Point symmetries in the Hartree-Fock approach. II. Symmetry-breaking schemes

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