Outstanding problems in the band structures of ${}^{152}\mathrm{Sm}$

The recent data on $B\left(E2\right)$ values, deduced from the multi-Coulex excitation of the low spin states in the decay of ${}^{152}\mathrm{Sm}$, and other experimental findings in the last two decades are compared with the predictions from the microscopic dynamic pairing plus quadrupole model of Kumar and Baranger. The 1292.8 keV $2^{+}$ state is assigned to the ${0_3}^{+}$ band, and the $K=2$ assignment of the 1769 keV $2^{+}$ state is confirmed. The anomaly of the shape coexistence of the assumed spherical β band versus the deformed ground band is resolved. The values from the critical point symmetry X(5) support the collective character of the β band. The problem with the two-term interacting boson model Hamiltonian in predicting β and γ bands in ${}^{152}\mathrm{Sm}$ leads to interesting consequences. The collective features of the second excited $K^{\pi }={0_3}^{+}$ band are preferred over the “pairing isomer” view. Also the multiphonon nature of the higher lying $K^{\pi }={2_2}^{+}\beta \gamma$ band and $K^{\pi }=4^{+}$ band are illustrated vis-à-vis the new data and the nuclear structure theory.

Figure 1

Partial energy level spectrum of ${}^{152}\mathrm{Sm}$ [3].

Figure 2

Partial energy level spectrum of ${}^{152}\mathrm{Sm}$ from the DPPQ model.

Figure 3

Potential energy curve for ${}^{152}\mathrm{Sm}$ from the DPPQ model. The zero point energy “ZPE” lies 1.37 MeV below the spherical barrier.

Figure 4

Variation of $B$($E2$, β-g) with $\varepsilon /k$ in ${}^{152}\mathrm{Sm}$. The experimental values are shown by open circles.

Figure 5

Variation of $B$($E2$, γ-g, γ-β) with $\varepsilon /k$ in ${}^{152}\mathrm{Sm}$. The experimental points are indicated by open circles.

Figure 6

Partial energy spectrum of ${}^{152}\mathrm{Sm}$ in IBM-1.

Figure 7

The wave functions $A_{100}$ and $A_{200}$ for the $0_g$ and $0_{\beta }$ states of ${}^{152}\mathrm{Sm}$ from the DPPQ model.

Figure 8

Partial ground band spectrum of ${}^{152}\mathrm{Sm}$ in power index formula.

Figure 9

The power index $b$ versus spin $I$ for ${}^{152}\mathrm{Sm}$ and ${}^{154}\mathrm{Gd}$.

Figure 10

Staggering index $S\left(I\right)$ for $N=88$, 90, and 92 in Sm, Gd, and Dy.