Symmetries of shapes, currents, and average angular momenta

In this section we discuss properties of average values of various operators, calculated for the HF many-particle state $\vert\Psi\rangle$. In particular, we consider the electromagnetic multipole operators and the total angular momentum; the quantities which are used to characterize properties of investigated systems. First of all, we enumerate transformation properties of these operators under the D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ or D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$ operators. Similarly as for the density matrix (Sec. 3), the one-body operators discussed in this section belong to one-dimensional ircoreps of D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {T}}}$ or D $_{\mbox{\rm\scriptsize {2h}}}^{\mbox{\rm\scriptsize {TD}}}$, and therefore, their properties do not depend on whether the system contains even or odd number of fermions.