Interacting boson approximation model analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>E</mml:mi><mml:mi/><mml:mn>2</mml:mn></mml:math>transition probabilities for transitions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Er</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mn>6</mml:mn><mml:mn>6</mml:mn><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mn>7</mml:mn><mml:mn>0</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The experimental results from Coulomb excitation of vibrational-like ${2}^{+}$ states in $^{166\ensuremath{-}170}\mathrm{Er}$ are compared with the predictions of the interacting boson approximation model. The breaking of the SU(3) symmetry by the pairing term plays a crucial role in giving a much better account of the $B(E2)$ values for decay of the $K$,${J}^{\ensuremath{\pi}}=0,{2}^{+}$ state. In general, the interacting boson approximation model provides a detailed quantitative description of the level energies and of the $E2$ transition probabilities.NUCLEAR STRUCTURE IBA model predictions of the $B(E2)$ values for the different decay modes of the ${2}^{+}$ states in $^{166\ensuremath{-}170}\mathrm{Er}$.

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