Lifetime measurements of 0+ states in Er168 with the Doppler-shift attenuation method

Abstract

Background: The lowest-lying shape oscillations of deformed nuclei have been described as quadrupole in nature $(\ensuremath{\lambda}=2)$, resulting in two types of vibrations or oscillations: $\ensuremath{\beta}$ vibrations with oscillations along the symmetry axis $({K}^{\ensuremath{\pi}}={0}^{+})$ and $\ensuremath{\gamma}$ vibrations breaking axial symmetry with a projection of ${K}^{\ensuremath{\pi}}={2}^{+}$ on the symmetry axis. The $\ensuremath{\gamma}$ vibration seems to be well characterized as the first ${K}^{\ensuremath{\pi}}={2}_{1}^{+}$ (or ${2}_{\ensuremath{\gamma}}^{+}$) band in deformed nuclei and exhibits a systematic behavior across the region. The nature of the ${K}^{\ensuremath{\pi}}={0}^{+}$ excitations, however, has remained poorly understood and has been open to debate for some decades.Purpose: The goal of this work is to understand the nature of ${0}^{+}$ states observed in $^{168}\mathrm{Er}$ through measurements of the lifetimes of these states and to determine if they are consistent with oscillations built on a deformed ground state, the minima of other coexisting shapes, single-particle states, or a mixture of effects.Method: Lifetimes of excited states in the $^{168}\mathrm{Er}$ nucleus were measured with the Doppler shift attenuation method (DSAM) and the inelastic neutron scattering reaction, $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$, at the University of Kentucky Accelerator Laboratory.Results: Numerous ${0}^{+}$ states had been observed by the ($p,t$) reaction [D. Bucurescu et al., Phys. Rev. C 73, 064309 (2006).]. We confirm the ${0}^{+}$ states at 1217.2, 1421.5, 1833.6, 2364.9, 2392.1, and 2643.0 keV in $^{168}\mathrm{Er}$. We could not, however, support the previous assignments of ${0}^{+}$ levels at 2114.1, 2200.6, 2572.5, and 2617.4 keV. We report measured lifetimes for six confirmed ${0}^{+}$ excitations and additional members of ${0}^{+}$ bands.Conclusions: The results for $^{168}\mathrm{Er}$ show that it is the third excited ${K}^{\ensuremath{\pi}}={0}^{+}$ $({0}_{4}^{+})$ excitation that carries the collective strength and, therefore, the potential to be an oscillation on the ground state. This result is similar to the case in $^{166}\mathrm{Er}$, where it was also the ${0}_{4}^{+}$ state that exhibited greater collectivity than the first excited ${K}^{\ensuremath{\pi}}={0}^{+}$ band. The Delaroche et al. [J.-P Delaroche et al., Phys. Rev. C 81, 014303 (2010).] prediction for a collective ${K}^{\ensuremath{\pi}}={0}^{+}$ band is at ${E}_{T}=1.818\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, which corresponds the third excited ${K}^{\ensuremath{\pi}}={0}^{+}$ band.