Investigation of the anomalously low $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio in ${}^{134}\mathrm{Ce}$ through lifetime measurements

The existing experimental value of the ratio $B_{4/2}\equiv B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ in ${}^{134}\mathrm{Ce}$ is less than unity, which is outside the range allowed by current collective models and is highly anomalous. In the present work, new lifetime measurements of excited states in ${}^{134}\mathrm{Ce}$ have been performed in order to clarify this discrepancy. Excited states of ${}^{134}\mathrm{Ce}$ were populated by the fusion-evaporation reaction ${}^{122}\mathrm{Sn}({}^{16}\mathrm{O},4n){}^{134}\mathrm{Ce}$. The recoil distance doppler shift method was employed, and reliable lifetimes for the $2_1^{+}, 4_1^{+}, {10}_2^{+}$, and ${12}_2^{+}$ states were derived from the differential decay curve method. The resulting $B_{4/2}$ value is larger than unity, resolving the disagreement with traditional collective models. The new experimental data is in very good agreement with the calculation in the framework of the interacting boson model. The systematic evolution in collectivity of the Ce isotopes is discussed.

Figure 1

Gated $\gamma$-ray spectra of ${}^{134}\mathrm{Ce}$ taken at different distances. On the left-hand side, the shifted and unshifted components of the $2_1^{+}\to 0_1^{+}$ transition are presented; on the right-hand side, the shifted and unshifted components of the $4_1^{+}\to 2_1^{+}$ transition are shown. In these spectra the shifted component lies lower in energy ($\theta$ = ${153}^{\circ }$) than the unshifted component.

Figure 2

Partial level scheme showing the main feeding transitions into the ground-state band according to Refs. [13, 14]. The widths of the arrows correspond to the intensities of each transition.

Figure 3

Lifetime values $\tau \left(x\right)$ and their average values for the $2_1^{+}\to 0_1^{+}$ transition at 409.1 keV (a) and $4_1^{+}\to 2_1^{+}$ transition (d) at 639.7 keV, measured by the detectors at backward angular ($\theta$ = ${153}^{\circ }$). The associated intensities of the shifted [(b) and (e)] and unshifted [(c) and (f)] components are also shown.

Figure 4

Top: the systematic of the $B(E2;2_1^{+}\to 0_1^{+})$ value in cerium isotopes. Middle: the systematic of the $R_{4/2}$ value in cerium isotopes. Bottom: the systematic of the $B_{4/2}$ value in cerium isotopes compared to the IBM-1 calculations. Data are taken from Refs. [7, 18, 19, 20, 21] and filled circles (blue) correspond to values measured in the present work.

Figure 5

Experimental level energies for ${}^{134}\mathrm{Ce}$ compared with IBM-1 calculations. Energies are normalized to the experimental $E\left(2_1^{+}\right)$ value.