High-spin states in the ${}_{68}^{165,166,167}\mathrm{Er}$ nuclei were populated in the incomplete fusion of 55-MeV ${}^7\mathrm{Li}$ ions with a ${}^{164}\mathrm{Dy}$ target. Previously known rotational sequences in ${}^{165,166,167}\mathrm{Er}$ have been extended, in some cases beyond the $i_{13/2}$ two-quasineutron crossing region. In ${}^{165}\mathrm{Er}$, four rotational sequences were observed up to a maximum $I^{\pi }$ of ($45/2^{+}$); in ${}^{166}\mathrm{Er}$, five decay sequences were observed to $I^{\pi }=({28}^{+}$); and in ${}^{167}\mathrm{Er}$, four decay sequences were populated to $I^{\pi }=(53/2^{-}$). Comparisons of the experimental data with the results of Cranked Shell Model calculations provide insight into the configuration dependence of the first two-quasineutron crossing frequencies and the blocking effects of the odd quasineutron in ${}^{165}\mathrm{Er}$ and ${}^{167}\mathrm{Er}$. The experimental high-spin decay sequences in ${}^{165}\mathrm{Er}$ and ${}^{167}\mathrm{Er}$ have also been compared with the results of Projected Shell Model (PSM) calculations; the overall agreement between experiment and theory is very good over the complete range of spins for all high-spin rotational sequences. In particular, the observed signature splitting in the $5/2^{+}\left[642\right]$ band in ${}^{165}\mathrm{Er}$ and in the $7/2^{+}\left[633\right]$ and $1/2^{-}\left[521\right]$ bands in ${}^{167}\mathrm{Er}$ together with the absence of signature splitting in the high-$K$ $11/2^{-}\left[505\right]$ band in ${}^{165}\mathrm{Er}$ are reproduced in the PSM calculations. For ${}^{166}\mathrm{Er}$, the Triaxial Projected Shell Model calculations yield satisfactory results for both the ground and $\gamma$-vibrational band. For the latter band, there is a one-to-one correspondence between the theoretical results and experimental data for all states with $I^{\pi }$ in the range from the $2^{+}$ bandhead to the ${21}^{+}$ state.

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• High spin states
• Nuclear structure & decays
• 150 ≤ A ≤ 189
• Radiation detectors
• Shell model