Two-phonon $\gamma$-vibrational states, with energy anharmonicity in the range $2.0\le R_a^{\gamma }$(a = 4, 0) $\le 3.5$, have been investigated in the well-deformed ${}^{164}\mathrm{Dy}$ nucleus using the ${}^{163}\mathrm{Dy}$($n_{\mathrm{th}},\gamma ){}^{164}\mathrm{Dy}$ reaction. The lowest-lying $K^{\pi }$ = $4^{+}$ state at 1978.5 keV ($R_4^{\gamma }$ = 2.60) has been identified. This, together with the one at $E_x$ = 2113.2 keV ($I^{\pi }$ = $5^{+}$), and the two other newly observed levels at 2261.4 ($I^{\pi }$ = $6^{+}$) and 2463.5 ($I^{\pi }$ = $7^{+}$) keVs likely constitute a candidate $K^{\pi }$ = $4^{+}$ two-phonon $\gamma$-vibrational band in this nucleus. Novel calculations in the framework of triaxial projected shell model have been carried out for the two-$\gamma$-phonon bandhead state and the band structure built above it. The results from the calculations have been found to be in fair agreement with the experimental findings.

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• Collective levels
• Collective models
• Electromagnetic transitions
• Energy levels
• Nuclear structure & decays
• Radiative capture
• 150 ≤ A ≤ 189
• Nuclear data analysis & compilation
• Shell model
• Spectrometers & spectroscopic techniques