Kπ=0+and4+Two-Phononγ-Vibrational States in166Er

The $\left({n,n}^{\prime }\gamma \right)$ reaction has been used to search for two-phonon $\gamma$-vibrational states in ${}^{166}\mathrm{Er}$. Levels at 1943 and 2028 keV have been observed with collective transitions to the $\gamma$ band. The latter, which has $B(E2;2028\mathrm{}\to 2_{\gamma }^{+})=7.4\mathrm{}\pm 2.5$ W.u. (Weisskopf unit) is interpreted as the ${I,K}^{\pi }{=4,4\mathrm{}}^{+}$ two- $\gamma$-phonon state. The former, for which the data indicate spin 0, has $B(E2;1943\mathrm{}\to 2_{\gamma }^{+})=21\mathrm{}\pm 6$ W.u. and is interpreted as the ${I,K}^{\pi }{=0,0\mathrm{}}^{+}$ two- $\gamma$-phonon state. This is the first observation of the $K^{\pi }{=0\mathrm{}}^{+}$ two- $\gamma$-phonon state in a well-deformed nucleus, and its identification places stringent limits on the nuclear models.