Efficient method for quantum number projection and its application to tetrahedral nuclear states

We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying the method, we have microscopically calculated, for the first time, the energy spectra based on the exotic tetrahedral deformation in ^108,110Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, α32 >∼ 0.25, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for ?32 ≈ 0.1 ? 0.2.