Extended tests of an SU(3) partial dynamical symmetry

Background: A recent survey of well-deformed rare earth nuclei showed that $B\left(E2\right)$ values from the $\gamma$ band to the ground band could be explained rather well by a parameter-free description in terms of a partial dynamical symmetry (PDS).

Purpose: Our purpose here is to extend this study to deformed and transitional nuclei in the actinide and $\mathrm{A}\sim 100$ regions to determine if the success of the PDS description is general in medium- and heavy-mass nuclei and to investigate further where it breaks down.

Method: As with the previous study we study the empirical relative $B$($E2:\gamma$ to ground) values in comparison to a pure rotor (Alaga) model and to the SU(3) PDS.

Results: The data for the actinides, albeit sparser than in the rare-earth region, are reasonably well accounted for by the PDS but with systematic discrepancies. For the Mo isotopes, the PDS improves on the Alaga rules but largely fails to account for the data.

Conclusions: As in the rare earths, the parameter-free PDS gives improved predictions compared to the Alaga rules for the actinides. The differences between the PDS predictions and the data are shown to point directly to specific mixing effects. In the Mo isotopes, their transitional character is directly seen in the large deviations of the $B\left(E2\right)$ values from the PDS in the direction of the selection rules of the vibrator.

Figure 1

Shown above are relative $B\left(E2\right)$ transition strengths for (a) $2_{\gamma }^{+}\to 0_g^{+}$, (b) $4_{\gamma }^{+}\to 2_g^{+}$, and (c) $6_{\gamma }^{+}\to 4_g^{+}$ transitions. As in the tables, all transition strengths are normalized to the strongest Alaga transition ($J_{\gamma }^{+}\to J_g^{+}$ for these cases). Error bars are shown for nuclei with reported uncertainties in NDS [10]. For visual clarity, ${}^{106}\mathrm{Mo}$ has been omitted from the $4_{\gamma }^{+}\to 2_g^{+}$ plot because the error bars were greater than 50%, severely limiting the information it provides. Plotted with the Mo and actinide data are ${}^{168}\mathrm{Er}$ for reference, the PDS for ${\mathrm{N}}_{\mathrm{val}}=20$ and ${\mathrm{N}}_{\mathrm{val}}=32$, and the Alaga rules.

Figure 2

Partial vibrator level scheme showing the phonon structure for the yrast and next lower spin nonyrast levels. The transitions shown as dashed lines in the figure are forbidden in the vibrator since they change the phonon number by two.