the g band. The latter, which has B͑E2; 2028 ! 2 1 g ͒ 7.4 6 2.5 W.u. (Weisskopf unit) is interpreted as the I, K p 4, 4 1 twog-phonon state. The former, for which the data indicate spin 0, has B͑E2; 1943 ! 2 1 g ͒ 21 6 6 W.u. and is interpreted as the I, K p 0, 0 1 two-g-phonon state. This is the first observation of the K p 0 1 two-g-phonon state in a well-deformed nucleus, and its identification places stringent limits on the nuclear models. [S0031-9007(97)03409-1] PACS numbers: 21.10.Tg, 23.20.En, 25.40.Fq, 27.70. + q The existence of two-phonon states in deformed nuclei has been the subject of considerable debate for over 30 years. The recent measurement [1] of enhanced E2 transitions from a level at 2055 keV in 168 Er, interpreted as the K p 4 1 two-phonon g vibration ͑4 1 gg ͒, has not silenced the controversy which is now centered on the magnitude of the two-g-phonon component in the wave function needed to reproduce the enhanced E2 rate and the extent to which these states appear in other nuclei [2][3][4][5][6][7]. Following the discovery of the 4 1 gg state in 168 Er, attempts [2] were made to locate candidates for these states in other nuclei, mainly by considering branching ratios and energy systematics. For many of these candidates, Burke [3] has argued that data exist which rule out the possibility that the main components in their wave functions are of two-phonon character. This demonstrated the need for absolute B͑E2͒-value measurements and for considering all data before assigning levels as two-phonon states.Certain models, such as the self-consistent collectivecoordinate model (SCCM) [8], the multiphonon method (MPM) [9], the dynamic-deformation model (DDM) [10], etc., predict that states with properties of 4 1 gg states should be widespread in the well-deformed rare-earth region. The quasiparticle-phonon nuclear model (QPNM) [4], on the other hand, predicts that 4 1 gg states should exist in a few special cases only, such as 164 Dy, 166 Er, and 168 Er. This limited set of nuclei arises from the behavior of the density of levels in the vicinity of the 4 1 gg states; these nuclei are predicted as being the only ones for which the density is sufficiently low that the two-gphonon states are not greatly fragmented.A feature common to many models is that they predict a relatively pure K p 0 1 two-phonon g vibration ͑0 1 gg ͒ should not exist. Bohr and Mottelson [11] suggested that for 168 Er these states should lie above the 4 1 gg excitation, in the vicinity of 2.5 MeV. In a more detailed treatment, Dumitrescu and Hamamoto [12] found that the positions of the two-g-phonon states depended on the anharmonicities introduced into the Hamiltonian. In particular, by introducing a g-dependent contribution to the moment of inertia, the 0 1 gg excitation could lie lower than the 4 1 gg state.As well, the introduction of a g-unstable ...
