Emergent dynamical symmetry at the triple point of nuclear deformations

Based on the boson realization of the Euclidean algebras, it is shown that the five-dimensional Euclidean dynamical symmetry may emerge at the triple point of the shape phase diagram of the interacting boson model, which thus offers a symmetry-based understanding of this isolated point. It is further shown that the low-lying dynamics in ${}^{108}\mathrm{Pd}$, ${}^{134}\mathrm{Ba}$, ${}^{64}\mathrm{Zn}$, and ${}^{114}\mathrm{Cd}$ may be dominated by the Euclidean dynamical symmetry.

Figure 1

Shape phase diagram in the IBM parameter space, where S represents the region with ${\beta }_{\mathrm{e}}=0$ corresponding to the spherical, P represents the region with ${\beta }_{\mathrm{e}}>0$ corresponding to the prolate, and O represents the region with ${\beta }_{\mathrm{e}}<0$ corresponding to the oblate. In addition, the dashed lines correspond to the critical points of the first-order QPTs, the two thin regions involving the dashed lines represent the two-phase coexisting regions [36], and the solid dot in the center represents the triple point.

Figure 2

The low-lying structure of ${}^{108}\mathrm{Pd}$ [49] and the results calculated for the Eu(5) Hamiltonian (40) with the $m=100$ truncation, where $0_{\tau }^{+}$ and $0_{\xi }^{+}$ represent the excited $0^{+}$ state with $\tau =3$ in the $\xi =1$ family and that with $\tau =0$ in the $\xi =2$ family, respectively, as those in the E(5) CPS [22]. The parameters involved in the Eu(5) Hamiltonian are set as $\alpha =49.4$ keV, $b=14.8$ keV, and $c=9.9$ keV.

Figure 3

The same as in Fig. 2 but for ${}^{134}\mathrm{Ba}$ [50] and the corresponding Eu(5) pattern, for which the parameters are set as $\alpha =74.9$ keV, $b=11.2$ keV and $c=13.5$ keV.

Figure 4

The same as in Fig. 2 but for ${}^{64}\mathrm{Zn}$ [51] and the corresponding Eu(5) pattern, for which the parameters are set as $\alpha =126$ keV, $b=12.6$ keV and $c=22.7$ keV.

Figure 5

The same as in Fig. 2 but for ${}^{114}\mathrm{Cd}$ [52] and the corresponding Eu(5) pattern, for which the parameters are set as $\alpha =79.9$ keV, $b=4.8$ keV and $c=4.8$ keV.