Figure 1

Energy levels in the ground band ($\mathrm{s}=1$) and $\beta$ band ($\mathrm{s}=2$) in the DX(3) CPS based on the X(3) even-even core coupled to a $g_{9/2}$ particle (for $h_{9/2}$, the parities should be reversed), normalized to the energy of the lowest excited $J=13/2^{+}$ state, together with $B\left(E2\right)$ transition rates, normalized to the transition $B(E2;13/2_1^{+}\to 9/2_1^{+})$. As a comparison, the level scheme of the X(3) CPS [3] is also shown. It should be noted that only the transitions rates involving the lowest two states in the $\beta$ band are shown as examples to illustrate the features of the interband transition.Reuse & Permissions

Figure 2

Energy levels, normalized to the $R=2$ results, and intraband $B\left(E2\right)$ ratios in the ground band of the DX(3) CPS for $j=7/2,9/2,11/2,$ and $13/2$ single-particle levels are shown as a function of the angular momentum $R=J-j$. It should be noted that the energy levels depend only on the $R$ values as discussed in the text. To identify the similarities and differences between the odd-$A$ and even-even system, the corresponding results in the X(3) CPS together with those in the vibrational and rotational cases, which are obtained from the U(5) and SU(3) limit of the interacting boson model [23], are also shown. For even-even systems, $R=L$.Reuse & Permissions

Figure 3

Energy levels for ground-band states of ${}^{172}$Os [25] (center) and two low-lying bands in ${}^{173}$Ir [26] with $J^{\pi }=9/2^{-}$ (left) and $13/2^{+}$ (right) band heads. The inset shows the normalized energy levels from experiment compared with the results calculated in the X(3) and DX(3) CPS signified as CPS together with those calculated in the vibrational and rotational cases, where all the energy levels are normalized to the $R=2$ result with $R$ being the difference between the spin $J$ of each level and the spin of the band head in a collective band. Note that the levels in the ground band of the X(3) and DX(3) CPS have the same functional dependence on $R$.Reuse & Permissions

Figure 4

Same as in Fig. 3 but for the ground band of ${}^{150}$Sm [27] as well as for states of the lowest negative parity band of ${}^{151}$Eu [28] built on $J^{\pi }=11/2^{-}$ band head configuration.Reuse & Permissions