Figure 1

(a) The potential surfaces as functions of $\beta$ with different $\xi$; (b) those at (${\xi }^{*},{\xi }_c,{\xi }^{**}$) on an expanded scale with the infinite well as approximation to the potential at ${\xi }_c$, where the $\gamma$ variable has been frozen as $\gamma =0$.Reuse & Permissions

Figure 2

The contribution of deformation to the two-neutron separation energies, $S{\left(2n\right)}_{\mathrm{def}}$ (in MeV) for both the even and odd Sm isotopes, plotted as a function of neutron boson number, $N_{\nu }$. The contribution is enhanced about 330 keV at $N_{\nu }=5$ in the odd Sm nuclei. Also the increase of $S{\left(2n\right)}_{\mathrm{def}}$ from $N_{\nu }=3$ to $N_{\nu }=4$ is sharper in the odd Sm nuclei than that in the even Sm nuclei. In the $N\to \infty$ limit of the IBM [27], $S{\left(2n\right)}_{\mathrm{def}}$ should be zero when $\xi \le {\xi }_c$ and finite but large when $\xi >{\xi }_c$. The expected behavior of $-\frac{\partial V_{\min }}{\partial \xi }$ is shown in the inset. The experimental data are taken from [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40].Reuse & Permissions

Figure 3

(a) The normalized experimental energy levels of the ground bands of the even Sm nuclei together with those calculated by several typical collective models shown in Table , in which Rot represents the results of the Rotor, Vib corresponds to the results of the Vibrator, and X(3), and X(5) represent those given by the X(3) and the X(5) CPS [14, 16]; (b) the same as (a) but for the ground band of the odd Sm nuclei, where Vib, X(3), X(5), and Rot represent the results of the corresponding collective modes in the weak-coupling limit, which are actually the same as those list in Table according to the discussion in Sec. 2, and the subpanel shows the spectra of ${}^{155,157}$Sm together with those following the $J(J+1)$ law solved from the particle-rotor model in the strong-coupling limit; (c) the same as those in (b) but for the first excited band of the odd Sm nuclei. It should be note that all the bandhead energies have been set to zero, and the levels in the band with $\Delta J=2$ are normalized to the levels with $J=J_0+2$, while the levels in the band with $\Delta J=1$ are normalized to the levels with $J=J_0+1$, where $L=J-J_0$ with $J$ being the total spin of the level and $J_0$ being the spin of the band head. The experimental data are taken from [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40].Reuse & Permissions

Figure 4

The experimental energy levels in the ground band and the $\beta$ band of ${}^{150}$Sm and those of ${}^{152}$Sm. The corresponding normalized results are shown in the insets, where the theoretical results of rotor and vibrator are also given to compare the experimental behaviors. The experimental data are taken from [33, 35].Reuse & Permissions

Figure 5

(a) The experimental energy levels of the lowest three $\Delta J=2$ collective bands and the lowest $\Delta J=1$ negative parity band in ${}^{151}$Sm and the subpanels showing the normalized results with $L=J-J_0$ and $J_0$ being the spin of bandhead as in Fig. 3. (b) Similar to those in (a) but for the experimental energy levels of the lowest four collective bands in ${}^{153}$Sm. The $\Delta J=2$ band denoted by A (short solid lines) and the one denoted by B (short dash lines) are often explained as the single $\Delta J=1$ strong-coupling band with the levels signified by the short solid and dash lines together under A. The experimental data shown (a) and (b) are taken from [34, 36].Reuse & Permissions