Conclusions

We have analyzed the "far end" of the symmetry breaking chain, namely, symmetries of mean-field nuclear states, which range from time-even, parity-even, signature conserving states, (nevertheless breaking the rotational and axial symmetry), to those which do not conserve any symmetries at all. We have shown that intermediate cases, between such two extremes, correspond to conserved subgroups of the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ or D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ point symmetry groups. A classification of all the subgroups has been proposed, and we have shown that there are 26 different non-trivial symmetry-breaking schemes, when names of Cartesian axes are irrelevant, and 65 different non-trivial symmetry-breaking schemes when names of axes are distinguished in the intrinsic frame of reference.

Consequences of conserving individual D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ symmetries have been enumerated for the construction of single-particle bases in which mean-field operators may have special simplified forms. We point out that the same forms of the mean-field Hamiltonian may correspond to different conserved symmetries, and hence to different physical consequences for observables obtained in the mean-field methods. We have also analyzed and compared various options for defining phase conventions of single-particle basis states.

This research was supported in part by the Polish Committee for Scientific Research (KBN) under Contract Nos. 2 P03B 034 08 and 2 P03B 040 14, and by the French-Polish integrated actions programme POLONIUM.