Point symmetries in the Hartree-Fock approach: Symmetry-breaking schemes

J. Dobaczewski,^1,2 J. Dudek,² S.G. Rohozinski,¹ and T.R. Werner^1,2
1Institute of Theoretical Physics, Warsaw University,
Hoza 69, PL-00681, Warsaw, Poland
²Institute de Recherches Subatomiques, CNRS-IN₂P₃/Université
Louis Pasteur, F-67037 Strasbourg Cedex 2, France

Abstract:

We analyze breaking of symmetries that belong to the double point group D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ (three mutually perpendicular symmetry axes of the second order, inversion, and time reversal). Subgroup structure of the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ group indicates that there can be as much as 28 physically different, broken-symmetry mean-field schemes -- starting with solutions obeying all the symmetries of the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ group, through 26 generic schemes in which only a non-trivial subgroup of D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ is conserved, down to solutions that break all of the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ symmetries. Choices of single-particle bases and the corresponding structures of single-particle hermitian operators are discussed for several subgroups of D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$.