Linking partial and quasi dynamical symmetries in rotational nuclei

Background: Quasi dynamical symmetry (QDS) and partial dynamical symmetry (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated.

Purpose: The goal of this paper is to establish a link between PDS and QDS and find an empirical manifestation.

Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei.

Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified.

Conclusions: PDS is more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.

Figure 1

Ground-state fluctuations $\Delta {\sigma }_{\mathrm{g}.\mathrm{s}.}$ (3) for the ECQF Hamiltonian (1) with $N=14$ bosons. The fluctuations vanish at the O(6) DS limit, saturate towards the U(5) DS limit, and are of the order ${10}^{-2}$ in the valley.

Figure 2

Squared amplitudes ${\alpha }_i^2$ in the expansion (2) of the $0_{\mathrm{g}.\mathrm{s}.}^{+}$ ground state of the ECQF Hamiltonian (1) for $\xi =0.84$ and $\chi =-0.53$ (indicated by the red star in the symmetry triangle and appropriate for ${}^{160}$Gd).

Figure 3

The ECQF symmetry triangle with the position of the nucleus ${}^{160}$Gd indicated by a star. The green area shows the region of low $\Delta {\sigma }_{\mathrm{g}.\mathrm{s}.}$, calculated from Eq. (3) for $N=60$. The red dashed line shows the same region of approximate ground-state O(6) symmetry, as predicted by Eq. (5) for large $N$. The blue dotted line shows the “arc of regularity” [37].

Figure 4

(a) The experimental spectrum of ${}^{160}$Gd compared with the IBM calculation using the ECQF Hamiltonian (1) with parameters $\xi =0.84$ and $\chi =-0.53$ taken from Ref. [32]. (b) The O(6) decomposition in $\sigma$ components of yrast states with $L=0,2,4$. (c) The SU(3) decomposition in $(\lambda ,\mu )$ components of the same yrast states.