Partial Dynamical Symmetry in Quantum Hamiltonians with Higher-Order Terms

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus ${}^{196}\mathrm{Pt}$.

Figure 1

Observed spectrum of ${}^{196}\mathrm{Pt}$ [16] compared with the calculated spectra of ${\widehat{H}}_{\mathrm{DS}}$ (4), with the SO(6) DS and of ${\widehat{H}}_{\mathrm{PDS}}$ (13) with PDS. The parameters in ${\widehat{H}}_{\mathrm{DS}}$ (${\widehat{H}}_{\mathrm{PDS}}$) are $A=174.2$ (122.9), $B=44.0$ (44.0), $C=17.9$ (17.9), and $\eta =0(34.9)\mathrm{keV}$. The boson number is $N=6$, and $\Sigma$ is an SO(6) label.