Conclusions

In the present study we have presented applications of point groups based on the three mutually perpendicular symmetry axes of the second order, inversion, and time reversal, to nuclear structure problems. We have discussed properties of the corresponding single D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ and double D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ groups in describing even and odd fermion systems, respectively. We have enumerated their representations, both for many-body states and for the single-particle operators, and reviewed properties of group operators when they are represented in the fermion Fock space.

Consequences of conserving individual D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ or D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ symmetries have been enumerated for: (i) space symmetries of local one-body densities, (ii) electric and magnetic multipole moments, and (iii) average values of the angular-momentum operators. This gives information about the nuclear shapes and matter-flow currents in states obeying one or more of the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ or D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ symmetries, and allows for selecting appropriate conserved symmetries in descriptions aiming at various physical phenomena.

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.