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 ${}^{108,110}$Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, ${\alpha }_{32}\text{gtsim}0.25$, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for ${\alpha }_{32}\approx 0.1-0.2$