Mixing of the Ground-State and Gamma-Vibrational Bands inEr166andEr168

Gamma-ray intensities were measured in ${\mathrm{Er}}^{166}$ and ${\mathrm{Er}}^{168}$ with an accuracy of a few percent, using a Ge(Li) detector. Several new $\gamma$ transitions, not previously reported, were observed. The half-life of the 1095-keV state in ${\mathrm{Er}}^{168}$ was measured to be 115.7±3.3 nsec. The $E2\mathrm{}$ branching ratios from the gamma band to the ground-state band are in excellent agreement with the band-mixing theory. Our $z_2$ values are 0.0460±0.0010 for ${\mathrm{Er}}^{166}$ and 0.0388±0.0015 for ${\mathrm{Er}}^{168}$. These $z_2$ parameters as well as some recent values for other even-even nuclei in the $150<A<\mathrm{}190\mathrm{}$ regions are compared with calculated values according to different theories. The theories and the experiments give the same mass dependence of $z_2$. However, the experimental values are up to a factor of 2 higher than the theoretical ones. The ratios of the intrinsic $E2\mathrm{}$ matrix elements, $\frac{〈2\left|M^{\prime }\mathrm{}\right(E2,0\mathrm{}\left)\right|2\mathrm{}〉}{〈0\left|M^{\prime }\mathrm{}\right(E2,-2\mathrm{}\left)\right|2\mathrm{}〉}$ are derived as 9.8±0.3 for ${\mathrm{Er}}^{166}$ and 9.2±0.7 for ${\mathrm{Er}}^{168}$. Using Coulomb-excitation data, we obtain for the ratio of the quadrupole moments, $\frac{Q_0\mathrm{}(K=2\mathrm{})\mathrm{}}{Q_0\mathrm{}(K=0\mathrm{})\mathrm{}}$, the values 1.38±0.15 for ${\mathrm{Er}}^{166}$ and 1.15±0.14 for ${\mathrm{Er}}^{168}$. Finally, the $\gamma$ transition rates from the negative-parity states are discussed in terms of the collective nuclear model.