  Electromagnetic and weak transitions tell us a great deal about the structure
of atomic nuclei. Yet modeling transitions can be difficult: it is often easier
to compute the ground state, if only as an approximation, than excited states.
One alternative is through transition sum rules, in particular the
non-energy-weighted and energy-weighted sum rules, which can be computed as
expectation values of operators. We investigate by computing sum rules for a
variety of nuclei, comparing the numerically exact full
configuration-interaction shell model, as a reference, to Hartree-Fock,
projected Hartree-Fock, and the nucleon pair approximation. These
approximations yield reasonable agreement, which we explain by prior work on
the systematics of transition moments.
