Chiral geometry in symmetry-restored states: Chiral doublet bands in ${}^{\mathbf{128}}\mathbf{Cs}$

The pairing-plus-quadrupole Hamiltonian is diagonalized in a symmetry-restored basis, i.e., the triaxial quasiparticle states with angular momentum and particle number projections, and applied for chiral doublet bands in ${}^{128}\mathrm{Cs}$. The observed energy spectra and electromagnetic transition probabilities are reproduced well without introducing any parameters. The orientation of the angular momentum in the intrinsic frame is investigated by the distributions of its components on the three principle axes ($K$ plot) and those of its tilted angles (azimuthal plot). The evolution of the chirality with spin is illustrated, and the chiral geometry is demonstrated in the angular momentum projected model for the first time.

Figure 1

Illustration of the relation between the tilted angles ($\theta ,\varphi$) of the angular momentum with respect to the intrinsic frame (labeled by 1, 2, and 3) and the Euler angles $\{{\psi }^{\prime },{\theta }^{\prime },{\varphi }^{\prime }\}$ describing the orientation of the intrinsic frame with respect to the laboratory frame (labeled by $x,y$, and $z$).

Figure 2

(a) The energy spectra, (b) the intraband $B\left(E2\right)$, (c) $B\left(M1\right)$, and (d) the interband $B\left(M1\right)$ of the doublet bands in ${}^{128}\mathrm{Cs}$ calculated by the AMP approach in comparison with the data available [14].

Figure 3

The $K$ plot, i.e., $K$ distributions for the angular momentum on the short ($s$), intermediate ($i$), and long ($l$) axes, calculated at $I=11$ (a)–(c), 14 (d)–(f), and $18\hslash$ (g)–(i), respectively.

Figure 4

The azimuthal plot, i.e., profile for the orientation of the angular momentum on the ($\theta ,\varphi$) plane, calculated at $I=11$ [(a), (b)], 14 [(c), (d)], and $18\hslash$ [(e), (f)], respectively.