Excited $0^{+}$ states are studied in the framework of the projected shell model, aiming at understanding the nature of these states in deformed nuclei in general, and the recently observed 13 excited $0^{+}$ states in ${}^{158}\mathrm{Gd}$, in particular. The model, which contains projected two- and four-quasiparticle states as building blocks in the basis, is able to reproduce reasonably well the energies for all the observed $0^{+}$ states. The obtained $B\left(E2\right)$ values, however, tend to suggest that these $0^{+}$ states might have a mixed nature of quasiparticle excitations coupled to collective vibrations.

• Received 3 September 2003

DOI:https://doi.org/10.1103/PhysRevC.68.061301