Reduced<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi><mml:mn>1</mml:mn><mml:mn/></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>E</mml:mi><mml:mn>1</mml:mn><mml:mn/></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>E</mml:mi><mml:mn>2</mml:mn><mml:mn/></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>E</mml:mi><mml:mn>3</mml:mn><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">Gd</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mn>5</mml:mn><mml:mn>6</mml:mn><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mn>6</mml:mn><mml:mn>0</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Dy</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>1</mml:mn><mml:mn>6</mml:mn><mml:mn>0</mml:mn><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mn>6</mml:mn><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

Direct $E2$ and $E3$ Coulomb excitation of ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states with 13.5-MeV $^{4}\mathrm{He}$ ions on isotopically enriched targets of $^{156\ensuremath{-}160}\mathrm{Gd}$ and $^{160\ensuremath{-}164}\mathrm{Dy}$ has been measured by means of $\ensuremath{\gamma}$-ray spectroscopy. Vibrational-like ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states were identified in each nucleus. The $B(E\ensuremath{\lambda},0\ensuremath{\rightarrow}J=\ensuremath{\pi})$ is obtained for excitation of each state, and information is given on the reduced transition probabilities for the different decay modes of these states. The experimental results are compared with theoretical predictions of nuclear models describing these states. A reasonable account of the reduced $E2$ transition probabilities is provided by the interacting boson model.NUCLEAR REACTIONS $^{156\ensuremath{-}160}\mathrm{Gd}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\gamma})$, $^{160\ensuremath{-}164}\mathrm{Dy}(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\gamma})$, $E=13.5$ MeV; measured ${I}_{\ensuremath{\gamma}}$, ${E}_{\ensuremath{\gamma}}$, $\ensuremath{\gamma}(\ensuremath{\theta})$, Doppler broadening. $^{156\ensuremath{-}160}\mathrm{Gd}$, $^{160\ensuremath{-}164}\mathrm{Dy}$ levels deduced $B(E2)$, $B(M1)$, $B(E3)$, $B(E1)$, ${T}_{\frac{1}{2}}({3}^{\ensuremath{-}})$, ${J}^{\ensuremath{\pi}}$, $\ensuremath{\delta}$. Enriched targets.

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