Point symmetries in the Hartree-Fock approach. I. Densities, shapes, and currents

Three mutually perpendicular symmetry axes of the second order, inversion, and time reversal can be used to construct a double point group denoted by $D_{2h}^{\mathrm{TD}}.$ Properties of this group are analyzed in relation to the symmetry and symmetry-breaking effects within the mean-field (Hartree-Fock) theories, both in even and odd fermion systems. We enumerate space symmetries of local one-body densities, and symmetries of electromagnetic moments, that appear when some or all of the $D_{2h}^{\mathrm{TD}}$ elements represent self-consistent mean-field symmetries.