Figure 1

Upper frame: energy levels in the odd system at the $E(5/12)$ critical point (normalized to the energy of the first excited state). Each (degenerate) state is characterized by the $\xi$, ${\tau }_1^B$, ${\tau }_1^F$, (${\tau }_1$, ${\tau }_2$) quantum numbers. The values $k=-1/4$, $k^{\prime }=5/2$ have been used in the Hamiltonian (1). The values of (twice) the angular momenta for each degenerate state can be extracted from the inset in the lowest panel. Some selected values of $B(E2)$’s, corresponding to the transitions between the highest spins of initial and final multiplets, are given in the figure [the $B(E2)$ associated with the lowest $5/2-1/2$ transition is normalized to 100]. Lower frame: energy levels in the odd system within the IBFM Hamiltonian (13) at the critical point. A number of bosons $N=7$ has been assumed. The values of $k$ and $k^{\prime }$ are the same as in the $E(5/12)$ Hamiltonian. For the $BE(2)$’s, see the upper frame.Reuse & Permissions

Figure 2

The lattice of algebras involved in the IBFM Hamiltonian (13).Reuse & Permissions