Multiphonon structure in a γ-unstable fermionic model

The multiphonon structure is shown for the ${\mathrm{SO}}_6$ limit of the Ginocchio model. We can see that the multiphonon description is valid strictly in this fermion system. The phonon states are created by the quadrupole operator ${\mathit{P}}^2$ with proper symmetrization. All the σ=N states can be described in this scheme in terms of phonon quanta and two-phonon anharmonicity. The dipole and octupole interactions are also included in the Hamiltonian for both the boson and fermion systems.