Anharmonicities inKπ=0+andKπ=0−coupled vibrational spectra of deformed nuclei discussed in a simple model

The multiphonon method—i.e., exact diagonalization in the restricted space of collective phonons of different types—is tested in a simple model allowing an exact solution for a many body system of fermions interacting via pairing plus quadrupole and octupole forces. It appears satisfactory for the description of the anharmonicities of the lowest-lying vibrational states with $K^{\pi }=0^{+} \mathrm{and} 0^{-}$ in deformed nuclei. In particular, it allows electromagnetic transitions between the different one phonon states which cannot be described in any harmonic treatments such as the Tamm-Dancoff or random-phase approximations.