Restoration of the Broken D2-Symmetry in the Mean Field Description of   Rotating Nuclei
  Signature effects observed in rotational bands are a consequence of an inherent D2-symmetry. This symmetry is naturally broken by the mean field cranking approximation when a tilted (non-principal) axis orientation of the nuclear spin becomes stable. The possible tunneling forth and back between the two symmetry-related minima in the double-humped potential-energy surface appears as a typical bifurcation of the rotational band. We describe this many-body process in which all nucleons participate by diagonalizing the nuclear Hamiltonian within a selected set of tilted and non-tilted cranking quasiparticle states. This microscopic approach is able to restore the broken D2 symmetry and reproduce the quantum fluctuations between symmetry- related HFB states which emerge as splitting of the band energies and in parallel staggering in intraband M1 transitions. 
F. D\"onau, Jing-ye Zhang, and L.L. Riedinger