Electromagnetic properties of excited states in the even-even erbium isotopes from Coulomb excitation studies

The reorientation effect in Coulomb excitation has been used to measure in $^{162,164,166,168,170}\mathrm{Er}$ the static quadrupole moments ${Q}_{{{2}^{+}}^{\ensuremath{'}}}$ of ${2}^{+}$\ensuremath{'} $\ensuremath{\gamma}$-vibrational states; and the branching ratio ${B}_{\ensuremath{\gamma}}$ for the decay of the ${2}^{+}$\ensuremath{'} state to the ${0}^{+}$ ground state and the first ${2}^{+}$ state. Both particle-$\ensuremath{\gamma}$ coincidence and particle spectroscopy experiments were carried out to extract these quantities, using 12.5 MeV $\ensuremath{\alpha}$ and 48 MeV $^{16}\mathrm{O}$ beams with enriched targets. The evaluation was based on the semiclassical Winther-deBoer code and corrected for quantum mechanical effects. The measured values of ${Q}_{{{2}^{+}}^{\ensuremath{'}}}$ agree well with the predictions of the rotation-vibration model, asymmetric rotor model, and, for $^{168}\mathrm{Er}$, the interacting boson approximation. For ${B}_{\ensuremath{\gamma}}$, all of the above models predict the increasing trend with increasing mass number seen in the measurements, but are unable to correctly predict the absolute magnitudes.NUCLEAR REACTIONS $^{162,164,166,168,170}\mathrm{Er}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\gamma})$, $E=12.5$ MeV, $^{162,164,166,168,170}\mathrm{Er}(^{16}\mathrm{O}, ^{16}\mathrm{O}^{\ensuremath{'}}\ensuremath{\gamma})$, $^{168}\mathrm{Er}$($^{16}\mathrm{O}$, $^{16}\mathrm{O}$\ensuremath{'}), $E=48$ MeV; measured particle-$\ensuremath{\gamma}$ coincidence $\ensuremath{\sigma}$, inelastic $\ensuremath{\sigma}$; deduced ${Q}_{{{2}^{+}}^{\ensuremath{'}}}$, ${B}_{\ensuremath{\gamma}}$. Enriched metal targets. Ge(Li) and silicon surface-barrier detectors. Coupled channel semiclassical and quantum mechanical analysis.

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