Anharmonicities in K/sup π/ = 0+ and K/sup π/ = 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/sup π/ = 0+ 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